1、第五章：净现值和投资评价的其他方法1.如果项目会带来常规的现金流，回收期短于项目的生命周期意味着，在折现率为0 的情况下，NPV 为正值。折现率大于0 时，回收期依旧会短于项目的生命周期，但根据折现率小于、等于、大于IRR 的情况，NPV 可能为正、为零、为负。折现回收期包含了相关折现率的影响。如果一个项目的折现回收期短于该项目的生命周期，NPV 一定为正值。2.如果某项目有常规的现金流，而且NPV 为正，该项目回收期一定短于其生命周期。因为折现回收期是用与NPV 相同的折现值计算出来的，如果NPV为正，折现回收期也会短于该项目的生命周期。NPV 为正表明未来流入现金流大于初始投资成本，盈利指
2、数必然大于1。如果NPV 以特定的折现率R 计算出来为正值时，必然存在一个大于R 的折现率R 使得NPV 为0，因此，IRR 必定大于必要报酬率。3.（1）回收期法就是简单地计算出一系列现金流的盈亏平衡点。其缺陷是忽略了货币的时间价值，另外，也忽略了回收期以后的现金流量。当某项目的回收期小于该项目的生命周期，则可以接受；反之，则拒绝。回收期法决策作出的选择比较武断。（2）平均会计收益率为扣除所得税和折旧之后的项目平均收益除以整个项目期限内的平均账面投资额。其最大的缺陷在于没有使用正确的原始材料，其次也没有考虑到时间序列这个因素。一般某项目的平均会计收益率大于公司的目标会计收益率，则可以接受；反
3、之，则拒绝。（3）内部收益率就是令项目净现值为0 的贴现率。其缺陷在于没有办法对某些项目进行判断，例如有多重内部收益率的项目，而且对于融资型的项目以及投资型的项目判断标准截然相反。对于投资型项目，若IRR 大于贴现率，项目可以接受；反之，则拒绝。对于融资型项目，若IRR 小于贴现率，项目可以接受；反之，则拒绝。（4）盈利指数是初始以后所有预期未来现金流量的现值和初始投资的比值。必须注意的是，倘若初始投资期之后，在资金使用上还有限制，那盈利指数就会失效。对于独立项目，若PI 大于1，项目可以接受；反之，则拒绝。（5）净现值就是项目现金流量（包括了最初的投入）的现值，其具有三个特点：使用现金流量；
4、包含了项目全部现金流量；对现金流量进行了合理的折现。某项目NPV 大于0 时，项目可接受；反之，则拒绝。4.对于一个具有永续现金流的项目来说，回收期为：内部收益率为： 所以可得：这意味着对一个拥有相对固定现金流的长期项目而言，回收期越短，IRR越大，并且IRR 近似等于回收期的倒数。5.原因有很多，最主要的两个是运输成本以及汇率的原因。在美国制造生产可以接近于产品销售地，极大的节省了运输成本。同样运输时间的缩短也减少了商品的存货。跟某些可能的制造生产地来说，选择美国可能可以一定程度上减少高额的劳动力成本。还有一个重要因素是汇率，在美国制造生产所付出的生产成本用美元计算，在美国的销售收入同样用美
5、元计算，这样可以避免汇率的波动对公司净利润的影响。6.最大的问题就在于如何估计实际的现金流。确定一个适合的折现率也同样非常困难。回收期法最为容易，其次是平均会计收益率法，折现法（包括折现回收期法，NPV 法，IRR 法和PI 法）都在实践中相对较难。7.可以应用于非盈利公司，因为它们同样需要有效分配可能的资本，就像普通公司一样。不过，非盈利公司的利润一般都不存在。例如，慈善募捐有一个实际的机会成本，但是盈利却很难度量。即使盈利可以度量出来，合适的必要报酬率也没有办法确定。在这种情况下，回收期法常常被用到。另外，美国政府是使用实际成本/盈利分析来做资本预算的，但需要很长时间才可能平衡预算。8.这
6、种说法是错误的，如果项目B 的现金流流入的更早，而项目A 的现金流流入较晚，在一个较低的折现率下，A 项目的NPV 将超过B 项目。不过，在项目风险相等的情况下，这种说法是正确的。如果两个项目的生命周期相等，项目B 的现金流在每一期都是项目A 的两倍，则B 项目的NPV 为A项目的两倍。9.尽管 A 项目的盈利指数低于B 项目，但A 项目具有较高的NPV，所以应该选A 项目。盈利指数判断失误的原因在于B 项目比A 项目需要更少的投资额。只有在资金额受限的情况下，公司的决策才会有误。10. （1）如果两个项目的现金流均相同，A 项目将有更高的IRR，因为A 项目的初期投资低于项目B。（2）相同，
7、因为项目B 的初始投资额与现金流量都为项目A 的两倍。11. B 项目将更加敏感。原因在于货币的时间价值。有较长期的未来现金流会对利率的变动更加敏感，这种敏感度类似于债券的利率风险。12. MIRR 的计算方法是找到所有现金流出的现值以及项目结束后现金流入的未来值，然后计算出两笔现金流的IRR。因此，两笔现金流用同一利率（必要报酬率）折现，因此，MIRR 不是真正的利率。相反，考虑IRR。如果你用初始投资的未来值计算出IRR，就可以复制出项目未来的现金流量。13. 这种说法是错误的。如果你将项目期末的内部现金流以必要报酬率计算NPV 和初始投资，你将会得到相同的NPV。但是，NPV 并不涉及内
8、部的现金流再投资的问题。14. 这种说法是不正确的。的确，如果你计算中间的所有现金的未来价值到项目结束流量的回报率，然后计算这个未来的价值和回报率的初步投资，你会得到相同的回报率。然而，正如先前的问题，影响现金流的因素一旦产生不会影响IRR。15. 1. a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment.Project A:Cumulative cash flows Year 1 = $6,500
9、 = $6,500Cumulative cash flows Year 2 = $6,500 + 4,000 = $10,500Companies can calculate a more precise value using fractional years. To calculate the fractional payback period, find the fraction of year 2s cash flows that is needed for the company to have cumulative undiscounted cash flows of $10,00
10、0. Divide the difference between the initial investment and the cumulative undiscounted cash flows as of year 1 by the undiscounted cash flow of year 2. Payback period = 1 + ($10,000 $6,500) / $4,000 = 1.875 years Project B: Cumulative cash flows Year 1 = $7,000 = $7,000 Cumulative cash flows Year 2
11、 = $7,000 + 4,000 = $11,000 Cumulative cash flows Year 3 = $7,000 + 4,000 + 5,000 = $16,000 To calculate the fractional payback period, find the fraction of year 3s cash flows that is needed for the company to have cumulative undiscounted cash flows of $12,000. Divide the difference between the init
12、ial investment and the cumulative undiscounted cash flows as of year 2 by the undiscounted cash flow of year 3. Payback period = 2 + ($12,000 7,000 4,000) / $5,000 Payback period = 2.20 years Since project A has a shorter payback period than project B has, the company should chooseproject A.b. Disco
13、unt each projects cash flows at 15 percent. Choose the project with the highest NPV.Project A:NPV = $10,000 + $6,500 / 1.15 + $4,000 / 1.152 + $1,800 / 1.153= $139.72Project B:NPV = $12,000 + $7,000 / 1.15 + $4,000 / 1.152 + $5,000 / 1.153= $399.11The firm should choose Project B since it has a high
14、er NPV than Project A has.16. When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: Value today of Year 1 cash flow = $6,000/1.14 = $5,263.16 Value today of Year 2 cash flow = $6,500/1.142 = $5,001.54
15、 Value today of Year 3 cash flow = $7,000/1.143 = $4,724.80 Value today of Year 4 cash flow = $8,000/1.144 = $4,736.64 To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is $5,263.16, so the discounted payback for an $8,000 initial cos
16、t is: Discounted payback = 1 + ($8,000 5,263.16)/$5,001.54 = 1.55 years For an initial cost of $13,000, the discounted payback is: Discounted payback = 2 + ($13,000 5,263.16 5,001.54)/$4,724.80 = 2.58 years Notice the calculation of discounted payback. We know the payback period is between two and t
17、hree years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the
18、fractional portion of the discounted payback. If the initial cost is $18,000, the discounted payback is: Discounted payback = 3 + ($18,000 5,263.16 5,001.54 4,724.80) / $4,736.64 = 3.64 years17. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defin
19、es the IRR for this project is: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = $11,000 + $5,500/(1 + IRR) + $4,000/(1 + IRR)2 + $3,000/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 7.46% Since the IRR i
20、s less than the required return we would reject the project.18. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this Project A is: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = $3,500 + $1,800/(1 + IRR) + $2,40
21、0/(1 + IRR)2 + $1,900/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 33.37% And the IRR for Project B is: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = $2,300 + $900/(1 + IRR) + $1,600/(1 + IRR)2 + $1,4
22、00/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 29.32%19. The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The cash flows from this project are an annuity, so the
23、 equation for the profitability index is: PI = C(PVIFAR,t) / C0 PI = $65,000(PVIFA15%,7) / $190,000 PI = 1.42320. a. The profitability index is the present value of the future cash flows divided by the initial cost. So, for Project Alpha, the profitability index is: PIAlpha = $800 / 1.10 + $900 / 1.
24、102 + $700 / 1.103 / $1,500 = 1.331 And for Project Beta the profitability index is: PIBeta = $500 / 1.10 + $1,900 / 1.102 + $2,100 / 1.103 / $2,500 = 1.441 b. According to the profitability index, you would accept Project Beta. However, remember the profitability index rule can lead to an incorrect
25、 decision when ranking mutually exclusive projects. Intermediate21. a. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR for each project is: Deepwater Fishing IRR: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = $750,000 + $310,000 / (1 + IRR)
26、 + $430,000 / (1 + IRR)2 + $330,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 19.83% Submarine Ride IRR: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = $2,100,000 + $1,200,000 / (1 + IRR) + $760,0
27、00 / (1 + IRR)2 + $850,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 17.36%Based on the IRR rule, the deepwater fishing project should be chosen because it has the higher IRR.b. To calculate the incremental IRR, w
28、e subtract the smaller projects cash flows from the larger projects cash flows. In this case, we subtract the deepwater fishing cash flows from the submarine ride cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the submarine ride are:Year
29、 0 Year 1 Year 2 Year 3 Submarine Ride $2,100,000 $1,200,000 $760,000 $850,000 Deepwater Fishing 750,000 310,000 430,000 330,000 Submarine Fishing $1,350,000 $890,000 $330,000 $520,000 Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is: 0 = C0 + C
30、1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = $1,350,000 + $890,000 / (1 + IRR) + $330,000 / (1 + IRR)2 + $520,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: Incremental IRR = 15.78%For investing-type projects, a
31、ccept the larger project when the incremental IRR is greater than the discount rate. Since the incremental IRR, 15.78%, is greater than the required rate of return of 14 percent, choose the submarine ride project. Note that this is not the choice when evaluating only the IRR of each project. The IRR
32、 decision rule is flawed because there is a scale problem. That is, the submarine ride has a greater initial investment than does the deepwater fishing project. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project.c. The NPV is the
33、sum of the present value of the cash flows from the project, so the NPV of each project will be: Deepwater fishing: NPV = $750,000 + $310,000 / 1.14 + $430,000 / 1.142 + $330,000 / 1.143 NPV = $75,541.46 Submarine ride: NPV = $2,100,000 + $1,200,000 / 1.14 + $760,000 / 1.142 + $850,000 / 1.143 NPV =
34、 $111,152.69 Since the NPV of the submarine ride project is greater than the NPV of the deepwater fishing project, choose the submarine ride project. The incremental IRR rule is always consistent with the NPV rule.22. a. The payback period is the time that it takes for the cumulative undiscounted ca
35、sh inflows to equal the initial investment.Board game: Cumulative cash flows Year 1 = $700 = $700Payback period = $600 / $700 = .86 yearsCD-ROM: Cumulative cash flows Year 1 = $1,400 = $1,400 Cumulative cash flows Year 2 = $1,400 + 900 = $2,300 Payback period = 1 + ($1,900 1,400) / $900 Payback peri
36、od = 1.56 years Since the board game has a shorter payback period than the CD-ROM project, the company should choose the board game.b. The NPV is the sum of the present value of the cash flows from the project, so the NPV of each project will be: Board game: NPV = $600 + $700 / 1.10 + $150 / 1.102 +
37、 $100 / 1.103 NPV = $235.46 CD-ROM: NPV = $1,900 + $1,400 / 1.10 + $900 / 1.102 + $400 / 1.103 NPV = $417.05 Since the NPV of the CD-ROM is greater than the NPV of the board game, choose the CD-ROM.c. The IRR is the interest rate that makes the NPV of a project equal to zero. So, the IRR of each pro
38、ject is:Board game: 0 = $600 + $700 / (1 + IRR) + $150 / (1 + IRR)2 + $100 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 42.43%CD-ROM: 0 = $1,900 + $1,400 / (1 + IRR) + $900 / (1 + IRR)2 + $400 / (1 + IRR)3Using a spre
39、adsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 25.03%Since the IRR of the board game is greater than the IRR of the CD-ROM, IRR implies we choose the board game. Note that this is the choice when evaluating only the IRR of each project. The IR
40、R decision rule is flawed because there is a scale problem. That is, the CD-ROM has a greater initial investment than does the board game. This problem is corrected by calculating the IRR of the incremental cash flows, or by evaluating the NPV of each project.d. To calculate the incremental IRR, we
41、subtract the smaller projects cash flows from the larger projects cash flows. In this case, we subtract the board game cash flows from the CD-ROM cash flows. The incremental IRR is the IRR of these incremental cash flows. So, the incremental cash flows of the CD-ROM are:Year 0 Year 1 Year 2 year3CD-
42、ROM $1,900 $1,400 $900 $400 Board game 600 700 150 100 CD-ROM Board game $1,300 $700 $750 $300 Setting the present value of these incremental cash flows equal to zero, we find the incremental IRR is: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = $1,300 + $700 / (1 + IRR) + $750 / (
43、1 + IRR)2 + $300 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: Incremental IRR = 18.78%23. a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment. AZM Mi
44、ni-SUV: Cumulative cash flows Year 1 = $270,000 = $270,000 Cumulative cash flows Year 2 = $270,000 + 180,000 = $450,000 Payback period = 1+ $30,000 / $180,000 = 1.17 years AZF Full-SUV: Cumulative cash flows Year 1 = $250,000 = $250,000 Cumulative cash flows Year 2 = $250,000 + 400,000 = $650,000 Pa
45、yback period = 1+ $350,000 / $400,000 = 1.88 years Since the AZM has a shorter payback period than the AZF, the company should choose the AZM. Remember the payback period does not necessarily rank projects correctly.b. The NPV of each project is: NPVAZM = $300,000 + $270,000 / 1.10 + $180,000 / 1.10
46、2 + $150,000 / 1.103 NPVAZM = $206,912.10 NPVAZF = $600,000 + $250,000 / 1.10 + $400,000 / 1.102 + $300,000 / 1.103 NPVAZF = $183,245.68 The NPV criteria implies we accept the AZM because it has the highest NPV.c. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the
47、IRR of the AZM is:0 = $300,000 + $270,000 / (1 + IRR) + $180,000 / (1 + IRR)2 + $150,000 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRRAZM = 51.43%And the IRR of the AZF is:0 = $600,000 + $250,000 / (1 + IRR) + $400,000 /
48、(1 + IRR)2 + $300,000 / (1 + IRR)3Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:IRRAZF = 26.04%The IRR criteria implies we accept the AZM because it has the highest IRR. Remember the IRR does not necessarily rank projects correctlyd. Inc
49、remental IRR analysis is not necessary. The AZM has the smallest initial investment, and the largest NPV, so it should be accepted.24. a. The profitability index is the PV of the future cash flows divided by the initial investment. The profitability index for each project is:PIA = $140,000 / 1.12 + $140,000 / 1.122 / $200,000 = 1.18PIB = $260,000 / 1.12 + $260,000 / 1.122 / $400,000 = 1.10PIC = $150,000 / 1.12 + $120,000 / 1.122 / $200,000 = 1.15b. The NPV of each project is:NPVA = $200,000 + $1
