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1、Chapter 6 Net Present Value and Other Investment Criteria(淨現值與投資決策)1 1Topics Covered Net Present Value (淨現值法與資本預算之評估) Other Investment Criteria (其他投資決策準則) Project Interactions (投資方案間相互的影響與決策) Capital Rationing (資本配額限制問題)2 2Payback Method(1) Payback Period(1) Payback Period ( (還本期間法還本期間法) )- - Time u
2、ntil cash flows recover the initial Time until cash flows recover the initial investment of the project.investment of the project.The The payback rulepayback rule specifies that a project be specifies that a project be accepted if its payback period is less than the accepted if its payback period is
3、 less than the specified cutoff period. The following specified cutoff period. The following example will demonstrate the absurdity of example will demonstrate the absurdity of this statement.this statement.優點優點: : 簡單易用易懂且計算成本低簡單易用易懂且計算成本低缺點缺點: (1): (1)未考慮所有現金流量未考慮所有現金流量 (2) (2)未考慮錢的時間價值未考慮錢的時間價值修正修
4、正: : Discounted Payback Period MethodDiscounted Payback Period Method3 3Payback MethodExampleExampleThe three project below are available. The company The three project below are available. The company accepts all projects with a 2 year or less payback period. accepts all projects with a 2 year or l
5、ess payback period. Show how this decision will impact our decision.Show how this decision will impact our decision.Cash FlowsCash FlowsPrjPrj. . C C0 0 C C1 1 C C2 2 C C3 3 PaybackPayback NPVNPV10%10%AA-2000-2000 +1000+1000 +1000+1000 +10000+100002 2+7,249+7,249B B-2000-2000 +1000+1000 +1000+1000 0
6、 02 2- 264- 264C C-2000-2000 0 0+2000+2000 0 02 2- 347- 3474 4Techniques that Ignore the Time Value of MoneyBut which is preferred?Payback is thesame!Payback WeaknessPayback Weakness: Failure to consider the : Failure to consider the time value of money (pattern of cash flows).time value of money (p
7、attern of cash flows).5 5Techniques that Ignore the Time Value of MoneyPayback WeaknessPayback Weakness: Failure to consider : Failure to consider allall relevant cash flows.relevant cash flows.But look at the total cash flows for Project 1!Payback sayspick Project 2!6 6Book Rate of Return(2) Book R
8、ate of Return (2) Book Rate of Return (會計報酬率法會計報酬率法) ) - - Average income divided by average book value Average income divided by average book value over project life. Also called over project life. Also called accounting rate of accounting rate of returnreturn. .Managers rarely use this measurement
9、 to make Managers rarely use this measurement to make decisions. The components reflect tax and decisions. The components reflect tax and accounting figures, not market values or cash accounting figures, not market values or cash flows.flows.缺點缺點: : 所考慮為非現金流量且未考慮錢的時間價值所考慮為非現金流量且未考慮錢的時間價值 7 7Accounti
10、ng Rate of Return甲案平均稅後會計盈餘甲案平均稅後會計盈餘 = (5000+1000-1000-2000)/4=$750 = (5000+1000-1000-2000)/4=$750乙案乙案 = (-2000+0+1000+6000)/4=$1,250 = (-2000+0+1000+6000)/4=$1,250甲案之會計報酬率甲案之會計報酬率: $750/$6,000 = 12.5%; : $750/$6,000 = 12.5%; 與公司標準比與公司標準比乙案之會計報酬率乙案之會計報酬率: $1,250/$6,000 = 20.83%: $1,250/$6,000 = 20.
11、83%假設投資假設投資4 4年無殘值年無殘值, ,直線折舊每期直線折舊每期$3,000,$3,000,平均投資平均投資$6,000$6,0008 8Net Present Value (淨現值法)Opportunity Cost of Capital - Expected rate of return given up by investing in a project. (4) Net Present Value - Present value of cash flows minus initial investments.9 9Net Present ValueExampleExample
12、Q: Suppose we can invest $50 today & receive $60 Q: Suppose we can invest $50 today & receive $60 later today. What is our increase in value?later today. What is our increase in value?InitialInvestmentInitialInvestmentAddedValueAddedValue$50$50$10$10A:Profit=-$50+$60=$101010Net Present ValueExampleE
13、xampleSuppose we can invest $50 today and receive $60 Suppose we can invest $50 today and receive $60 in one year. What is our increase in value given in one year. What is our increase in value given a 10% expected return?a 10% expected return?This is the definition of NPVThis is the definition of N
14、PVInitialInvestmentAddedValue$50$4.551111Net Present ValueNPV = PV - required investment1212Net Present ValueTerminologyC = Cash Flowt = time period of the investmentr = “opportunity cost of capital” The Cash Flow could be positive or negative at The Cash Flow could be positive or negative at any ti
15、me period. Normally it is negative at time any time period. Normally it is negative at time 0 to represent initial capital investment or cash 0 to represent initial capital investment or cash out flow (usually the cash flow change sign, the out flow (usually the cash flow change sign, the number of
16、IRR will increase)number of IRR will increase)1313Net Present ValueNet Present Value RuleNet Present Value RuleManagers increase shareholders wealth by Managers increase shareholders wealth by accepting all projects that are worth more than accepting all projects that are worth more than they cost.
17、Therefore, they should accept all they cost. Therefore, they should accept all projects with a positive net present value.projects with a positive net present value.優點優點: (1): (1)考慮了投資方案的所有現金流量考慮了投資方案的所有現金流量 (2) (2)考慮了現金流量之時間價值考慮了現金流量之時間價值 (3) (3)符合企業追求價值最大之原則符合企業追求價值最大之原則(4)(4)The only best rule to
18、 follow by the The only best rule to follow by the manager manager 1414Time Value TechniquesNet Present Value (NPV)Net Present Value (NPV). Net Present Value is . Net Present Value is found by subtracting the present value of the after-found by subtracting the present value of the after-tax outflows
19、 from the present value of the after-tax tax outflows from the present value of the after-tax inflows.inflows.Decision CriteriaIf NPV 0, accept the projectIf NPV k, accept the projectIf IRR 1, accept the projectIf PI 1); note the project scalePI1); note the project scale甲案與乙案若為互斥則選甲案甲案與乙案若為互斥則選甲案( (
20、甲甲PIPI乙乙 PI)PI)Note: PI Note: PI 最大之方案可能不是最大之方案可能不是NPVNPV最大之方案最大之方案2727Project Interactions When you need to choose between mutually When you need to choose between mutually exclusive projects, the decision rule is simple. exclusive projects, the decision rule is simple. Calculate the NPV of each pr
21、oject, and, from Calculate the NPV of each project, and, from those options that have a positive NPV, choose those options that have a positive NPV, choose the one whose NPV is highest.the one whose NPV is highest. 獨立案件獨立案件: :一投資方案接受與否將不會影響到另一投資方案接受與否將不會影響到另一投資方案接受與否之決策一投資方案接受與否之決策 互斥案件互斥案件: :一投資方案接
22、受將會影響到另一投資一投資方案接受將會影響到另一投資方案接受與否之決策方案接受與否之決策2828Mutually Exclusive ProjectsExampleExampleSelect one of the two following projects, based Select one of the two following projects, based on highest NPV. on highest NPV. ProjProj0 01 12 23 34 4NPVNPVAA-15-155.55.55.55.55.55.55.55.52.822.82 B B-20-209 99
23、 99 92.782.78assume 9% discount rateassume 9% discount rate2929Investment TimingSometimes you have the ability to defer an Sometimes you have the ability to defer an investment and select a time that is more ideal investment and select a time that is more ideal at which to make the investment decisi
24、on. A at which to make the investment decision. A common example involves a tree farm. You common example involves a tree farm. You may defer the harvesting of trees. By doing so, may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet you defer the receipt of the
25、 cash flow, yet increase the cash flow.increase the cash flow.Investment now vs. Investment in the futureInvestment now vs. Investment in the future Decision rule: choose the investment date that Decision rule: choose the investment date that results in the highest net present value todayresults in
26、the highest net present value today3030Investment TimingExampleExampleYou may purchase a computer anytime within the next five years. You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of While the computer will save your company
27、 money, the cost of computers continues to decline. If your cost of capital is 10% and computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the given the data listed below, when should you purchase the computer?computer?YearYearCost
28、CostPV SavingsPV SavingsNPV at PurchaseNPV at PurchaseNPV NPV TodayToday0 050507070202020.020.01 145457070252522.722.72 240407070303024.824.83 3363670703434Date to purchase Date to purchase 25.525.54 433337070373725.325.35 531317070393924.224.23131Long vs. Short-lived Equipment: Equivalent Annual Co
29、st (等額成本法)Equivalent Annual Cost (EAC)Equivalent Annual Cost (EAC) - The cost per - The cost per period with the same present value as the cost of period with the same present value as the cost of buying and operating a machine.buying and operating a machine.Decision rule: select the machine that ha
30、s the Decision rule: select the machine that has the lowest equivalent annual costlowest equivalent annual costEACEAC*PVIFA(n, r%) = PV cost of the project*PVIFA(n, r%) = PV cost of the project3232Equivalent Annual CostExampleExampleGiven the following costs of operating two Given the following cost
31、s of operating two machines and a 6% cost of capital, select the machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost lower cost machine using equivalent annual cost method.method.YearYearMachMach. .1 12 23 34 4PVPV6%6%Ann. CostAnn. CostDD-15-15-4-4-4-4-4-4-2
32、5.69-25.69-9.61-9.61E E-10-10-6-6-6-6-21.00-21.00-11.45-11.4525.69 = EAC*PVIFA(=2.673) 25.69 = EAC*PVIFA(=2.673) EAC = 9.61 EAC = 9.6121.00 = EAC*PVIFA(=1.834) 21.00 = EAC*PVIFA(=1.834) EAC = 11.45 EAC = 11.453333Equivalent Annual CostExample (with a twist) Example (with a twist) 等額年金法等額年金法Select on
33、e of the two following projects, based Select one of the two following projects, based on highest “equivalent annual annuity” (r=9%). on highest “equivalent annual annuity” (r=9%). ProjProj0 01 12 23 34 4NPVNPVEqEq. Ann. AnnAA-15-155.55.55.55.55.55.55.55.52.822.82.87 .87 B B-20-209 99 99 92.782.781.
34、101.10Decision Rule: for evaluating costs Decision Rule: for evaluating costs lower EAC lower EAC for evaluating revenues for evaluating revenues higher EAA higher EAA3434Internal Rate of ReturnExample You have two proposals to choice between. The initial proposal (H) has a cash flow that is differe
35、nt than the revised proposal (I). Using IRR, which do you prefer?3535Internal 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?3636Internal Rate of Return5040302010
36、0-10-20NPV$,1,000sDiscountrate,%810 121416RevisedproposalInitialproposalIRR=12.96%IRR=14.29%IRR=12.26%3737Internal Rate of ReturnPitfall 1 - Mutually Exclusive ProjectsPitfall 1 - Mutually Exclusive ProjectsIRR sometimes ignores the magnitude of the project. IRR sometimes ignores the magnitude of th
37、e project. The following two projects illustrate that problem.The following two projects illustrate that problem.Pitfall 2 - Lending or Borrowing? Pitfall 2 - Lending or Borrowing? (when IRR (when IRR KcKc) )With some cash flows (as noted below) the NPV of With some cash flows (as noted below) the N
38、PV of the project increases as the discount rate increases. the project increases as the discount rate increases. This is contrary to the normal relationship between This is contrary to the normal relationship between NPV and discount rates. NPV and discount rates. Pitfall 3 - Multiple Rates of Retu
39、rnPitfall 3 - Multiple Rates of ReturnCertain cash flows can generate NPV=0 at two Certain cash flows can generate NPV=0 at two different discount rates.different discount rates.The following cash flow generates NPV=0 at both The following cash flow generates NPV=0 at both (-50%) and 15.2%. (-50%) a
40、nd 15.2%. 3838Capital RationingCapital RationingCapital Rationing ( (資本配額資本配額) - ) - Limit set on the Limit set on the amount of funds available for investment.amount of funds available for investment.Soft RationingSoft Rationing ( (軟性配額軟性配額) - ) - Limits on available Limits on available funds impos
41、ed by management.funds imposed by management.Hard RationingHard Rationing ( (硬性配額硬性配額) - ) - Limits on available Limits on available funds imposed by the unavailability of funds in funds imposed by the unavailability of funds in the capital market.the capital market.3939Profitability IndexCapital av
42、ailable = 20 million Capital available = 20 million choose N, L, O, and P choose N, L, O, and PCapital available = 10 million Capital available = 10 million choose N and L choose N and LDecision rule: pick high NPV per dollar of investment first Decision rule: pick high NPV per dollar of investment first 4040
