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Irwin/McGraw-HillChapter 6Fundamentals of Corporate FinanceThird EditionNet Present Value and Other Investment CriteriaBrealey Myers Marcusslides by Matthew WillIrwin/McGraw-HillThe McGraw-Hill Companies,Inc.,2001Topics CoveredNet Present ValueOther Investment CriteriaProject InteractionsCapital RationingNet Present ValueOpportunity Cost of Capital-Expected rate of return given up by investing in a project.Net Present Value-Present value of cash flows minus initial investments.Net Present ValueExampleSuppose we can invest$50 today and receive$60 in one year.What is our increase in value given a 10%expected return?This is the definition of NPVProfit=-50+601.10$4.55Initial InvestmentAdded Value$50$4.55Net Present ValueNPV=PV-required investmentNPVCCrtt01()NPVCCrCrCrtt01122111()().()Net Present ValueTerminologyC=Cash Flowt=time period of the investmentr=“opportunity cost of capital”The Cash Flow could be positive or negative at any time period.Net Present ValueManagers increase shareholders wealth by accepting all projects that are worth more than they cost.Therefore,they should accept all projects with a positive net present value.Net Present ValueExampleYou have the opportunity to purchase an office building.You have a tenant lined up that will generate$16,000 per year in cash flows for three years.At the end of three years you anticipate selling the building for$450,000.How much would you be willing to pay for the building?Net Present Value0 1 2 3$16,000$16,000$16,000$450,000$466,000Present Value 14,953 14,953 380,395$409,323Example-continuedNet Present ValueExample-continuedIf the building is being offered for sale at a price of$350,000,would you buy the building and what is the added value generated by your purchase and management of the building?Net Present ValueExample-continuedIf the building is being offered for sale at a price of$350,000,would you buy the building and what is the added value generated by your purchase and management of the building?NPVNPV 350 00016 00010716 000107466 000107323123,(.),(.),(.)$59,Other Investment CriteriaInternal Rate of Return(IRR)-Discount rate at which NPV=0.Rate of Return Rule-Invest in any project offering a rate of return that is higher than the opportunity cost of capital.Rate of Return=C-investmentinvestment1Internal Rate of ReturnExampleYou can purchase a building for$350,000.The investment will generate$16,000 in cash flows(i.e.rent)during the first three years.At the end of three years you will sell the building for$450,000.What is the IRR on this investment?0350 00016 000116 0001466 0001123,(),(),()IRRIRRIRRIRR=12.96%Internal Rate of Return-200-150-100-5005010015020005101520253035Discount rate(%)NPV(,000s)IRR=12.96%Payback MethodPayback Period-Time until cash flows recover the initial investment of the project.The payback rule specifies that a project be accepted if its payback period is less than the specified cutoff period.The following example will demonstrate the absurdity of this statement.Payback MethodExampleThe three project below are available.The company accepts all projects with a 2 year or less payback period.Show how this decision will impact our decision.Cash FlowsPrj.C0 C1 C2 C3 Payback NPV10%A-2000+1000+1000+100002+7,249B-2000+1000+1000 02-264C-2000 0+2000 02-347Book Rate of ReturnBook Rate of Return-Average income divided by average book value over project life.Also called accounting rate of return.Managers rarely use this measurement to make decisions.The components reflect tax and accounting figures,not market values or cash flows.Book rate of return=book incomebook assetsProject InteractionsWhen you need to choose between mutually exclusive projects,the decision rule is simple.Calculate the NPV of each project,and,from those options that have a positive NPV,choose the one whose NPV is highest.Mutually Exclusive ProjectsExampleSelect one of the two following projects,based on highest NPV.Proj01234NPVA-155.55.55.55.5 B-20999assume 9%discount rateMutually Exclusive ProjectsExampleSelect one of the two following projects,based on highest NPV.Proj01234NPVA-155.55.55.55.52.82 B-209992.78assume 9%discount rateInvestment TimingSometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision.A common example involves a tree farm.You may defer the harvesting of trees.By doing so,you defer the receipt of the cash flow,yet increase the cash flow.Investment TimingExampleYou may purchase a computer anytime within the next five years.While the computer will save your company money,the cost of computers continues to decline.If your cost of capital is 10%and given the data listed below,when should you purchase the computer?YearCostPV SavingsNPV at PurchaseNPV Today050702020.0145702522.7240703024.83367034Date to purchase 25.5433703725.3531703924.2Equivalent Annual CostEquivalent Annual Cost-The cost per period with the same present value as the cost of buying and operating a machine.Equivalent annual cost=present value of costsannuity factorEquivalent Annual CostExampleGiven the following costs of operating two machines and a 6%cost of capital,select the lower cost machine using equivalent annual cost method.YearMach.1234PV6%Ann.CostD-15-4-4-4-25.69-9.61E-10-6-6-21.00-11.45Equivalent Annual CostExample(with a twist)Select one of the two following projects,based on highest“equivalent annual annuity”(r=9%).Proj01234NPVEq.AnnA-155.55.55.55.52.82.87 B-209992.781.10Internal Rate of ReturnExample You have two proposals to choice between.The initial proposal(H)has a cash flow that is different than the revised proposal(I).Using IRR,which do you prefer?ProjectC0C1C2C3IRRNPV7%H-35040014.29%24,000$I-350161646612.96%59,000$Internal Rate of ReturnExample You have two proposals to choice between.The initial proposal(H)has a cash flow that is different than the revised proposal(I).Using IRR,which do you prefer?%29.140)1(4003501IRRNPV%96.120)1(466)1(16)1(16350321IRRIRRIRRNPVInternal Rate of Return50403020100-10-20NPV$,1,000sDiscount rate,%8 10 12 14 16Revised proposalInitial proposalInternal Rate of ReturnPitfall 1-Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project.The following two projects illustrate that problem.Pitfall 2-Lending or Borrowing?With some cash flows(as noted below)the NPV of the project increases s the discount rate increases.This is contrary to the normal relationship between NPV and discount rates.Pitfall 3-Multiple Rates of Return Certain cash flows can generate NPV=0 at two different discount rates.The following cash flow generates NPV=0 at both (-50%)and 15.2%.內部報酬率法內部報酬率法內部報酬率(Internal Rate of Return Md.;簡稱 IRR)法方法:內部報酬率:使淨現值(NPV)為0之折現率NPV=或CFt：t 期淨現金流量(即各期稅後現金入)IRR：內部報酬率(即投資人之報酬率)nnIRRCFIRRCFIRRCFC)1(.)1()1(22110)1(0NPVRCFnttt內部報酬率法內部報酬率法(續續)決策準則:單一計劃:IRR R;互斥計劃:Max(IRR1,IRR2,)R優劣:缺:(1)複雜(2)某些狀況未符合價值最大化原則(3)可能無解或(4)有多重解(5)再投資報酬率問題 優點:(1)考慮風險因素（2）考慮整時間價值因素 (3）考慮投資人之機會成本 （4）考慮整個投資期間之現金流量 (5)考慮整個投資期末處分資產之現金流量修正內部報酬率法修正內部報酬率法修正內部報酬率(Modified Internal Rate of Return Md.;簡稱 MIRR)法方法:修正內部報酬率:使各期淨現金流出現值之和等於未來各期現金流入現值之和之折現率PV cost=PV(terminal value)nnttntntttMIRRRCIFRCOF)1()1()1(00修正內部報酬率法修正內部報酬率法(續續)決策準則:單一計劃:MIRR R;互斥計劃:Max(MIRR1,MIRR2,)R優劣:缺:(1)複雜(2)某些狀況未符合價值最大化原則 優點:(1)考慮風險因素（2）考慮整時間價值因素 (3）考慮投資人之機會成本 （4）考慮整個投資期間之現金流量 (5)考慮整個投資期末處分資產之現金流量Capital RationingCapital Rationing-Limit set on the amount of funds available for investment.Soft Rationing-Limits on available funds imposed by management.Hard Rationing-Limits on available funds imposed by the unavailability of funds in the capital market.Profitability IndexProfitabilityProjectPVInvestmentNPVIndexL4311/3=.33M6511/5=.20N10733/7=.43O8622/6=.33P5411/4=.25
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