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# CORPORATION FINANCE I FIN 3322

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This 40 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 George Cashman in Fall. Since its upload, it has received 14 views. For similar materials see /class/226366/fin-3322-texas-tech-university in Finance at Texas Tech University.

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Date Created: 10/22/15

Chapter 13 Corporate Financing and Market Efficiency 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 flows 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 flows of these assets Principal and interest payments are the portion of a firm s cash flow 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 flow 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 N39PV 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 De nition of an ef cient market An efficient market is one where prices for securities and other assets re ect all relevant and available information The three forms of ef ciency I Weakfarm efficiency security prices re ect only past price and return information I Semisl rangfarm efficiency security prices re ect all publicly available information I Sl rangfarm efficiency security prices re ect 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 ef cient 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 3 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 nance 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 inefficiencies imperfections and disequilibrium can make nancing 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 2 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 re ects 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 lnvestors 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 immediatelyfall to its new lower value based on the private information Assume that the FDA has just rejected ABC Pharmaceuticals lnc 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 economy 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 CorrecIAnswer 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 N 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 whic 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 N39PV B The equity security has the higher financing NPV C Both securities have the same financing NPV Correct answer 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 N 9 He Generation of investment proposals researchmarketing department Types of projects investments associated with Lal assets A New products or expansionmodification of existing products B Replacement of equipment or buildi 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 flows 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 flows 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 I 10000 600011 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 If 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 re ect 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 LRR 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 1 i httpwww ta admin u 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 Year 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 1Liami 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 cash ow 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 112 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 Rev enue 12000000 13200000 14520000 15972000 17569200 Change inAR Cash Revenue Cash Expense Calc Inventory purchases 100000 9000000 9900000 10890000 11979000 13076900 Change in AP Income tax 0 1020000 1122000 1234200 1357620 1493382 Change in cash Cash Expense Cash Flow Calc Cash Revenue Cash Expense Cash Flow V 0 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 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 outflow 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 t en Use tax depreciation in the calculation of project cash flows Tax depreciation of an asset is not a cash flow and therefore it does not directly affect project cash flows 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 inflation rate 29411765 per year Expected inflation 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 31131 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 1111500 13529500 4600030 8929470 Adj ustm ents Depreciation 4999500 2221500 1111500 Initial Investment 15000000 Cash Flow 15000000 8959830 9539910 10040970 NPV at 5 19334563 0 H 0 Expected in ation is an important component of the determination of the project NPV Use the nominal discount rate to discount cash ow estimates that include in ation or Use the real discount rate to discount cash ow estimates that do not account for inflation ie cash ows in constant dollars Equation 1 rnomiml 1 rm11 expected in ation What is the real discount rate in the previous problem Use the overall in ation rate in the above equation the cash ows by the overall in ation rate This gives you real cash ows To calculate N39PV discount the real cash ows at the real discount rate Converting to real constant dollar cash ows Adjust all cash ows including depreciation by discounting 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 1 500 0000 Cash Flow 15000000 8703835 9675437 8745344 8941681 NPV 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 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 500 real sale39s price 50010294117653 54543 nominal sale39s price p A W PV of the aftertax cash ow using the nominal sale39s price Nom Sale s Price 54543 Less Adjust 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 AdjustedBasis 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 1500 10294117653 137507 137507 X 03333 45831 137507 X 04445 61122 137507 x 01481 x 05 10182 Financing cash ows iNotice 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 modification 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 oflumber 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 Sale s 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 N 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 inyear 12 year 18 year 24 etc Machine 0 1 2 5 6 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 515 Equivalent annual cash ow 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 1941561 1 11022 002 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 ows would need to be adjusted for in ation See book for a discussion Note The above analysis assumes that the real cost and cash ows 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 the xture I Selling the old machine this year will probably result in a higher sales price than if it is sold next year 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 oldmachine 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 sa1vage 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 ows with EAC Replace now 0 l 2 3 4 5 a SV old machine 46200 New machine 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 machine 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 Its 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 A 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 38831 22 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 tin 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 DJ 4 Lquot 0 00 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 N39PV 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 Intuitively 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 19 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 StockB 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 Assume you invest 5 million into either Stock A or Stock B 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 Divestment of 5 million in Stock A CarrecIAnswer B Divestment 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 CarreclAnswer mUowgt 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 3650 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 4080 D Use the short method to check your answer to C Additional taxable income 12000 marginal tax rate 34 12 000034 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 29900 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 4 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 26420 H 9 A perpetual project requires an initial investment of 1000 It has cash ows of 0 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 of the project 25856 0 1 2 3 4 5 6 a l 1000 I 0 I 0 I 0 I 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 ow 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 61710000 67881000 74669100 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 14166667 27500000 28750000 30125000 316375 00 19134583 000 19 An accrual basis corporation is considering the following threeyear project What is the cash ow for year 2 133 400 0 1 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 l 045 500 l 065 900 l 091 400 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 300 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 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 401000 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 of accounting expects to have revenue of 1300000 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 ow 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 ow constant this increase in the accounts payable balance will mean that A Firm cash ow will be lower than 1000000 B Firm cash ow 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 rm TAKES the project Beg Balance End Balance Accounts Receivable 1000 1000 Inventory 4000 5000 Accounts Payable 6000 7000 Account balances if the rm DOES NOT TAIGZ 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 flow 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 I 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 CarrecIAnswer 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 CarrecIAnswer 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 macthe Machine purchased 5 years ago for 200000 Accumulated tax depreciation 170000 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 macthe Machine purchased 5 years ago for 500000 Accumulated tax depreciation 425000 Tax basis 75000 Current market value l 13000 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 549550 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 3400 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 in ation 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 1 62240000 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 101 0 9452 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 1800 00 180000 180000 Price per unit 148571429 147156463 145754972 144366830 Revenue 2674285 7 2648 81 63 2623 5895 2598 6029 Depreciation 7935714 10079365 319 8359 1524056 Taxable Income 1880 7143 16408798 2303 7536 24461973 Income Tax at 34 6394429 5578991 7832762 831 7071 Subtotal 12412714 1082 9807 15204774 1614 4902 Adjustments Depreciation 7935714 10079365 3198359 1524056 Initial Investment 2500 0000 Cash Flow 2500 0000 2034 8429 2090 91 72 18403133 17668959 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 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 Depryr two 3 111125 95994 Depryr three 3 18513 15992 Adjusted Basis 3 70 38 31 9 94 Gain 3 1 018 78 880 06 Tax 34638 29922 After Tax CF 3 1 042 77 900 78 PV 3 82434 82434 3 Lquot Similar to the example given in class assume that A Young trees grow faster than mature trees Assumption board feet 100 bd feet x square root age Trees are currently 10 years old B Price of lumber increasing at 5 per year Current price 500 per 1000 board feet or 050 per bd foot b C Cost of harvest included in sale39s price of lum er D Use an 815 nominal discount rate Fill out the following table 27 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 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 al 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 219 5304500 8 1837533 8 1635398 758 13 3605551 8 5463635 8 1969942 8 1654001 721 28 4 O Lquot O 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 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 quotevaluating two mutually exclusive projects with unequal lives 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 l0 l1 I2 I3 l4 l5 6000 1860 I1860 I1860 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 0 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 inflation 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 17000 3000 3000 3000 3000 3000 3000 3000 3000 17000 17000 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 95 7 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 inflation ie they are real cash flows The following shows the real cash flows through year 10 lo 1 I2 I3 I4 Is I6 l7 I8 l9 10 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 790758 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 Accept project Reject Project 0 l 2 3 4 5 6 7500 7500 7500 7500 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

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