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1、,Irwin/McGraw-Hill,Chapter 6,Fundamentals of Corporate FinanceThird Edition,Net Present Value and Other Investment Criteria,Brealey Myers Marcusslides by Matthew Will,Irwin/McGraw-Hill,The McGraw-Hill Companies, Inc.,2001,Topics Covered,Net Present ValueOther Investment CriteriaProject InteractionsC
2、apital Rationing,Net Present Value,Opportunity 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 Value,ExampleSuppose we can invest $50 today and receive $60 in one year. What is our in
3、crease in value given a 10% expected return?This is the definition of NPV,Net Present Value,NPV = PV - required investment,Net Present Value,TerminologyC = Cash Flowt = time period of the investmentr = “opportunity cost of capital”The Cash Flow could be positive or negative at any time period.,Net P
4、resent Value,Net Present Value RuleManagers 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 Value,ExampleYou have the opportunity to purchase an office building. You h
5、ave 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 Value,0 1 2 3,$16,000,$16,000,$16,000,$450,000,$466,000,Present Valu
6、e 14,953 14,953 380,395$409,323,Example - continued,Net Present Value,Example - 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 Value,Example - con
7、tinuedIf 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?,Other Investment Criteria,Internal Rate of Return (IRR) - Discount rate at which NPV = 0.Rate of Return Rule - Inv
8、est in any project offering a rate of return that is higher than the opportunity cost of capital.,Internal Rate of Return,ExampleYou 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 s
9、ell the building for $450,000. What is the IRR on this investment?,IRR = 12.96%,Internal Rate of Return,IRR=12.96%,Payback Method,Payback 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 t
10、han the specified cutoff period. The following example will demonstrate the absurdity of this statement.,Payback Method,ExampleThe 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.
11、C0 C1 C2 C3 PaybackNPV10%A-2000+1000+1000+100002+7,249B-2000+1000+1000 02- 264C-2000 0+2000 02- 347,Book Rate of Return,Book 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.
12、The components reflect tax and accounting figures, not market values or cash flows.,Project Interactions,When 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
13、 NPV is highest.,Mutually Exclusive Projects,ExampleSelect one of the two following projects, based on highest NPV. Proj01234NPVA-155.55.55.55.5 B-20999assume 9% discount rate,Mutually Exclusive Projects,ExampleSelect one of the two following projects, based on highest NPV. Proj01234NPVA-155.55.55.5
14、5.52.82 B-209992.78assume 9% discount rate,Investment Timing,Sometimes 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 r
15、eceipt of the cash flow, yet increase the cash flow.,Investment Timing,ExampleYou 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, w
16、hen should you purchase the computer?YearCostPV SavingsNPV at PurchaseNPV Today050702020.0145702522.7240703024.83367034Date to purchase 25.5433703725.3531703924.2,Equivalent Annual Cost,Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a mac
17、hine.,Equivalent Annual Cost,ExampleGiven 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-10-6-6-21.00-11.45,Equivalent Annual Cost,Example (with a twist)Select
18、one of the two following projects, based on highest “equivalent annual annuity” (r=9%). Proj01234NPVEq. AnnA-155.55.55.55.52.82.87 B-209992.781.10,Internal Rate of Return,Example You have two proposals to choice between. The initial proposal (H) has a cash flow that is different than the revised pro
19、posal (I). Using IRR, which do you prefer?,Internal Rate of Return,Example 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?,Internal Rate of Return,50403020100-10-20,NPV $, 1,000s,Disco
20、unt rate, %,8 10 12 14 16,Revised proposal,Initial proposal,Internal Rate of Return,Pitfall 1 - Mutually Exclusive ProjectsIRR 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
21、 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 ReturnCertain cash flows can generate NPV=0 at two different discount rates.The following cash flow generates NPV=0 at both (-50%) an
22、d 15.2%.,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),內部報酬率法(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
23、 (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(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),修正內部報酬率法(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
24、現金流量 (5)考慮整個投資期末處分資產之現金流量,Capital Rationing,Capital 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 Index,