问一道题：NO.PZ201601200500000801 第1小题

NO.PZ201601200500000801 问题如下 The capitbueting committee for Laroche Instries is meeting. Laroche is a North Americconglomerate thhsevervisions. One of these visions, Laroche Livery, operates a large fleet of vans. Laroche’s management is evaluating whether it is optimto operate new vans for two, three, or four years before replacing them. The managers have estimatethe investment outlay, annuafter-toperating expenses, anafter-tsalvage cash flows for eaof the servilives. Because revenues ansome operating costs are unaffectethe choiof servilife, they were ignorein the analysis. Laroche Livery’s opportunity cost of fun is 10 percent. The following table gives the cash flows in thousan of Canallars (C$).SchoemProcts, another vision of Laroche, hevaluateseverinvestment projects annow must choose the subset of them thfits within its C$40 million capitbuet. The outlays anNPVs for the six projects are given below. Schoemcannot buy fractionprojects, anmust buy all or none of a project. The currenamounts are in millions of Canallars. Schoemwants to termine whisubset of the six projects is optimal.A finproposcomes from the vision Society Services, whihinvestment opportunity with a reoption to invest further if contions warrant.The crucitails are follows: The originproject: •outlof C$190 million time zero. •Cash flows of C$40 million per yefor Years 1–10 if manis \"high.\" •Cash flows of C$20 million per yefor Years 1–10 if manis \"low.\" Aitioncash flows with the optionexpansion project: •outlof C$190 million time one. •Cash flows of C$40 million per yefor Years 2–10 if manis \"high.\" •Cash flows of C$20 million per yefor Years 2–10 if manis \"low.\" Whether manis \"high\" or \"low\" in Years 1–10 will revealering the first year. The probability of \"high\" manis 0.50, anthe probability of \"low\" manis 0.50. The option to make the expansion investment pen on making the initiinvestment. If the initiinvestment is not ma, the option to expanes not exist. The requirerate of return is 10 percent.Society Services wants to evaluate its investment alternatives.The internautor for Laroche Instries hma seversuggestions for improving capitbueting processes the company. The internautor’s suggestions are follows:Suggestion 1\"In orr to put all capitbueting proposals on equfooting, the projects shoulall use the risk-free rate for the requirerate of return.\"Suggestion 2\"Because you cannot exercise both of them, you shoulnot permit a given projeto have both abannment option anexpansion/growth option.\"Suggestion 3\"When rationing capital, it is better to choose the portfolio of investments thmaximizes the company NPV ththe portfolio thmaximizes the company IRR.\"Suggestion 4\"Projebetshoulusefor establishing the requirerate of return whenever the project’s beta is fferent from the company’s beta.\"1. Whis the optimservilife for Laroche Livery’s fleet of vans? A.Two years. B.Three years. C.Four years. B is correct.The wto solve the problem is to calculate the equivalent annuannuity anchoose the servilife with the lowest annucost. For a two-yeservilife, the NPV isNPV=−40000+−120001.101+−150001.102+200001.102=−46776.86NPV=-40000+\frac{-12000}{1.10^1}+\frac{-15000}{1.10^2}+\frac{20000}{1.10^2}=-46776.86NPV=−40000+1.101−12000​+1.102−15000​+1.10220000​=−46776.86The E(PV = –46,776.86, N = 2, ani = 10%) is –26,952.38.For a three-yeservilife, the NPV isNPV=−40000+−120001.101+−150001.102+−200001.103+170001.103\mathrm{NPV}=-40000+\frac{-12000}{1.10^1}+\frac{-15000}{1.10^2}+\frac{-20000}{1.10^3}+\frac{17000}{1.10^3}NPV=−40000+1.101−12000​+1.102−15000​+1.103−20000​+1.10317000​=-65559.73The E(PV = –65,559.73, N = 3, ani = 10%) is –26,362.54.For a four-yeservilife, the NPV isNPV=−40000+−120001.101+−150001.102+−200001.103+−250001.104+120001.104\mathrm{NPV}=-40000+\frac{-12000}{1.10^1}+\frac{-15000}{1.10^2}+\frac{-20000}{1.10^3}+\frac{-25000}{1.10^4}+\frac{12000}{1.10^4}NPV=−40000+1.101−12000​+1.102−15000​+1.103−20000​+1.104−25000​+1.10412000​=-87211.26The E(PV = –87,211.26, N = 4, ani = 10%) is –27,512.61.The three-yeservilife hthe lowest annucost. Laroche shoulreplathe vans every three years. 老师，我的过程和答案全部一样，算出来PV是一样的，带进去算EAA的时候，怎么都算不出来答案的数，比如第4年的PMT我的计算结果是25011.46（N=4, I/Y=10, FV=0, PV=-87211.26）您看是我过程出问题了还是计算器出问题了同理，其他两个我也算不出答案给的PMT

NO.PZ201601200500000801 问题如下 1. Whis the optimservilife for Laroche Livery’s fleet of vans? A.Two years. B.Three years. C.Four years. B is correct.The wto solve the problem is to calculate the equivalent annuannuity anchoose the servilife with the lowest annucost. For a two-yeservilife, the NPV isNPV=−40000+−120001.101+−150001.102+200001.102=−46776.86NPV=-40000+\frac{-12000}{1.10^1}+\frac{-15000}{1.10^2}+\frac{20000}{1.10^2}=-46776.86NPV=−40000+1.101−12000​+1.102−15000​+1.10220000​=−46776.86The E(PV = –46,776.86, N = 2, ani = 10%) is –26,952.38.For a three-yeservilife, the NPV isNPV=−40000+−120001.101+−150001.102+−200001.103+170001.103\mathrm{NPV}=-40000+\frac{-12000}{1.10^1}+\frac{-15000}{1.10^2}+\frac{-20000}{1.10^3}+\frac{17000}{1.10^3}NPV=−40000+1.101−12000​+1.102−15000​+1.103−20000​+1.10317000​=-65559.73The E(PV = –65,559.73, N = 3, ani = 10%) is –26,362.54.For a four-yeservilife, the NPV isNPV=−40000+−120001.101+−150001.102+−200001.103+−250001.104+120001.104\mathrm{NPV}=-40000+\frac{-12000}{1.10^1}+\frac{-15000}{1.10^2}+\frac{-20000}{1.10^3}+\frac{-25000}{1.10^4}+\frac{12000}{1.10^4}NPV=−40000+1.101−12000​+1.102−15000​+1.103−20000​+1.104−25000​+1.10412000​=-87211.26The E(PV = –87,211.26, N = 4, ani = 10%) is –27,512.61.The three-yeservilife hthe lowest annucost. Laroche shoulreplathe vans every three years. 计算出来的PMT正负号，是不是跟原本计算得到的NPV正负号一致呀？比如NPV算出来是−46776.86，那么通过计算器得到PMT=26952.38124之后，也应该再加上负号变成-26952.38124，以此来跟NPV正负一致？然后这道题中，选–26,362.54，就是选三个计算结果中的最大值？

NO.PZ201601200500000801 计算EAA时，都默认FV=0吗？

NO.PZ201601200500000801 你好 这个题我按答案按的计算器 但是结果都是正的 想问下问题出在哪里？

NO.PZ201601200500000801 老师好 这题 是不是计算器里PV 应该打入正的 不是负的 （比如正的46，776.86）， 因为 NPV 和E的符号一致。 PV 键和PMT 在计算器第三例 是符号相反， 如果这题里输入负的NPV， 算出的PMT 或EAA会是正的 而不是负的 （cost). 谢谢。