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# CORPORATION FINANCE I FIN 3322

TTU

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This 128 page Class Notes was uploaded by Micah Klocko on Thursday October 22, 2015. The Class Notes belongs to FIN 3322 at Texas Tech University taught by John William Cooney in Fall. Since its upload, it has received 31 views. For similar materials see /class/226368/fin-3322-texas-tech-university in Finance at Texas Tech University.

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Date Created: 10/22/15

Chapter 9 Capital Budgeting and Risk In this chapter we will further develop our understanding of how to determine the discount rate for a proj ect s cash flows In particular we will Learn why discounting at the WACC or the proj ect s financing cost is only appropriate in limited circumstances Learn how to calculate the WACC and asset betas Understand how changes in capital structure affect the expected returns required returns and betas of the firm39s securities Understand how acceptance of a project affects the expected returns required returns and betas of the firm39s securities Learn how to estimate stock betas and how to use these estimates to calculate asset betas Learn how to use the WACC and asset betas of comparable companies to determine the discount rate Learn how to estimate beta in tough situations Understand why projects with different degrees of risk over time cause special problems Chapter 9 Capital Budgeting and Risk Summary so far Chapter 1 7 Why most large businesses operate as a corporation Chapter 2 7 Overview of investment decisions cash flows risk opportunity cost of capital as they relate to the objective of the firm Chapter 3 7 Time value of money Chapter 5 7 NPV should be used to make investment decisions Chapter 6 7 How to calculate project cash flows Chapter 7 amp 8 7 Risk and return and the CAPM Chapter 9 is a continuation of Chapters 7 and 8 The ultimate goal is to answer the question What discount rate should the corporation use to evaluate a project Note In this chapter we will assume financial markets are perfect efficient and in equilibrium What do we want Project cash flows should be discounted at the project s opportunity cost of capital De nition The opportunity cost of capital for the cash flows of a project is the expected rate of return for investments in the financial markets that have the exact same amount of risk as the proj ect s cash flows Riskfree cash ows Use the riskfree interest rate The current onemonth Treasury Bill rate is a good estimate of the risk free rate We have been using 5 as the risk free rate What about risky cash ows From Chapters 7 and 8 1 We calculated risk of the project s cash flows we used beta as a measure of risk 2 We used the CAPM to calculate the required expected return for financial assets with the same beta risk as the project s cash flows Remember with perfect efficient and in equilibrium markets a financial asset s expected rate of return equals its required rate of return 3 We used the CAPM required expected return as the discount rate for the project s cash flows The WACC weightedaverage cost of capital or company cost of capital can also be used in certain circumstances as the discount rate for a project s cash flows The WACC is the required return and expected return for a portfolio of all of the firm39s securities The WACC tells us what it will cost the firm on average to raise new capital to fund a project In this chapter we ignore income taxes Assuming no income taxes ram WACC debt In t equity IE Important The effect of income taxes on the WACC is discussed in Chapter 19 The with tax formula is raw WACC debt 1 i T In t equity IE I use the terms WACC and company cost of capital interchangeably The book appears to only use WACC as the withtax formula above Example of the calculation of the WACC ABC Inc s market value balance sheet Asset 1 has a market value of 300 and a beta of 090 Asset 2 has a market value of 600 and a beta of 027 Debt has a market value of 540 The debt is risk free Beta Equity has a market value of 360 The beta of the equity is 12 Current firm market value 900 The riskfree interest rate is 5 The expected required return for the market is 134 The market risk premium is 84 Questions 1 What are the debt and equity percentages 2 What is rD and rE Use CAPM 3 What is the WACC for ABC Inc When can the WACC be used as the discount rate for project cash flows Assume the firm has two potential projects projects A and B from the Chapter 7 and 8 notes I ProjectA has an expected t 1 cash flow of 120 SpunA 180887 discount rate 201945 I ProjectB has an expected t 1 cash flow of 932 SpunB 163175 discount rate 87067 From the previous chapter we determined that Project B had a positive NPV and Project A had a negative NPV Correct NPV of Project A 100 120 1 0201945 100 998382 01618 Correct NPV of Project B 100 9320 1 7 0087067 100 1020885 20885 What would happen if we incorrectly used the firm s WACC as the discount rate for both projects A and B Incorrect NPV of Project A 100 120 109032 1006 Incorrect NPV ofProject B 100 9320 109032 1452 As you can see if we evaluate all projects at one discount rate such as the WACC we do not take into account the riskiness of the project We could incorrectly Accept a bad project or Reject a good project As discussed we should use a discount rate that re ects the riskiness of the project s cash ows with the CAPM giving us a reasonable approximation for that discount rate A Graphical Explanation of when the WACC can be used as a discount rate Assuming the CAPM is correct the CAPM SML security market line plots the riskrequired return relationship given by the CAPM equation Projects that plot above the SM should be undertaken and those below should not be undertaken Plot the WACC the CAPM SM and projects A and B on the following graph Return Risk beta How do you graphically determine if a project has a positive or negative NPV How do you know where a project plots on the above graphically Example Project A Example Project B Initial Investment 100 Expected t 1 cash flow 125 ta 15 Example Exp Ret based on initial investment What are the implications of incorrectly using the WACC instead of the SM to evaluate projects First where does the company make mistakes Region 1 Region 2 Region 3 Region 4 How do the mistakes affect the company Risk Expected return Value at time 0 I When if ever is it proper to use the WACC as the discount rate for a project s cash flows The average beta risk for the rm39s assets The average beta for a firm s assets equals the weightedaverage beta for each of the firm39s individual assets I 3mm assetl Basset 1 asset2 Basseta assetN Bassetm It is also equal to the weightedaverage of the betas of the firm39s securities 39 Basset debt BD t equity BE What is the average beta for the assets of ABC Inc 3mm Use the CAPM to calculate the required return for the firm s assets I Using CAPM rams Therefore the WACC for ABC Inc can be used to discount a project with a beta equal to 7 I Describe What this type of project looks like I How often would you expect to find such a project Expanded Market Value Balance Sheet Some intuition concerning why Project A is a bad project and Project B is a good project Why is Project A unacceptable even though it has a 20 expected return With Project B the firm invests 100 and receives on average 9320 in one year The IR for Project B is negative 68 Why should the firm accept Project B even if it is expected to lose money Can you think of another good investment that companies or individuals make that has a negative expected return How does a change in capital structure affect the WACC of a corporation Example Assume that ABC Inc issues 180 of additional debt Because ABC is more highly levered the newly issued debt has a beta of 04 The existing debt remains riskfree Assume the 180 is used to repurchase 180 of ABC39s stock There is no change in ABC39s assets 1 What are the new debt and equity percentages 2 What is the new rm What is rDa Use CAP1I 3 What is the new beta for ABC39s assets Hint remember that there is no change in the composition or riskiness of ABC39s assets What is the new WACC for ABC Inc 4 What is the new rE What is the new BE Is the new beta for ABC39s equity consistent with the new rE and CAPM Summary Expanded Market Value Balance Sheet Should the cost of funds used to finance the project be considered in the analysis No The opportunity cost of capital for a project reflects where the funds are used not where the funds come from Example Assume that Project A will be accepted and financed with a riskfree debt issue and B rejected Assume that the interest rate on the riskfree debt issue is 5 Aside Is it reasonable to assume that ABC Inc can issue riskfree debt to finance a risky project What are the expected after nancing cash ows for Project A What is the NPV of the project after financing cash ows What about the IRR However the NPV of Project A is 01618 Shouldn t acceptance of the project be bad for the firm39s stockholders Perhaps the low interest rate on the financing changed the project NPV from negative to positive Information on risk and required returns Average beta of existing assets 048 Required return for the existing assets 9032 Beta ofProject A 180887 Required return for Project A 201945 ProjectA cash ows boom 155 normal 135 recession 40 expected t 1 cash flow 120 Present value of Project A s expected time 1 cash flow 120 1201945 998382 5 Analysis 7 Complete the expanded balance sheet Calculations 1 What is the market value of the debt and equity ie the righthandside of the balance sheet 2 What is the market value of the equity 3 What is the average beta for ABC39s assets and WACC 4 What is the new rE What is the new BE Is the new beta for ABC39s equity consistent with the new rE and CAPM Do stockholders benefit from the acceptance of the project To answer compare the market value of the stock assuming 1 The project is accepted and 2 The project is rejected Based on this stockholders stock has decreased in value by What did we learn 1 The risk of the equity Why 2 The required return of the equity 3 The expected return of the equity 4 Firm value 5 Stock value The combined projectfinancing arrangement looks profitable What39s going on Examine the total project and financing cash flows for time one across the three economic states The afterfinancing cash flow is negative when How might this fact in uence whether the firm finds the project acceptable Conclusion Since the expected return on the debt is equal to its required return 5 the NPV of the financing is zero Therefore the financing choice can be disregarded in the capital budgeting decision Does the same hold true if we had financed with equity in the above example Yes Is the financing NPV always 0 No Will we talk about this more in Chapter 9 No Some real world information on the determination of the riskadjusted discount rate using the CAPM First 7 an example to work with Our goal is to calculate the NPV of the following projects Project A 1000 initial investment 1250 expected cash flow in one year Project B 1000 initial investment 250 per year for years 1 7 4 1250 expected cash flow at year 5 Project C 1000 initial investment 250 per year for years 1 7 19 1250 expected cash flow at year 20 Assume each cash flow for each of the three projects has the following risk pmmj 23 opmj 060 om 020 How do we determine the discount rate for these projects According to the CAPM equation the discount rate is r rf 3 W 1 Beta 3m pmin Opioj 0m We will discuss methods for estimating this from sample data later in the notes 2 Market Risk Premium rm rf What do you want The expected return for the market portfolio minus the riskfree interest rate ie the premium investors require to own the market portfolio I US corporations should use the US market risk premium As discussed Brealey Myers and Allen suggest a US market risk premium in the 5 8 range We will use 84 in this class 3 RiskFree Rate rf What do you want The rate of return on a security with no risk Here are some possibilities I Interest rate yield to maturity on corporate bonds I Interest rate yield to maturity on longterm 20year US Treasury Bonds I Interest rate yield to maturity on mediumterm 5year US Treasury Bonds I Interest rate yield to maturity on shortterm 30day US Treasury Bills Which one should we select What s wrong with the other three 4 Maturity risk premium If evaluating a medium or longterm project we need to make an adjustment to the risk free rate used in the CAPM equation See footnote 8 in the textbook First some numbers from lbbotson Associates SBBI 1998 yearbook 7 data from 19261997 I Longterm maturity risk premium Avg difference in returns for 20year TBond and onemonth TBill I Mediumterm maturity risk premium Avg difference in returns for 5year TBond and onemonth TBill Risk free rate for the longterm 20year project Risk free rate for the mediumterm 5year project 5 CAPM Plug this information into the CAPM to determine a discount rate for the project Make the maturity adjustment as needed Discount rate for Project A cash flows Project NPV Discount rate for Project B cash flows Project NPV Discount rate for Project C cash flows Project NPV 6 Is the CAPM the best most sophisticated method for determining a discount rate No The APT is an alternative method for determining the discount rate More details on estimating the beta and discount rate for a project s cash ows For illustration purposes we calculated the exact beta for a project s cash flows in Chapter 7 notes based on project cash flows in different states of the economy Since this information is rarely available we need to estimate beta What you need The beta for the project ie how risky is the project under consideration General procedure calculate the beta of the assets of a company whose assets are just as risky as the project cash flows Use the CAPM to get the discount rate What do you need For a simple comparable company debt debt beta equity equity beta asset beta So we need four pieces of information MV of debt beta of debt MV of equity and beta of equity What s available Let s start with the equity MV of Equity Beta of equity typically estimated using historical stock returns and market returns The historical stock beta is estimated by regressing the historical stock returns against the historical market returns For example regress monthly stock returns against monthly market returns using data from the last five years Beta for the stock is equal to the slope of the regression line Alpha for the stock is equal to the intercept of the regression line Average return for the stock when market return equals 0 Graphical examples are on page 220 of the text Stability of Beta How much do betas change over time Again refer to page 220 of the text However it is best to use the most recent stock beta estimates in your calculations What about debt MV of debt is rarely known This causes two problems and MV of debt estimate as equal to the BV of debt Beta of debt debt betas for large safe firms range from 01 7 03 Brealey and Myers Pg 229 7d1 ed Finishing the calculation Example XYZ Corporation is considering a project that is similar in risk to the assets of ABC Corporation What discount rate should XYZ use to evaluate the project ABC Inc Asset 1 has a market value of 300 and a beta of 09 Asset 2 has a market value of 600 and a beta of 027 Debt has a market value of 540 The debt is risk free and therefore has a beta 0 Equity has a market value of 360 The beta of the equity is 12 Discount rate for XYZ s project The problem with estimates Remember that our calculation of the asset beta is estimated The true beta could be above or below the estimated beta More estimates diversify away the estimation errors Because of this it is best to calculate the average asset beta from several firms in the project s industry These industry betas give a better estimate of asset betas See the Ibbotson Web site wwwibbotsoncom for a compilation of individual firm and industry betas Use this industry estimate for the project beta to plug into the CAPM equation to determine the discount rate As an alternative calculate the WACC of each comparison firm The average of these WACCs will provide an estimate of the discount rate Computational hints when it is difficult to determine project beta Possible reasons suggestions I Difficulty in quantifying a particular aspect of the project39s risk Avoid fudge factors don39t arbitrarily increase the discount rate because there is difficulty in determining cash ows If risk is diversifiable then the discount rate should not be adjusted Properly calculate possible cash flows and the probability of these cash flows See example in text on pages 223224 I Difficulty in assigning project to a particular industry Solution Understand what in uence asset betas i Projects with cyclical cash flows tend to have positive betas A project with cyclical cash flows has high returns in periods when the market has high returns and vice versa What about projects with countercyclical cash flows ii Projects with a high percentage of fixed costs with cyclical cash flows tend to have high positive betas Similar to stock betas increasing when leverage is high iii High project standard deviation does not necessarily mean high positive beta Remember the formula for the project39s beta is BPYOJ ppmm opmj om Need to estimate pmypmj Skip discussion on Certainty Equivalents only skim section 94 Final thoughts Income taxes Remember that we have been ignoring income taxes in this chapter s discussion of the determination of the discount rate A detailed discussion is included in Chapter 19 Foreign projects can have a very high variance of returns but a low beta Why How do you compute beta for a foreign project 1 US corporation with a US project 7 compute project beta with respect to US market returns 3 ij pusprojmus Gusproj 0musl 2 Germ an corporation with a German project 7 compute project beta with respect to German market returns Bgmmn roj P german projmgermany Ggenmn proj 0mgenmny 3 How about a US corporation with a German project Bgerman proj P german projmus 0 german proj 0musl Once the beta is calculated use the home country s risk free rate and market risk premium to determine the discount rate Some questions How does 2 compare to 3 Why do we compute betas in this way When would we want to use a world market risk premium and a beta calculated with respect to a world market portfolio LongTerm Risky Projects Cash flows from longterm risky projects may be unduly penalized if their risk decreases over time This is likely if uncertainty is resolved as the project progresses 7 see pages 230231 Note Properly understanding this example involves an understanding of certainty equivalents The effects of using the wrong discount rate Assume that a project has two expected positive cash flows one in one year 50 and another in ten years 180 The first cash flow is risky beta l and the second cash flow is risk free Initial investment 100 Using 84 as the market risk premium 5 as a riskfree rate and the CAPM what is the NPV of the project Correct Calculations NPV Consider the following incorrect calculations NPV 100 39501051 1801051 5812 NPV 100 215011341 18011341 472 Observation Compare the relative impact of using the wrong discount rates gtxlt Selected quiz questions from the textbook for Chapter 9 91 93 95 96 97 Chapter 9 Review Questions 1 N 9 gt V gt1 O H 0 N L 4 What is the WACC How do you calculate the WACC Be able to calculate the required return for the firm39s equity debt and assets Using the graph drawn in class how can you determine if a project has a positive negative or zero NPV Using the graph drawn in class when will the use of the WACC as the discount rate give the same acceptancerejection recommendation as using the SML to determine the discount rate In what areas will the firm accept a bad project or reject a good project using the WACC as a discount rate What implications does this have for the composition of a firm39s assets Know how to calculate the average beta for a firm39s securities and assets How does a change in capital structure affect the firm Understand the intuition of Why is it inappropriate to use the cost of financing as the discount rate for a project How does acceptance of a project affect a firm What quotriskfreequot rate should be used in the CAPM What quotmarketrisk premium should be used in the CAPM Where would you look to get current figures What adjustment should be used to evaluate projects with long term cash flows What is the purpose of this adjustment When should the US market risk premium be used as opposed to the German or some other country s market risk premium When should beta be calculated with respect to the US market as opposed to the German market or some other country s market How do you estimate the beta for a stock Why is it better to use an industry beta than an individual stock beta How do you convert stock betas to asset betas How do you use this estimate to determine the beta and discount rate for a project s cash flows Understand the discussion in the section titled quotComputational hints when it is difficult to determine project beta quot What does it mean to quot avoid fudge factors Why do cyclical cash flows tend to have positive betas Why do countercyclical cash flows tend to have negative betas What if project cash flows are uncorrelated with market factors Remember that high variance does not necessarily mean a high positive beta What is the relationship between fixed costs and betas Understand why high variance risky foreign projects can have a low beta risk Understand the discussion on quotlongterm risky projects quot Be able to calculate the net present value of a long term risky project Chapter 9 Practice Problems Problems 1 7 5 use a common set of assumptions 1 N 9 gt V 0 Assume that the riskfree rate is 5 and the market risk premium is 84 If XYZ Inc has 700 of debt beta 02 and 300 of equity beta 15 what is the WACC for this firm 9956 What is the average beta for XYZ s securities 0 5900 Crosscheck your answer with the CAPM Assume that XYZ has three assets a riskfree Treasury Bill market value 100 a risky corporate bond of another company beta 04 market value 200 and an existing project beta 7 market value 700 A What is the beta of the existing project 0 72857 B What is the required return for the existing project 1112 C What is the average required return for the firm39s assets 9 95 6 Assume that XYZ Inc issues 100 of debt and uses the proceeds of the debt issue to retire 100 of its stock This new debt has a beta of 04 The beta of the existing debt stays at 02 Assume that the composition and riskiness of the firm39s assets remains the same Compute the following A Required rate of return for the firm39s new debt 836 B Average beta for the firm39s assets 05900 C WACC for the firm 9956 D Required rate of return for the firm39s equity 2222 E Beta for the firm39s equity 2 05 Assume that XYZ Inc has 700 of debt and 300 of equity as described in the original problem XYZ Inc issues 100 of new stock and uses the proceeds of the stock issue to invest in Project B Project B is described in the Chapter 7 notes has a beta of163175 a PV of future cash flows of1020885 and a NPV of 20885 Assume that the beta of the 700 of debt remains at 02 Compute the following A Market value of the firm and equity 1102 0885 and 4 02 0885 respectively B Average asset beta 038420 Notice the risk reducing bene ts afPrajecI Bf C WACC 822 72 D Required rate of return for the firm39s equity 109209 E Beta for the firm39s equity 0 70486 Using of the following information what is the average beta for Green Inc s assets 115 Green Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 500 12 15080 Debt 1 500 0 5000 Asset 2 300 05 9200 Debt 2 100 03 7520 Asset 3 200 2 21 800 Equity 400 2 8 28520 Total 1000 Answer 1000 Using of the following information what is the beta for Blue Inc s equity 1843 Blue Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 400 07 10880 Debt 1 200 0 5000 Asset 2 300 15 17600 Debt 2 100 01 5840 Asset 3 300 19 20960 Equity 700 Answer Total 1000 13 15920 1000 13 15920 12 L O i N Using of the following information what is the average beta for the AAA Inc s assets 094 AAA Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 500 Debt 1 250 0000 5000 Asset 2 200 Debt 2 350 0400 8360 Asset 3 300 Equity 400 2000 21 800 Total 1000 Answer 1000 Using of the following information what is the beta for the BBB Inc s equity 2 652 BBB Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 200 05 9200 Debt 1 400 0000 5000 Asset 2 300 1 13400 Debt 2 180 0200 6680 Asset 3 500 15 17600 Equity 420 Answer Total 1000 1000 1150 14660 Using of the following information what is the WACC for Alpha Inc Assume that the risk free rate 5 the market risk premium 84 and the CAPM is used to determine required returns 12 392 Alpha Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 500 100 Debt 1 50000 000 Asset 2 400 050 Debt 2 20000 020 Asset 3 100 180 Equity 30000 2 800 Total 1000 088 100000 Answer Using of the following information what is the required return for the Zeta Inc s equity Assume that the risk free rate 5 the market risk premium 84 and the CAPM is used to determine required returns 2096 Zeta Inc Assets Market Beta Req Liabilities Market Beta Re Value Return Equity Value Return Asset 1 300 120 1508 Debt 1 30000 000 5 00 Asset 2 500 070 1088 Debt 2 20000 020 668 Asset 3 200 140 1676 Equity 50000 Answer Total 1000 099 13316 100000 099 13316 Using the following information what is the beta of the firm s equity 2476 13 Using of the following information what is the beta for Brown Inc s equity 178 Brown Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 500 020 6680 Debt 1 400 000 5000 Asset 2 300 140 16760 Debt 2 100 030 7520 Asset 3 200 200 21 800 Equity 500 Answer Total 1000 092 12728 1000 092 12728 L gt Using of the following information what is the required return for Brown Inc s equity Assume that the risk free rate 5 the market risk premium 84 and the CAPM is used to determine required returns 20204 Brown Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 400 020 6680 Debt 1 400 010 5840 Asset 2 250 200 21800 Debt 2 100 020 6680 Asset 3 350 110 14240 Equity 500 Answer Total 1000 0965 13106 1000 0965 13106 15 Using of the following information what is the beta for XYZ Inc s equity 175 XYZ Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 300 04 8360 Debt 1 400 01 5840 Asset 2 500 08 11720 Debt 2 200 04 8360 Asset 3 200 15 17600 Equity 400 Answer Total 1000 0820 11888 1000 0820 11888 16 Using of the following information what is the required rate of return for XYZ Inc s equity Assume that the risk free rate 5 the market risk premium 84 and the CAPM is used to determine required returns 22 64 XYZ Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 400 02 668 Debt 1 300 01 584 Asset 2 100 08 1172 Debt 2 200 04 836 Asset 3 500 20 2180 Equity 500 Answer Total 1000 1160 14744 Total 1000 1160 14744 17 Refer back to the facts of the previous problem Assume that the beta risk of debt 1 was 0 instead of 01 and the required rate of return was 50 instead of 584 All the other numbers presented in the previous problem stay the same How do these changes in assumption affect your answer to the previous problem A The required rate of return for equity is higher than the correct answer to the previous problem Correct B The required rate of return for equity is the same as the correct answer to the previous problem C The required rate of return for equity is lower than the correct answer to the previous problem so 0 O i 19 Using of the following information what is the beta for XYZ Inc s equity 288 XYZ Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 900 0200 6680 Debt 1 1100 0100 5840 Asset 2 600 1300 15920 Debt 2 400 0400 8360 Asset 3 500 1500 17600 Equity 500 Answer Total 2000 0855 12182 Total 2000 0855 12182 Refer back to the facts of the previous problem Assume that the market value of debt 1 was 1200 instead of 1100 and the market value of the equity was 400 instead of 500 All the other numbers presented in problem 1 stay the same How do these changes in assumption affect your answer to problem 1 A The beta for equity is the same as the correct answer to problem 1 B The beta for equity is higher than the correct answer to problem 1 Correct C The beta for equity is lower than the correct answer to problem 1 Assume that the risk free rate 5 the market risk premium 84 and the CAPM is used to determine required returns and discount rates What is the WACC for AAA Inc 12 644 AAA Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 900 0800 11720 Debt 1 1200 0100 Asset 2 700 0600 10040 Debt 2 300 0400 Asset 3 400 1700 19280 Equity 500 3160 Total 2000 Total 2000 Answer What is the equity beta for BBB Inc 134 BBB Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 1200 0600 10040 Debt 1 600 0000 5000 Asset 2 500 0800 11720 Debt 2 400 0200 6680 Asset 3 300 1000 13400 Equity 1000 Answer Total 2000 0710 10964 Total 2000 What is the equity beta for AAA Inc 194 AAA Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 800 07 1088 Debt 1 700 01 584 Asset 2 1200 08 1172 Debt 2 800 02 668 Asset 3 500 13 1592 Equity 1000 Answer Total 2500 0868 122912 Total 2500 23 Assume that the risk free rate 5 the market risk premium 84 and the CAPM is used to determine N N N l required returns and discount rates Consider two firms Both firms have a market value of 1000 assets with an average beta of 15 and a WACC of 176 The difference between the two firms is on the right hand side of the balance sheet The first firm has 700 of riskfree debt and 300 of equity The second firm has 300 of riskfree debt and 700 of equity Which of the two firms has the higher risk ie higher beta equity A The first firm CorrectAnswer B The second firm C The beta of the equity of firm one is the same as the beta of the equity of firm two D There is not enough information to determine the beta risk of the equities of these two firms Assume that the risk free interest rate is 5 and the market risk premium is 84 ABC Inc has a WACC of 12 ABC is considering four projects These are not mutually exclusive projects Each project will require an initial investment of 100 and produce one expected cash flow in one year The future cash flow and the beta of that cash flow for each of the projects are listed below A What are the projects NPVs Use the CAPM to determine the discount rate Project A NPV I48 Project B NPV 3 85 Project C NPV 5 75 Project D NPV 646 B Plot the four projects on a beta risk return graph Note 7 all four projects will plot below the SML C Which of the four projects will the firm accept if it incorrectly used the WACC to evaluate projects Project1 D Which of the four projects will the firm accept if it used the CAPM discount rate to evaluate projects None of the four projects Assume that the risk free interest rate is 5 and the market risk premium is 84 The WACC for a firm is 10 This firm is considering four possible projects and it correctly uses the CAPM to determine discount rates for these projects Cash flows and discount rates for the four projects are given below Which of the four projects would plot in region 3 on the graph drawn on the board below the WACC below the SML Project1 rate Project Z requires an initial investment of 100 and has a time one expected cash flow of 103 Therefore its expected return based on the 100 initial investment is 3 The company s WACC is 10 The company correctly uses the CAPM to determine a discount rate Using this discount rate the project NPV is 100 Where does Project Z plot on the graph described in class Below the WACC above the SML ProjectX requires an initial investment of 100 and has a time one expected cash flow of 118 Therefore its expected return based on the 100 initial investment is 18 The company s WACC is 10 The company correctly uses the CAPM to determine a discount rate Using this discount rate the project NPV is 100 Similar to the discussion in class where does Project X plot on the graph described in class Above the WACC above the SML 16 28 ProjectX requires an initial investment of 100 and has a time one expected cash flow of 112 Therefore its expected return based on the 100 initial investment is 12 The company s WACC is 10 The company correctly uses the CAPM to determine a discount rate Using this discount rate the project NPV is 100 Similar to the discussion in class where does Project X plot on the graph described in class Above the WACC below the SML N O Assume a firm decides whether to accept or reject a project based on its NPV That is it accepts projects with positive NPVs and rejects projects with negative NPVs To calculate the NPV this firm uses its WACC equal to 10 as the discount rate for all projects Assume however that the correct discount rate should be based on the CAPM security market line This firm is faced with the following two projects Determine in each case whether the firm using the WACC as the discount rate will make a mistake in its project selection rejection decision The risk free rate is 5 and the market risk premium is 84 Project A beta 02 Time 0 1 I Expected Cash Flows I 100 I 108 I A The firm will make a mistake by accepting this project when it really has a negative NPV B The firm will make a mistake by rejecting this project when it really has a positive NPV Correct C The firm will not make a mistake with this project ie it will make the correct decision Project B beta 15 Time 0 1 I Expected Cash Flows I 100 I 120 I A The firm will make a mistake by accepting this project when it really has a negative NPV B The firm will make a mistake by rejecting this project when it really has a positive NPV C The firm will not make a mistake with this project ie it will make the correct decision Correct L O The following are basecase financing and afterfinancing cash flows for a project Discount rates are given in the last column Based on this information and using the procedure discussed in Chapter 9 what is the after financing NPV for the project 24 48 U N Assume that the annual yield for a onemonth TBill is 5 The fiveyear Treasury Note has a yield of 68 Using a fiveyear maturity premium of 1 and a market risk premium of 84 what discount rate should the firm use for a fiveyear project with a beta of one 142 L N Using the following information what is the discount rate for a fiveyear project 1580 I The yieldtomaturity for onemonth Treasury Bills is currently as of today s Wall Street Journal 220 I The yieldtomaturity for a 5year Treasury bond is currently as of today s Wall Street Journal 480 I The mediumterm maturity risk premium ie the average difference in yields between 5year Treasury Bonds and onemonth Treasury Bills as calculated by lbbotson Associates 16 The beta for the year 5 cash flow 15 I The market risk premium 84 33 Consider the following information L L Lquot Project beta 15 Market risk premium 84 From the latest issue of the Wall Street Journal I Onemonth Treasury Bill yieldtomaturity 175 I Fiveyear Treasury Bond yieldtomaturity 510 From the latest issue of the brown book by lbbotson Associates I Average annual return since 1926 from investment in onemonth Treasury Bills 38 I Average annual return since 1926 from investment in fiveyear Treasury Bonds 54 I Mediumterm 5year maturity risk premium 54 38 16 Using the CAPM and the type of analysis we discussed in Chapter 9 what discount rate should be used for a 5 year project 161 Consider the following information Project beta 12 Market risk premium 84 From the latest issue of the Wall Street Journal I Onemonth Treasury Bill yieldtomaturity 105 I Fiveyear Treasury Bond yieldtomaturity 398 From the latest issue of the brown book by lbbotson Associates I Average annual return since 1926 from investment in onemonth Treasury Bills 38 I Average annual return since 1926 from investment in fiveyear Treasury Bonds 54 I Mediumterm 5year maturity risk premium 54 38 16 Using the CAPM and the type of analysis we discussed in Chapter 9 what discount rate should be used for a 5 year project 1246 Consider the following information Project beta 13 Market risk premium 84 From the latest issue of the Wall Street Journal I Onemonth Treasury Bill yieldtomaturity 095 I Fiveyear Treasury Bond yieldtomaturity 273 Historical information from lbbotson Associates I Average annual return since 1926 from investment in onemonth Treasury Bills 38 I Average annual return since 1926 from investment in fiveyear Treasury Bonds 54 I Mediumterm 5year maturity risk premium 54 38 16 Using the CAPM and the type of analysis we discussed in Chapter 9 what discount rate should be used for a 5 year project 1205 36 Consider the following information L so Project beta 125 Market risk premium 84 From the latest issue of the Wall Street Journal I Onemonth Treasury Bill yieldtomaturity 150 I Fiveyear Treasury Bond yieldtomaturity 370 From the latest issue of the brown book by lbbotson Associates I Average annual return since 1926 from investment in onemonth Treasury Bills 38 I Average annual return since 1926 from investment in fiveyear Treasury Bonds 54 I Mediumterm 5year maturity risk premium 54 38 16 Using the CAPM and the type of analysis we discussed in Chapter 9 what discount rate should be used for a 5 year project 126 Consider the following information Project beta 13 Market risk premium 84 From the latest issue of the Wall Street Journal I Onemonth Treasury Bill yieldtomaturity 265 I Fiveyear Treasury Bond yieldtomaturity 394 Historical information from lbbotson Associates I Average annual return since 1926 from investment in onemonth Treasury Bills 38 I Average annual return since 1926 from investment in 5year Treasury Bonds 55 I Mediumterm 5year maturity risk premium 55 38 17 Using the CAPM and the type of analysis we discussed in Chapter 9 what discount rate should be used for the 5year project 1316 Consider the following information Project beta 085 Market risk premium 84 From the latest issue of the Wall Street Journal I Onemonth Treasury Bill yieldtomaturity 45 I Fiveyear Treasury Bond yieldtomaturity 52 Historical information from lbbotson Associates I Average annual return since 1926 from investment in onemonth Treasury Bills 38 I Average annual return since 1926 from investment in 5year Treasury Bonds 54 I Mediumterm 5year maturity risk premium 54 38 16 Using the CAPM and the type of analysis we discussed in Chapter 9 what discount rate should be used for the 5year project 1074 39 4 O 4 4 N 4 L 4 4 Consider the following information for a fiveyear project Project beta 14 Market risk premium 84 From the latest issue of the Wall Street Journal I Onemonth Treasury Bill yieldtomaturity 518 I Fiveyear Treasury Bond yieldtomaturity 564 Historical information from lbbotson Associates I Average annual return since 1926 from investment in onemonth Treasury Bills 38 I Average annual return since 1926 from investment in 5year Treasury Bonds 54 I Mediumterm 5year maturity risk premium 54 38 16 Using the CAPM and the type of analysis we discussed in Chapter 9 what discount rate should be used for the fiveyear project 1580 What is the yieldtomaturity of the following Treasury Bond Similar to the example in class give the yield to maturity as an annual rate with semiannual compounding 5277 Current price for a 100 face bond 90 1532 Yearly coupon interest rate 45 Coupon payments are made semiannually every 6 months The bond matures in 20 years What is the yieldtomaturity of the following Treasury Bond Similar to the example in class give the yield to maturity as an annual rate With semiannual compounding 5139 Current price for a 100 face bond 90 732 Yearly coupon interest rate 430 Coupon payments are made semiannually every 6 months The bond matures in 18 years What is the yieldtomaturity of the following Treasury Bond Similar to the example in class give the yield tom aturity as an annual rate with semiannual compounding 4800 Current price for a 100 face bond 95 1732 Yearly coupon interest rate 445 Coupon payments are made semiannually every 6 months The bond matures in 20 years What is the yieldtomaturity of the following Treasury Bond Similar to the example in class give the yield tomaturity as an annual rate with semiannual compounding 5 787 Current price for a 100 face bond 105 332 Yearly coupon interest rate 622 Coupon payments are made semiannually every 6 months The bond matures in 20 years What is the yieldtomaturity of the following Treasury Bond Similar to the example in class give the yield tomaturity as an annual rate with semiannual compounding 5383 Price 111 2432 for a bond with a face amount of 100 Yearly coupon interest rate 635 Coupon payments are made semiannually every 6 months The bond matures in 20 years 20 4 4 4 4 4 O 11 Lquot What is the yieldtomaturity of the following Treasury Bond Similar to the example in class give the yield tomaturity as an annual rate with semiannual compounding 4277 Price 10506 for a bond with a face amount of 100 Note that the price is 1 05 06 not 10506 Yearly coupon interest rate 544 Coupon payments are made semiannually every 6 months The bond matures in 5 years Your bank is considering lending 100 to a firm for one year to finance a project Project X This will be a nonrecourse loan meaning that payment on the loan must come from project cash flows The bank wants to earn a 6 expected return on the loan What interest rate does the bank need to charge to earn the 6 expected return 25 ProjectX time one cash flows Boom 200 20 probability Normal 145 60 probability Recession 30 20 probability Expected 133 Which of the following securities has the greatest price risk also called interest rate risk maturity risk or inflation risk A A twentyyear Treasury Bond paying a fixed coupon payment rate of 25 every 6 months Correct answer B A veyear Treasury Bond paying a fixed coupon payment rate of 25 every 6 months Which of the following securities has the least amount of price risk also called interest rate risk maturity risk or inflation risk A A sixmonth Treasury Bill paying a fixed coupon rate of 25 for the next 6 months Correct B A veyear Treasury Bond paying a fixed coupon payment rate of 25 every 6 months C A twentyyear Treasury Bond paying a fixed coupon payment rate of 25 every 6 months A project has the following expected cash flows Using the following information what discount rate should the firm use to calculate NPV As in class make the adjustment for the fact that this is a fiveyear project Answer the discount rate 174 0 1 2 3 4 5 1000 200 200 200 200 I 2500 I The latest edition of the book the lbbotson book passed around in class and shows that the maturity risk premium for fiveyear Treasury securities is 12 In other words the average yearly difference since 1926 between the returns for fiveyear Treasury Securities and onemonth Treasury Securities has been 120 I Today s Wall Street Journal shows the current yield to maturity for fiveyear US Treasury Bonds 600 I Today s Wall Street Journal shows the current yield to maturity for onemonth US Treasury Bills 450 I The market risk premium 84 I Beta for the time 5 cash flow 15 Assume that the beta for a company39s stock is 25 and the beta for its debt is 03 If the market value of equity as a percent of the market value of assets is 30 what is the beta for the firm39s assets 096 Using a riskfree interest rate of 5 and a market risk premium of 84 what discount rate should you use to evaluate a project with a beta of 096 13 064 21 Lquot L Lquot 5 Lquot Lquot Lquot 9 AAA Inc has assets with an average beta of 075 AAA is financed part with debt and part with equity lts debt is risky The debt pays an annual interest rate of 836 and has a beta 04 ABC s equity has a beta of 15 Assume that management undertakes actions to reduce the beta of the debt Holding the market values of the debt and equity constant and assuming the asset beta remains at 075 what effect will the reduction in the debt beta have on the equity beta A The equity beta will decrease B The equity beta will increase Correct answer C The equity beta will stay the same As explained in class the average beta for Ford Motor Company s assets is estimated by calculating the weightedaverage beta of Ford s debt and equity Ideally these weights are based on the market values of Ford s debt and equity In practice is it easier to get reliable figures for the market value of Ford s equity or Ford s debt A It is easier to get reliable figures for the market value of Ford s equity CarrecIAnswer B It is easier to get reliable figures for the market value of Ford s debt In practice the beta of Ford s equity is calculated by A Estimating the returns for Ford s stock in a boom normal and recessionary economy then using the methods described in Chapter 7 and 8 to calculate beta B Performing a regression analysis of Ford s stock returns yaxis against the market s returns xaxis The estimate of beta is the slope for the regression line CarrecIAnswer C Performing a regression analysis of Ford s stock returns yaxis against the market s returns xaxis The estimate of beta is the intercept of the regression line Beta for a stock say Ford stock is often estimated by using regression analysis In the regression analysis A Ford stock returns are plotted on the Yaxis market returns on the Xaxis The estimate of beta is the intercept of the regression line B Ford stock returns are plotted on the Xaxis market returns on the Yaxis The estimate of beta is the intercept of the regression line C Ford stock returns are plotted on the Yaxis market returns on the Xaxis The estimate of beta is the slope of the regression line CarrecIAnswer D Ford stock returns are plotted on the Xaxis market returns on the Yaxis The estimate of beta is the slope of the regression line Which of the following two firms has the lower weighted average cost of capital WACC A AAA Inc has the lower WACC B BBB Inc has the lower WACC Correct answer C Both companies have the same WACC 22 57 Which of the following two firms assets have the higher beta A The beta of the assets of AAA Inc is highest B The beta of the assets of BBB Inc is highest Correct answer C The beta of both company s assets are the same 58 Your corporation is considering a new project Project X The beta risk of the project is the same as the beta risk of the assets of AAA Inc Using the following balance sheet information for AAA Inc what is beta risk of ProjectX Use the method we discussed in Chapter 9 The risk free rate is 5 and the market risk premium is 84 Use the CAPM to calculate required returns 092 AAA Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 400 Debt 1 30000 01 584 Asset 2 500 Debt 2 30000 752 Asset 3 100 Equity 40000 20 2180 Total 1000 Answer 100000 59 Your firm is considering a project that is just as risky as the assets of Green Inc Therefore the average beta of Green Inc s assets should be same as the project beta and can be plugged into the CAPM equation to determine the project discount rate Green Inc Assets Market Beta Req Liabilities Market Beta Req Value Return Equity Value Return Asset 1 Debt 1 300 00 Asset 2 Debt 2 200 02 Asset 3 Equity Total Total Other information reen Inc s current stock price 750 per share Shares outstanding 270 Estimated stock beta ie equity beta from a regression using returns over the last 5 years 14 Risk free rate 5 Market risk premium 84 Use the CAPM to determine required rates of return Using the CAPM and the type of analysis we discussed in Chapter 9 what discount rate should be used for the project 14564 60 Gamma Inc has assets with a market value of 1000 and an average beta of 20 The market value of Gamma s debt is 300 The beta of the debt is 05 The market value of Gamma s equity is 700 What is the beta of Gamma s equity 2643 23 61 Refer back to the previous problem However now assume that the market value of the debt is 700 and the market value of the equity is 300 All other information in the previous problem remains the same What is the beta of the equity after this change in assumption A The beta of the equity is less than the answer to the previous problem B The beta of the equity is greater than the answer to the previous problem Correct answer equity beta 55 C The beta of the equity is the same as answer to the previous problem 62 A US corporation is considering a highrisk project in another country More specifically the standard deviation of returns for this project is 60 but the correlation of project returns with the SampP 500 returns is relatively low the correlation is only 02 Assuming the standard deviation of the SampP 500 returns is 20 what is the beta of the project with respect to the SampP 500 06 24 Chapter 10 Project Analysis Section 101 the first page of 102 and pages 257 to the top of 262 of section 103 In this chapter we will discuss other methods of assessing project risk In particular we will 1 Define standalone risk and withinfirm risk 2 Reemphasize that welldiversified investors are only concerned with nondiversifiable risk beta risk 3 Identify decision makers who are concerned about standalone risk and withinfirm risk 4 Learn how to measure standalone risk and when it is beneficial to buy additional information 5 Brie y discuss sensitivity analysis scenario analysis breakeven analysis MonteCarlo simulations and using decisiontrees Chapter 10 Project Analysis In the previous chapter we learned that beta is the appropriate measure of risk used to determine the discount rate for a project s cash flows This assumes that the CAPM is the correct model in calculating expected and required returns for assets Beta is the portion of a project s risk that affects a welldiversified investor Project beta is estimated by averaging the asset betas of other firms doing business in a similar industry Computer spreadsheet programs can be used to provide additional information regarding project risk particularly an assessment of standalone risk Standalone risk reflects the total riskiness of the project without consideration of any diversification benefits It is measured by examining the uncertainty of the project NPV Example ProjectX beta 00 the riskfree rate is 5 and the market risk premium is 84 discount rate 5 Initial investment 1000 Time one cash flow 50 chance 116550 Time one cash flow 50 chance 114450 NPV Project Y beta 00 the riskfree rate is 5 and the market risk premium is 84 discount rate 5 Initial investment 1000 Time one cash flow 50 chance 1302 Time one cash flow 50 chance 1029 NPV Side note Obviously there is risk with these two projects but the beta is zero How come Lowest Possible NPV Highest Possible NPV NPV 50 chance 50 chance Project X Project Y Which of the two projects has the higher standalone risk Which of the two projects has the higher NPV Important There is only one NPV for a project It is determined by discounting the project39s expected cash flows at the opportunity cost of capital We will call the highest and lowest NPVs in the above example whatif NPVs Whatif NPVs tell us how acceptance of the project will affect our firm if the worst set or best set of assumptions were realized The two extreme values for the whatif NPV give one measure for a proj ect s standalone risk More calculation methods are discussed later Within rm risk measures how the project contributes to the overall riskiness of the firm Withinfirm risk is related to the correlation of the new project s returns with the returns of the existing assets of the firm In most circumstances a project with high standalone risk will have high withinfirm risk However it is possible that a project with high standalone risk might actually reduce firm risk For example is it possible that Project X is risk increasing for the firm and Project Y is risk reducing Firm cash flows are high Firm cash flows are low Project X NPV Project Y NPV Welldiversified investors are concerned with nondiversifiable risk beta risk The beta risk of the project is not necessarily related to the standalone risk or withinfirm risk of a project For instance a project with high standalone risk and high withinfirm risk might depending on the correlation of the project s returns with the market s returns have a beta close to zero or even have a negative beta Consider the windmill project discussed during the rst few days of this class Does the windmill project have high standalone risk Does the windmill project have high withinfirm risk Does the windmill project have high beta risk Who is concerned about a project39s standalone risk within rm risk or beta risk Consider the following set of concerned individuals 1 The project manager and other employees that work on the project Firm employees that work on other projects Managers of the firm President VP Treasurer etc Investors in the firm39s stock not diversified Investors in the firm39s stock welldiversified mgww VVVV Consider the project manager 1 above How can this project manager hurt the firm by being too concerned about the proj ect s standalone risk Consider the president of the rm 3 above How can this president hurt the firm by being too concerned about the project s withinfirm risk How can we get the project manager and rm president to think more like a welldiversified stockholder Even though standalone risk does not take into account diversification it provides valuable information about the project39s total riskiness For example it might force managers to make better estimates or find ways to prevent bad outcomes Methods of Assessing StandAlone Risk I Sensitivity Analysis I Scenario Analysis I BreakEven Analysis I Monte Carlo Simulations Sensitivity Analysis How much does project NPV change when a single variable is changed Example A project involves purchasing a product for resale to the public The time zero initial investment 3770 Sales price 1450 20 chance 1400 50 chance or 1350 30 chance Unit sales 1080 20 chance 1010 50 chance or 930 30 chance Variable cost per unit 10 V eP Nf Perform a sensitivity analysis on the project s sales price and unit sales The beta of the time one expected cash flow 00 the riskfree rate is 5 and the market risk premium is 84 Use the CAPM Sales Price Sensitivity Analysis Be able to calculate the numbers in italics I What is the most likely sale39s price What is the expected sale39s price I What are the highest and lowest possible 39what if NPVs for the project I What is the NPV of the project Unit Sales Sensitivity Analysis Be able to calculate the numbers in italics Which of the two variables sales price or units presents the most standalone risk for the project Some questions How does the firm determine the above distributions of possible sales prices and unit sales Should the firm spend time and money to further refine these figures Wait 7 isn t the NPV negative 7 shouldn t we just reject the project If we plan to gather more information which variable sales price or unit sales should the firm address The value and costs of gathering more information What are the costs and benefits of gathering information eg a marketing survey Costs The fee charged by the marketing research firm and other costs incurred by your firm Benefits Assume that the marketing survey will reveal the exact sales price for the product Typically the marketing survey will not reveal a precise solution How would this benefit your firm You know whether the project will be good or bad pm to investing the 3770 initial investment The reason the NPV is negative is because there is a 30 chance of 3770 3500 105 43667 the pessimistic whatif NPV Eliminating this possibility will raise the NPV of the project Another potential benefit is from a reduction in risk This could mean a reduction in the discount rate Is this a benefit in this problem Scenario analysis here the manager is asked to supply several sets of assumptions scenarios such as pessimistic mostlikely and optimistic scenarios with probabilities of each Unlike sensitivity analysis assumptions are not changed one at a time but all assumptions are modified to fit a particular scenario Advantage variables are likely to be interrelated Therefore it often doesn39t make sense to analyze variables oneatatime The pessimistic scenario will provide the worse case N39PV What if the worstcase NPV is positive Breakeven analysis is similar to sensitivity analysis Variables are adjusted oneatatim e up or down to determine what value produces a 0 N39PV 1n the example above you would determine the sales price that makes the NPV exactly equal to zero The breakeven point is in terms of N39PV not accounting income accounting income ignores time value of money see example in book on pages 251 Breakeven analysis is well suited to a graphical presentation Monte Carlo Simulations is a more sophisticated technique of estimating the probability distribution or frequency distribution of possible project cash flows based on the probability distributions of the assumptions see figure 104 for an example This is used to help assess the riskiness of the project The book39s discussion in section 102 goes beyond the scope of this course We will not discuss this topic further Decision Tree analysis can be used to evaluate projects that require decisions over several time periods or over several stages See figures 105 gives a simple example and 106 and 107 more complicated examples Again the discussion in the section 103 of the book goes beyond the scope of this course However it is important to understand that a project with several stages gives managers a valuable real option A nancial option gives the owner the right to buy or sell a financial asset at a certain price for a certain period of time Example An option to purchase IBM stock at 100 per share at any time for the next three months A real option gives the owner a similar right to do something or not do something Just like a financial option has value a real option also has value Each project usually comes with two real options 1 to expand the project if the project is successful and 2 abandon the project if the project is unsuccessful Some also come with timing options the opportunity to postpone investment Exam le A firm is considering selling a new product The firm can either market the product nationwide at considerable expense or sell first in a test market at a lower expense The testmarket decision gives the firm a valuable real option Describe the real option How should the company decide whether to go directly to the expensive fullscale project or if it should use the smaller testmarket project first What are the incremental costs of the testmarketing project What are the incremental benefits of the testm arketing project This example can be presented in a decision tree framework gtxlt Selected Quiz Questions from the Textbook for Chapter 10 101 102 a b c and d 103 104 Chapter 10 Review Questions 1 Understand the difference between a proj ect s standalone risk withinfirm risk and beta risk Be able to determine whether the different groups of individuals listed towards the beginning of the Chapter 10 notes would be concerned or unconcerned with these various types of risk 2 What factors would cause a proj ect s withinfirm risk to be low in relation to its standalone risk What factors would cause a proj ect s beta risk to be low in relation to its standalone risk or withinfirm risk 3 Know the methods used to calculate standalone risk sensitivity analysis scenario analysis and breakeven analysis We skipped the discussion of how MonteCarlo simulations could be used to evaluate standalone risk 4 Understand the difference between a project s quotmost likely outcome and its quotexpected outcomequot for a particular variable Know how to use expected outcomes to calculate the NPV of a project Know how to use pessimistic most likely and optimistic outcomes to calculate quotwhatifquot NPVs 5 Understand how to determine the benefits of obtaining additional information 6 Understand how a decision tree analysis can assist a manager in analyzing projects that require decisions to be made in several steps What are the factors that would make it beneficial or detrimental for a firm to use a testmarket Chapter 10 Practice Problems 1 Assume that Project XYZ has a beta 00 the riskfree rate is 5 and the market risk premium is 84 Therefore the discount rate for Project XYZ 5 Initial investment 1350 Highest possible time one cash flow 60 chance 1650 Lowest possible time one cash flow 40 chance 1100 What is the NPV for Project XYZ 11 905 What is the highest possible whatif NPV for Project XYZ 3221429 2 ABC Corporation is considering Project Z Identify which measure of risk is the most relevant measure of risk for each of the following individuals on Project Z s stand alone risk Project Z s within firm risk Project Z s beta risk The chairman of the board of directors of ABC Corporation The chairman does not receive any salary or other benefits from the corporation and only owns a small amount of the stock of ABC Corporation The vast majority of the chairman s wealth is invested in a welldiversified mutual fund Answer Project Z s beta risk A stockholder that has most of her wealth invested in the stock of the corporation Answer Project Z s within rm n39sk An employee that works in the firm s Treasury department and does not work on Project Z This employee does not have any investments besides the stock she owns in ABC Corporation Answer Project Z s within rm n39s 9 Similar to the example given in the notes the following project requires an initial investment of 3500 and will end in one year The project s beta is 0 What is the NPV of the project using a 5 riskfree opportunity cost of capital Be able to calculate the numbers in italics using the other numbers Expected sale sprice 13 40 NPV 26I90 Therefore reject the project 4 ABC Corporation is considering Project ZZZ Project ZZZ involves the sale of TTU souvenir basketballs You have calculated the NPV of Project ZZZ using an opportunity cost of capital of 10 and the project s expected cash flows The NPV is 1000 Determine if the breakeven point for the following variables is above or below each of these variables expected values I The expected sale s price for TTU basketballs is 20 Answer The breakeven paint is below 20 I The expected cost of purchasing the TTU basketballs from the manufacturer is 10 Answer The breakeven paint is above 10 5 Consider the following information for a oneyear project Expected sales price 15 Expected variable costs per unit 12 Expected unit sales 2400 Time one expected cash flow 15122400 7200 Initial investment 5000 Discount rate 5 Using the 5 discount rate the NPV of the project 7200 105 5000 185714 What is the breakeven point for variable costs per unit rounded to the nearest penny 1281 6 Consider the following information for a oneyear project Expected sales price 179 Expected variable costs per unit 138 Expected unit sales 2000 Time one expected cash flow 1791382000 8200 Initial investment 5250 Discount rate 5 Using the 5 discount rate the NPV of the project 8200 105 5250 255952 What is the breakeven point for unit sales rounded to two decimal places 1344 51 7 Consider the following information for a oneyear project Expected sales price 187 Expected variable costs per unit 132 Expected unit sales 2200 Time one expected cash flow 1871322200 12100 Initial investment 10000 Discount rate 5 Using the 5 discount rate the NPV of the project 12100105 10000 152381 What is the breakeven point for unit sales rounded to two decimal places 190909 7 Chapter 13 Corporate Financing and Market Ef ciency 331 7 337 bottom of 348 to the middle of 349 In this chapter we define market efficiency and discuss how market efficiency applies to financing choices of a firm At this point of the course we shift the focus from capital budgeting decisions which projects should the firm select to financing decisions how do we acquire the funds to finance good projects These financing decisions will also determine who receives the cash ows from the accepted projects I The capital budgeting decision affects the asset side of the balance sheet I The financing decision typically determines the makeup of the liability and equity side of the balance sheet The owners of the debt and equity are combined the owners of the firm s assets and therefore share in the cash ows of these assets Principal and interest payments are the portion of a firm s cash ow paid to the owners of debt These payments are set by contract What happens if the company cannot meet the contractual obligations of the debt contract What can the firm do with the excess cash ow ie cash flows above the payments owed to the owners of debt Pay a dividend to the owners of equity 1 2 3 4 5 Let s apply this concept to financing a project Consider the following firm Cash flow from assets financial and real eg interest dividends CF from projects 1000 Sale of assets financial and rea 0 New financing 0 Total 1000 Principle and interest payments 6000 perpetual debt 5 interest rate 300 Dividend payment to stockholders 50 Investment in new positive NPV projects 500 Cash deposited in the firm s checking account 50 Investment in TBills 100 Repurchase of debt or equity 0 Total 1000 Assume that we have identified another valuable project one with a positive NPV using the tools learned in the first half of this course This project requires a 400 initial investment in land and machinery What financing method should the firm use to acquire the 400 of funds for the project Cash flow from assets financial and real eg interest dividends CF from projects 1000 Sale of assets financial and real 0 New financing 0 Total 1000 Principle and interest payments 6000 perpetual debt 5 interest rate 39 300 Dividend payment to stockholders 50 Investment in new positive NPV projects 39 900 Cash deposited in the firm s checking account 39 50 Investment in TBills 100 Repurchase of debt or equity 3 0 Total 1400 How can we balance out the cash in ows and cash out ows V eP Nf Which is the best method The answer to this last question affects 1 Capital structure policy I Should the firm borrow money or sell new stock to meet its needs for cash I Should the firm borrow with shortterm or longterm debt I Should the firm borrow with straight debt or convertible debt 2 Dividend policy Should the firm reduce its scheduled dividend payments to stockholders and use these savings to invest into the new project or should it continue to pay high dividends forcing the firm to raise cash in some other way 3 Sale of assets 7 Should the firm sell off some of its financial or real assets to finance the project 4 Lease versus buy decisions Should the firm buy land machinery and other assets needed for the project or should the firm rent these assets 5 Mergers and acquisitions Should a cashrich firm acquire a cashpoor firm which has a lot of good projects These questions are important even if the firm does not have a particular project to finance I Should the firm issue debt to retire equity or vice versa I Should the firm restrict its current dividends to pay for unidenti ed future projects I Should the firm sell off some of its financial or real assets that it thinks are overvalued I Should the firm sell its assets and lease them back from the purchaser I Should the firm seek to acquire undervalued merger candidates If nancial markets are perfect efficient and in equilibrium then the answer to these questions is simple The firm39s value will not be affected by the decision Therefore Finance the project with debt or equity the firm39s value will not be affected by the choice Pay high or low dividends the firm39s value will not be affected by the choice Sell or don t sell financial or real assets the firm39s value will not be affected by the choice Lease or buy assets the firm39s value will not be affected by the choice Here the rental market is perfect efficient and in equilibrium I Acquire or don39t acquire another firm the firm39s value will not be affected by the choice Here the market value of the acquired firm is established in a perfect efficient and in equilibrium market 2 In essence the NPV of each of these decisions is zero For example if the financial markets are perfect efficient and in equilibrium then NPV of debt financing 0 NPV of equity financing 0 So either financing choice has the same effect on firm value A quick review why would the NPV be zero for each choice For example why would the NPV of debt financing be zero If the NPV of borrowing money is positive then what does this imply about the NPV of lending money Thus competition in the financial markets forces the NPV to zero Therefore the important decisions for the firm are those that affect the asset side of the balance sheet such as project selectionrejection Firm value cannot be increased by the financing decision Definition of an efficient market An efficient market is one where prices for securities and other assets re ect all relevant and available information The three forms of efficiency I Weakfarm efficiency security prices re ect only past price and return information I Semislrangfarm efficiency security prices reflect all publicly available information I Strangfarm efficiency security prices reflect all relevant information There is currently a debate as to the degree of efficiency of the security markets Therefore market efficiency deals with the degree to which information is re ected in a security s price Implications of an efficient and perfect and in equilibrium market an example Firms can fund positive NPV projects using a wide variety of financing choices As stated above each of the possible financing choices will have no affect on the value of the firm since all have a zero NP Using this assume a financial manager is trying to decide how to finance a new project The project requires a time zero initial investment of 100 and produces an expected cash ow of 110 in one year The opportunity cost of capital is 7 and the project NPV is 280 The firm has two financing choices for raising the 100 a oneyear riskfree debt issue with a 5 interest rate or a common stock issue with a 15 expected return to stockholders Base case NPV Base case NPV Financing NPV debt Financing NPV equity After Financing Project NPV After Financing Project NPV Conclusion 7 What does market efficiency have to do with the above example Each security has a market price of 100 What do these prices re ect according to market efficiency Market value of the debt security 100 PV of the future debt payments based on relevant and available information Market value of the equity security 100 PV of the future equity payments based on relevant and available information Since both securities have the same PV equal to 100 and therefore their NPVs are both equal to 0 then both securities are equivalent in terms of valuation and either one can be used to finance the project That is firm value at time 0 is not affected by the choice of the type of financing if the financial market is perfect efficient and in equilibrium However in retrospect one choice is likely to be better than the other For example assume that there is a recession over the next year Would you rather have financed the project with debt or equity Now assume that there is a booming economy over the next year Would you rather have financed the project with debt or equity Market inef ciencies imperfections and disequilibrium can make financing decisions important An example Assume the security markets are only semistrong form efficient and managers who know the true present value of the firm s securities need to raise 100 for the initial investment in a project Security A PV calculated by the firm s managers 110 Security B PV calculated by the firm s managers 90 Investors based on public information think that both securities have a PV 100 If managers can sell either security to investors for 100 which security Will they select to fund the project To answer calculate the NPV of the two financing choices From the managers perspective NPV Security A NPV Security B From the investors perspective NPV Security A NPV Security B What Will managers do Note 7 insiders and outsiders having the same information is one of the assumptions used in defining market perfection Coordination with Chapter 9 In chapter 9 we assumed that the financial markets were perfect efficient and in equilibrium This affects a couple of key points from the chapter 1 As discussed in the previous example if financial markets are not perfect efficient and in equilibrium then the financing NPV may not be equal to zero In this case the after financing NPV is not equal to the base case The main tool we learned from Chapter 9 is that we can use the WACC of another firm as the discount rate for a project eg use the WACC of Ford as the discount rate for an automobile manufacturing project What happens to the WACC if the financial markets are inefficient 4 The WACC formula Without taxes is WACC debt rD equity rE Market efficiency implies that the current price of a security reflects relevant and available information about the security If the market is inefficient then the security s current price could be almost anything How does this affect the calculation of the WACC Selected quiz questions from Chapter 13 of the textbook l34a c d l36a 137 Chapter 13 Review Questions 1 Understand how cash flows from assets are paid to the owners of debt and equity and the financing sources for projects 2 Understand the definition of an efficient market 3 Remember that in a perfect efficient and in equilibrium market the present value of a security39s expected future cash flows is equal to the current market price for that security NPV 0 4 Assume that a firm has a project to finance What are the implications of being able to raise funds for that project by issuing securities in a perfect efficient and in equilibrium market What happens if the market is not efficient Chapter 13 Practice Problems 1 Similar to the discussion in class assume that security markets are only semistrong form efficient and managers who know the true present value of the firm s securities need to raise 5000 for the initial investment in a project Managers have two financing choices Security AA and Security BB The following shows the valuation of the securities using information available to mangers also called insiders and investors also called outsiders Security AA Managers valuation 4800 lnvestors valuation 5000 Security BB Managers valuation 5200 lnvestors valuation 5000 Assume that managers can issue either of the two securities to investors for 5000 Using managers information the financing NPV for Security AA is A Positive Correct answer B Negative C Zero N 9 gt V 0 gt1 Similar to the discussion in class assume that financial markets are only semistrong form efficient and managers who know the true present value of the firm s securities need to raise 10000 for the initial investment in a project Managers are considering issuing Security X Managers valuation of Security X 9500 Investors valuation of Security X 10000 Assume that managers plan to issue Security X to investors for 10000 ie what investors think Security X is worth Using managers information what is the financing NPV for Security X 5 00 In each case determine the correct statement 1A The semistrong form of market efficiency states that A Prices of financial securities re ect all information public and private B Prices of financial securities re ect all publicly available information CorrectAnswer 1B If a financial market is efficient then A All financial securities will have the same expected return B Financial assets could have different expected returns CorrectAnswer Assume that the president of a corporation knows that the corporation is going to release some bad news tomorrow Further assume that the market is strong form efficient Can the president take advantage of this inside information by selling the stock today ie before the bad news is released to the public No 7 the price will immediately fall to its new lowervalue based on the private information Assume that the FDA has just rejected ABC Pharmaceuticals 1nc s application for a new cancer drug Without FDA approval the company will not be able to sell the drug Everyone had thought that the drug would be approved This extremely bad and disappointing news about the company will be made public tomorrow Assume that you are planning to buy stock in ABC Pharmaceuticals Inc today ie before the public announcement Which form of market efficiency would enable you to buy the stock for the lowest price A Semistrong form efficiency B Strong form efficiency CorrectAnswer XYZ Corporation plans to issue some stock to finance a project Assume that the investing public thinks that the stock is worth 10 per share but managers of the corporation know that the stock is overvalued ie they know that the true value of the stock is only 9 per share If the corporation can issue one million shares of stock at 10 per share then managers know that the financing NPV of this stock issue is A 1000000 CorrectAnswer B l000000 XYZ Corporation plans to issue some stock to finance a project Assume that the investing public thinks that the stock is worth 10 per share but managers of the corporation know that the stock is undervalued ie they know that the true value of the stock is 11 per share If the corporation can issue one million shares of stock at 10 per share then managers know that the financing NPV of this stock issue is A 1000000 B 1000000 CorrectAnswer Assume that financial markets are perfect efficient and in equilibrium This means that the NPV of all financing choices are equal to zero A firm is considering two financing choices to finance a positive NPV project Debt expected return and required return 5 Equity expected return and required return l5 Assume that either of the two possible financing choices will be outstanding for one year You are trying to make a decision today time 0 about which of the two financing choices is best in terms of impact on firm value not knowing what the state of the economy is going to be over the next year Given this information which of the following statements is true concerning the financing choice at time 0 A Debt is a better financing choice because the expected and required return is lower Thus debt financing will have a more favorable impact on firm value than equity financin B Equity is a better financing choice because of its added exibility Thus equity financing will have a more favorable impact on firm value than debt financing C Both financing choices would have the same impact on firm value at time 0 Correct Assume that financial markets are perfect efficient and in equilibrium This means that the NPV of all financing choices are equal to zero A firm is considering two financing choices to finance a project Debt required return 5 Equity required return l5 Assume that either of the two financing choices will be outstanding for one year Under what economic conditions over the next year would the firm be better off issuing equity rather than debt A A recession economy CarrecIAnswer B A booming econom C Since the NPV 0 for both financing choices it doesn t matter what the economy is like over the next year A firm needs funds to finance a project Assume that financial markets are perfect efficient and in equilibrium This means that the NPV of all financing choices calculated at time 0 are equal to zero A firm is considering two financing choices to finance a project Debt required return 5 Equity required return l5 Assume that either of the two financing choices will be outstanding for one year Under what economic conditions over the next year would the firm be better off issuing debt rather than equity A The economy is booming over the next year causing the firm s cash flows and value to increase significantly CarrecIAnswer B The economy is in a recession over the next year causing the firm s cash flows and value to decrease significantly C Since the NPV 0 for both financing choices it doesn t matter what the economy is like over the next year i i i i i i Assume that financial markets are perfect efficient and in equilibrium This means that the NPV of all financing choices are equal to zero Today is January 1 2006 and you don t know what the economy will be like over the next year recession normal or boom A firm is considering two financing choices to finance a positive NPV project Debt expected return and required return 5 Equity expected return and required return 15 Assume that either of the two possible financing choices will be outstanding for one year from January 1 2006 to December 31 2006 Further assume that one year from today on December 31 2006 you realize that there had been a booming economy in 2006 In retrospect ie given that the economy was booming which financing choice would have been best A Debt financing would have been better if the economy is booming in 2006 CarrecIAnswer B Equity financing would have been better if the economy is booming in 2006 C Both financing choices would have the same impact on firm under the assumption that the economy is booming in 2006 A firm needs funds to finance a project Assume that financial markets are perfect efficient and in equilibrium This means that the NPV of all financing choices calculated at time 0 are equal to zero A firm is considering two financing choices to finance a project Debt required return 5 Equity required return 15 Assume that either of the two financing choices will be outstanding for one year Under what economic conditions over the next year would the firm be better off issuing equity rather than debt A The economy is in a recession over the next year causing the firm s cash flows and value to decrease significantly CorrectAnswer B The economy is booming over the next year causing the firm s cash flows and value to increase significantly C Since the NPV 0 for both financing choices it doesn t matter what the economy is like over the next year Assume that the FDA has just accepted ABC Pharmaceuticals Inc s application for a new cancer drug With FDA approval the company will be able to sell the drug Everyone had thought that the drug would not be approved This extremely good news about the company will be made public tomorrow Assume that you are planning to buy stock in ABC Pharmaceuticals Inc today ie before the public announcement Which form of market efficiency would enable you to buy the stock for the lowest price A Semistrong form efficiency Correct answer B Strong form efficiency Assume that the FDA has just rejected ABC Pharmaceuticals Inc s application for a new cancer drug Without FDA approval the company will not be able to sell the drug Everyone had thought that the drug would be approved This extremely bad news about the company will be made public tomorrow Assume that you are planning to sell stock in ABC Pharmaceuticals Inc today ie before the public announcement Which form of market efficiency would enable you to sell the stock for the highest price A Strong form efficiency B Semistrong form efficiency Correct answer Assume the financial markets are perfect efficient and in equilibrium A firm has the choice of issuing either debt or equity to finance a project Both securities will be outstanding one year More specifically the debt matures in one year If the company issues equity the company plans to repurchase the equity in one year The expected oneyear returns for the debt and equity are 5 and 15 respectively Which of these two securities has the higher financing NPV A The debt security has the higher financing NPV B The equity security has the higher financing NPV C Both securities have the same financing NPV Correct answer Chapter 12 Agency problems Management Compensation and Measuring Performance This chapter is a practical discussion of how we can make sure managers are following the NPV rule accept positive NPV projects and reject negative NPV projects We will discuss V The capital budgeting process Agency problems associated with gathering information needed to make good decisions How to correct these problems Measuring project performance using accounting income 2 3 4 5 Measuring project performance using economic income The main topic of this chapter is How can we get managers to select positive NPV projects and reject negative NPV projects We start the discussion with an outline of how capital budgeting decisions are made The capital budgeting process Capital budgeting decisions ie what projects the firm invests in are made by employees at different levels of the firm Lower level managers make a significant number of small project decisions More expensive projects typically require higherlevel approval A significant number of projects are not in the capital budget IT RampD marketing expenses employee training but they are still projects and should be analyzed as projects Evaluation of the project after acceptance 7 Post audits Why do we look at a project after acceptance 1 Fix any unanticipated problems avoid costly delays determine the accuracy of forecasts to help in making more accurate forecasts for future projects 2 Typically ask I Were the estimates of initial investment accurate I Are the first few years of cash flow estimates accurate Overall profitability of the project is probably not evaluated since postaudits are typically conducted prior to the project39s completion Need to consider the affect of the economy of project cash flows L V Some projects are difficult to evaluate separately because they are interwoven with other projects Example Advertisements for a new product is done in three forms TV radio and newspaper Should the firm continue advertising in the newspaper What was the incremental impact of the newspaper advertisement on product sales Agency problems can cause firms to make bad project selection decisions What are agents An agent is someone that works for a principal For example a real estate agent works for a home seller the principal Principals want agents to work in their best interests However sometimes they don t What does a home seller want a real estate agent to do How might a real estate agent fail to work in the best interests of the home seller For a corporation managers and employees of the corporation are the agents of the firm s stockholders the principals Just like the real estate agent example stockholders want managers and employees to work in their best interests How agency problems distort the information that is given to senior managers 1 Biased forecasts provide bad information to senior managers Forecasts can come in two forms Biased economic forecasts Suggestion Rather than having each project manager put together an independent economic forecast it is probably better to have a companywide economic forecast that can be applied to all projects Also rather than one economist s forecast a consensus forecast of a team of economists can further reduce biases Biased noneconomic based forecasts 2 Agency problems ie con icts of interests between decisionmakers agents and firm owners can cause biased forecasts and therefore suboptimal investment decisions Describe how the following examples can result in the acceptance of a bad project or rejection of a good project I Project acceptance allows the project manager to over consume perks I Project acceptance increases the size of manager s division think about the manager s compensation I Manager is overly concerned with shortterm profitability of his her division I Project manager has an incentive to invest in projects that require his her specialized skills I Project manager needlessly wants to avoid risk when deciding which projects to select I The project manager may not expend the effort needed to make the project successful 3 Many of these problems can also apply to senior management as well 4 Can senior managers avoid agency problems by disclosing the opportunity cost of capital See Brealey Myers and Allen s second law page 303 How to correct these agency problems Increased monitoring 7 but you need to compare the benefits with the costs of monitoring Benefits of monitoring I Reduced agency costs Costs and problems of monitoring I Monitoring costs money and takes time Senior management can t review projects they don t know about Micro management by senior management Too many constraints or too much time spent on monitoring can result in the firm being prevented from undertaking positive NPV projects Diminishing returns Need to review projects that are most likely to contain errors in assumptions or analysis that would hurt the firm Example You are a senior level manager in charge of reviewing projects prior to acceptance rejection A junior analyst has computed the NPV of two nonmutually exclusive projects NPV Project A 10 NPV Project B 10 Assume that you know that the junior analyst is pessimistic in making forecasts and calculating NPVs If you have only the time to review one project which would you review I Who monitors senior management Shareholders are the primary beneficiaries of reduced agency costs but do they have the incentive to monitor Primary responsibility the board of directors stockholders lenders hired monitors e g auditors O hanging incentives for managers ie use compensation to provide incentives Usually determined by outputs performance rather than inputs ie effort Why In the US CEOs are often paid relatively low base salaries with the rest being incentive based bonuses stock and stock options Only 1 million of regular compensation is deductible by the corporation Compensation in the form of stock options is not included in this restriction The amount of incentives should depend on how much firm value is influenced by managers efforts Two examples A Firm value is primarily influenced by factors beyond the manager s control eg a power plant B Firm value is prim arily influenced by factors in manager s control e g real estate brokerage I The magnitude of gains and losses for large 1 39 require and to share risk I Incentives are often linked to stock performance Problems A Too much concern with the Within firm risk of the project B Large fluctuations in the firm s stock value could be caused by 1 changes in the overall stock market and or 2 firm specific changes in stock value C Abnormal stock price increases may occur too early example the problem with hiring a hotshot manager D Enron and WorldCom type problems Accounting measures are often used for evaluating employees Advantages 1 Objective 2 Can be used to evaluate junior managers who are in charge of a division or project ie stock performance isn t the best measure Disadvantages 1 Subject to manipulation 2 Accounting profits do not always equate to adding value through accepting positive NPV projects Measures 1 Book or accounting return on investment Accounting net income Investment Compare this fraction to the opportunity cost of capital 2 Economic Valued Added EVA Net accounting operating profit after taxes 7 opportunity cost of capital investment See httpwwwstemstewartcom for more information 3 Disadvantages of both methods They use accounting income as a starting point and They use current profits from a project instead of the present value of future expected cash flows from the project What if the bad performance is due to factors beyond the employee s control Measuring the pro tability of the rm39s assets using economic income versus accounting income Accounting book net income Revenue minus expenses minus accounting book depreciation minus taxes Economic income cash flow minus economic depreciation Cash flow computation is described in Chapter 6 Economic depreciation re ects the decrease in the present value of the asset over time Example Accounting book depreciation 1 1000 initial investment in a factory 2 Factory has a useful life of 3 years and a zero salvage value 3 Expected factory accounting revenue and expected cash flows Year 1 300 Year 2 300 Year 3 700 4 Accounting depreciation method Straightline depreciation 5 No other expenses other than depreciation Ignore income taxes Expected accounting income per year Year 1 300 333 33 Year 2 300 333 33 Year 3 700 334 366 Expected accounting return on investment ROI per year Year 1 33 1000 33 Year 2 33 667 495 Year 3 366 334 10958 Performance Evaluation using Accounting Figures Assume that you are the project manager and under your management you are able to exactly meet expectations How will the firm39s senior management view your performance using accounting ROI as a measure Performance evaluation at the end of year 1 Performance evaluation at the end of year 2 Performance evaluation at the end of year 3 Example Economic depreciation using a 10 cost of capital 1 What is the expected economic investment att 0 ie PV at t 0 10465815 2 What is the expected economic investment at time 1 2 and 3 PV t l PVt2 PVt3 L V Economic depreciation equals the change in economic investment or PV by year Since we are calculating these figures at time zero we are calculating expected economic depreciation Ideally you would recalculate the present value from the previous step each year in order to calculate the previous year s actual economic depreciation Expected economic depreciation ear 1 Expected economic depreciation ear 2 Expected economic depreciation ear 3 Total expected economic depreciation is 10465815 PV att 0 of the project 4 V Expected economic income per year factory cash flow minus economic depreciation Year 1 Year 2 Year 3 Lquot V Expected economic return on investment ROI Year 1 Year 2 Year 3 Performance evaluation using economic income gures Assume that you are the project manager and under your management you are able to exactly meet expectations How will the firm39s officers view your performance using economic ROI as a measure Performance evaluation at the end of year 1 Performance evaluation at the end of year 2 Performance evaluation at the end of year 3 Lessons 1 Accounting depreciation distorts the yearbyyear ROI Managers compensated based on accounting ROI may be reluctant to take projects similar to the example given above 2 1f actual cash ows equal expected cash flows then economic income results in a constant ROI equal to the cost of capital Side note What would actual economic ROI look like if you exceeded expectations For example assume that actual cash ows are Year 1 300 Year 2 300 Year 3 725 What is the actual economic ROI for years 1 2 and 3 How to correct the accountingeconomic depreciation problem 1 Adjust accounting depreciation to re ect economic depreciation 2 Compare yearbyyear accounting ROI with accounting ROIs from similar successful projects 3 Change manager compensation package 4 1n the long run when the firm has a mixture of old and new projects accounting return on investment will be closer to economic return on investment But see Table 125 showing that the two measures can still be different Selected quiz questions from Chapter 12 of the textbook 121 c d and e122123124127128 Chapter 12 Review Questions 1 Understand the basics of the capital budgeting process Remember that many project acceptance rejection decisions are made by lowerlevel managers Understand why a project should be evaluated after acceptance What is the purpose of a post audit 2 Understand the management agency problems as they relate to the capital budgeting process How can monitoring address these problems Who benefits from monitoring Who monitors corporate managers What are the limitations costs and problems of monitoring How can changing incentives reduce agency problems What are the limitations costs and problems of changing incentives 3 How is accounting ROI different that EVA 4 What is economic depreciation Understand how to calculate returnoninvestment ROI using both accounting and economic depreciation What are the advantages of using economic depreciation instead of using an accounting depreciation method such as the straightline or the smnoftheyearsdigits or tax depreciation methods In particular what is the problem with using accounting depreciation in performance evaluation for a manager 5 What are the various ways a corporation can adapt accounting depreciation to correctly evaluate the performance of a manager Chapter 12 Practice Questions 1 Assume that a project requires an initial investment of 5000 and is expected to produce cash flows and revenue of 2100 per year for three years The expected project net income is calculated by subtracting depreciation for revenue Ignore income taxes A What is the expected economic depreciation per year if the discount rate is 10 1577 76 173554 190909 What is the expected economic R01 per year 10f0r each of the three years What is the expected accounting ROI if straightline depreciation is used 3 year life no salvage value 8667 13 26 D What is the actual economic ROI in year 3 if cash flows exceed expectations in year 3 More than 10 B C 2 Assume a divisional manager39s compensation contract is designed as follows 50000 per year base salary plus a bonus equal to 5 of the difference between the actual cash flows for the division and the division39s projected cash flows Since the base salary is relatively low the manager expects most of her his yearly salary from the bonus If this manager is responsible for reviewing and approving new projects for the division it is likely that A The manager will have an incentive to overestimate project cash flows B The manager will have an incentive to underestimate project cash flows CorrectAnswer 3 Four junior analysts have the responsibility to calculate NPV for four different projects Unfortunately and as discussed in class the person calculating the project NPV may let their biases enter into their calculations Assume the following Biased NPV calculated for Project A 5 This junior analyst tends to overestimate project NPV Biased NPV calculated for Project B 5 This junior analyst tends to overestimate project NPV Biased NPV calculated for Project C 5 This junior analyst tends to underestimate project NPV Biased NPV calculated for Project D 5 This junior analyst tends to underestimate project N39PV A senior analyst has enough time to evaluate and check the assumptions and NPV calculations for only two projects Taking into account the junior analysts biased NPV calculations and their known tendency to overestimate or underestimate N39PV which two projects should the senior analyst review Projects A and D 4 As described in class the accounting return on investment for a project is calculated by dividing the year39s net income for the project by A The book value of the project at the beginning of the year CorrectAnswer B The book value of the project at the end of the year V 0 gt1 00 O In class we discussed Brealey Myers and Allen s second law regarding project cost of capital According to that second law if a company increases the minimum rate of return required for its projects eg if they increase the discount rate they will use to evaluate projects from 10 to 15 A The proportion of projects that have a positive NPV for that company calculated at the new higher discount rate will increase B The proportion of projects that have a positive NPV for that company calculated at the new higher discount rate will decrease C The proportion of projects that have a positive NPV for that company calculated at the new higher discount rate will stay the same CarrecIAnswer As discussed in class a senior manager needs to recognize that a project manager will typically prefer that the firm select a project that other things equal A Requires his or her specialized skills CarrecIAnswer B Does not require his or her specialized skills ie anyone could manage the project As discussed in class incentive based compensation for a manager eg giving the manager stock in the firm as part of his or her compensation package is most effective in which of the following two situations A The manager is the president of a company where firm value is influenced by factors beyond the manager s control B The manager is the president of a company where firm value is influenced by factors within the manager s control Correct Answer In class we discussed how stock can be used to provide the proper incentives for managers and thereby reduce agency costs One of the problems of using stock as an incentive is the problem of the hotshot manager As described in class the problem of the hotshot manager is that A Stock prices often rise at announcement of the hiring of the hotshot manager which is before the manager starts working for the firm ie before the manager s date of hire Correct B Stock prices usually don t rise at announcement of the hiring of the hotshot manager Instead the increase in stock price typically occurs after the hotshot manager starts working for the firm ie after the manager s date of hire A threeyear project requires an initial investment of 2000 It will produce expected cash flows of 1500 at time one 1200 at time two and 500 at time three The opportunity cost of capital is 10 A What is the NPV of the project 731 03 B What is the economic depreciation for the second year 1 049 59 C If actual cash flows are less than expected cash flows for the third year what will the economic return on investment be for the third year Less than 10 ABC Corporation will invest in a twoyear project Expected cash flows are listed below 0 1 2 l 190000 88000 145200 Using a 10 discount rate the PV of the project s future expected cash flows is 200000 Therefore the NPV for the project is 10000 Using the expected cash flows what is the economic depreciation for the first year 68 000 1 N 9 He The following are expected cash flows for a project Using a discount rate of 10 what is the expected economic depreciation for the first year of the project 50526 o 1 2 3 1000 650 400 700 The following are expected cash flows for a project Using a discount rate of 6 what is the expected economic depreciation for the first year of the project 32043 3 0 1 1000 400 500 600 The following are expected cash flows for a project Using a discount rate of 9 what is the expected economic depreciation for the first year of the project 188 71 0 1 2 3 1000 300 500 700 The following are expected cash flows for a project Using a discount rate of 9 what is the expected economic depreciation for the first year of the project 90 01 3 0 1 1000 200 500 800 The following are expected cash flows for a project Using a discount rate of 5 what is the expected economic depreciation for the second year of the project 54921 3 0 1 1000 200 610 700 The following are expected cash flows for a project Using a discount rate of 12 what is the expected economic depreciation for the second year of the project 13520 3 0 1 2 1000 400 250 920 The following are expected cash flows for a project Using a discount rate of 8 what is the expected economic depreciation for the second year of the project 50754 3 0 1000 300 600 700 18 The following are expected cash flows for a project Using a discount rate of 8 what is the expected economic income for the second year of the project Note 7 this question asks for expected economic income not expected economic depreciation 92 46 0 2 3 1000 100 600 700 19 The following are expected cash flows for a project Using a discount rate of 8 what is the expected economic income for the first year of the project Note 7 this question asks for expected economic income not expected economic depreciation 11181 0 1 2 3 1000 400 550 700 Using the following numbers what is the expected economic return on investment ie expected economic ROI for the second year of the following project 3F 1 3 N O N You are considering a project The project requires an initial investment of 900 in a factory that will last three years no salvage value The firm was originally planning to use the straightline depreciation method to calculate accounting depreciation The following summarizes accounting net income for the project under straightline depreciation Assume the firm wants to switch to the sumoftheyears digits depreciation method for the project Under the sumoftheyears digits method the depreciation will be 450 for year 1 300 in year 2 and 150 in year 3 How will this change in the accounting depreciation method from straight line to sumoftheyears digits affect the accounting ROI for the third year A The account ROI for the third year will be the same under both methods B The account ROI for the third year will be lower using the sumoftheyears digits method C The account ROI for the third year will be higher using the sumoftheyears digits method Correct answer 22 The following are expected cash flows for a project Using a discount rate of 8 what is the expected economic depreciation for the first year of the project 198 78 0 1 2 3 1000 300 550 650 23 Refer back to the facts of the previous problem What would happen to the expected economic depreciation for the first year if the discount rate was changed from 8 to 9 You can solve this problem by using your intuition Here s a hint remember that expected economic ROI the discount rate So the expected economic R01 is 8 in the first problem and 9 in the second problem A The expected economic depreciation for the first year would increase B The expected economic depreciation for the first year would decrease Correct answer C The expected economic depreciation for the first year would stay the same Assume a project is expected to produce revenue of 600 per year for four years This project requires an investment of 1000 in a factory that will be depreciated over the project s four years using the straight line method for accounting purposes The factory has no salvage value at the end of the fourth year Other than accounting depreciation the project has no other expenses and there are no income taxes Using the straight line method the accounting depreciation will be 250 a year for each of the four years and net income will be 600 250 350 a year for each of the four years Over the four years accounting return on investment will A Stay the same each year B Increase each year CarrecIAnswer C Decrease each year Chapter 17 Corporate Capital Structure Foundations Sections 171 172 174 skim section 173 but read pages 459 through the top of 461 The primary focus of the next two chapters will be to examine the debtequity choice by firms In particular we will discuss possible advantages and disadvantages to debt versus equity financing In Chapter 17 we will 1 Learn the perfect capital market assumptions needed to demonstrate capital structure irrelevance 2 Learn the arbitrage proof for capital structure irrelevance 3 Learn how investors can manipulate capital structure of any firm to suit their own tastes 4 Review the effect of leverage changes on the return on equity return on debt return on assets and WACC Chapter 9 stuff The purpose of the discussion of this chapter is to lay the foundations for a higher level real world discussion in Chapter 18 Capital Structure Analysis in a Nutshell I If the firm is all equity the firm39s stockholders are the owners of 100 of the firm39s cash flows Cash flows be Be paid to stockholders as a dividend or stock repurchase or Be reinvested by the corporation in projects or Be put in a bank checking account or invested in securities I If there is debt and equity and perhaps other types of securities such as preferred stock convertible debt etc on the righthandside of its balance sheet then the firm39s cash flows must be split among the various claimants I Capital structure analysis attempts to find the particular combination of debt and equity and other types of securities that maximizes firm value and stockholder value I Based on the assumptions discussed below a firm39s capital structure decision is irrelevant In other words a firm cannot increase or decrease its value by making changes to the righthandside of its balance sheet I Starting with the foundation of capital structure irrelevance Chapter 18 will incorporate real world assumptions and examine the effects of these real world assumptions on the firm39s capital structure decision Chapter 17 quotPerfect Capital Marketquot Assumptions 1 No income taxes Therefore no income tax deduction for interest payments 2 No bankruptcy costs N o attorneyaccountanttrustee fees or other costs from going bankrupt 3 No transaction costs There is no cost to the corporation for issuing and repurchasing securities Investors can also buy and sell securities for free 4 Unlimited borrowing and lending at the riskfree interest rate for corporations and investors 5 No asymmetric information Outside investors know as much as corporate insiders 6 Managers and employees work to maximize stockholder wealth Also managers and employees of the firm are not affected by the amount of debt versus equity in a firm For instance managers and employees do not let the amount of leverage affect the criteria they use to select projects how they manage the firm s assets etc Modigliani and Miller 1958 Proposition 1 With the above assumptions the value of the firm in equilibrium is independent of the proportion of debt and equity in the firm39s capital structure Stating the proposition in another way If two firms Firm A and Firm B have identical assets then with perfect capital markets DA EA DB EB If not identical it is possible to earn an arbitrage pro t More specifically if the market values of these two firms are not identical then it is possible to make a series of investments in the firm s securities that require no net cash outlay and have no risk but pays the investor a positive cash flow Earning money because you make a cash investment or take on some risk of loss is consistent with market equilibrium However in equilibrium a riskfree investment that requires no cash outlay should not pay a positive cash flow to the investor 1f the market is out of equilibrium and arbitrage profits are available then investors taking advantage of the arbitrage opportunity would quickly force prices back into equilibrium and eliminate the arbitrage opportunity A simple example of an almost arbitrage pro t Gold dealer on 42nd Street in New York says that he will buy gold at 501ounce and sell at 501 50ounce Gold dealer on 43quoti Street in New York says that she will buy gold at 49950ounce and sell at 500ounce I Notice that each gold dealer has prices set up to earn 050ounce on each roundtrip transaction But will they really earn 050 with the prices outlined above What can you do to earn a 1 profit per ounce of gold Does this meet our definition of an arbitrage profit Have you invested any cash for even a short period of time Does this investment have any risk of loss Since this doesn t exactly meet our definition what would you have to do to make a 1 arbitrage profit Assuming you can structure your purchases and sales of gold to earn a arbitrage profit what should happen to the market prices of gold ie prices to buy and sell gold on 42nd and 43quoti streets In equilibrium if an investment requires no cash outlay for even a short period of time and no risk of loss then you should not expect to make money If the market is out of equilibrium and an arbitrage profit opportunity existed then prices should quickly move back to equilibrium so that the arbitrage opportunity is eliminated Application of perfect capital markets and a no arbitrage condition to corporate capital structure policy An example 1 Two identical firms except one firm has perpetual debt U is the unlevered firm and L is the levered firm 2 The required rate of return for Firm L s perpetual debt 5 5 rD rt 3 The investment policy common to each firm generates a perpetual stream of the following yearly cash flows from the firm s assets 13 probability of a 225 cash flow optimistic outcome 13 probability of a 45 cash flow middle outcome 13 probability of a 30 cash flow pessimistic outcome The expected cash flow is 100 per year in perpetuity 4 Cash flows from assets are first used to pay interest to the owners of debt if any The residual is paid as a dividend to stockholders Notation DL is the market value of the debt bonds in the levered firm EL is the market value of the equity stock in the levered firm EU is the market value of the stock in the unlevered firm Market value of the two rms VL DL EL The market value of the levered firm VU EU The market value of the unlevered firm Analysis of cash flow to owners of Firm U All cash ows to stockholders Asset cash ows Liability cash ows with 0 of debt 225 13 chance 0 13 chance 45 13 chance 0 13 chance m 13 chance M 13 chance 100 expected 0 expected Equity cash ows 225 13 chance 45 13 chance m 13 chance 100 expected Analysis of cash ows to owners of Firm L Cash ows split between stockholders and bondholders Asset cash ows Liability cash ows with 600 of debt 225 13 chance 30 13 chance 45 13 chance 30 13 chance M 13 chance M 13 chance 100 expected 30 expected Equity cash ows 195 13 chance 15 13 chance M 13 chance 70 expected With the perfect capital market assumptions given above the equilibrium pricing relationship is VU VL What happens if this relationship doesn39t hold exactly That is What happens if 1 VU gt VL or 2 VU lt VL Case 1 VU gt VL Firm U VU EU 1000 Firm L EL 300 DL 600 VL DL EL 900 How can you earn an arbitrage pro t At time 0 1 Sell short ocEU 2 Invest CDL VL ocEU into the debt of firm L 3 Invest EL VL ocEU into the equity of firm L Using the above numbers and on 10 What is the cash ow from the three position at time 0 1 Cash ow 2 Cash ow 3 Cash ow Total At time 1 2 3 etc 1 Pay missed dividends for firm U stock to cover obligation from the short position 2 Receive cash flow from investment in firm L debt 3 Receive cash flow from investment in firm L equity Using the above numbers and on 10 What is the cash flow from the three position at time 1 2 3 etc Notice that there is no cash investment at time 0 and you make money in all future years no matter What dividend Firm U pays This is an arbitrage profit Investors taking advantage of this arbitrage profit opportunity will cause I The price of firm L39s stock to increase I The price of firm US stock to decrease The price movement will continue until VU VL Case 2 VU ltVL Same assumptions as Case 1 except EL 500 At time 0 1 Sell short ocEL 2 Borrow ocDL 3 Invest ocEL ocDL into the equity of firm U Using the above numbers and on 10 What is the cash flow from the three position at time 0 1 Cash flow 2 Cash flow 3 Cash flow Tota At time 1 2 3 etc 1 Pay missed dividends for firm L stock to cover obligation from the short position 2 Pay interest on amount borrowe 3 Receive cash flow from investment in firm U equity Using the above numbers and on 10 What is the cash flow from the three position at time 1 2 3 etc Notice that there is no cash investment at time 0 and you make money in all future years no matter What dividend Firm L pays This is an arbitrage profit Investors taking advantage of this arbitrage profit opportunity will cause I The price of firm US stock to increase I The price of firm L39s stock to decrease The price movement Will continue until VU VL In equilibrium there should be no arbitrage profits available so VU cannot be greater than VL and VU cannot be less than VL Therefore VU must equal VL This means that with perfect capital markets the equilibrium value of a rm is independent of its capital structure That is the proportion of debt and equity on its balance sheet does not affect firm value Therefore I Financing a project with debt is equivalent to financing a project with equity I Capital structure changes ie issuing debt to buy back equity or vice versa will not affect firm value Another reason that capital structure does not affect rm value With perfect capital markets and assuming market equilibrium investors can buy levered or unlevered firms and manipulate the cash flows to suit their particular capital structure tastes Example r All equity firm with 100 shares outstanding 19 The firm s assets earn one of the three possible cash flows each year in perpetuity 13 probability of a 225 cash flow optimistic outcome 13 probability of a 45 cash flow middle outcome 13 probability of a 30 cash flow pessimistic outcome Expected yearly cash flow in perpetuity 100 9 Cash flows from assets are first used to pay interest to the owners of debt if any The residual is paid as a dividend to stockholders Expected year dividend in perpetuity 100 100 1 4 r 5 MRP 84 beta of equity 0595238 The required rate of return for the firm39s equity using the CAPM is 10 Obviously there is a lot of stand alone risk With these cash flows Why is the beta and discount rate so low What is the market value of the firm39s stock per share V The value of the firm outstanding shares x price per share 0 What are the dividends per share and return on investment across the three possible states Assume the firm changes its capital structure by issuing 600 of default riskfree perpetual debt rD 5 The firm uses the 600 of cash to repurchase 600 60 shares of stock The firm is now 60 debt and 40 equity DL 600 and SL 400 Are stockholders better off with debt in the rm39s capital structure 1 Expected return on the equity investment Expected R01 100 equity Expected R01 40 equity General formula is proposition 2 of Modigliani Miller 1958 rE rA rA rD CD E 2 Equity beta Equity beta 100 equity Equity beta 40 equity General formula 3E 3A BA BD CDE 3 Required rate of return for the stock using CAPNI Required return 100 equity Required return 40 equity 4 Market Value of the Stock Price per share 100 equity Price per share 40 equity Conclusion How did the change in capital structure affect the stockholders of the firm I Expected return increased but I Beta risk and required return also increased I End result no change in stockholder s wealth Before change in capital structure stockholder wealth After change in capital structure stockholder wealth However should a rm lever up if its stockholders prefer high expected return highrisk cash ows No because the stockholders of the firm can create these same risky cash flows using quothomemade leverage Assume an investor has 16 to invest but can purchase stock on margin at 5 interest perpetual debt With 24 of borrowed funds the investor can purchase four shares 40 of the unlevered firm Therefore purchasing stock on margin in the unlevered firm can make the ROI and risk the same as from ownership of stock in the levered firm A similar procedure can be used to quotunleverquot a levered firm For example take your 16 of cash and buy 640 of stock 064 shares of the levered firm and lend 960 5 perpetual debt Implications 1 Investors can take unlevered stock and create levered stock cash flows by buying stock on margin 2 Investors can buy levered stock and debt and create unlevered stock cash flows 3 In fact anything the firm can do investors can do Lesson Since a firm39s capital structure decision does not affect investors cash flow opportunities capital structure is irrelevant In summary with perfect capital markets the equilibrium value of a firm and investor cash flows opportunities are independent of the firm s capital structure choice Therefore I Capital structure changes issue debt to buy back equity or vice versa will not affect firm value I Financing a project with debt is equivalent to financing a project with equity Perfection ef ciency equilibrium and financing projects A project requires a time zero investment of 100 and produces an expected cash flow of 110 in one year The opportunity cost of capital is 7 and the project NPV is 280 The firm has two financing choices for raising the 100 a oneyear riskfree debt issue with a 5 interest rate or a common stock issue with a 15 required return to stockholders Assume the risk free opportunity cost of capital is 5 1 Perfect and in equilibrium financial markets mean that the choice of debt versus equity financing has no effect on firm value Therefore NPV debt financing NPV equity financing 77 2 An efficient market that is in equilibrium implies that the current value of the firm s securities re ect available and relevant information about those securities Available and relevant information about the debt security The debt security Will pay 105 in one year risk free The riskfree opportunity cost of capital is 5 PV of105 time 1 cash flow This means that the NPV debt financing Therefore NPV of equity financing must also Conclusion Base case NPV 280 Financing NPV 0 for both debt and equity financing After Financing Project NPV 280 0 280 Complication The ModiglianiMiller capital structure irrelevance proposition centers on the ability of individual investors to replicate or reverse actions by firms What if they can39t Examples 1 What if individual investors are limited to 50 margin but firms can borrow a higher percentage of money say 60 2 What if firms can borrow at a lower interest rate than individuals perhaps due to economies of scale In both examples there is an advantage to firms borrowing money rather than individuals borrowing money Therefore stocks of levered firms should sell at a premium However 1 Investors can borrow money from other sources besides the broker to make stock investments Compare home mortgage interest rates with longterm corporate bond interest rates 3 It is likely that the supply of levered firms would rise to meet the demand eliminating any premium 19 How close does the ModiglianiMiller theory t the real world or is capital structure really irrelevant Evidence against ModiglianiMiller The capital structure decisions of companies do not appear to be random In fact companies in certain industries are primarily debt financed and in other industries they are primarily equity financed The reason for this pattern may be Managers of successful companies set the standard in the industry for capital structure Other firms mimic Since capital structure doesn39t affect firm value there is no real benefit penalty Or The assumptions used in the model are unreasonable this is the primary topic of Chapter 18 Selected quiz questions from Chapter 17 of the textbook 171 172 173 174 175 except b 176 178 Chapter 17 Review Questions 1 Understand the perfect capital market assumptions used in the capital structure irrelevance proof 2 Understand the arbitrage proof for capital structure irrelevance Be able to demonstrate the method of generating arbitrage profits if market prices are out of equilibrium Remember that when investors take advantage of an arbitrage opportunity their actions quickly force prices back into equilibrium thereby eliminating the arbitrage opportunity 3 Understand how changes in leverage affect Expected equity return Beta risk of the equity Required return using the CAPM Price per share and market value of a firm39s stock 4 Be able to show how an individual investor can take an unlevered firm39s stock and create levered stock cash flows by buying on margin Be able to show how an individual investor can take a levered firm39s stock and create unlevered stock cash flows by buying stock and lending money Understand the significance of being able to manipulate capital structure with respect to the issue of capital structure irrelevance 5 Understand the implications of a financial market that is perfect efficient and in equilibrium with respect to financing projects In such a market the financing NPV 0 for any financing choice Chapter 17 Practice Problems 1 2 3 Assume that the market value of the equity of Firm X is 800 Firm X is an all equity firm Firm Y has the exact same assets as Firm X managed in exactly the same way that Firm X manages its assets The only difference between Firm X and Firm Y is that Firm Y has both debt and equity in its capital structure The market value of Firm Y s debt 200 Using the perfect capital market assumptions listed in Chapter 17 notes which of the following statements are correct A In equilibrium the market value of Firm Y s equity 800 B In equilibrium the market value of Firm Y s equity 600 correct answer Assume that Firm U an all equity firm has a market value of 2000 Firm L is a firm with both debt and equity The market value of its debt is 1600 and the market value of its equity is 600 So the market value of Firm L is 2200 Both Firm U and Firm L have the exact same assets managed in exactly the same manner Using the Chapter 17 perfect capital market assumptions how can you earn an arbitrage profit Since VU ltVL then at time 039 A Sell short ocEL B Borrow 11D L C Invest zEL ocDL into the equity of rm U Using the numbers in the problem and 0c 10 then A Sell short 60 of rm L stock B Borrow 160 C Invest 220 in rm U stock Refer back to the previous problem and assume that at time 0 you have correctly taking the three steps to earn an arbitrage profit What are the future cash flows associated with these transactions A Future cash flows will always be positive Correct answer B Future cash flows will on average be positive The next five problems 4 8 have a common set of assumptions 4 The assets of ABC Inc produce a perpetual stream of 150 expected cash flows The beta of these cash flows is 56 With a riskfree interest rate of 5 and a marketrisk premium of 84 the appropriate discount rate for these cash flows using the CAPM is 12 This implies that the assets of ABC Inc are worth 1250 Since ABC Inc is all equity then the beta for the equity is also 56 the required rate of return for the equity is 12 and the market value of the equity is 1250 XYZ Inc has the exact same assets as ABC Inc managed in exactly the same way as ABC Inc manages its assets However XYZ Inc has 900 of perpetual default risk free debt 5 interest rate zerobeta and stock with a current market value of 300 So the market value of XYZ Inc is 1200 Both companies have a 100 dividend payout ratio Using the Chapter 17 assumptions describe the steps necessary to earn an arbitrage profit at time 0 ABC Inc is an unlevered rm call it rm U XYZ Inc is a levered rm call it rm L Since VU gtVL then at time 039 V 0 l 00 A Sell shart aEU B InvestDLVL aEU inta the debt af rm L C Invest ELVL aEU inta the equity af rm L Using the numbers in the prablem and a 10 then A Sell shart 125 af rm U stack B Invest 93 75 in rm L debt C Invest 3125 in rm L stack Repeat the analysis assuming that the market value of XYZ lnc stock is 400 instead of 300 Now XYZ Inc has a market value of 900 400 1300 ABC Inc still has a market value of 1250 All other numbers remain the same ABC Inc is an unlevered rm call it rm U XYZ Inc is a levered rm call it rm L Since VU ltVL then at time 039 A Sell shart aEL B Barraw 11D L C Invest aEL aDL inta the equity af rm U Using the numbers in the prablem and a 10 then39 A Sell shart 40 af rm L stack B Barraw 90 C Invest 130 in rm U stack Assume that the market is in equilibrium ie no arbitrage profits are available and we are in a Chapter 17 world Therefore when two firms eg levered and unlevered have the exact same assets managed in exactly the same way the market values of the securities of a levered and unlevered firm are identical Using the information from problem 4 assume that ABC39s stock has a market value of 1250 and the stock and debt of XYZ Inc have market values of 350 and 900 respectively Both firms will pay dividends equal to firm cash flows less interest payments if any I What are the expected dividend payments for ABC Inc and XYZ lnc stock ABC Inc 150 XYZInc 105 I What are the expected returns for the stocks of the two companies ABC Inc 120 X YZ Inc 30 0 I What are the betas of the stocks of the two companies ABC Inc 56 ar 08333 XYZ Inc 29762 Hint The beta risk farX YZ s debt is 0 0 Use this ta salve far the stack beta risk I What are the required rates of return for the two stocks using CAPM ABC Inc 120 XYZ Inc 300 I Using the expected dividend payments and required returns what are the market values for the two stocks ABCInc 150012 1250 XYZInc 105030 350 I What if the debt beta for XYZ s debt was 04 instead of 00 Keeping the asset beta at 56 what is XYZ s stock beta 19476 For all of the remaining questions assume that XYZ debt is risk free You have 60 and want the risk and return characteristics of XYZ stock However XYZ stock is not for sale but ABC stock is available What can you do Take yaur 60 af cash and barraw an additianal 1542857 perpetual debt 5 interest rate Use the 2142857 ta buy 1714286 2142857 divided by 1250 afthe tatal autstanding stack afABC The annual expected return an this 60 investment is 30 and the beta risk is 29762 You have 60 and want the risk and return characteristics of ABC stock However ABC stock is not for sale but XYZ stock is available What can you do Take yaur 60 and buy 1680 an Y Z stack Take the remaining 4320 af cash and invest in default risk ee perpetual debt with a 5 interest rate and a zera beta The annual expected return an this 60 investment is 12 and the beta risk is 56 10 O l l l 1 Assume the capital markets are perfect as described in Chapter 17 Firm U and Firm L have the exact same assets managed in exactly the same way Firm U has no debt The market value ofFirm US equity is 2000 Firm L has debt with a market value of 800 and equity with a market value of 1400 Therefore the market values of firm U and firm L are 2000 and 2200 respectively Since these firms do not have the same market value you should be able to earn an arbitrage profit What are the three positions you need to take at time zero to earn an arbitrage profit Use the procedures we discussed in class Also as in class assume alpha 10 A Sell short 220 of Firm L equity Sell short 140 of Firm L equity Sell short 200 of Firm U equity Invest 80 into the debt of Firm L Borrow 80 Invest 200 in Firm U equity Invest 220 in Firm U equity Invest 220 in Firm L equity Invest 140 in Firm L equity HEQTJP JUOW Note 7 remember there are three positions you need to take to earn the arbitrage profit that we discussed in class Circle the three correct answers above and also put these answers below Correct answers B E G Refer back to the facts of the previous problem and assume that people take positions to earn arbitrage profits based on the difference in market values of firm U and firm L What effect should these transactions have on market prices A The market value of firm U stock should decrease and the market value of firm L stock should increase B The market value of firm U stock should increase and the market value of firm L stock should decrease Answer B is correct Assume the capital markets are perfect as described in Chapter 17 Firm U and Firm L have the exact same assets managed in exactly the same way Firm U has no debt The market value of Firm US equity is 2000 Firm L has debt with a market value of 800 and equity with a market value of 1000 Therefore the market values of Firm U and Firm L are 2000 and 1800 respectively Since these firms do not have the same market value you should be able to earn an arbitrage profit What are the three positions you need to take at time zero to earn an arbitrage profit Use the procedures we discussed in class Also as in class assume alpha 10 Sell short 100 of Firm L equity Sell short 200 of Firm L equity Sell short 200 of Firm U equity Invest 80 into the debt of Firm L Invest 8889 into the debt ofFirm L Invest 100 into the equity of Firm U Invest 11111 into the equity of Firm U Invest 100 into the equity of Firm L Invest 11111 into the equity of Firm L Hmommcowgt Note 7 remember there are three positions you need to take to earn the arbitrage profit that we discussed in class Circle the three correct answers above and also put these answers below Correct answers C E Assume the capital markets are perfect as described in Chapter 17 Firm U and Firm L have the exact same assets managed in exactly the same way Firm U has no debt The market value of Firm US equity is 8500 Firm L has debt with a market value of 3000 and equity with a market value of 5000 Therefore the market values of Firm U and Firm L are 8500 and 8000 respectively Since these firms do not have the same market value you should be able to earn an arbitrage profit What are the three positions you need to take at time zero to earn an arbitrage profit Use the procedures we discussed in class Also as in class assume alpha 10 H E H gt H V H O H gt1 Pick One A Sell short 850 of Firm U equity B Sell short 850 of Firm L equity C Sell short 500 of Firm L equity Pick One D Invest 31875 into the debt ofFirm L E Invest 300 into the debt of Firm L F Invest 850 into the debt of Firm L Pick One G Invest 500 into the equity of Firm U H Invest 500 into the equity of Firm L I Invest 53125 into the equity of Firm U J Invest 53125 into the equity of Firm L Note 7 remember there are three positions you need to take to earn the arbitrage profit that we discussed in class Circle the three correct answers above and also put these answers below Correct answers A D J Assume that there are two firms Firm U and Firm L Both firms have the exact same assets managed in exactly the same way Firm U has no debt and its equity has a market value of 1000 Firm L has debt with a market value of 350 In equilibrium and with perfect capital markets the market value of Firm L s equity A equals 650 Correct B equals 1000 C Can be anywhere within the range of 650 to 1000 Assume that there are two firms Firm U and Firm L Both firms have the exact same assets managed in exactly the same way Firm U has no debt Firm L has debt with a market value of 400 and equity with a market value of 600 In equilibrium and with perfect capital markets the market value of Firm US equity A equals 1000 Correct B equals 600 C Can be anywhere within the range of 600 to 1000 Assume that there is an unlevered firm U Corporation The market value of this firm s equity is 1500 and the beta of its equity is 15 L Corporation has the exact same assets as U Corporation managed in exactly the same way The market value of L Corporation s debt is 475 and the market value of its equity is 1025 The beta of L Corporation s debt is zero What is the beta of L Corporation s equity Assume the financial markets are perfect efficient and in equilibrium 21951 You have 30 to invest Firm A is an unlevered firm The market value of Firm A s equity is 1000 Firm B is a levered firm The market value of its debt and equity are 800 and 200 respectively Firm A and Firm B have the exact same assets managed in the same way How can you purchase Firm A equity ie the unlevered firm and make it look like an investment in Firm B equity ie the levered firm Use the Chapter 17 perfect capital market assumptions and assume the market is efficient and in equilibrium Thus when you borrow or lend money you get the same interest rate and same terms as corporations do Answer Take your 30 borrow an additional 120 andbuy 150 ofthe equity ofFirm A You have 150 to invest Firm A is an unlevered firm The market value of Firm A s equity is 6000 Firm B is a levered firm The market value of its debt and equity are 5000 and 1000 respectively Firm A and Firm B have the exact same assets managed in exactly the same way How can you purchase Firm A equity ie the unlevered firm and make it look like an investment in Firm B equity ie the levered firm Use the Chapter 17 perfect capital market assumptions and assume the market is efficient and in equilibrium Thus when you borrow or lend money you get the same interest rate and same terms as corporations do Answer Take your 150 borrow an additional 750 andbuy 900 ofthe equity ofFirm A 12 Chapter 6 Using the NPV Rule In this chapter we will learn 1 How to construct a proforma cash flow statement for a project The project NPV is calculated by discounting these cash flows back to time 0 2 How to use the NPV rule in complicated but common situations Steps in the capital investment capital budgeting process 1 N 9 He Generation of investment proposals researchmarketing department Types of projects investments associated with gal assets A New products or expansionmodification of existing products B Replacement of equipment or buildin C Comparison of alternative manufacturing processes D Safety and environmental projects E New advertising expenditures F Abandonment of an existing project G Other Estimation of the project s expected cash ows Chapter 6 In this chapter we will keep things simple by assuming that future project cash flows are known with certainty ie they are risk free This allows us to concentrate on the many complications of project cash flow calculations In reality future cash flows are almost never known with certainty If there is uncertainty you need to first calculate the project s future cash flow in each state of nature then calculate the expected future cash flows and use these expected future cash flows in the NPV analysis We learned how to calculate expected future cash flows with the windmill project Cash flow with light winds 4091 M 20 chance Cash flow with normal winds 9091 M 50 chance Cash flow with strong winds 15455 M 30 chance Expected cash flow 10 M Evaluation of cash ows Determine the riskiness of the project s expected cash flows and the project s opportunity cost of capital Chapters 7 9 Higher risk cash flows have a higher opportunity cost of capital Remember from Chapter 125 notes that each of the project s cash flows can have a different risk level and therefore a different opportunity cost of capital Example from Chapter 125 notes NPV for Project J 10000 6000 11 60001152 859 Project acceptance or rejection should be based on the NPV method using the opportunity cost of capital as a discount rate Chapter 5 1f the NPV is positive then you should accept the project39 if negative then reject Projects investments in lal assets versus investment in nancial assets A project can have a positive or a negative NPV although projects with a positive NPV are difficult to find What about investments in financial assets Assuming the financial markets are perfect efficient and in equilibrium the present value of the future expected cash flows from a financial asset is equal to the financial asset s current price Perfect Chapter 17 7 No taxes transaction costs etc Efficient Chapter 13 7 Prices reflect information Based on this What is the NPV from an investment in the financial markets How does competition explain this Current stock price 9 Expected dividend in one year 1 Growth rate in dividends in perpetuity 2 Opportunity cost of capital discount rate 12 What is the present value of the stocks future dividends What is the NPV What is the expected return ie IRR for the stock How should competition affect the stock price Change the current stock price to 11 What is the present value of the stocks future dividends What is the NPV What is the expected return ie IRR for the stock How should competition affect the stock price Based on this discussion What is the equilibrium stock price What is the NPV What is the expected return ie IRR for the stock using its equilibrium stock price What implications does this have for allocating firm resources to evaluating investments in real versus financial assets What about financial assets of different risk levels Risk Level I Opp Cost of Capital I IRR I NPV High Low Estimation of cash ows is probably the most important task in capital budgeting Examine cash flows rather than income Need cash to pay for operating expenses capital investment interest dividends Remember income taxes are an additional cash flow Example 1 Assume a project requires a 10000 initial investment for the purchase of inventory The inventory will be sold at the end of the period for 16000 sold on credit collected at time two Cash wages paid to employees at time one 4000 Income tax rate 34 Corporation is an accrualbasis taxpayer The opportunity cost of capital is 8 Example 2 What happens if the 16000 is received at time 1 Corporate Income Taxes Taxes on project income should be computed based on the corporation39s incremental or marginal income tax rate Make sure you include the incremental income taxes as an additional project cash ow Corporate Tax Rates Federal Bracket Tax Rate 0 50000 15 50000 75000 25 75000 100000 34 100000 335000 39 335000 10000000 34 10000000 15000000 35 15000000 18333333 38 Above 18333333 35 The incremental tax rate should be the combination of federal and state marginal income tax rates Most states have a corporate income tax and the state corporate tax rates vary from state to state See httpwww ta admin inchtml for a summary Texas does not have a corporate income tax It does have a franchise tax that works like an income tax 3 The computation of the Texas franchise tax is somewhat complicated but is approximately equal to 45 of Federal taxable income To simplify the discussion we will ignore state taxes However in practice both federal and state taxes need to be considered in any project selection decision Examples of the computation of federal taxes for a project Example 1 The year is 2007 What is the federal income tax for a project if the corporation has 70000 of taxable income without the project and 71000 of taxable income with the project In other words the project produces 1000 of additional taxable income Long method Calculate the federal taxes at the two different amounts of taxable income A What is the federal tax with 70000 of taxable income 15 50000 25 20000 B What is the federal tax with 71000 of taxable income 15 50000 25 21000 C How much more income tax will the firm pay if it takes the project D Thus the marginal tax rate for the project is Short method A What is the tax bracket for 70000 of taxable income B What is the tax bracket for 71000 of taxable income 0 Since the firm s tax bracket is the same with the project as it is without the project then Calculate the incremental income tax by multiplying the additional taxable income by the tax bracket rate Incremental taxable income Tax rate for bracket Incremental income tax A corporation s incremental tax rate might change from year to year Why would this rate change 1 2 Example 2 In 2008 taxable income will be 5000000 without the project and 5100000 with the project Does the project cause a change in tax brackets How much additional income taxes must be paid Example 3 In 2009 taxable income will be 9800000 without the project and 10200000 with the project Does the project cause a change in tax brackets For purpose of the examples given in class we will assume that the corporation39s marginal tax rate T is 34 Determination of Project Cash Flows When evaluating a project the relevant cash flows are the incremental 0r marginal cash ows Incremental cash flows are equal to the difference in the firm s cash flows with and without the project 1quot N We calculated the incremental corporate income taxes in the above examples Another simple example of incremental cash flows Average pro tability versus incremental cash ows 7 Always evaluate projects based on the incremental cash flows without regard to average profitability Example 7 Assume that on average Factory X is currently unprofitable and is expected to remain unprofitable However Factory X produces a positive cash flow Expected yearly cash revenues 1010000 Expected yearly cash expenses 1000000 Yearly A a 39 r A s 50 000 Expected yearly net income 40000 Expected yearly cash flow 10000 A machine critical to operating Factory X breaks down Without the machine the factory cannot operate With the machine which costs 30000 Factory X should operate for 5 more years producing expected cash flows of 10000 a year Expected firm cash flows from its other projects 500000 Should the machine be replaced Incidental effects When evaluating a new project you must consider the incidental effects of the project s acceptance on the firm s cash flows from other projects Example Hallmark Cards Inc is contemplating a new greeting card Unlike the traditional greeting cards that retail for 2 these cards will sell for 50 cents Example Compare the relative value of hosting the Super Bowl for Detroit and Miami In the previous discussion we have emphasized analyzing incremental cash ows for a project Firm cash flows with the project Firm cash flows without the project Project cash flows The following discussion emphasizes other issues in determining cash flows To simplify these tough subjects I will only show the incremental cash flows from the acceptance of the project rather than showing the detailed analysis of firm cash flows with the project versus firm cash flows without the project 4 Working capital adjustments Increases and decreases in working capital need to be considered in calculating cas Working capital shortterm assets e g cash AR inventory minus shortterm liabilities e g AP taxes payable wages payable An increase in working capital is treated as a negative cash flow A decrease in working capital is treated as a positive cash flow Analysis for calculating yearly cash flows for a project Step 1 7 Calculate yearly taxable income Step 2 7 Calculate the corporate income tax Step 3 7 Subtract income tax from taxable income Step 4 7 Calculate the amount of working capital as of the end of each year Step 5 7 Calculate the change in working capital from year to year Step 6 7 If there was an increase in working capital from the previous year this increase in working capital is a negative adjustment in calculating cash flow If there was a decrease in working capital from the previous year the decrease in working capital is a positive adjustment in calculating cash flow Step 7 7 Make the working capital adjustment to calculate the cash flow for the year taxable income 7 income tax working capital adjustment cash flow An example I An accrualbasis corporation is considering a project In the project the firm buys inventory and resells the inventory to the public Assume the firm wants to maintain 100000 of inventory at all times throughout the 5year prOject I The project will produce revenue of 12000000 expenses cost of goods sold of 9000000 and taxable income of 3000000 for year one No depreciation I Revenues expenses and taxable income are expected to grow at 10 a year for five years ear 5 is the last year of the project The growth is from an increase in sales ie assume the in ation rate equals 0 I Cash of 50000 is needed to start the project and is maintained throughout the life of the project I End of period accounts receivable balance is equal to 1 12 of the year s revenue and accounts payable is equal to 1 12 of the year s inventory purchases Income taxes are paid in the current year Fill in the missing cells in the table to determine yearly project cash flow 0 1 2 3 4 5 6 Revenue 12000000 13200000 14520000 15972000 17569200 Cost of Goods Sold 9000000 9900000 10890000 11979000 13176900 Taxable Income 0 3000000 3300000 3630000 3993000 4392300 Income Tax 0 1020000 1122000 1234200 1357620 1493382 Subtotal 0 1980000 2178000 2395800 2635380 2898918 Adjustments Working Capital Cash Flow Inventory Purchases 100000 9000000 9900000 10890000 11979000 13076900 Account Balances Cash 50000 50000 50000 50000 50000 0 0 Inventory 100000 100000 100000 100000 100000 0 0 Accounts Receivable 0 1000000 1100000 1210000 1331000 1464100 0 Accounts Payable 8333 750000 825000 907500 998250 1089742 0 Working Capital To check calculate cash revenue and cash expenses Cash revenue Revenue 7 change in AR from previous year to this year Cash expenses Inventory purchases 7 change in AP from previous year to this year income tax change the cash account from the previous year to this year Note 7 The formulas for cash revenue and cash expenses are simplified because of the simple nature of the problem A more complicated problem would mean more complicated formulas for cash revenue and cash expenses Cash Revenue Calc Revenue 12000000 13200000 14520000 15972000 17569200 ChangeinAR Cash Rev enue Cash Expense Calc Inventorypurchases 100000 9000000 9900000 10890000 11979000 13076900 ChangeinAP 1ncometax 0 1020000 1122000 1234200 1357620 1493382 Change in cash Cash Expense Cash Flow Calc Cash Revenue Cash Expense Cash Flow 5 Ignore sunk costs Project cash flows should not consider past expenditures for equipment land or other assets that will be used on the project These are sunk casts and are irrelevant to the project selection decision Only future incremental cash flows should be considered in your analysis of the project Example Equipment purchased several years ago for 100000 will be used on a new project The 100000 is a sunk cost and should be ignored in calculating the NPV for the project Example 7 Assume that the company purchased the equipment several years ago for 100000 but instead of paying cash the firm agreed to make ten payments of 10000 once a year It currently has one remaining payment of 10000 The first 90000 of payments are clearly a sunk cost What about the 10000 6 Take into account opportunity costs The current market value of equipment land and any other assets that will be used on the project should be considered as a time zero cash out ow Why If the assets are not used on the project they can be sold Therefore by using the assets on the project the firm is forgoing the opportunity to receive the positive cash flow from the sale of those assets Make sure you take into account the tax effects of sale Example A project will require a cash initial investment of 1000000 In addition it will use equipment purchased several years ago for 100000 This asset has been fully depreciated and therefore has a tax basis tax book value of 0 The current market value for the asset is 20000 If the asset is not used on the project it will be sold it has no other use to the corporation If sold the corporation will pay tax at the rate of 34 on the 20000 gain How should the use of this asset be considered in evaluation of the project Sunk cost The 100000 purchase price is a sunk cost and is irrelevant to the project selection decision Opportunity cost The following amount will be treated as a time zero negative cash flow in addition to any other time zero cash flows gt1 00 Current market value Tax basis Tax gain or loss on sale Tax effect of sale Time zero opportunity cost cash out ow What if the accumulated tax depreciation was 40000 leaving a tax basis of 60000 Current market value Tax basis Tax gain or loss on sale Tax effect of sale Time zero opportunity cost cash out ow Note 7 this is actually more complicated than presented Specifically if you use the asset on the project you can continue depreciating the asset Of course if you sell you can no longer depreciate Ignore allocated overhead Accountants often allocate indirect expenditures to the firm s revenue sources These allocated expenses should be ignored in the analysis An exception would be if the acceptance of the project causes these indirect expenditures to change Example Corporate headquarter expenses totaling 10 million per year are allocated to the various projects of the firm based on the revenue of these projects Project X s allocation is 100000 If corporate headquarter expenses are the same whether the project is accepted or rejected then If acceptance of the project requires the firm s corporate headquarters to hire clerical staff at 40000 per year then Use tax depreciation in the calculation of project cash ows Tax depreciation of an asset is not a cash ow and therefore it does not directly affect project cash ows However tax depreciation will affect the amount of income tax the firm will have to pay if the project is selected Therefore because of this indirect effect tax depreciation must be considered in the analysis of the project Make sure you use tax depreciation to calculate the tax effects of the asset s depreciation rather than accounting depreciation Example A Acceptance of a project will require the purchase of equipment on January 1 Cost 1500 3year tax depreciation life see page 122 of the textbook The equipment is expected to run for four more years with a no salvage value at the end of its useful life The corporation is a calendaryear taxpayer Project sales 1000 units sold per year current price 1 per unit Customers pay cash Ignore expenses other than depreciation and income taxes Assume the marginal tax rate is 34 Expected overall economywide in ation rate 29411765 per year Expected in ation rate in price per unit 10 per year Discount rate 5 The firm uses straightline depreciation for financial statement reporting purposes Therefore accounting depreciation r year If the asset had a 500 salvage value then accounting depreciation would e per year U053 131 Analysis fill in the missing numbers for year 2 Unit sales Price per unit Revenue Depreciation Taxable Income Income tax at 34 Subtotal 0 1 2 3 1000 1000 1000 11000 13310 11000000 13310000 4999500 2221500 6000500 11088500 2040170 3770090 3960330 7318410 4 1000 14641 14641000 1 1 1 1500 13529500 4600030 8929470 Adj ustm ents Depreciation 4999500 2221500 1111500 Initial Investment 15000000 Cash Flow 15000000 8959830 9539910 10040970 N39PV at 5 19334563 9 Expected in ation is an important component of the determination of the project NPV I Use the nominal discount rate to discount cash ow estimates that include in ation or I Use the real discount rate to discount cash ow estimates that do not account for in ation ie cash ows in constant dollars Equation 1 rnomiml 1 rmiXl expected in ation What is the real discount rate in the previous problem Use the overall in ation rate in the above equation 10 Converting to real constant dollar cash ows Adjust all cash ows including depreciation by discounting the cash ows by the overall inflation rate This gives you real cash ows To calculate N39PV discount the real cash ows at the real discount rate 0 1 2 3 4 Unit sales 100000 100000 100000 100000 Price per unit 106857143 114184490 122014283 130380977 Revenue 10685714 11418449 12201428 13038098 Depreciation 4856657 6291943 2036474 989813 Taxable Income 5829057 5126506 10164954 12048285 Income Tax at 34 1981879 1743012 3456084 4096417 Subtotal 3847178 3383494 6708870 7951868 Adjustments Depreciation 4856657 6291943 2036474 989813 Initial Investment 15000000 Cash Flow 15000000 8703835 9675437 8745344 8941681 N39PV at 2 19334563 i Computations 7 Adjust price per unit to real dollars Year 1 11000 10294117651 106857143 Year 2 12100 10294117652 114184490 Year 3 1331010294117653 122014283 Year 4 14641 10294117654 130380977 Adjust yearly depreciation to real dollars Year 1 49995 10294117651 4856657 Year 2 66675 10294117652 6291943 Year 3 22215 10294117653 2036474 Year 4 11115 10294117654 989813 500 real sale39s price 50010294117653 54543 nominal sales price Sale of an asset nominal versus real discount rates A similar correction can be made to account for the sale of an asset Example Assume that the asset described above is sold at the end of the 3rd year for N W PV of the aftertax cash ow using the nominal sale39s price Nom Sale s Price 54543 Less Adjusted Basis 22223 1500 49995 66675 11108 Gain on Sale 32320 Tax at 34 10989 Net Cash Flow 43554 PV 3years at 5 37623 PV of the aftertax cash ow using the real sale39s price Real Sale s Price 50000 Less Adjusted Basis 20372 137507 45831 61122 10182 Gain on Sale 29628 Tax at 34 10074 Net Cash Flow 39926 PV 3years at 2 37623 Calculation Hints Only onehalf of the regular tax depreciation is allowed in the year of sale 150010294117653 137507 137507 x 03333 45831 137507 x 04445 61122 137507 x 01481 x 05 10182 Financing cash flows 7 Notice that we have assumed that the project has been financed with available cash This might not always be the case Sometimes the company might borrow money or issue stock to raise the funds needed undertake the project The format for analysis is the same However an adjustment to the project NPV might need to be made for financing effects The proper analysis discussed in Chapter 19 looks like this Base case NPV A Financing NPV B Project NPV A B Evaluation of projects by foreign corporations A Use the foreign country s currency B Use the foreign country s in ation rate C Use the foreign country s tax laws tax rates depreciation schedules etc D Use the foreign country s opportunity cost of capital Four situations when the simple NPV rule needs modi cation 1 Optimal Timing of Investment Should the project be undertaken now or should it be delayed and undertaken in the future Solution Which alternative yields the highest NPV Example Tree Harvests single harvest Assumptions A Young trees grow faster than mature trees Assumption board feet 80 bd feet x square root age Trees are currently 10 years old B Price oflurnber increasing at 29411765 per year Current price300 per 1000 board feet or 030 per bd foot C Cost of harvest included in sale39s price of lumber D Use a 5 nominal discount rate Age Board Feet Lumber Price Sale39s Price PV 5 Return 10 2529822 3000000 758947 758947 11 2653300 3088235 819401 780382 797 12 13 2884441 3272568 943953 815422 714 14 2993326 3368820 1008398 829611 683 15 3098387 3467903 1074490 841891 655 16 3200000 3569900 1142368 852453 632 17 3298485 3674897 1212159 861459 611 18 3394113 3782982 1283987 869053 593 19 3487119 3894246 1357970 875360 576 20 3577709 4008783 1434226 880490 562 21 3666061 4126688 1512869 884543 548 22 3752333 4248061 1594014 887607 536 23 3836665 4373004 1677775 889760 525 24 3919184 4501622 1764268 891075 516 25 4000000 4634023 1853609 891618 506 26 4079216 4770318 1945915 891446 498 27 4156922 4910621 2041307 890615 490 28 4233202 5055051 2139905 889175 483 19 Which year should the company harvest the trees We assumed away any uncertainty However What if estimates are wrong ie prices only increase at 2 a year trees grow slower than expected how about a fire How should uncertainty be included in the analysis In addition a multiple harvest problem is much more complicated Earlier harvest allows the next set of trees to be planted earlier This is advantageous because young trees grow faster Evaluating two mutually exclusive projects with unequal lives The problem discussed in this section only applies in a special case when you are evaluating mutually exclusive projects with unequal lives and when each project will be replaced with a new identical project at the end of its useful life in perpetuity Example 7 a firm is considering purchasing one of two different machines Using a 2 real discount rate which is the best machine to purchase if these machines Will be replaced at the end of their useful lives in perpetuity Note The book s example uses only costs or cash out ows This example is more general it uses both positive and negative cash flows Here are the cash flows from a single purchase 0 1 2 3 Machine X 6000 2600 2600 2600 Machine Y 4000 2600 2600 NPVX 2 one purchase 14980965 NPVY 2 one purchase 10480584 Should you take Machine X First 7 what happens if the facts are a bit different I What happens if these two projects are not mutually exclusive I What happens if these two projects are mutually exclusive but they are not replaced at the end of their useful lives Go back to the original facts T0 properly analyze Make the two machines comparable by equalizing the lives Two methods Replacement Chains and Equivalent Annual Cash Flows A Replacement Chains Lives equal in year 6 also equal in year 12 year 18 year 24 etc Machine 0 1 2 3 5 6 X 6000 2600 2600 3400 2600 2600 2600 Y 4000 2600 1400 2600 1400 2600 2600 NPVX 2 290979 NPVY 2 302366 Pick Y it has the higher NPV over 6 years also over 12 years 18 years 24 years etc W Equivalent annual cash flow EAC Use the single purchase NPV in the following formula NPV PV Ordinary Annuity Factor for N years PV annuity factor 2 3 years 2883883 1 11023 002 PV annuity factor 2 2 years 1941561111022002 EACX EACY 104805841941561 5398020 Pick Y because it has the higher EAC The PV of a perpetual stream of Machine X or Y purchases is X Y 5398020002 2699010 Therefore over the long term Machine Y is more valuable than Machine X Note The above analysis assumes no in ation Therefore you would want to use a real as opposed to a nominal discount rate I If a real discount rate is used make sure that the depreciation deduction is adjusted for in ation I If a nominal discount rate is used project cash flows would need to be adjusted for inflation See book for a discussion Note The above analysis assumes that the real cost and cash flows associated with operating the two assets are constant However it is likely that the real cost will change in the future For example assume that the real cost of the machine falls at a rate of 20 per year How should this additional piece of information affect the analysis 12 3 Replacement Analysis 7 Should an old machine be replaced with a new machine today or in thefmure I Selling the old machine this year will probably result in a higher sales price than if it is sold next year I A new machine may run more efficiently require less maintenance produce more goods etc To analyze compare cash flows assuming the machine is replaced today with cash flows assuming the machine is replaced in the future e g in one year Use the new machine s equivalent annual annuity EAC in the calculations Example A Today is January 1 calendaryear taxpayer You purchased the old machine nine years ago for 100000 tax depreciation life of 7 years see page 122 of the text It will last five more years and will produce an aftertax cash flow of 15000 per year at the end of each year The old machine is worthless at the end of its useful life B The old machine is fully depreciated and therefore has a tax book value of 0 Its current market value 70000 Market value in one year 57000 C New machine tax depreciation life of 7 years will cost 150000 and has a remaining useful life of 10 years It produces an aftertax cash flow of 40000 per year The 40000 per year includes the cash flow effects of the depreciation deductions and sale at the end of its useful life At the end of its useful life an identical new machine will be purchased with identical cash flows Replacement every 10 years will continue in perpetuity D Marginal tax rate 34 E All numbers are in constant dollars ie no adjustment for in ation Use a 2 real discount rate to determine present values Preliminary calculations To determine the best alternative you need to do some preliminary calculations A What are the aftertax salvage values associated with selling the old machine now versus in one year Selling now Selling in one year B What is the EAC associated with the new machine NPV single purchase EAC Initial presentation of cash ows Replace now 0 1 2 3 4 5 a SV old machine 46200 New machine 150000 40000 40000 40000 40000 40000 40000 Replace in 1 year 0 1 2 3 4 5 a Old machine CF 15000 SV old machine 37620 New machine 150000 40000 40000 40000 40000 40000 Now substitute new machine cash flows with EAC Replace now 0 l 2 3 4 5 a SV old machine 46200 New In achine 0 EAC EAC EAC EAC EAC EAC Replace in 1 year 0 l 2 3 4 5 a Old machine CF l5000 SV old machine 37620 New In achine 0 EAC EAC EAC EAC EAC What is the NPV associated with replacing now versus in one year NPV replacing now N PV replacing in one year Difference in NPVs Decision 4 Cost of Using Excess Capacity Basic Issue Does the use of the quot excess capacity of a machine cause it to wear out earlier If so consider the additional cost of an early purchase of a new replacement machine Example A Preliminary calculation of the project NPV A project requires an initial investment of 100000 and produces real cash flows of 2700 per year in perpetuity Using a 2 real discount rate the preliminary project NPV is 35000 In addition to the above cash flows this project will cause an old machine that the firm owns to wear out two years early B Old machine will last 4 years without the project low usage but only 2 years if the above project is accepted high usage lts salvage value is 0 once it wears out After tax costs of operating the old machine over 2 years high usage or 4 years low usage are as follows Q l 2 3 4 12000 12000 12000 12000 20000 20000 PV of operating costs at 2 assuming low usage 4569274 PV of operating costs at 2 assuming high usage 3883l22 o The replacement machine has a life of 4 years and will be replaced every 4 years with the same costs The new replacement machine has more than enough capacity to handle the new project and all existing projects Aftertax costs of purchasing and operating the new machine are 14 t m E E M 50000 10000 10000 10000 10000 Note time t in the above cash flow statement is the date of the purchase of the replacement machine 7 ie either time 2 or time 4 NPV of a single purchase at the real discount rate of 2 8807728699 EAC 23l3l18763 Analysis 7 The preliminary calculation of the project NPV is 35000 But the costs of wearing out the old machine needs to be determined and used to calculate the correct project NPV NPV take project 1 Preliminary NPV 35000 2 PV of operating costs of old machine assuming high usage 3883l22 3 PV of a perpetual purchase of new replacement machine starting at time 2 Total NPV reject project 1 PV of operating costs of old machine assuming low usage 4569274 2 PV of a perpetual purchase of new replacement machine starting at time 4 Total Should the project be accepted Compare the NPV take project with the NPV reject project NPV take project NPV reject project Difference this is the NPV of the project Since NPV reject project is greater then reject the project Alternative Accept project and abandon in year 2 or consider scaling back project to avoid early purchase Change facts of the problem 7 project produces 3000 per year cash flows in perpetuity instead of 2700 Preliminary NPV 50000 ie l5000 greater than before NPV take project NPV reject project Difference this is the NPV of the project Since NPV accept project is greater it is now better to accept the project Wait the NPV take project is negative Doesn t that mean we should reject the project 5 Fluctuating Load Factors can be summarized as follows consider all alternatives Read this section on your own Not on the test Selected quiz questions from the textbook for chapter 6 You should be able to answer all of the quiz questions ie quiz questions 1 7 9 Chapter 6 Review Questions 1 2 gt1 00 O H 0 H 19 L 4 V 0 Know how to calculate the NPV of a project based on its expected future cash flows Why is it important to calculate the NPV of a project but not the NPV of an investment in the capitalmoney markets eg stock bonds Treasury Securities Note In discussing this topic I assumed that the financial markets were perfect efficient and in equilibrium What are some of the reasons a project s yearly income could be different than its yearly cash flow Which should be used future income or future cash flows in determining the NPV of a project What is a corporation39s marginal income tax rate Be able to use a federal tax bracket schedule and a corporation39s taxable income with and without the project to calculate a corporation39s marginal income tax rate and the incremental amount of taxes the corporation must pay if it accepts a project What is meant by a project39s incremental cash flows What is meant by incidental effects How should incidental effects be considered in analyzing a project Know how to calculate working capital adjustments in order to determine project cash flows What is a sunk cost and why should it be ignored What is an opportunity cost and how should it be considered in the analysis of a project Know how to calculate the aftertax opportunity cost of an asset used in a project How should allocated overhead be considered in analyzing a project Know how to compute tax depreciation for depreciable assets used on a project Know the formula relating nominal interest rates nominal discount rates real interest rates real discount rates and the expected inflation rate Be able to calculate one value given the other two values Know what real cash flows and nominal cash flows mean Remember that real discount rates should be used to discount real cash flows and nominal discount rates should be used to discount nominal cash flows Know how to convert nominal cash flows for a project to real cash flows so they can be discounted using a real discount rate Know how to calculate the present value of nominal aftertax salvage values Know how to adjust salvage values to real cash flows so that they can be discounted using a real discount rate Understand in brief the terms basecase NPV and financing NPV Understand how a foreign company should evaluate a project Know when trees should be harvested Know how to use replacement chains and equivalent annual cash flows EAC to evaluate two mutually exclusive projects with uneven lives Remember that this problem only exists if the two projects are mutually exclusive and the machines will be replaced in perpetuity at the end of their useful lives Remember that the analysis usually uses real constant dollar cash flows so a real discount rate with a depreciation salvage value adjustment must be used lntuitively how should a project with increasing or decreasing real cash flows be handled Know when a machine should be replaced Similar to the example given in class know how to incorporate the cost of using excess capacity Chapter 6 Practice Problems 1 Assume that a project requires an initial investment of 5000 The time 1 cash flow is 12000 10 probability 6000 50 probability or 2500 40 probability A What is the time one expected cash flow for the project 5200 00 B What is the NPV of the project using a 10 discount rate 272 73 2 Big Red Corporation a retailer of Texas Tech University merchandise has 5 million of extra cash that it plans to invest It is considering two possible investments Stock A or Stock B Use the following information to answer the next two questions I Both stocks pay annual dividends next dividend in one year See time one expected dividend payments below The dividends for both stocks are expected to grow at a constant rate in perpetuity See growth rates below I Assume you invest 5 million into either Stock A or Stock B I Assume financial markets are perfect efficient and in equilibrium Information about each stock Compare the NPV of investment of 5 million in Stock A or Stock B Which of the two investments has the higher NPV A Investment of 5 million in Stock A B Investment of 5 million in Stock B C Both investments have the same NPV CarrecIAnswer Compare the expected return associated with investment of 5 million in Stock A or Stock B Which of the two investments is expected to have the highest return A Investment of 5 million in Stock A CarrecIAnswer B Investment of 5 million in Stock B C Both investments have the expected return 3 A firm is considering investing in a stock that currently trades in the financial markets Assume that the financial markets are perfect efficient and in equilibrium The opportunity cost of capital for the stock is 10 The Stocks current price is 100 What is the answer to the following questions A The NPV of the investment in the stock is A Equal to 0 Correct B Less than 0 C Greater than 0 B The expected return or IR of the investment in the stock is A Equal to 0 B Less than 0 C Greater than 0 Correct gt V P gt1 00 Assume that financial markets are perfect efficient and in equilibrium You are comparing two investments Investment A is low risk and has a low opportunity cost of capital equal to 5 Investment B is high risk and has a high opportunity cost of capital equal to 15 What can be said about the NPVs and expected returns ie IRRs for these two investments Both investments have the same NPV and also have the same IRR Investment A has a higher NPV and it also has a higher expected return Investment B has a higher NPV and it also has a higher expected return Both investments have the same NPV Investment A has a higher expected return Both investments have the same NPV Investment B has a higher expected return CarrecIAnswer mcowgt Assume that a corporation s 2007 taxable income is 80000 without the project and 81000 with the project There is no change in tax bracket in this problem A What is the corporation s federal income tax if the project is rejected 15450 B What is the corporation s federal income tax if the project is accepted 15 790 C How much more federal income tax must the corporation pay if the project is accepted 340 D Use the short method to check your answer to Additional taxable income 1000 marginal tax rate 34 1000034 340 Assume that a corporation s 2007 taxable income is 95000 without the project and 105000 with the project There is a change in the federal tax bracket in this problem A What is the corporation s federal income tax if the project is rejected 20550 B What is the corporation s federal income tax if the project is accepted 24200 C How much more federal income tax must the corporation pay if the project is accepted 3 650 D You cannot use the simple formula to calculate the additional federal and state taxes because the federal tax bracket changes if the project is accepted from the 34 bracket to the 39 bracket How much more income tax will XYZ Inc need to pay for the year 2007 if it takes Project A 2007 federal taxable income if the firm does not take Project A 1988000 2007 federal taxable income if the firm takes Project A 2000000 A What is the corporation s federal income tax if the project is rejected 675920 B What is the corporation s federal income tax if the project is accepted 680 000 C How much more federal income tax must the corporation pay if the project is accepted 4 080 D Use the short method to check your answer to Additional taxable income 12 000 marginal tax rate 34 12000034 4080 Use the tax rate schedule given in the notes As in class ignore state taxes For 2007 a corporation will have 135000 of taxable income if it undertakes a project If it rejects the project the taxable income will be 40000 Since there is a change in tax brackets you need to use the long method Complete the calculations Calculations for the long method Federal income tax with 40000 of taxable income 6 000 Federal income tax with 135000 of taxable income 35900 How much more income tax will the firm pay if it takes the project 29 900 O For 2007 a corporation will have 130000 of taxable income if it undertakes a project If it rejects the project the taxable income will be 115000 How much additional ie incremental marginal income tax will the corporation need to pay if it accepts the project Hint You can use the short method to answer this question Additional taxable income 15000 marginal tax rate 39 15 0000 39 5850 H O For 2007 a corporation will have 122000 of taxable income if it undertakes a project If it rejects the project the taxable income will be 50000 Since there is a change in tax brackets you need to use the long method Complete the calculations Federal income tax with 50000 of taxable income 7500 Federal income tax with 122000 of taxable income 30830 How much more income tax will the firm pay if it takes the project 23330 H H Use the tax rate schedule given in the notes As in class ignore state taxes For 2007 a corporation will have 92000 of taxable income if it undertakes a project If it rejects the project the taxable income will be 43200 How much additional income tax must the firm pay in 2007 if it decides to accept this project 13 050 H 19 Use the tax rate schedule given in the notes As in class ignore state taxes For 2007 a corporation will have 234000 of taxable income if it undertakes a project If it rejects the project the taxable income will be 40000 How much additional income tax must the firm pay in 2007 if it decides to accept this project Federal income tax with 40000 of taxable income 6 000 Federal income tax with 234000 of taxable income 74510 How much more income tax will the firm pay if it takes the project 68510 H 9 Use the tax rate schedule given in the notes As in class ignore state taxes For 2007 a corporation will have 189000 of taxable income if it undertakes a project If it rejects the project the taxable income will be 45000 How much additional income tax must the firm pay in 2007 if it decides to accept this project 50210 H gt Use the tax rate schedule given in the notes As in class ignore state taxes For 2007 a corporation will have 195000 of taxable income if it undertakes a project If it rejects the project the taxable income will be 41000 Since there is a change in tax brackets you need to use the long method How much more income tax will the firm pay in 2007 if it takes the project 53150 H 9quot Use the tax rate schedule given in the notes As in class ignore state taxes For 2007 a corporation will have 128000 of taxable income if it undertakes a project If it rejects the project the taxable income will be 45000 How much additional income tax must the firm pay in 2007 if it decides to accept this project 26 420 H 9 A perpetual project requires an initial investment of 1000 It has cash ows 0f0 for time 1 2 3 and 4 The cash ow is 105 at time 5 The time 6 cash ow is 3 more than the time 5 cash ow Cash ows continue to grow at a 3 rate in perpetuity The opportunity cost of capital is 12 The following outlines the project cash ows through time 6 Remember the cash ows continue beyond time 6 What is the NPV ofthe project 258 56 0 1 2 3 4 5 I6 a 1000 I 0 0 0 0 105 3 3 I 17 Using the following what are the project s cash flows 18 Similar to the example of working capital adjustments in the notes calculate the working capital balance working capital adjustment and project cash flow Answers in italics 0 1 2 3 4 5 6 Revenue 600000000 660000000 726000000 798600000 878460000 Cost of Goods Sold 450000000 495000000 544500000 598950000 658845000 Taxable Income 150000000 165000000 181500000 199650000 219615000 Income Tax at 34 51000000 56100000 6l710000 67881000 74669l00 Subtotal 99000000 108900000 119790000 131769000 144945900 Adjustments Working Capital 141666 67 13333333 12500 00 13750 00 15125 00 12502917 19134583 CashFlow 14166667 85666667 107650000 118415000 130256500 157448817 19134583 Inventory Purchases 10000000 450000000 495000000 544500000 598950000 648845000 Account Balances Cash 5000000 5000000 5000000 5000000 5000000 000 000 Inventory 10000000 10000000 10000000 10000000 10000000 000 000 Accounts Receivable 000 50000000 55000000 60500000 66550000 73205000 000 Accounts Payable 833333 37500000 41250000 45375000 49912500 54070417 000 Working Capital 141666 67 27500000 28750000 30125000 31637500 19134583 0 00 19 An accrual basis corporation is considering the following threeyear project What is the cash ow for year 2 1 33 400 0 l 2 3 Revenues 1000000 1100000 1210000 Expenses 800000 880000 968000 Taxable Income 200000 220000 242000 Income Tax at 34 68000 74800 82280 Subtotal 132000 145200 159720 Adjustments Working Capital Cash Flow Answer Working Capital Balance 70000 91200 103000 115500 20 An accrual basis corporation is considering the following threeyear project What is the cash ow for year 2 0 l 2 3 Revenues 1000000 1100000 1210000 Expenses 800000 880000 968000 Taxable Income 200000 220000 242000 Income Tax at 34 68000 74800 82280 Subtotal 132000 145200 159720 Adjustments Working Capital Cash Flow Answer Working Capital Balance 100000 138250 145000 155000 Answer 138 450 20 21 Similar to the example given in the notes an accrual basis corporation is considering the following veyear project Accounts receivable is expected to be 12 of revenue and accounts payable is expected to be 18 of inventory purchases What is cash ow for year 4 2 070300 0 l 2 3 4 5 6 Revenue 10000000 10100000 10250000 10450000 10700000 Expenses CGS 7 000 000 7 070 000 7 175 000 7 315 000 7 490 000 Taxable Income 3000000 3030000 3075000 3135000 3210000 Income Tax 34 l 020 000 l 030 200 1045 500 1065 900 1 091400 Subtotal 0 1980000 1999800 2029500 2069100 2118600 Adjustments Working Capital Cash Flow Answer Inventory Purchases 500000 7000000 7070000 7175000 7315000 6990000 0 Account Balances Cash 100000 100000 100000 100000 100000 0 0 Inventory 500000 500000 500000 500000 500000 0 0 Accounts Receivable 0 1200000 1212000 1230000 1254000 1284000 0 Accounts Payable 90000 1260000 1272600 1291500 1316700 1258200 0 Working Capital 0 22 The following are working capital balances for a project What is the working capital adjustment for year 2 for determining project cash ows Working capital increased by 300 so the working capital adjustment is 3 00 0 1 2 3 Accounts Receivable 0 5000 I 6000 I 7000 I Accounts Payable 0 4400 I 5100 I 6500 I N L Today is January 1 2007 AAA Inc is a calendaryear accrualbasis corporation The following are balances at the beginning and end of the year for various working capital accounts The first set of balances is calculated under the assumption that the firm does not take Project Y The second set of balances is calculated under the assumption that the firm does take Project Y What is the working capital adjustment for 2007 that will be made in determining cash ows for Project Y Answer 500 00 Do not take project Beg Balance End Balance Accounts Receivable 1000 1200 Inventory 5000 6000 Accounts Payable 4000 7000 Take project Beg Balance End Balance Accounts Receivable 1000 2700 Inventory 5000 7000 Accounts Payable 4000 9000 21 24 N o N l N Go An accrual basis corporation is considering the following threeyear project What is the cash ow for year 3 Notice there is no inventory 401 000 0 1 2 3 4 Revenue 2300000 2800000 3250000 Expenses 1840000 2240000 2600000 Taxable Income 460000 560000 650000 Income Tax at 34 156400 190400 221000 Subtotal 0 303600 369600 429000 0 Adjustments Working Capital Cash Flow Answer Working Capital Accounts Cash 29000 29000 29000 0 0 Accounts Receivable 0 276000 336000 390000 0 Accounts Payable 0 150000 175000 172000 0 Working Capital Balance 0 A rm using the accrual basis ofaccounting expects to have revenue of1300000 for a project for year 2 The following shows working capital balances for the project for years 0 to 3 What is cash revenue year 2 1280 000 A rm has two expenditures each year taxes and inventory purchases Using the accrual basis of accounting the rm expects to pay 1000000 in taxes in year two Using the following information what are cash expenditures for year 2 Hint calculate cash expenditures for inventory purchases Add the 1000000 tax expenditure to get your nal answer 3 785 000 Firm cash flow for 2007 is expected to be 1000000 Assume that your corporation has just hired a new purchasing manager This manager plans to start purchasing more supplies on credit Based on this the firm s end of the year accounts payable balance ie accounts payable balance on 12312007 will be higher than originally anticipated Holding other factors besides cash flow constant this increase in the accounts payable balance will mean that A Firm cash flow will be lower than 1000000 B Firm cash flow will be higher than 1000000 Correct answer Today is January 1 2007 BBB Inc is a calendaryear accrualbasis corporation The following are balances at the beginning and end of the year for various working capital accounts The first set of balances is calculated under the assumption that the firm takes Project Z The second set of balances is calculated under the assumption that the firm does not take Project Z What is the working capital adjustment that will be made in determining cash flows for Project Z for 2007 Answer 950 22 Account balances if the firm TAKES the project Beg Balance End Balance Accounts Receivable 1000 1000 Inventory 4000 5000 Accounts Payable 6000 7000 Account balances if the firm DOES NOT TAKE the project Beg Balance End Balance Accounts Receivable 1000 Inventory 4000 3100 Accounts Payable 6000 4000 29 ABC corporation uses the accrual basis of accounting It primarily sells items to customers on credit The following table gives revenue and accounts receivable balances through the third year of the project What are cash revenues for year 2 1180 000 0 1 2 3 Revenue 0 1000000 1200000 1400000 Accounts receivable 0 190000 210000 260000 30 CCC Inc is considering Project XXX Use the following information to calculate the cash ow for Project XXX for the month of May Answer 40200 31 Similar to the example given in the notes an accrual basis corporation is considering the following veyear project Accounts receivable is expected to be 8 of revenue and accounts payable is expected to be 15 of inventory purchases 0 l 2 3 4 5 6 Revenue 10000000 11000000 12100000 13310000 14641000 Expenses CGS 7 000 000 8 250 000 9 075 000 9 982 500 10 980 750 Taxable Income 3000000 2750000 3025000 3327500 3660250 Income Tax 34 l 020 000 935 000 l 028 500 l 131 350 l 244 485 Subtotal 0 1980000 1815000 1996500 2196150 2415765 Adjustments Working Capital Cash Flow 23 Inventory Purchases 400000 7000000 8250000 9075000 9982500 10580750 Account Balances Cash 75000 75000 75000 75000 75000 0 Inventory 400000 400000 400000 400000 400000 0 Accounts Receivable 0 800000 880000 968000 1064800 1171280 Accounts Payable 60000 1050000 1237500 1361250 1497375 1587113 0000 Working Capital L U L L What is cash ow for year 3 2 032250 What is cash revenue for year 4 13213200 XYZ Corporation is trying to decide whether to construct a new factory The land on which the factory will be built is already owned by XYZ Corporation However if the company decides to build the new factory it will need to prepare the land for the factory s construction In each case determine if the item should be considered a sunk cost and therefore ignored in the calculation of project cash flows The cost of preparing the land for the factory s construction A Sunk cost ie do not include in project cash flows B Not sunk cost ie include in project cash flows CorrectAnswer The amount due on architectural plans for the new factory The plans were recently completed and XYZ has been billed for the work Payment on the bill is not due until next month A Sunk cost ie do not include in project cash flows CorrectAnswer B Not sunk cost ie include in project cash flows A building was purchased several years ago for 500000 To date 350000 of tax depreciation has been taken on the building Therefore the tax book value is 150000 lts current market value is 600000 If the project is rejected the building will be sold it has no other use to the corporation Therefore if the corporation did not take the project it will receive 600000 from the sale of the building less any income taxes it will need to pay because of the sale Use the corporation s marginal income tax rate of 34 to compute the amount of income tax it owes if the building is sold What is the time zero aftertax opportunity cost of using the building on the project 44 7 000 a negative cash ow at time 0 A project will use a building purchased several years ago for 250000 So far the corporation has taken a total of 190000 of tax depreciation Therefore the tax book value is 60000 The current market value of the building is 95000 1f the project is rejected the building will be sold it has no other use to the corporation Therefore if the corporation did not take the project it will receive 95000 from the sale of the building less any income taxes it would need to pay because of the sale Use the corporation s marginal income tax rate of 34 to compute the amount of income tax it owes if the building is sold What is the time zero aftertax opportunity cost of using the building on the project The time zero aftertax opportunity cost 83100 treated as a 83100 cash aw at time zero A project will require an initial cash investment of 2500000 In addition the project will use the following mac 1ne Machine purchased 5 years ago for 250000 Accumulated tax depreciation 210000 Tax basis 40000 24 L L L 0 Current market value 65000 Tax rate 34 If the project is not accepted the machine will be sold What amount should you use as the time zero cash flow for the project 2 556500 A project will require an initial cash investment of 2000000 In addition the project will use the following machine Machine purchased 5 years ago for 200000 Accumulated tax depreciation l70000 Tax basis 30000 Current market value 75000 Tax rate 34 If the project is not accepted the machine will be sold What amount should you use as the time zero cash flow for the project 2 059 700 Refer back to the previous problem Assume that the current market value of the machine was 70000 instead of 75000 This change in assumption will make the time zero cash flow for the project the correct answer to question number one A Greater than ie less negative CarrecIAnswer B Less than ie more negative C The same as A project will require an initial cash investment of 1400000 In addition the project will use the following machine Machine purchased 5 years ago for 500000 Accumulated tax depreciation 425000 Tax basis 75000 Current market value 1 1 3000 Tax rate 34 If the project is not accepted the machine will be sold What amount should you use as the time zero cash flow for the project I500 080 A project will require an initial cash investment of 2250000 In addition the project will use the following machine Machine purchased 5 years ago for 750000 Accumulated tax depreciation 495000 Tax basis 255000 Current market value 322500 Tax rate 34 If the project is not accepted the machine will be sold What amount should you use as the time zero cash flow for the project 2 549 550 25 40 A project will require an initial cash investment of 3000000 In addition the project will use the following machine Machine purchased 5 years ago for 900000 Accumulated tax depreciation 750000 Tax basis 150000 Current market value 188600 Tax rate 34 If the project is not accepted the machine will be sold What amount should you use as the time zero cash ow for the project 3 175476 41 A firm is considering two possible projects The firm has a marginal income tax rate of 34 Both projects are identical in all aspects except Project A will use a fullydepreciated asset purchased 10 years ago for 10000 with a current market value of 6000 Project B will use a fullydepreciated asset purchased 10 years ago for 10000 with a current market value of 5000 Which of the two projects has the higher NPV A Project A B Project B CarrecIAnswer C Both projects have the same NPV 42 A firm is considering two possible projects The firm has a marginal income tax rate of 34 Both projects are identical in all aspects except Project C will use a fullydepreciated asset purchased 10 years ago for 12000 with a current market value of 5000 Project D will use a fullydepreciated asset purchased 10 years ago for 10000 with a current market value of 5000 Which of the two projects has the higher NPV A Project C B Project D C Both projects have the same NPV CarrecIAnswer 4 L Similar to the depreciation example given in the notes assume I Equipment purchased on January 1 Cost 2500 3year tax depreciation life The equipment is expected to run for four more years with no salvage value at the end of its useful life The corporation is a calendaryear taxpayer 1800 units sold per year current price 150 per unit Ignore expenses other than depreciation and income taxes Assume the marginal tax rate is 34 Expected overall in ation rate 5 per year Expected inflation rate in price per unit 4 per year Discount rate 3 real 815 nominal Tax depreciation rates 3333 for year 1 4445 for year 2 1481 for year 3 741 for year 4 A What are the yearly nominal cash flows What is the NPV using the nominal discount rate B What are the yearly real cash flows C What is the NPV using a real discount rate 26 Analysis Using Nominal Figures 1 2 0 3 4 Unit Sales 1800 1800 1800 1800 Price per unit 156000000 162240000 168729600 1 75478784 Revenue 2808 0000 2920 3200 30371328 3158 6181 Depreciation 8332500 11112500 3702500 1852500 Taxable Income 1974 7500 1809 0700 2666 8828 2973368 Income Tax at 34 6714150 615 0838 906 7402 10109452 Subtotal 1303 3350 1193 9862 17601426 1962 4230 Adjustments Depreciation 8332500 11112500 3702500 1852500 Initial Investment 2500 0000 Cash Flow 2500 0000 21365850 23052362 21303926 2147 6730 NPVat 815 47004770 Analysis Using Real Constant Dollar Figures 0 1 2 3 4 Unit Sales 180000 180000 180000 180000 Price per unit 148571429 147156463 145754972 144366830 Revenue 2674285 7 2648 81 63 2623 5895 2598 6029 Depreciation 7935714 10079365 3198359 1524056 Taxable Income 1880 7143 1640 8798 2303 7536 24461973 Income Tax at 34 639 4429 557 8991 7832762 831 7071 Subtotal 12412714 1082 9807 15204774 1614 4902 Adjustments Depreciation 793 5714 1007 9365 319 8359 1524056 Initial Investment 2500 0000 Cash Flow 2500 0000 2034 8429 2090 91 72 1840 3133 1766 8959 NPVat 3 47004770 44 Similar to the example given in class assume that the asset purchased in the previous example is sold at the end of the third year The real sale s price is expected to be 1200 Compute the present value of the aftertax 3 V salvage value using both nominal and real figures Nominal Real Sale sPrice 138915 120000 Purchase Price 2500 00 215959 Depr yr one 3 83325 719 79 Depryrtwo 111125 95994 Depryr three 3 18513 15992 Adjusted Basis 3 70 38 31994 Gain 3 1018 78 88006 Tax 34638 29922 After Tax CF 3 1 042 77 900 78 PV 3 82434 82434 Similar to the example given in class assume that A Trees are currently 10 years old B C D Cost of harvest included in sale39s price of lumber Use an 815 nominal discount rate Fill out the following table 27 Young trees grow faster than mature trees Assumption board feet 100 bd feet x square root age Price of lumber increasing at 5 per year Current price 500 per 1000 board feet or 050 per bd foot Age Board Feet Price Sale s Price NPV 815 Return 10 3162278 50000 15811 15811 11 3316625 52500 17412 16100 1012 12 3464102 55125 19096 16326 967 13 3605551 57881 20869 16498 929 14 3741657 607 75 22740 16622 896 15 3872983 63814 24715 16704 869 16 4000000 67005 26802 16750 844 17 4123106 70355 29008 167 62 823 18 4242641 738 73 31342 16746 804 19 4358899 77566 33810 167 04 788 20 4472136 81445 36423 16638 7 73 21 4582576 85517 39189 16553 759 22 4690416 89793 42117 16449 747 23 4795832 94282 45216 16329 736 24 4898979 98997 48498 16194 726 Harvest in year 17 46 Similar to the tree harvest example discussed in class which of the following years should the company plan to harvest the trees Note that the discount rate is 7 Age Board Feet Price Sale39s Price NPV 7 Return 10 3952847 4000000 1581139 1581139 11 4145781 4192000 1737911 1624216 992 12 4330127 4393216 1902318 1661559 946 13 4506939 4604090 2075035 1693847 908 14 4677072 4825087 2256728 1721647 876 15 4841229 5056691 2448060 1745433 848 16 5000000 5299412 2649706 1765611 824 17 5153882 5553784 2862355 1782531 803 18 5303301 5820365 3086715 1796496 784 19 5448624 6099743 3323520 1807775 767 20 5590170 6392531 3573533 1816603 752 21 5728220 6699372 3837547 1823191 739 22 5863020 7020942 4116392 1827727 727 23 5994789 7357947 4410934 1830381 716 24 6123724 7711129 4722083 1831305 705 25 6250000 8081263 5050789 1830638 696 Harvest when the tree is 7 years old Answer harvest when the tree is 24 years old 47 Refer back to the previous problem Which year should the company harvest the tree if the discount rate was 75 instead of 7 Answer harvest when the tree is 20years old 48 Similar to the tree harvest example which of the following years should the company plan to harvest the trees Note that the discount rate is 6 Age Board Feet Price Sale39s Price NPV 6 Return 10 3162278 8 5000000 8 1581139 8 1581139 11 3316625 8 5150000 8 1708062 8 1611379 803 12 3464102 8 5304500 8 1837533 8 1635398 758 13 3605551 8 5463635 8 1969942 8 1654001 721 28 4 O Lquot Lquot 1 Lquot 11 Lquot 14 3741657 5627544 2105634 1667859 689 15 3872983 5796370 2244925 1677538 662 16 4000000 5970261 2388105 1683520 638 17 4123106 6149369 2535450 1686219 617 18 4242641 6333850 2687225 1685998 599 19 4358899 6523866 2843687 1683174 582 20 4472136 6719582 3005088 1678026 568 21 4582576 6921169 3171678 1670801 554 22 4690416 7128804 3343706 1661719 542 23 4795832 7342669 3521420 1650979 531 24 4898979 7562949 3705073 1638757 522 25 5000000 7789837 3894919 1625213 512 Harvest when the tree is 7 years old 17 years old Refer back to the previous problem Which year should the company harvest the tree if the discount rate was 55 instead of 6 21 years old Similar to the quot evaluating two mutually exclusive projects with unequal livesquot example given in class assume that Asset A costs 6000 and produces aftertax real cash flows of 2600 per year in years 1 and 2 and 2800 in year 3 Asset B costs 4000 and produces aftertax real cash flows of 2600 in year 1 and 2 Use a 3 real discount rate What the EAC of Asset A using the 3 discount rate 54352 What the EAC of Asset B using the 3 discount rate 50956 What is the PV of a perpetual stream of Asset A purchases 1811746 A B C D Which of the two assets should the firm purchase Asset1 A project has the following real constant dollar cash flows Using a 3 real discount rate what is the equivalent annual cash flow EAC for the project Answer 10254 0 1 2 3 4 2000 0 0 1000 I 1650 Using a 6 discount rate what is the equivalent annual cash flow EAC for the following cash flow stream Answer 1075 62 0 1 2 3 4 5 6000 I 2500 I 2500 I 2500 I 2500 I 2500 Using a 3 discount rate what is the equivalent annual cash flow EAC for the following cash flow stream Answer 54987 0 1 2 I3 4 5 6000 I 1860 I 1860 I 1860 I 1860 I 1860 Refer back to the previous problem If the time zero cash flow was 5500 instead of 6000 the EAC would be than the correct answer to the previous problem A Higher Carreclanswer B Lower 29 Lquot Lquot Lquot O u gt1 Using a 5 discount rate what is the equivalent annual cash flow EAC for the following cash flow stream 29415 0 1 2 I3 4 5 6000 I 1680 I 1680 I 1680 I 1680 I 1680 Refer back to the previous problem If the time zero cash flow was 5500 instead of 6000 the EAC would be than the correct answer to the previous problem Higher Assume that you will buy a new car in two years and every 4 years thereafter forever ie time 2 time 6 time 10 time 14 etc The car will cost 17000 to buy and cost 3000 to operate and maintain for each of the four years These cash flows do not include in ation ie they are real cash flows The following shows the real cash flows through year 10 0 1 2 3 4 5 6 7 8 9 10 0 0 l7000 3000 3000 3000 3000 3000 3000 3000 3000 l7000 l7000 Hint the EAC for the cash flows for the car ie 17000 3000 3000 3000 3000 using a 3 real discount rate is 77573459768 Using a 3 real discount rate what is the present value of a perpetuity of cash flows from buying and operating maintaining the car 23 7 957 07 58 Assume that you will buy a new car in two years and every 4 years thereafter forever ie time 2 time 6 time 10 time 14 etc The car will cost 15000 to buy and cost 3500 to operate and maintain for each of the four years These cash flows do not include in ation ie they are real cash flows The following shows the real cash flows through year 10 0 1 I2 3 4 l5 l6 l7 I8 I9 I10 I 0 0 I 15000 I 3500 3500 3500 3500 3500 3500 3500 3500 15000 15000 Hint the EAC for the cash flows for the car ie 15000 3500 3500 3500 3500 using a 4 real discount rate is 77632350680 Using a 4 real discount rate what is the present value of a perpetuity of cash flows from buying and operating maintaining the car I 76413 59 Similar to the quotreplacement analysis example given in class assume 1 an old machine produces cash flows of 15000 per year for the next 5 years at which time it will be worthless 2 old machine s sale s price today 66000 3 old machine s sale s price in one year 58000 4 old machine is fully depreciated 5 new machine will cost 200000 produce aftertax cash flows of 28000 for the next 12 years At the end of this 12year period an identical machine with the same cash flows will be purchased This will continue every 12 years forever 6 Cash flows are in constant dollars 7 use the real discount rate of 3 7 The marginal tax rate is 34 A What is the t 0 aftertax salvage value of the old machine if it is sold today 43560 B What is the t 1 aftertax salvage value of the old machine if it is sold in one year 38280 C What is the EAC for the new machine 7907 58 D What is NPV replace today 7 NPV replace in one year 490 89 do not replace today 60 A project requires an initial investment of 100000 and produces real cash flows of 3600 per year in perpetuity In addition to the above cash flows this project will cause an old machine that the firm owns to wear out two years early More specifically if the project is accepted this existing machine will last only four more years The new replacement machine will handle the capacity of the new project and all existing projects will 30 cost 30000 to purchase at t 4 and will cost 5000 per year to operate for eight years t 5 to t 12 At the end of this eightyear period an identical machine with the same cash flows will be purchased This will continue every eight years forever If the firm rejects the project the old machine will need to be replaced in six years with the new replacement machine Cash flows for the replacement machine are the same as above but the 30000 purchase of the replacement machine would be in year 6 and the 5000 operating cash out flows would be for years 7 14 Again this will continue every eight years forever The costs of operating the old machine are as follows 0 l 2 3 4 5 6 Accept project 7500 7500 7500 7500 Reject Project 5500 5500 5500 5500 5500 5500 Assume all cash flows are after tax Also all figures presented are real cash flows so use a 3 real discount rate A FEED What is the preliminary NPV In other words what is the NPV ignoring the costs of causing the old machine to wear out 2 years early 20 000 What is the PV of operating the old machine assuming the project is accepted 2787824 What is the PV of operating the old machine assuming the project is rejected 29 79455 What is the EAC for the new replacement machine 9273 69 What is the NPV take project 7 NPV reject project 615018 Take project 31 Chapter 12 Agency problems Management Compensation and Measuring Performance This chapter is a practical discussion of how we can make sure managers are following the NPV rule accept positive NPV projects and reject negative NPV projects We will discuss V The capital budgeting process Agency problems associated with gathering information needed to make good decisions How to correct these problems Measuring project performance using accounting income 2 3 4 5 Measuring project performance using economic income The main topic of this chapter is How can we get managers to select positive NPV projects and reject negative NPV projects We start the discussion with an outline of how capital budgeting decisions are made The capital budgeting process Capital budgeting decisions ie what projects the firm invests in are made by employees at different levels of the firm Lower level managers make a significant number of small project decisions More expensive projects typically require higherlevel approval A significant number of projects are not in the capital budget IT RampD marketing expenses employee training but they are still projects and should be analyzed as projects Evaluation of the project after acceptance 7 Post audits Why do we look at a project after acceptance 1 Fix any unanticipated problems avoid costly delays determine the accuracy of forecasts to help in making more accurate forecasts for future projects N V Typically ask I Were the estimates of initial investment accurate I Are the first few years of cash flow estimates accurate Overall profitability of the project is probably not evaluated since postaudits are typically conducted prior to the project39s completion Need to consider the affect of the economy of project cash flows L V Some projects are difficult to evaluate separately because they are interwoven with other projects Example Advertisements for a new product is done in three forms TV radio and newspaper Should the firm continue advertising in the newspaper What was the incremental impact of the newspaper advertisement on product sales Agency problems can cause firms to make bad project selection decisions What are agents An agent is someone that works for a principal For example a real estate agent works for a home seller the principal Principals want agents to work in their best interests However sometimes they don t What does a home seller want a real estate agent to do How might a real estate agent fail to work in the best interests of the home seller For a corporation managers and employees of the corporation are the agents of the firm s stockholders the principals Just like the real estate agent example stockholders want managers and employees to work in their best interests How agency problems distort the information that is given to senior managers 1 Biased forecasts provide bad information to senior managers Forecasts can come in two forms Biased economic forecasts Suggestion Rather than having each project manager put together an independent economic forecast it is probably better to have a companywide economic forecast that can be applied to all projects Also rather than one economist s forecast a consensus forecast of a team of economists can further reduce biases Biased noneconomic based forecasts 2 Agency problems ie con icts of interests between decisionmakers agents and firm owners can cause biased forecasts and therefore suboptimal investment decisions Describe how the following examples can result in the acceptance of a bad project or rejection of a good project I Project acceptance allows the project manager to over consume perks I Project acceptance increases the size of manager s division think about the manager s compensation I Manager is overly concerned with shortterm profitability of his her division I Project manager has an incentive to invest in projects that require his her specialized skills I Project manager needlessly wants to avoid risk when deciding which projects to select I The project manager may not expend the effort needed to make the project successful 3 Many of these problems can also apply to senior management as well 4 Can senior managers avoid agency problems by disclosing the opportunity cost of capital See Brealey Myers and Allen s second law page 303 How to correct these agency problems Increased monitoring 7 but you need to compare the benefits with the costs of monitoring Benefits of monitoring Reduced agency costs Costs and problems of monitoring 0 ha Monitoring costs money and takes time Senior management can t review projects they don t know about Micro management by senior management Too many constraints or too much time spent on monitoring can result in the firm being prevented from undertaking positive NPV projects Diminishing returns Need to review projects that are most likely to contain errors in assumptions or analysis that would hurt the firm Example You are a senior level manager in charge of reviewing projects prior to acceptance rejection A junior analyst has computed the NPV of two nonmutually exclusive projects NPV Project A 10 NPV Project B 10 Assume that you know that the junior analyst is pessimistic in making forecasts and calculating NPVs If you have only the time to review one project which would you review Who monitors senior management Shareholders are the primary beneficiaries of reduced agency costs but do they have the incentive to monitor Primary responsibility the board of directors stockholders lenders hired monitors e g auditors nging incentives for managers ie use compensation to provide incentives Usually determined by outputs performance rather than inputs ie effort Why In the US CEOs are often paid relatively low base salaries with the rest being incentive based bonuses stock and stock options Only 1 million of regular compensation is deductible by the corporation Compensation in the form of stock options is not included in this restriction The amount of incentives should depend on how much firm value is influenced by managers efforts Two examples A Firm value is primarily in uenced by factors beyond the manager s control eg a power plant B Firm value is primarily in uenced by factors in manager s control eg real estate brokerage The magnitude of gains and losses for large require and to share risk 1 I Incentives are often linked to stock performance Problems A Too much concern with the Within fir39m risk of the project B Large uctuations in the firm s stock value could be caused by 1 changes in the overall stock market and or 2 firm specific changes in stock value C Abnormal stock price increases may occur too early example the problem with hiring a hotshot m D Enron and WorldCom type problems Accounting measures are often used for evaluating employees Advantages 1 Objective 2 Can be used to evaluate junior managers who are in charge of a division or project ie stock performance isn t the best measure Disadvantages 1 Subject to manipulation 2 Accounting profits do not always equate to adding value through accepting positive NPV projects Measures 1 Book or accounting return on investment Accounting net income Investment Compare this fraction to the opportunity cost of capital 2 Economic Valued Added EVA Net accounting operating profit after taxes 7 opportunity cost of capital investment See httpwwwsternstewartcom for more information 3 Disadvantages of both methods They use accounting income as a starting point and They use current profits from a project instead of the present value of future expected cash flows from the project What if the bad performance is due to factors beyond the employee s control Measuring the pro tability of the rm39s assets using economic income versus accounting income Accounting book net income Revenue minus expenses minus accounting book depreciation minus taxes Economic income cash flow minus economic depreciation Cash flow computation is described in Chapter 6 Economic depreciation reflects the decrease in the present value of the asset over time Example Accounting book depreciation 1 1000 initial investment in a factory 2 Factory has a useful life of 3 years and a zero salvage value 3 Expected factory accounting revenue and expected cash flows Year 1 300 Year 2 300 Year 3 700 4 Accounting depreciation method Straightline depreciation 5 No other expenses other than depreciation Ignore income taxes Expected accounting income per year Year 1 300 333 33 Year 2 300 333 33 Year 3 700 334 366 Expected accounting return on investment ROI per year Year 1 33 1000 33 Year 2 33 667 495 Year 3 366 334 10958 Performance Evaluation using Accounting Figures Assume that you are the project manager and under your management you are able to exactly meet expectations How will the firm39s senior management view your performance using accounting ROI as a measure Performance evaluation at the end of year 1 Performance evaluation at the end of year 2 Performance evaluation at the end of year 3 Example Economic depreciation using a 10 cost of capital 1 What is the expected economic investment at t 0 ie PV att 0 10465815 2 What is the expected economic investment at time 1 2 and 3 PV t 1 PVt 2 PVt 3 L V Economic depreciation equals the change in economic investment or PV by year Since we are calculating these figures at time zero we are calculating expected economic depreciation Ideally you would recalculate the present value from the previous step each year in order to calculate the previous year s actual economic depreciation Expected economic depreciation clear 1 Expected economic depreciation clear 2 Expected economic depreciation clear 3 Total expected economic depreciation is 10465815 PV at t 0 of the project 4 V Expected economic income per year factory cash flow minus economic depreciation Year 1 Year 2 Year 3 Lquot V Expected economic return on investment ROI Year 1 Year 2 Year 3 Performance evaluation using economic income gures Assume that you are the project manager and under your management you are able to exactly meet expectations How will the film39s officers view your performance using economic ROI as a measure Performance evaluation at the end of year 1 Performance evaluation at the end of year 2 Performance evaluation at the end of year 3 Lessons 1 Accounting depreciation distorts the yearbyyear ROI Managers compensated based on accounting ROI may be reluctant to take projects similar to the example given above 2 1f actual cash flows equal expected cash flows then economic income results in a constant ROI equal to the cost of capital Side note What would actual economic ROI look like if you exceeded expectations For example assume that actual cash flows are Year 1 300 Year 2 300 Year 3 725 What is the actual economic ROI for years 1 2 and 3 How to correct the accountingeconomic depreciation problem 1 Adjust accounting depreciation to reflect economic depreciation 2 Compare yearbyyear accounting ROI with accounting ROIs from similar successful projects 3 Change manager compensation package 4 1n the long run when the firm has a mixture of old and new projects accounting return on investment will be closer to economic return on investment But see Table 125 showing that the two measures can still be different Selected quiz questions from Chapter 12 of the textbook 121 c d and e122123124127128 Chapter 12 Review Questions 1 Understand the basics of the capital budgeting process Remember that many project acceptance rejection decisions are made by lowerlevel managers Understand why a project should be evaluated after acceptance What is the purpose of a post audit 2 Understand the management agency problems as they relate to the capital budgeting process How can monitoring address these problems Who benefits from monitoring Who monitors corporate managers What are the limitations costs and problems of monitoring How can changing incentives reduce agency problems What are the limitations costs and problems of changing incentives 3 How is accounting ROI different that EVA 4 What is economic depreciation Understand how to calculate returnoninvestment ROI using both accounting and economic depreciation What are the advantages of using economic depreciation instead of using an accounting J 39 39 method 1 l 1 as the N i N 1quotquot or the quotm f h r quoti it or tax depreciation methods In particular what is the problem with using accounting depreciation in performance evaluation for a manager 5 What are the various ways a corporation can adapt accounting depreciation to correctly evaluate the performance of a manager Chapter 12 Practice Questions 1 Assume that a project requires an initial investment of 5000 and is expected to produce cash flows and revenue of 2100 per year for three years The expected project net income is calculated by subtracting depreciation for revenue Ignore income taxes A What is the expected economic depreciation per year if the discount rate is 10 1577 76 1 73554 190909 What is the expected economic R01 per year 10f0r each aflhe three years What is the expected accounting ROI if straightline depreciation is used 3 year life no salvage value 8667 13 26 D What is the actual economic ROI in year 3 if cash flows exceed expectations in year 3 More than 10 B C 2 Assume a divisional manager39s compensation contract is designed as follows 50000 per year base salary plus a bonus equal to 5 of the difference between the actual cash flows for the division and the division39s projected cash flows Since the base salary is relatively low the manager expects most of her his yearly salary from the bonus If this manager is responsible for reviewing and approving new projects for the division it is likely that A The manager will have an incentive to overestimate project cash flows B The manager will have an incentive to underestimate project cash flows CarrecIAnswer 3 Four junior analysts have the responsibility to calculate NPV for four different projects Unfortunately and as discussed in class the person calculating the project NPV may let their biases enter into their calculations Assume the following BiasedNPV calculated for Project A 5 This junior analyst tends to overestimate project NPV BiasedNPV calculated for Project B 5 This junior analyst tends to overestimate project NPV BiasedNPV calculated for Project C 5 This junior analyst tends to underestimate project NPV BiasedNPV calculated for Project D 5 This junior analyst tends to underestimate project NPV A senior analyst has enough time to evaluate and check the assumptions and NPV calculations for only two projects Taking into account the junior analysts biased NPV calculations and their known tendency to overestimate or underestimate NPV which two projects should the senior analyst review Projectsl andD 4 As described in class the accounting return on investment for a project is calculated by dividing the year39s net income for the project by A The book value of the project at the beginning of the year CarrecIAnswer B The book value of the project at the end of the year V 0 gt1 00 In class we discussed Brealey Myers and Allen s second law regarding project cost of capital According to that second law if a company increases the minimum rate of return required for its projects eg if they increase the discount rate they will use to evaluate projects from 10 to 15 A The proportion of projects that have a positive NPV for that company calculated at the new higher discount rate will increase B The proportion of projects that have a positive NPV for that company calculated at the new higher discount rate will decrease C The proportion of projects that have a positive NPV for that company calculated at the new higher discount rate will stay the same CarrecIAnswer As discussed in class a senior manager needs to recognize that a project manager will typically prefer that the firm select a project that other things equal A Requires his or her specialized skills CarrecIAnswer B Does not require his or her specialized skills ie anyone could manage the project As discussed in class incentive based compensation for a manager eg giving the manager stock in the firm as part of his or her compensation package is most effective in which of the following two situations A The manager is the president of a company where firm value is influenced by factors beyond the manager s control B The manager is the president of a company where firm value is influenced by factors within the manager s control Correct Answer In class we discussed how stock can be used to provide the proper incentives for managers and thereby reduce agency costs One of the problems of using stock as an incentive is the problem of the hotshot manager As described in class the problem of the hotshot manager is that A Stock prices often rise at announcement of the hiring of the hotshot manager which is before the manager starts working for the firm ie before the manager s date of hire Correct B Stock prices usually don t rise at announcement of the hiring of the hotshot manager Instead the increase in stock price typically occurs after the hotshot manager starts working for the firm ie after the manager s date of hire A threeyear project requires an initial investment of 2000 It will produce expected cash flows of 1500 at time one 1200 at time two and 500 at time three The opportunity cost of capital is 10 A What is the NPV of the project 73103 B What is the economic depreciation for the second year 1 049 59 C If actual cash flows are less than expected cash flows for the third year what will the economic return on investment be for the third year Less than 10 ABC Corporation will invest in a twoyear project Expected cash flows are listed below 0 1 2 l 190000 88000 145200 Using a 10 discount rate the PV of the project s future expected cash flows is 200000 Therefore the NPV for the project is 10000 Using the expected cash flows what is the economic depreciation for the first year 68 000 1 1 The following are expected cash flows for a project Using a discount rate of 10 what is the expected economic depreciation for the first year of the project 50526 1 N 0 3 1000 650 400 700 1 N The following are expected cash flows for a project Using a discount rate of 6 what is the expected economic depreciation for the first year of the project 32043 0 1 2 3 1000 400 500 600 13 The following are expected cash flows for a project Using a discount rate of 9 what is the expected economic depreciation for the first year of the project 188 71 0 3 1000 300 500 700 1 4 The following are expected cash flows for a project Using a discount rate of 9 what is the expected economic depreciation for the first year of the project 90 01 o 1 2 I3 1000 200 500 800 15 The following are expected cash flows for a project Using a discount rate of 5 what is the expected economic depreciation for the second year of the project 54921 0 1 2 3 1000 200 610 700 16 The following are expected cash flows for a project Using a discount rate of 12 what is the expected economic depreciation for the second year of the project 13520 0 3 1000 400 250 920 17 The following are expected cash flows for a project Using a discount rate of 8 what is the expected economic depreciation for the second year of the project 50754 0 1 2 3 1000 300 600 700 00 The following are expected cash flows for a project Using a discount rate of 8 what is the expected economic income for the second year of the project Note 7 this question asks for expected economic income not expected economic depreciation 9246 0 3 1000 100 600 700 19 The following are expected cash flows for a project Using a discount rate of 8 what is the expected economic income for the first year of the project Note 7 this question asks for expected economic income not expected economic depreciation 11181 0 1 2 I3 1000 400 550 700 N O Using the following numbers what is the expected economic return on investment ie expected economic ROI for the second year of the following project F 1 B N You are considering a project The project requires an initial investment of 900 in a factory that will last three years no salvage value The firm was originally planning to use the straightline depreciation method to calculate accounting depreciation The following summarizes accounting net income for the project under straightline depreciation Assume the firm wants to switch to the sumoftheyears digits depreciation method for the project Under the sumoftheyears digits method the depreciation will be 450 for year 1 300 in year 2 and 150 in year 3 How will this change in the accounting depreciation method from straight line to sumoftheyears digits affect the accounting ROI for the third year A The account ROI for the third year will be the same under both methods B The account ROI for the third year will be lower using the sumoftheyears digits method C The account ROI for the third year will be higher using the sumoftheyears digits method Correct answer Q N The following are expected cash flows for a project Using a discount rate of 8 what is the expected economic depreciation for the first year of the project 198 78 0 1 2 I3 1000 300 550 650 23 Refer back to the facts of the previous problem What would happen to the expected economic depreciation for the first year if the discount rate was changed from 8 to 9 You can solve this problem by using our intuition Here s a hint remember that expected economic ROI the discount rate So the expected economic R01 is 8 in the first problem and 9 in the second problem A The expected economic depreciation for the first year would increase B The expected economic depreciation for the first year would decrease Correct answer C The expected economic depreciation for the first year would stay the same Assume a project is expected to produce revenue of 600 per year for four years This project requires an investment of 1000 in a factory that will be depreciated over the project s four years using the straight line method for accounting purposes The factory has no salvage value at the end of the fourth year Other than accounting depreciation the project has no other expenses and there are no income taxes Using the straight line method the accounting depreciation will be 250 a year for each of the four years and net income will be 600 250 350 a year for each of the four years Over the four years accounting return on investment will A Stay the same each year B Increase each year CarrecIAnswer C Decrease each year Chapter 7 Introduction to Risk Return and the Opportunity Cost of Capital Chapter 8 Risk and Return section 82 and 83 skim These chapters describe how risk is measured and is part of a threechapter sequence describing how the risk of a proj ect s cash flows determines the discount rate the opportunity cost of capital for these cash flows We then use the discount rate to calculate the present value of the project s future expected cash flows Subtracting the initial investment gives us the project NPV You will notice a slight difference in notation between these notes and the text Please take this into account in your studying Through most of our discussion of Chapter 6 we assumed that the future cash ows of a project are known with certainty However in most circumstances future cash flows are uncertain When a corporation s future cash flows are uncertain Step one Calculate expected future cash flows Calculation of project cash flows under certainty was discussed in Chapter 6 This involved determining project revenues expenses tax depreciation corporate income taxes working capital adjustments in ation etc To calculate expected cash flows for risky projects the types of calculations done in Chapter 6 may have to be performed many times resulting in something like this Project A s time one cash flow in a booming economy 155 Project A s time one cash flow in a normal economy 135 Project A s time one cash flow in a recession economy 40 To calculate expected cash flows you need to determine the probabilities Probability of a booming economy 20 Probability of a normal economy 60 Probability of a recession economy 20 What is the expected project cash flow for time one in the above example If the initial investment is 100 what is the IRR for this project In the above example 1 have assumed that project cash flows depend only on the type of economy This is obviously a simplification Several other factors can affect project cash flows each with their own cash flows and probabilities For example consider consumer demand Project A s time one cash flow in a booming economy and high consumer demand 200 10 prob Project A s time one cash flow in a booming economy and low consumer demand 110 10 prob Project A s time one cash flow in a normal economy and high consumer demand 165 30 prob Project A s time one cash flow in a normal economy and low consumer demand 105 30 prob Project A s time one cash flow in a recession economy and high consumer demand 60 10 prob Project A s time one cash flow in a recession economy and low consumer demand 20 10 prob Step two Discount expected cash flows at the opportunity cost of capital to determine their present value The opportunity cost of capital is based on the cash flow s risk higher risk higher opportunity cost of capital Notice that the above example gives project cash flows and probabilities We use these to calculate expected project cash flows and the present value of these cash flows Sometimes you might want to calculate present values of individual parts of the project For example Economy Probability Project Product 1 Product 2 Boom 020 155 115 40 Normal 060 135 95 40 Recession 020 40 0 40 Expected 120 80 40 PV of cash flows from product 1 PV of cash flows from product 2 PV of project cash flows Separate present value calculations of the two parts will give you the same answer as you would get by calculating the PV of the project cash flows However separate calculations may allow you to focus on the risks of the different parts of the project How could you use this concept in the above example The opportunity cost of capital for cash flows is the expected return for financial assets with the exact same amount of risk as these cash flows I Riskfree cash flows should use a discount rate equal to the expected return for riskfree securities eg the onemonth TreasuryBill interest rate We are using 5 as the riskfree rate in this class I Higher risk cash flows should be discounted at a higher discount rate to re ect their higher level of risk For example consider a project with cash flows that are just as risky as large US firm common stocks Examine Table 71 page 149 of the textbook Then describe how the opportunity cost of capital would be determined for the risky cash flows of this particular project Relevant Table 71 information Average annual return for the large US firm common stocks 1900 7 2003 117 Average annual return for Treasury Bills 1900 7 2003 41 Source Yahoo Finance SampP 500 for 2004 107 Treasury Bills for 2004 15 approximate SampP 500 for 2005 30 Treasury Bills for 2005 30 approximate SampP 500 for 2006 152 Treasury Bills for 2006 50 approximate Note For purposes of class discussion ignore what has happened so far in 2007 ie assume we are at the beginning of the year Updated approximate averages including information from 2004 2006 age annual return for large US firm common stocks 1900 7 2006 116 Average annual return for Treasury Bills 1900 7 2006 41 Average difference 1900 7 2006 75 I Arithmetic versus geometric averages Assume you buy a stock for 100 att 0 The stock falls 50 in year 1 but increases 50 in year 2 What is your stock selling for att 2 What do you need to earn in the second year to get you back to 100 We should use arithmetic averages for estimating risk premiums discussed below We should use geometric averages for computing growth in investment Example stock without dividends Arithmetic average Geometric average Example stock with dividends Arithmetic average Geometric average Compounding and the growth in investment values Assume your greatgreat grandparents put 1000 in the bank for you in 1900 earning 40 per year geometric average for TBills What is the value of this 1000 investment today 107 years later Assume your greatgreat grandparents put 1000 in the bank for you in 1900 earning 97 per year geometric average for large US firm common stocks What is the value of this 1000 investment today 107 years later Some questions and observations about the market risk premium 1 What is the market risk premium The extra return investors expect for the stock market eg large US firm common stocks over the riskfree rate Based on the law of one price what investors expect for the stock market should in equilibrium be equal to what investors require for the stock market In general what investors require for a particular investment should be based on the investm ent s opportunity cost of capital ie the expected rate of return on other investments with the same risk level Now applied to the stock market eg large US firm common stocks 1f investors expected return for the stock market is higher than what they require ie the stock market s opportunity cost of capital then If investors expected return for the stock market is lower than what they require ie the stock market s opportunity cost of capital then So to have both buyers and sellers in the market expected required 2 What is the expected return over the next year for an investment in large US firm common stocks To approximate add I Current shortterm Treasury Bill rate I Market risk premium for large US firm common stocks estimated as the avg historical premium 3 1n the previous equation we assumed two things I The average historical premium is a good approximation of the unobservable market risk remium I The market risk premium is constant across time 4 Based on this what would happen if Treasury Bill interest rates increased from 5 to 10 I Expected large US firm common stock return with a 5 riskfree interest rate I Expected large US firm common stock return with a 10 riskfree interest rate 5 Problems with using historical data for the period 19002006 to approximate the market risk premium Is the average historical premium a good approximation for what investor s expect for the future I Perhaps events have occurred that have caused previous market returns to be different than what investor expected What are some surprise events that could have caused the actual market return to differ from expected I Maybe the high average historical return for large US firm common stocks is due to a decrease in the market risk premium Examp e Price for a portfolio of large US firm common stocks 1000 Expected dividend in one year 100 Opportunity cost of capital 134 Growth rate in dividend in perpetuity 34 What is the expected return for large US firm common stocks using the above information What happens if over the next year the opportunity cost of capital for large US firm common stocks declines to 94 Keep everything else the same New large US firm common stock price New expected return for large US firm common stocks What happens to the average annual return for large US firm common stock when this most recent year is included in the average I Results from recent surveys of financial economists and corporate CFOs imply a market risk premium between 55 and 7 see footnote 11 page 152 I Using analysis from dividend yields and dividend growth rates results in a risk premium of 53 I Brealey Myers and Allen suggest the use of a market risk premium in the range of a 5 8 Note 7 this is lower than the range of 6 85 given in the previous edition of the text In class we will use 5 as the riskfree interest rate and 84 as the market risk premium Computing the opportunity cost of capital for risky cash flows of a project From the above we know how to calculate the opportunity cost of capital for risk free cash flows and for cash flows that are just as risky as large US firm common stocks What about cash flows of different amounts of risk In this class we will I Use the CAPM model I In the CAPM risk is measured by beta the portion of total risk that cannot be diversified away I We will initially use a variation of the CAPM to solve for the PV of the project s cash flows With this number we will also calculate the NPV I With the PV we will calculate the project s risk and opportunity cost of capital and use the opportunity cost of capital to verify our calculation of the project PV and NPV Statistical and other tools used in the calculation of the beta of a project s risky cash ows I Calculation of expected cash flows Calculation of returns and expected returns Calculation of the variance and standard deviation of returns Calculation of the covariance and correlation of returns This next section of the notes is meant to build up your intuition of the determinants of beta and project value A detailed example follows You are expected to review most of this detailed example on your own ABC Corporation is considering an investment of 100 at t 0 in either project A or project B Each project will last only one year Time 1 cash flows from these projects depend on the state of the economy Cash flows for a 100 riskfree investment and for a 100 investment in the market are provided for comparison purposes 1 What is the expected time one cash flow from the four investments Ecrf 10502 1050 6 10502 105 ECFM 14302 1160 6 7602 1134 ECFA 15502 1350 6 4002 120 ECFB 1502 1050 6 13602 932 Based on the initial investment of 100 we can calculate a oneperiod rate of return 2 What is the expected return based on the initial investment ErYf using initial investment 502 50 6 502 105 100 71 5 ErM using initial investment 4302 160 6 2402 1134 100 71 134 ErA using initial investment 5502 350 6 6002 120100 71 20 ErB using initial investment 8502 50 6 3602 932 100 71 68 Calculation of the PV of the project s time one cash ow Step one 7 calculate the variance of the market s returns Step two 7 calculate the covariance between the project s cash flows and the market s returns Step three 7 use the above two numbers to calculate the PV 3 What is the variance of the market s returns N 2 0M 2er EUM Zpl 71 02M 7 043 0134 02 016 0134 06 024 0134 02 7 0045904 1quot What is the covariance between the project s cash ow and the market s returns Cov CFA rM i CFh ECFArM ErM 11 C0vCFArM 7155 120043 013402 1351200160340 6 40120 024 013402 7 8290000 C0vCFBrM 715932043013402 105932016 0 1340 6 136932 024013402 7 7 646800 5quot What is the PV of the projects time one cash ows See footnote 16 page 227 of the textbook C0vCF r Er 7r A M M f PVA ECFA 2 1rf WA 7 120 7 8290084 0 045904 105 7 998382 NPVA 7 100 998382 7 01618 13vB 7 932 7 764680084 0 045904 105 7 1020885 NPVB 7 100 1020885 7 20885 Calculation of beta the CAPM opportunity cost of capital and the veri cation of the project PV and NPV Step one calculate the project returns using the PV and the expected return using the PV Step two 7 calculate the variance and standard deviation of the market s returns Step three 7 calculate the variance and standard deviation of the proj ect s returns using the PV Step four calculate the correlation coefficient between the project s returns using the PV and the market s returns Step five 7 use the above three numbers to calculate the beta Step six 7 use the beta to calculate the CAPM opportunity cost of capital and the PV and NPV 6 What are the returns for the two projects using the PV 7 What is the expected return for the two projects using the PV ErA using PV 55251202 3521880 6 59935202 120998382 7 201945 ErB using PV 85306902 285190 6 3321 7702 39123102 0885 7 I 8 7067 8 What is the variance of returns for the market and for the two projects using the PV 02M 0045904 calculated above 7 variance is the same as based on the initial investment 02A 0552512 02019452 02 03521887 02019452 06 0599352 02019452 02 0166539 623 0 853069 00870672 02 0 028519 00870672 06 0 3321 77 00870672 02 0160521 9 What is the standard deviation of returns for the market and for the two projects using the PV GM 0214252 0A 0408091 03 0400651 Aside What is the variance and standard deviation for the riskfree asset 10 What is the correlation coef cient between the project s returns using the PV and the market s return Note The correlation coefficient measures the tendency of two asset39s returns to move in the same direction The maximum correlation coefficient is 10 perfect positive correlation and the minimum is l 0 perfect negative correlation A correlation coefficient of 0 means that the two asset39s returns are uncorrelated pAM Cav r1 rM 0quotA 6M 0552512 0201945 043 0134 02 0352188 0201945 016 0134 06 0 599352 0201945 024 0134 02 0408091 0214252 0949675 pBM Cav WM 763 6M 0853069 0 087067 043 0134 02 0028519 0 087067 016 0134 06 0332177 0 087067 024 0134 02 0400651 0214252 0872593 T maximum correlation coefficient is 10 perfect positive correlation and the minimum is l 0 perfect negative correlation A correlation coefficient of 0 means that the two asset39s returns are uncorrelated Aside 7 What is the correlation coefficient between the riskfree asset and the market The market investment and project A have a very high positive correlation This indicates that when the market has a return that is higher than its expected return project A should also have a return that is higher than its expected return and vice versa The opposite relationship a negative correlation is found between the market investment and project B The returns of the market investment and the riskfree investment are uncorrelated ll What is the beta for the cash flows of Project A and Project B Investors in ABC Corp want the corporation s managers to only invest in positive NPV projects To calculate the NPV we need to discount the expected t 1 cash flow at the opportunity cost of capital for each of the projects NPVA 100 120 l opportunity cost of capital for project A NPVB 100 932 l opportunity cost of capital for project B As stated above the opportunity cost of capital depends on the riskiness of the projects How risky are these two projects Welldiversified investors in ABC Corp are concerned with how these projects will affect their investment portfolio s risk They are not concerned with risk that will be diversified away If an investor is invested in the market the market portfolio then beta is the relevant risk measure not variance or standard deviation Beta measures the contribution of an asset to the riskiness of the market portfolio The market portfolio has a beta of one Betas greater than one are more risky than the market and vice versa Calculation of beta BA pAM 5A C5M 3A 0949675 0408091 02I4252 180887 BB 0872593 04006510214252 463175 6 00 000214252 00 3M 10 0214252 0214252 10 Project A is more risky than the market portfolio Project B is less risky than the market portfolio 12 A quick look at the Capital Asset Pricing Model CAPM Using certain semireasonable assumptions it can be shown that all riskaverse investors will want to invest in two assets i the market portfolio and ii a riskfree asset The market portfolio is a portfolio of all risky assets stocks bonds real estate fine art human capital etc held in proportion to their market value The riskfree asset could be Treasury Bills or some other riskfree asset bank savings account bank CD39s moneymarket mutual funds etc Example 10000 total investment 2000 in a bank certificate of deposit riskfree investment 8000 in a global mutual fund market investment Based on the discussion in the notes so far we learned that beta is the appropriate measure of risk for investors that own a portion of the market portfolio This also applies to an investment such as the one above ie part investment in the market portfolio and part in a riskfree investment Remember Beta measures the contribution of an asset to the riskiness of the market portfolio after taking into account the reduction in risk from diversification Betas greater than one are more risky than the market portfolio Betas less than one are less risky than the market portfolio Riskaverse investors will not want to own highrisk assets unless they are compensated with a low price or equivalently a high expected return Example Price Expected T 1 Cash Flow Beta Assetl 100 110 High Asset J 100 110 Low Notice that both assets have the same expected return 10 but assetl has more risk This is not an equilibrium relationship Investors will not want to own asset 1 if they can own asset I that has the same expected return but lower risk What will happen to asset 139s price and expected return Based on this if an asset has aboveaverage risk then investors will require an aboveaverage expected return and vice versa 1 L The Capital Asset Pricing Model CAPM is one finance model that takes into account this riskreturn tradeoff According to this model the required return for asset a is ra r 3 Erm rf r 3 Notice that the CAPM uses beta for a measure of risk In a CAPM setting the required return means the expected return required by investors based on the asset39s risk beta and marketwide expected returns r and Erm Graphically the CAPM equation gives the formula for the Security Market Line SML see Figure 87 in the text page 195 For example assume that If 5 and ErM rf 84 The intercept of the SML is the risk free rate 5 The slope is the market risk premium 84 What is the required return for the following investments projects Also how are these required returns related to expected returns Assuming the CAPM is correct fe rf50845 13M1 rM5184134 3A 180887 rA 5 180887 84201945 3B 163175 rB 51631758487067 Expected Return calculated using the initial investment Em 105 100 71 5 ErM 1134 100 71 134 E01 120100 71 20 ErB 932 100 71 68 Notice that for nancial assets Required return using CAPlVl expected return based on the initial investment Required return using CAPlVl expected return based on the PV of the future expected cash flows Notice that for the two projects Required return using CAPlVl 5 expected return based on the initial investment Required return using CAPlVl expected return based on the PV of the future expected cash flows As discussed earlier competition in the nancial markets plus market perfection and efficiency causes The cost of the financial asset reflected in the initial investment to equal the present value of the future expected cash flows NPV 0 Resulting in required returns expected returns based on initial investment However this should also happen for any asset that trades in an active and competitive market place land fine art coins 14 Graphical presentation of the CAPM the SML 15 Expected rates of return can differ from required rates of return for Assets that do not trade on an active and competitive secondary market greater probability of mis pricing Projects the expected return based on the initial investment for a project can be more or less than the required return implied by the CAPM 16 As an estimate of the opportunity cost of capital we will use the required return based on the CAPM In other words to determine the appropriate discount rate for a project Calculate the project39s beta Use the CAPM equation to determine the expected return and required return for financial assets with the same amount of beta ris Use this expected return required return as the discount rate for calculating the NPV of the project or as the cutoff rate used with the IRR method For projects A and B NPVA PV of expected time 1 cash flow 7 initial investment 120 1 0201945 100 998382 100 01618 NPVB PV of expected time 1 cash flow 7 initial investment 9320 1 7 0087067 100 1020885 100 20885 We have verified our earlier calculations of the PV and N39PV Plot the SM and projects A and B on the same graph Selected quiz questions from the textbook for Chapters 7 and 8 71 72 see footnote 17 page 156 74 75 78 85 86 88 Chapter 7 and 8 Review Questions 1 What is the opportunity cost of capital What is typically used as the opportunity cost of capital for projects with risk free cash flows What is meant by a constant market risk premium Assuming a constant market risk premium What happens to the expected return for large US firm common stocks if there is an increase in the risk free interest rate 2 Historically What has been the average difference between the returns on large US firm common stocks and Treasury Bills Is this a good estimate for the market risk premium According to Brealey Myers and Allen What is a good estimate for the market risk premium 3 Know how to calculate A Expected cash flows B Expected returns C Variance of returns D Standard deviation of returns E Covariance and correlation coefficient F Beta G The CAPM discount rate H The PV of cash flows 4 What is the maximum and minimum correlation coefficient How is the maximum and minimum correlation coefficient related to the maximum and minimum possible beta 5 What are quotreal life examples of the riskfree security and the market portfolio 6 What is the beta risk of the market portfolio What is the beta of the risk free asset What does it mean in terms of risk if the beta is a greater than one b less than one or c less than 0 7 How is the beta riskiness of an asset related to its market value and expected return Be able to use the CAPM equation to calculate required rates of return for assets based on their beta risk This graphs the security market line What are examples of assets that fall on the SM How do market forces ensure that these assets locate on the SM 8 What does it mean if a project locates above or below the SML with respect to the project39s NPV Chapter 7 and 8 Practice Problems Plenty of practice problems are given in the notes Here are a couple more practice problems 1 Using the following annual returns over a 4 year period What is the geometric average return 717 Year 1 50 Year 2 10 Year 3 10 Year 4 50 N 9 gt V 0 gt1 The following are stock prices for a nondividend paying stock Using these prices what is the geometric average return over this 3year period 1380 Time m 0 95 1 105 2 165 3 140 The following are stock prices for a dividend paying stock Using these prices and dividends what is the geometric average return over this 3year period 8 74 The following are stock prices for a nondividend paying stock Using these prices what is the geometric average return over this 3year period 858 The following are stock prices and dividends for a stock Using these prices and dividends what is the geometric average return over this 3year period 2167 The following are stock prices and dividends for a stock Using these prices and dividends what is the geometric average return over this 3year period 0 84 The following are stock prices and dividends for a stock Using these prices and dividends what is the geometric average return over this 3year period 242 00 O O N N N The following are stock prices and dividends for a stock Using these prices and dividends what is the geometric average return over this 3year period 13 68 Project X is a oneyear project The standard deviation of ProjectX s returns based on its present value is 20 The standard deviation of the market s returns is 15 What is the lowest possible beta for Project X Hint think about the formula for beta I33 Project X is a oneyear project The standard deviation of ProjectX s returns based on its present value is 15 The standard deviation of the market s returns is 25 What is the highest possible beta for Project X Hint think about the formula for beta 06 If an asset s standard deviation of returns is 20 and the market s standard deviation of returns is 25 what is the maximum and m1nimum possible beta for the asset Maximum 080 minimum 080 Consider the following returns based on present values of future cash flows for the riskfree asset the market and Project X Based on this information Project X s returns have a correlation with the market returns A Negative B Positive Correct Answer C Zero Which of the following two assets has the highest beta The difference between the two assets is bolded Standard deviations and correlations are calculated based on the present value of future cash flows Asset A Expected cash flow 130 Initial investment 100 Standard deviation of Asset A s returns 30 Standard deviation of the Market s returns 20 Correlation between Asset A s returns and the market s returns 05 Asset B Expected cash flow 130 Initial investment 100 Standard deviation of Asset B s returns 40 Standard deviation of the Market s returns 20 Correlation between Asset B s returns and the market s returns 05 A Asset A has the highest beta CarrecIAnswer B Asset B has the highest beta C Both assets have the same beta 14 Which of the following two assets has the highest beta The difference between the two assets is bolded Standard deviations and correlations are calculated based on the present value of future cash flows Asset AA Expected cash flow 130 Initial investment 100 Standard deviation of Asset AA s returns 30 Standard deviation of the Market s returns 20 Correlation between Asset AA s returns and the market s returns 00 Asset BB Expected cash flow 130 Initial investment 100 Standard deviation of Asset BB s returns 40 Standard deviation of the Market s returns 20 Correlation between Asset BB s returns and the market s returns 00 A Asset AA has the highest beta B Asset BB has the highest beta C Both assets have the same beta CarrecIAnswer H V Which of the following two assets has the highest beta The difference between the two assets is bolded Standard deviations and correlations are calculated based on the present value of future cash flows Asset A Expected cash flow 130 Initial investment 100 Standard deviation of Asset A s returns 30 Standard deviation of the Market s returns 20 Correlation between Asset A s returns and the market s returns 00 Asset B Expected cash flow 130 Initial investment 100 Standard deviation of Asset B s returns 40 Standard deviation of the Market s returns 20 Correlation between Asset B s returns and the market s returns 00 A Asset A has the highest beta B Asset B has the highest beta C Both assets have the same beta CarrecIAnswer H 0 Using the following information what is the beta for project X 09170 Initial investment cash flow at time 0 for the project 100 Time 1 expected cash flow for the project 126 Standard deviation of the project s returns using the PV 20862355 Standard deviation of the market s returns 21425219 Expected return for the market 134 Risk free interest rate 5 Correlation between the market s returns and the project s returns using the PV 0941731739 Correlation between the market s returns and the risk free asset s returns H gt1 Project X is a oneyear project Using the following information what is the PV of the project s time one cash flow 1 1457 Initial investment cash flow at time 0 for the project 100 Time 1 expected cash flow for the project 127 1 1 N N N Variance of the project s returns using the PV 002635916 Standard deviation of the project s returns using the PV 016235503 Variance of the market s returns 004590400 Standard deviation of the market s returns 021425219 Expected return for the market 0134 Risk free interest rate 005 Covariance between the project s cash flows and the market s returns 36620 Correlation between the market s returns and the project s returns using the PV 091887202 Correlation between the market s returns and the risk free asset s returns 0 You are calculating the beta for a project s time one cash flow This is a oneyear project and the time one cash flow is expected to be 150 Assume that the correlation between project returns and market returns is equal to 050 Both the standard deviation of the project s returns and the standard deviation of the market s returns are positive The correlation and standard deviations are correctly calculated using the present value of the project s cash flows Holding other things constant what is the effect of a higher standard deviation of project returns on the beta of project s time one cash flow A The beta will become higher B The beta will become lower Correct answer C This change will have no affect on the beta Assume that the riskfree interest rate is 5 and the market risk premium is 84 What is the required rate of return for the following financial assets Beta for financial asset AAA 15 Answer 7 6 Beta for financial asset BBB 15 Answer 17 6 What is the expected return based on the initial investment for the two financial assets described above if the market is in equilibrium and perfect and efficient 7 6 and 176 respectively Project Z requires an initial investment of 100 and has a time one expected cash flow of 95 The beta of Project Z s time one cash flow is 15 The risk free rate is 5 the market risk premium 84 Using the CAPM what is the NPV of Project Z 281 Both Project X and Y require an initial investment of 1000 and both have an expected oneyear return of 10 Using this information and the other information provided below which project has the higher NPV 0 1 I Project X expected cash flows I 1000 I 1100 I I Project Y expected cash flows I 1000 I 1100 I Riskfree interest rate 5 Market risk premium 84 Discount rates determined by the CAPM equation Correlation between the market returns and ProjectX returns 02 Correlation between the market returns and Project Y returns 02 Annual standard deviation of returns for the market 20 Annual standard deviation of returns for the Project X 40 Annual standard deviation of returns for the Project Y 20 Hint You have enough information to calculate the NPV of the two projects But you can also answer the problem without calculations if you correctly use some finance intuition Solution The betaforProjectX 02040020 04 The betaforProject Y 02020020 02 With a lowerbeta ProjectXwill have a lower discount rate and a higher NPV 15 23 You are considering the following two mutually projects Projects X and Y Expected cash flows 0 1 ProjectX 100 130 ProjectY 100 130 Standard deviation of project returns and correlation of project returns with market returns both using the PV of cash flows I Std Deviation I Correlation I ProjectX 40 06 ProjectY 30 04 Other information The standard deviation of the market 20 The risk free rate 5 The market risk premium 84 Use the CAPM to calculate the opportunity cost of capital Using the information above which of these two mutually exclusive projects should the firm select A ProjectX CarrecIAnswer B Project Y C Either Project X or Project Y they both have the same positive NP D Neither Project X or Project Y they both have the a negative NP 24 A project will produce one of two possible cash flows in one year cash flows and probabilities given below The beta for these cash flows is 12 The risk free rate is 5 and the market risk premium is 84 Using the CAPM what is the present value of the project s time one cash flow 9211 I Type of Economy I Good I Bad Probability 60 40 I Project Cash Flow I 130 I 70 Hint Calculate the expected time one cash flow Then calculate the discount rate using the CAPM Use the discount rate to calculate the present value 25 A project has the following cash flows 1 100 150 Assume that the correlation between project returns and the market returns is equal to 050 Both the standard deviation of the proj ect s returns and the standard deviation of the market s returns are positive The correlation and standard deviations are correctly calculated using the present value Holding other things constant what is the effect of a higher correlation on the NPV of the project Hint assume the correlation is increased to 060 Use the CAPM to calculate the discount rate A This will increase the NPV of the project B This will decrease the NPV of the project CarrecIAnswer C This will have no affect on the NPV of the project Chapter 11 Where do Positive NPV Projects come from Capital Budgeting and Economics Skip section 113 This chapter is concerned with answering the question Where do positive NPV projects come from In a competitive world positive NPV projects should be difficult to find Therefore you should carefully evaluate projects that purport to produce a positive N39PV We focus on using our quot economic intuition in order to critically evaluate the assumptions used in calculating the project NPV In particular we will 1 Understand why and when we should trust market values 2 Understand when it is likely we might earn quotpositive economic rents and why in general they should not be expecte In order to determine a proj ect s N39PV we need to determine the initial investment expected future cash flows and the discount rates Estimation errors are unavoidable For example consider Project A from the Chapter 7 notes Time 0 cash flow initial investment 100 Project A time one expected cash flow calculation from Chapter 7 notes Boom economy cash flow 155 probability 20 Normal economy cash flow 135 probability 60 Recession economy cash flow 40 probability 20 Expected time one cash flow 120 Beta 180887 Discount rate 201945 N39PV 100 120 1201945 01618 Based on the project N39PV the project is rejected Now consider the estimation error Assume that the economy for the next year ends up being a booming economy So the project s time 1 cash flow would have been 155 In retrospect the project should have been accepted However based on the information available at time 0 the project was correctly rejected In general the expected cash flows that you calculate for an individual project are likely to be an overestimate or an underestimate of actual project cash flows In the previous example the actual cash flow would have been higher than the expected cash flow However over time and over many projects overestimates from some projects should cancel out underestimates with other projects Therefore these estimation errors are diversified away to a certain extent Even though you can t estimate with 100 accuracy the estimates of the expected future cash flows need to be unbiased That is actual cash ows should on average be equal to the expected cash ow In the same way you need to make an unbiased estimate of the discount rate How do you know if a person is making unbiased estimates of future cash ows If you make unbiased estimates of future cash ows then these unbiased estimates should on average be equal to actual future cash ows assuming you have enough observations across many projects and many years Evidence of unbiased estimates of future cash ows 7 refer back to Project A and ignore in ation Over a 100year period of time you would expect to see roughly 20 booming years with a 155 cash ow 60 normal years with a 135 cash ow 20 recession years with a 40 cash ow Total cash ows for 100 projects 12000 Average per project 120 Example of biased estimates of future cash flows 7 an overly optimistic manager makes the following estimates for the cash ows in the three different types of economies Another possible error for the optimistic manager would have been to overestimate the probability of a booming economy Boom economy cash ow 160 Normal economy cash ow 140 Recession economy cash ow 45 Effects on the NPV calculation for Project A Only over time and many projects will we be able to determine that the manager is making biased estimates Problems associated with making a biased estimate No problem exists if there is no change in project selection due to the bias A bias towards overestimating expected cash flows or underestimating the discount rate will make a good project look great Project is still accepted A bias towards underestimating expected cash ows or overestimating the discount rate will make a bad project look horrible Project is still rejected Problems occur in the following two circumstances A bias towards overestimating expected cash flows or underestimating the discount rate can make a bad project look good Negative NPV project accepted This problem is compounded if a manager has an incentive to overestimate cash ows or underestimate the discount rate When would a manager have the incentive to do this A bias towards underestimating expected cash ows or overestimating the discount rate can make a good project look bad Positive NPV project rejected This problem is compounded if a manager has an incentive to underestimate cash ows or overestimate the discount rate When would a manager have the incentive to do this How do you prevent or minimize forecast errors 1 Use market values In other words use the information that is available from the current market value as established by investors that buy and sell the asset in question in your analysis of the project To use this approach you need current market values from an asset that trades in an active and competitive market Why do we want to use market values If you try to estimate expected future cash ows and discount rates for an asset that trades in an active and competitive market you might let your optimistic or pessimistic estimates bias your NPV calculations This could cause you to accept a bad project or reject a good project We are assuming that the current market value established by numerous investors is a more reliable estimate of the asset s true value than your own estimate An example 7 You plan to invest in ABC stock and sell in one year ABC stock does not currently pay dividends and will not for the next several years Assume the financial market where ABC stock trades is perfect efficient and in equilibrium Current stock price 10 Expected sales price at time 1 Beta Riskfree rate 5 Market risk premium 84 What is the NPV of the oneyear investment To answer you need to know What is the expected time 1 sale s price What is the discount rate However take advantage of the fact that ABC stock trades is perfect efficient and in equilibrium market Thus What is the NPV of the investment Therefore what is the present value of the time one stock price Another example 7 Joe is offering the sale of the mining rights for gold on his property for 40 million The right to mine gold will be for 10 years and the purchaser must restore the property after the end of the 10year period The expected extraction and restoration costs and PVs of these costs have already been estimated Geologists have determined that 100000 ounces of gold can be extracted from the land You plan to extract 10000 ounces of gold each year for 10 years Assume that the gold market is perfect efficient and in equilibrium Present value of extraction costs 4 million Present value of restoration costs 2 million NPV 40 million 4 million 2 million PV of revenue You work for a potential purchaser and your job is to estimate the PV of revenue To determine the PV of the revenue and ultimately the NPV of the project you need The expected price of gold at the end of each of the next 10 years The beta of the gold revenue cash flows and associated discount rate Additional fact the current price of gold What is the NPV of the project Does the present value of the expected cash revenue increase or decrease if you extract the gold quicker ie 20000 ounces of gold per year for 5 years What if the market is not active or competitive Then the price is not necessary an equilibrium price Example 7 A house has been for sale for the last six months for 150000 Should you buy the house for the pquose of reselling at a later date What is the expected future selling price What is the discount rate What is the NPV of this project Example 7 A house just went on the market for 150000 Should you buy the house for the purpose of reselling at a later date Does it make a difference that the house hasn t been exposed to the market yet 2 Economic Rents Summary of this section Why hasn39t anyone else thought of this idea In a competitive industry that has been operating for a long period of time projects that involve entering and exiting this industry have a zero NPV ie the IRR equals the opportunity cost of capital Why If entering the industry really had a positive N39PV then competitors will also enter the industry The impact of this is I Supply of items to be sold will I This will cause a in price I This will cause a in the NPV of a project that involves entering this industry The opposite would occur if entering and staying in the industry were a negative NPV project In this case competitors will withdraw from the industry The impact of this is I Supply of items to be sold will I This will cause a in price I This will cause a in the NPV of a project that involves entering this industry The competitive equilibrium would therefore occur when there is no advantage to entering or exiting the industry NPV 0 In this case economic rents equal zero Example Based on current cotton prices and the costs of farming land used for cotton farming should be priced such that the NPV of cotton farming is a zeroNPV project Therefore there is no incentive to purchase land to farm cotton

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