Finance B A 301
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BA 301 Discounted Cash Flow Valuation Woolridge amp Gray Text Chapter 10 Discounted Cash Flow Valuation Chapter Objectives Learn to calculate future and present value of level cash flow streams and uneven cash flow streams Learn to calculate loan payments effective interest rates and amortization schedules Learn to value stocks and bonds using the DCF approach Discounted Cash Flow Valuation Chapter Overview 101 Introduction to DCF Valuation 102Valuing Level Cash Flows 103Vauing Uneven Cash Flows 104 Summary Introduction to DCF Valuation I DCF determines the value of an investment I The markets determine the price of an investment I You decide based on price or cost if the investment is undervalued overvalued or fairlyvalued I Your buysell decision should be based solely on Qrice versus value Introduction to DCF Valuation Definitions The value of an investment stock bond mortgage etc equals the present value of its expected cash ows discounted reduced for their risk and timing I Expected cgsh ows are the most likely cash payments dividends interest capital gain or loss that you can expect not hope to receive Introduction to DCF Valuation Definitions uquot uquot uquot Hquot I Discount multiply a number by less than one I Discount rate a function of time and risk discount rate f time risk I Discount factor a function of both time and the discount rate discount factor f time discount rate I Present value PV of an investment is the sum of the expected cash ows multiplied by their respective discount factors Introduction to DCF Valuation Loans I Level cgsh ows the interest rate and cash ows associated with the loans mortgages and annuities are xed and do not change I A loan is an obligation under which a person borrows money from a lender I Terms of the loan state an interest rate and a repayment or gmortizgtion schedule Introduction to DCF Valuation Mortgages I Home mortgage an obligation under which a person borrows money from a bank and uses the proceeds to purchase a house or condominium I Amortization schedule Level payments over a long time period usually 20 to 30 years Introduction to DCF Valuation Annuities I A life annuity is contract sold by pension funds and life insurance companies I Pays a speci ed amount of money per year to owner I Amortization schedule more complex than loans or mortgage I Investor makes a single payment or multiple payments then Withdraws funds upon her retirement Introduction to DCF Valuation Mortgage Example Table 97 Gary borrows 100000 from a bank at 8 and 25 year mortgage What is his annual payment 39 Calculator n 25 years PV 100000 r or i 8 FV 0 Solve for PMT 936788 39Using Tables PV PMT PVMP Factor 25 8 39100000 PMT 106748 39100000106748 PMT 39PMT 9368year ITotal Payments 25 9368 234197 39Interest 134197 Principal Repayment 100000 Introduction to DCF Valuation Mortgage EX Rates up 2 to 10 Interest rates on mortgages increase by 2 to 10 What is Gary s annual payment on a 10 loan 39 Calculator n 25 years PV 100000 r or i 10 FV 0 Solve for PMT 1101680 39Using Tables PV PMT PVMP Factor 25 10 100000 PMT 90770 10000090770 PMT 39PMT 10608year ITotal Payments 25 10608 265200 39Interest 165200 Principal Repayment 100000 Introduction to DCF Valuation Mortgage EXRates drop 2 to 6 If interest rates on mortgages decrease by 2 to 6 What is Gary s annual payment on a 6 loan 39 Calculator n 25 years PV 100000 r or i 6 FV 0 Solve for PMT 782267 39Using Tables PV PMT PVMP Factor 25 6 100000 PMT 127834 39100000127834 PMT 39PMT 7823year ITotal Payments 25 7823 195567 39Interest 95567 Principal Repayment 100000 Introduction to DCF Valuation The ThreeStep Approach 1 Develop a set of expected cash ows 2 Estimate the discount rate and calculate the discount factors 3 Multiply the cash ows by the discount factors and add them to determine the value of the asset Decision Rule I If the value of an asset is greater than its price Buy it I If the value is less than its price Sell it Valuing Level Cash Flows Amortizing a Loan I Example Randy likes fast women Budweiser and expensive cars He wants to buy a BMW for 50000 He can nance it with a bank loan at 10 for 4 years His annual payment is 15774 What is his amortization schedule Interest Rate 1000 Discount Rate 1000 Beginning Interest Principal Annual Discount Ending Princial Pament Pament Pament Factor DCF Princial 50000 5000 10774 15774 09091 14340 39226 39226 3923 11851 15774 08264 13036 27375 27375 2737 13037 15774 07513 11851 14338 14338 1434 14340 15774 0683 10774 13094 50002 63096 50001 Valuing Level Cash Flows Spreadsheet An Excel Spreadsheet makes the DCF calculation easy Assume interest rates on similar car loans increase to 11 What s Randy s 10 loan now worth Discount the cash ows now at 11 Plug 11 into the discount rate slot and the DCF value of Randy s 50000 car loan is 48938 Interest Rate Discount Rate Discount Factor 09009 08116 07312 06587 Beginning Interest Princial Pament 50000 Principal Annual Pament Pament 10774 15774 11851 15774 13037 15774 14340 15774 50 002 63096 E 14211 12803 11534 10391 48938 5000 3923 2737 1434 13094 39226 27375 14 338 1000 1100 Ending Princial 39226 27375 14338 Valuing Level Cash Flows Calculator I Using a nancial calculator for PV Five nancial function keys n number of periods r or i interest rate or yield PV present value PMT payment and FV future value I Randy s Car Loan Valuing a fouryear 10 loan with a payment of 1577354 discounted 11 I Inputs are n 4 i 11 FV 0 PMT 1577354 solve for PV which is equal to 4893655 Valuing Uneven Cash FlowsProjects Most real world investments such as projects stocks and bonds do not have a single cash ow or level expected cash ows A groiect or venture is an investment to produce a product or provide a service that Will generate money in the future Cash In ow additional revenues coming into the company as a result of the project Cash Out ow additional expenses being spent by the company as a result of the project Valuing Uneven Cash Flows Bonds A bond is a debt instrument Corporations the US Government and municipalities issue bonds Bonds are payable from taxes from US government or the general revenues of a corporation Cash in ows to an investor are bond interest payments usually every 6 months and repayment of principal Valuing Uneven Cash FlowsStocks A stock represents ownership interest in a corporation The cash in ows consist of dividends and increase or decrease in stock price There is no maturity associated With a stock n the life of a stock is in nite quot The risk of a stock is hard to quantify making it dif cult to determine the proper discounting rate Valuing Uneven Cash Flows Using a Calculator Most popular nancial calculators have their own speci c systems for entering uneven sequential cash ows and then discounting those cash ows at a uniform discount rate I HP10BII model 39First input the initial cash out ow or cost in CFj button 39Then input the subsequent cash ows one at a time in CFj button 39Then hit the gold button and NPV for the answer 39Refer to pages 8082 of Instruction Book I TI BAII owners referto pages 4149 of Instruction Book Valuingjln ere ws of a Proj ect eet New lIachinew j Bill wants to ncrease paper production r year initially Cost of pulp for the project is 2500000 u ff Pquot f Y ense of the project will 39 39 Bill estimat year and th year The n1 salvage val rate of 6 per r rate of 4 per years and have no Projects of L rate of 14 How much 39 103 Valuing Uneven Cash Flows Using a Spreadsheet Lemont Paper Project Discount Rate 14 Cash Cash Net Cash Discount Year Inflow Outflow Flow Factor DCF 1 3000 2600 400 08772 351 2 3180 2704 476 07695 366 3 3 371 2812 559 0675 377 4 3573 2925 648 05921 384 5 3787 3042 746 05194 387 6 4015 3163 851 04556 388 7 4256 3290 966 03996 386 8 4511 3421 1089 03506 m Total 5735 3 021 Valuing Uneven Cash Flows of a Bond Using a Spreadsheet Assume that the US Government has issued a Bond with an 8 interest rate ve years to the maturity of the Bond and a principal payment of 1000 The Bond pays interest in the amount of 40 dollars equal to 1000 8 12 year two times per year April 1 and October 1 plus the 1000 repayment of the principal at maturity Also assume that the interest rate associated With this type of bond has increased to 10 in today s market What is the current value of this 8 Bond Valuing Uneven Cash Flows of a Semi Annual Rate Cash Discount Period Flow Factor 1 40 09524 40 0907 40 08638 40 08227 40 07835 40 07462 40 07107 40 06768 40 06446 06139 140000 2 3 4 5 6 7 8 9 10 Valuing Uneven Cash Flows of a Stock Using a Spreadsheet Valuing a stock involves the same analysis as valuing a xedrate mortgage loan or the US Government Bond However in estimating future cash ows there are two important exceptions The Bond and the mortgage have cash ows that are known with certainty while the range of future cash ows for a stock can be enormous Common stock represents ownership in a corporation which has an in nite life unlike bonds and mortgages jFra Edi Mium Wrnduw Heb Valuahon Date Valuel m 2002 General Invut Screen Intxinsic Stuck Value 5929 n ral Inputs Company Trcker Excess Return Permd years 0 Deprecratron Rate Va of Rev Revenues m EIEB nvestment Rate u of Rev Growth Rate 3 3 DE Workrng Caprta u of Rev Net Operatrng Prom Marng Us 26 DU Swan Term Assets mr x Rate 23 3 r Shoanerm Lrabrhtresmr Stock Rrrce 47 75 Equrtv Rrsk Premrum u Shares Outstandng m 694 U Companv Beta UrvearTreasurerem 23 5 92 Vaue of Debt Out WM Bond Spread to Treasury 2 mt Vaue or Pref Stock Out WM Preferred Smkmm 1 750 Companvvacc 03242005 valuePro 2002 1020023013 39 7 j File Edit IilaluePro Window Help Valuation Date ValuePro 2002 General Pro Forma Screen Illveer Excess Return Period ABC Corp Disc Excess Return Period FCFF 0521 Total Corporate Value 45459 Discounted Residual Value 39943 Less Debt 4931 ShortTerm Assets 000 Less Preferred Stock 11350 Total Corporate Value 45409 Less ShortTerm Liabilities 0 Total Value to Common Equity 41100 Intrinsic Stock Value 121 131 111 151 151 171 101 191 1121 Chanqein 1211110n1h3 Adj Change in Working Discount Ending Revenues NOR Taxes NDPAT Invest Caital Factor 0312412005 10001 0312412000 12010 3140 910 2103 09203 0312412001 13040 3540 1 103 2445 1 0312412000 15420 4009 1 241 2102 39 39 03942009 1425 1530 mg m Intrmsw Stock Value Result 0312412010 19590 5119 1592 3521 Corp has a current 0312412011 22250 5105 1 199 3900 0312412012 25112 3531 2033 1501 prolected worth of 59 29 0312412013 2041 1 1301 2291 5090 0312412014 32104 0341 2595 5151 2 0312412015 35210 9432 2933 5499 1413 2512 4051 50 04150 30 210 9432 2933 0499 2012 2012 0 0 04150 0312412005 FCFF Discounted BA 301 Risk and Return and the Capital Asset Pricing Model Woolridge amp Gray Text Chapter 12 An Important Principle of Finance CAPMThe Trade Off Between Return and Risk Tradeoff between the expected return on an investment and its risk Low risk Treasury Bills have lower expected returns 24 Stocks large price volatility have higher expected returns eg 610 Risk measured by price or return volatility More pricereturn movement greater risk A rational investor requires a higher expected return to accept additional risk Model that describes this tradeoff is the CAPM Risk and Return and the Capital Asset Pricing Model Risk Return Relationship Direct tradeoff between the expected rate of return and risk Tradeoff represented by the diagonal line Expected Return As the inherent risk increases in an investment so does the expected return Risk Risk and Return and the Capital Asset Pricing Model 123 Historic Returns by Asset Class Historically lower risk investments have lower returns and higher risk investments have higher returns Ibbotson and Sinque eld study Return Std Deviation Treasury Bills 38 32 Government Bonds 53 94 Corporate Bonds 58 86 Large Company Stock 107 202 Small Company Stock 125 332 LongTerm Return and Risk of US Securities 19261999 Small Co Common Stocks 126 X 12 10 Common Stocks 113 X g v 8 E 3 6 LT Corp Bonds 56 a X X 0 X LT Gov Bonds 51 4 Treasury Bills 38 2 o 10 20 30 Risk Source Ibbotson Associates 2000 What is Rate of Return Rate of Return Cash Payment Change in PricePrice Paid Buy IBM 90 receive a cash dividend of 4 and sell it one year later at 104 Rate of Return 4 14 90 2 20 Components of Rate of Return Cash PaymentsDividends and Interest taxed as ordinary income ie up to 35 Dividends quarterly payments made on some stocks ownership Interest semiannual payments made on bonds debt Change in Price Capital Gain or Capital Loss Realized you sell your asset and incur gain or loss Unrealized you continue to own your asset If realized the gains or losses are taxed Longterm gains and losses are taxed at a lower rate eg 20 Shortterm gains and losses taxed at a higher rate eg 35 What do we mean by Risk Riskmeasured by the possible range of returns arogbd an expected return the standard deviation of v rquot T Risk has both negative a positive outcomes returns that are lower 39 expected or higher than expected Risk and Return and the Capital Asset Pricing Model 122 De nitions Relating to Return and Risk Standard Deviation of Return 039 I Risk on an asset is measured by the variability of returns I Standard deviation is the statistic that is that measures how Wildly or tightly observed stock returns cluster around the average stock return I Greater standard deviation means more uctuations and greater risk Risk and Return and the Capital Asset Pricing Model 122 Definitions Relating to Return and Risk Calculation of Standard Deviation of Return 039 Example The annual returns of stock of XYZ Inc for the last three years was Year 1 8 Year 2 1 Year 3 2 Risk and Return and the Capital Asset Pricing Model 122 De nitions Relating to Return and Risk Calculation of Standard Deviation of Return 62 Step 1 Take the simple average return of the distribution of returns Year Return Average Return 1 8 3 2 1 3 3 2 3 Total 9 Risk and Return and the Capital Asset Pricing Model 122 De nitions Relating to Return and Risk Calculation of Standard Deviation of Return 6 Step 2 Take each individual observed return and subtract the average of the returns Year Return Average Deviation Return of Return 1 8 3 5 2 1 3 4 3 2 3 1 Total 9 Risk and Return and the Capital Asset Pricing Model 122 De nitions Relating to Return and Risk Calculation of Standard Deviation of Return 039 Step 3 Square the resulting difference and add the squares to get the sum of the squares Year Return Average Deviation Squared Return of Return Deviation 1 8 3 5 00025 2 1 3 4 00016 3 2 3 1 00001 Total 9 00042 Risk and Return and the Variance 122 De nitions Relating to Return and Calculation of Standard Deviation of Return 039 Step 4 Divide the sum of the squares by the total number of observations minus 1 the result is the variance of the distribution Variance 0004231 00021 Step 5 The square root of the variance is the standard deviation of the returns Standard Deviation 00021 A 12 458 What Do We Mean by Returns Simple versus Compound Averages of Returns When Analyzing Returns Simple Averages are Never Simple I Many investment managers and advisors use simple averages to portray their historic performance I However simple averages are a misleading way to assess investment returns compound or geometric averages are far more representative of actual investment performance Geometric average is calculated as below Value at the end of the period 1T Value at the beginning of the period Where T is the number of years in the compounding period Simple Averages of Percentages are Never Simple The math underlying investment returns and percentages computes investment gains more favorably than comparable losses Problem is embedded in calculation of simple averages If there is a negative percentage return the calculation of a simple average is biased upwards Simple average returns can hide very poor performance Q Simple Averages of Percentages are Never Simple Martha s Investment Perfermenee Simple 3 Cempeuntl uerege Returns Beginning Ending nnuel Tear 1Lnl39elue 1Lnl39elue Return 1 10 20 IIIIIII39E39rE 2 2 4 20 Simple uerege Fleturn 1l39l u Cemneund uerene Return 355 l u Risk and Return Highrisk Stock Expected R t e um Lowrisk Stock 0vt Bond A Market P0rtf01i0Includes all stocks TBills E Corporate Bonds Risk Capital Asset Pricing Model CAPM From the RiskReturn Line we can estimate the expected return on a stock ERi Expected return on stock i ERi equals the Risk Free Rate Rf the stock s Beta lo times the Market l Risk Premium the return I th k t Rm 39 81 e mar e m1nus p R I C m ERi Rf i Rm Rf Sample Averages for Investments Risk Premium Treasury Bills 0 o o o o 4 Government Bonds 0 o o o o o o 5 100 Corporate Bonds o 600 200 Average Common Stock 12 8 Our Questions For Today How do we measure risk of an asset Answer Beta I I What s the relatlon it between beta and H I return 7 quot Answer It s very positive What is Beta Market IBM Stock Portfolio Return 10 00 12 00 10 12 IBM s stock return tends to be the 9 IBM S beta ls 1392 market return multiplied by 12 What is Beta Market ATampT Stock Portfolio Return 10 8 40 8 ATampTos beta is ATampT s stock return tends to be the market return multiplied by A Quick Quiz on Beta Firm Market up 20 Market down 20 Firm s Beta Intel 30 30 150 GE 15 15 075 Apple 20 20 100 Why is beta a measure of Market Magnification A stock With a beta of 2 will tend to double market movements up or down A stock with a beta of 050 will tend to have movements up or down equal to 12 the market Isn t there more to Risk than Beta Yes Unsystematic or rm speci c risk risk that affects the return of that rm or industry only On average the rm speci c risks average out to be zero if an investor holds a diversi ed portfolio Finance theory assumes that investors are rational and own diversi ed portfolios How to Measure Beta Graph 60 months of returns as done below IBM s Return O O 0 o I Slope 18 Beta SampP500 Return 0 g 0 O Using Beta to Determine Expected Returns What is a risk premium The amount by which an investment is expected to outperform TBills The Market has averaged 12 a year TBills have averaged 4 a year The market risk premium is 8 An investment s beta determines its risk premium TBill Rate 4 Expected return on Market 8 Market riskpremium 4 AOL has a beta of 16 AOL s riskpremium AM E R l A 16 4 64 AOL s expected return 4 64 104 An investment s beta determines its risk premium TBill Rate 4 Expected return on Market 8 Market risk premium 4 ATT has a beta of 06 ATT s riskpremium 06 4 24 ATT s expected return 4 24 64 The RiskReturn Line T Bill Rate is 5 Market Risk Premium has averaged 8 Expected Return on the Market ie SampP500 is 8513 Expected Return 5 I 1 Beta Let s Draw Today s RiskReturn Line Put half your money in T Bills and half in the SampP500 Your portfolio has a beta of 050 Your portfolio has an expected return of 9 Expected Return quotn I l 1 Beta Let s Draw Today s RiskReturn Line By splitting your money between T Bills and the market portfolio you can obtain any point on the riskreturn line below Expected Return 1 Beta Let s Draw Today s RiskReturn Line By putting all your money in the SampP 500 and borrowing still more and putting that money in the SampP 500 leveraging you can obtain any point on the riskreturn line below Expected Return 1 Beta Let s Draw Today s RiskReturn Line Any point on the riskreturn line can be obtained with the SampP 500 and T Bills Expected Return 1 Beta Evaluating Mutual Fund Performance Using the RiskReturn Line lWhich fund provided the better performance A or B I Average Return Fund B 1 Beta Alpha measures performance A positive alpha is g00da negative alpha is not so good 39 39 A h Average Return Posmve p a 4Negative Alpha 1 Beta Alpha measures performance Remember the RiskReturn line is also called the zero talent line so performance below the line is poor 1 Beta Practice Problem TBills averaged 4 over last few years SampP 500 averaged 14 The XYZ Fund had an average return of 16 and a beta of 14 Find XYZ s alpha The CAPM riskreturn line for a beta of 14 is 4 14 10 18 XYZ s alpha is 1618 2 Alpha measures performance 2 Average Return 1 Beta Practice Problem TBills averaged 4 over last few years SampP500 averaged 14 The Nittany Lion Fund had an average return of 16 and a beta of 080 Find Nittany Lion s alpha Alpha measures performance Alpha is 4 Good job Average Return Q 1 Beta BA 301 Capital Budgeting and Measures of Investment Return Woolridge amp Gray Text Chapter 11 Capital Budgeting and Measures of Investment Return Chapter Objectives I Learn the process of capital budgeting and estimation of incremental cash costs and bene ts I Learn the standard techniques for measuring investment returns relating to capital budgeting problems I Understand the contribution of capital budgeting towards increasing stock prices of a company and maximizing shareholder value Capital Budgeting and Measures of Investment Return Chapter I 111 I 112 I 113 eturn I 114 elating t0 Capltal urn Pro tability Index Capital Budgeting and Measures of Investment Return 111 Capital Budgeting I Capital budgetingprocess of planning and managing a rm s longterm investment in projects and ventures I Capital Budgeting involves estimating the amount timing and risk of future cash ows I Capital budgeting Istarts With estimation of incremental cash ows from a project Icreate a time line of expected cash ows and Ic0mpare the present value of the cash ows with cost of project Capital Budgeting and Measures of Investment Return 112 Net Present Value NPV I NPV of an investmentdifference between the value and cost of investment I The value of any project is equal to the present value of its expected cash ows discounted for risk and timing I NPV Ruleinvest in projects if NPV is positive Reject if NPV is negative Capital Budgeting and Measures of Investment Return Net Present Value Example Textile Inc is considering buying a new machine The machine requires an initial outlay of 250000 and is expected to generate incremental cash in ows of 120000 for the next 5 years and requires 30000 yearly cash out ows for maintenance At the end of ve years the machine will have no disposable value Calculate the Net Present Value of the project if the discount rate is m per year Capital Budgeting and Measures of Investment Return Procedure for solving the NPV Problem 1 Estimate cash ows from the new machine Year 0 1 2 3 4 5 In ows 120 120 120 120 120 Out ows 250 30 30 30 30 30 Net Cash 250 90 90 90 90 90 Flows Capital Budgeting and Measures of Investment Return Procedure for solving the NPV Problem 2 Calculate the discounted cash ows Year 0 1 2 3 4 5 Net 250 90 90 90 90 90 PVFactor 1000 0870 0756 0658 0572 0497 Discounted 250 7826 6805 5918 5146 4475 Cash Flow PV Factor 11 r t Capital Budgeting and Measures of Investment Return Procedure for solving the NPV Problem 3 Calculate N PV and make the on NPV Rule Year 0 KL Discounted w We sed E 2 3 4 6805 5918 5146 4475 5169 s of W 7 D f Capital Budgeting and Measures of Investment Return Internal Rate of Return Example I Let s continue with the same example of Textile Inc Textile Inc is considering buying a new machine for spinning The machine requires an initial outlay of 250000 and L is expected to generate incremental cash in ows of 120000 for the next 5 years and requires 30000 yearly cash out ows for maintenance At the end of ve years the machine will have no disposable value Calculate the IRR of the project Capital Budgeting and Measures of Investment Return Procedure for solving the IRR 1 Estimate NPV from the machine based on a discount rate In our case let us start With 15 per year Year 0 1 2 3 4 5 Net Cash 250 90 90 90 90 90 Flows PV Factor 1000 0870 0756 0658 0572 0497 Discounted 250 7826 6805 5918 5146 4475 Cash Flow NPV 5169 Capital Budgeting and Measures of Investment Return Procedure for solving the IRR 2 Since the NPV calculated at step 1 is positive we increase the discount rate because IRR is the rate at which NPV of the project is 0 Now we take a discount rate of 25 per year Year 0 1 2 3 4 5 Cash Flows 250 90 90 90 90 90 PVFactor 1000 0800 0640 0512 0410 0328 Discounted 250 7200 5760 4608 3686 2949 Cash Flow NPV 796 Capital Budgeting and Measures of Investment Returl Procedure for solving the IR 3 We continue the process till V the rate at Which NPV is 0 In this example a disc te of 2344 gives an NPV of0 and hence IRR is 2 er ear Yer 0 1 3 4 5 gt 1000 0810 0656 0532 0431 0349 H quot39 qs 250 90 90 90 90 90 d 250 7291 5907 4785 3876 3140 0 Capital Budgeting and Me ures of Invesl39fnt Return Procedi for solving thr t 4 We 11 calculated determined i ate 0f IRR of 2344 is greater than the required rate of return of 15 per year Invest in the new machine Capital Budgeting and Measures of Investment Return 114 Other Measures Payback Period I Payback periodlength of time for the return on an investment takes to cover the cost of the investment I Payback periodinvolves only gross cash ows and not discounted cash ows I Payback rule as an investment criterion Iaccept the investment if its payback period is less than a predetermined number of years Irej ect the investment if its payback period is greater than the predetermined number of years 399 J 3 Measures of generate cas year Calcul quot I 2 frquot A i l I V h 39 39 y r r17 39 quot a l 439 Iquot 5 Payback perr years 9 gr 8 p If the compa V V payback peri quotW the estimateq accept the pr the project Capital Budgeting and Measures of Investment Return 114 Other Measures Book Rate of Return I Book Rate of Returnan accounting ratio calculated by dividing the company s accounting pro ts by the book value of the company s assets I Book rate of return rule as an investment criterion 39accept the investment if its book rate of return exceeds a predetermined target book return 39reject the investment if its book rate of return is less than a target book return Capital Budgeting and Measures of Investment Return Book Rate of Return Problem Continuing with Tools Inc problem and given that Tools Inc will depreciate the machine fully over the ve year period Calculate the book rate of return Book Value Beg Income Book Rate of Return 100000 20000 20000100000 20 80000 20000 20000 80000 25 60000 20000 20000 60000 33 40000 20000 20000 40000 50 20000 20000 20000 20000 100 Capital Budgeting and Measures of Investment Return 114 Other Measures Pro tability Index PI I PI The NPV of an investment divided by its cost I PI is used to identify projects that will receive the best return associated with the amount of dollars invested by ranking the projects by P1 I PI rule is Iaccept the venture with the highest pro tability index rst Ithen accept ventures with lower and lower positive PI s until the projects expend the capital budget Ido not accept projects with a negative PI Capital Budgeting and Measures of Investment Return Pro tability Index Problem Calculate the pro tability Index for the 3 projects given below Project PV Cost NPV Pro tability Index 1 5000 4200 800 8004200 019 2 2500 2000 500 5002000 025 3 3000 2700 300 3002700 011 Based on Pro tability Index Project 2 will be chosen rst followed by project 1 and then by project 3