第六章：投资决策1.机会成本是指进行一项投资时放弃另一项投资所承担的成本。

选择投资和放弃投资之间的收益差是可能获取收益的成本。

2. （1）新的投资项目所来的公司其他产品的销售下滑属于副效应中的侵蚀效应，应被归为增量现金流。

（2）投入建造的机器和厂房属于新生产线的成本，应被归为增量现金流。

（3）过去3 年发生的和新项目相关的研发费用属于沉没成本，不应被归为增量现金流。

（4）尽管折旧不是现金支出，对现金流量产生直接影响，但它会减少公司的净收入，并且减低公司的税收，因此应被归为增量现金流。

（5）公司发不发放股利与投不投资某一项目的决定无关，因此不应被归为增量现金流。

（6）厂房和机器设备的销售收入是一笔现金流入，因此应被归为增量现金流。

（7）需要支付的员工薪水与医疗保险费用应被包括在项目成本里，因此应被归为增量现金流。

3. 第一项因为会产生机会成本，所以会产生增量现金流；第二项因为会产生副效应中的侵蚀效应，所以会会产生增量现金流；第三项属于沉没成本，不会产生增量现金流。

4. 为了避免税收，公司可能会选择MACRS，因为该折旧法在早期有更大的折旧额，这样可以减免赋税，并且没有任何现金流方面的影响。

但需要注意的是直线折旧法与MACRS 的选择只是时间价值的问题，两者的折旧是相等的，只是时间不同。

5. 这只是一个简单的假设。

因为流动负债可以全部付清，流动资产却不可能全部以现金支付，存货也不可能全部售完。

6. 这个说法是可以接受的。

因为某一个项目可以用权益来融资，另一个项目可以用债务来融资，而公司的总资本结构不会发生变化。

根据MM 定理，融资成本与项目的增量现金流量分析无关。

7. ECA 方法在分析具有不同生命周期的互斥项目的情况下比较适应，这是因为ECA 方法可以使得互斥项目具有相同的生命周期，这样就可以进行比较。

ECA 方法在假设项目现金流相同这一点与现实生活不符，它忽略了通货膨胀率以及不断变更的经济环境。

8. 折旧是非付现费用，但它可以在收入项目中减免赋税，这样折旧将使得实际现金流出的赋税减少一定额度，并以此影响项目现金流，因此，折旧减免赋税的效应应该被归为总的增量税后现金流。

9. 应考虑两个方面：第一个是侵蚀效应，新书是否会使得现有的教材销售额下降？第二个是竞争，是否其他出版商会进入市场并出版类似书籍？如果是的话，侵蚀效应将会降低。

出版商的主要需要考虑出版新书带来的协同效应是否大于侵蚀效应，如果大于，则应该出版新书，反之，则放弃。

10. 当然应该考虑，是否会对保时捷的品牌效应产生破坏是公司应该考虑到的。

如果品牌效应被破坏，汽车销量将受到一定影响。

11. 保时捷可能有更低的边际成本或是好的市场营销。

当然，也有可能是一个决策失误。

12. 保时捷将会意识到随着越来越多产品投入市场，竞争越来越激烈，过高的利润会减少。

13. We will use the bottom-up approach to calculate the operating cash flow for each year. We also must be sure to include the net working capital cash flows each year. So, the net income and total cash flow each year will be:Y ear01 Y ear02 Y ear03 Year04Sales $8,500 $9,000 $9,500 $7,000Costs 1,900 2,000 2,200 1,700 Depreciation 4,000 4,000 4,000 4,000EBT $2,600 $3,000 $3,300 $1,300Tax 884 1,020 1,122 442Net income $1,716 $1,980 $2,178 $858OCF $5,716 $5,980 $6,178 $4,858Capital spending -$16000NWC –200 –250 –300 –200 950–$16,200 $5,466 $5,680 $5,978 $5,808 Incrementalcash flowThe NPV for the project is:NPV = –$16,200 + $5,466 / 1.12 + $5,680 / 1.12⌒2 + $5,978 / 1.12⌒3 + $5,808 / 1.12⌒4 NPV = $1,154.5314.First, we will calculate the annual depreciation of the new equipment. It will be: Annual depreciation charge = $850,000/5 = $170,000The aftertax salvage value of the equipment is:Aftertax salvage value = $75,000(1 – 0.35)= $48,750Using the tax shield approach, the OCF is:OCF = $320,000(1 – 0.35) + 0.35($170,000)= $267,500Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Y ear 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We also must include the aftertax salvage value at the end of the project. The IRR of the project is:NPV = 0 = –$850,000 + 105,000 + $267,500(年金现值表IRR%,5) + [($48,750 – 105,000) / (1+IRR)5] IRR = 22.01%15. We will begin by calculating the initial cash outlay, that is, the cash flow at Time 0. To undertake the project, we will have to purchase the equipment and increase net working cap ital. So, the cash outlay today for the project will be:Equipment –$1,800,000NWC –150,000Total –$1,950,000Using the bottom-up approach to calculating the operating cash flow, we find the operating cash flow each year will be:Sales $1,100,000Costs 275,000Depreciation 450,000EBT $375,000Tax 131,250Net income $243,750The operating cash flow is: OCF = Net income + Depreciation =$243,750 + 450,000 = $693,750To find the NPV of the project, we add the present value of the project cash flows. We must be sure to add back the net working capital at the end of the project life, since we areassuming the net working capital will be recovered. So, the project NPV is:NPV = –$1,950,000 + $693,750(PVIFA16%,4) + $150,000 / 1.16⌒4 = $74,081.4816. We will need the aftertax salvage value of the equipment to compute the EAC. Even though the equipment for each product has a different initial cost, both have the same salvage value. The aftertax salvage value for both is:Both cases: aftertax salvage value = $20,000(1 – 0.35) = $13,000To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I is: OCF=（Sales-Cash）*（1-t c）+ Depreciation* t cOCF = – $45,000(1 – 0.35) + 0.35($270,000/3) = $2,250NPV = –$270,000 + $2,250(PVIFA12%,3) + ($13,000/1.123) = –$255,342.74EAC = –$255,342.74 / (PVIFA12%,3) = –$106,311.69And the OCF and NPV for Techron II is:OCF = – $48,000(1 – 0.35) + 0.35($370,000/5) = –$5,300NPV = –$370,000 – $5,300(PVIFA12%,5) + ($13,000/1.125) = –$381,728.76EAC = –$381,728.76 / (PVIFA12%,5) = –$105,895.27The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II because it has the lower (less negative) annual cost.17. If we are trying to decide between two projects that will not be replaced when they wear out, the proper capital budgeting method to use is NPV. Both projects only have costs associated with them, not sales, so we will use these to calculate the NPV of each project. Using the tax shield approach to calculate the OCF, the NPV of System A is:OCF A = –$105,000(1 – 0.34) + 0.34($360,000/4) = –$38,700NPV A = –$360,000 – $38,700(PVIFA11%,4) = –$480,064.65And the NPV of System B is:OCF B = –$65,000(1 – 0.34) + 0.34($480,000/6) = –$15,700NPV B = –$480,000 – $15,700(PVIFA11%,6) = –$546,419.44If the system will not be replaced when it wears out, then System A should be chosen, because it has the less negative NPV.18. When we are dealing with nominal cash flows, we must be careful to discount cash flows at the nominal interest rate, and we must discount real cash flows using the real interest rate. Project A‘s cash flows are in real terms, so we need to find the real interest rate. Using the Fisher equation, the real interest rate is:1 + R = (1 + r)(1 + h) 1.15 = (1 + r)(1 + .04) r = .1058 or 10.58%So, the NPV of Project A‘s real cash flows, discounting at the real interest rate, is:NPV = –$50,000 + $30,000 / 1.1058 + $25,000 / 1.1058⌒2 + $20,000 / 1.1058⌒3 = $12,368.89 Project B‘s cash flow are in nominal terms, so the NPV discounted at the nominal interest rate is:NPV = –$65,000 + $29,000 / 1.15 + $38,000 / 1.15⌒2 + $41,000 / 1.15⌒3 = $15,909.02We should accept Project B if the projects are mutually exclusive since it has the highest NPV.19. To determine the value of a firm, we can sim ply find the present value of the firm‘s future cash flows. No depreciation is given, so we can assume depreciation is zero. Using the tax shield approach, we can find the present value of the aftertax revenues, and the present value of the aftertax costs. The required return, growth rates, price, and costs are all given in real terms. Subtracting the costs from the revenues will give us the value of the firm‘s cash flows. We must calculate the present value of each separately since each is growing at a different rate. First, we will find the present value of the revenues. The revenues in year 1 will be the number of bottles sold, times the price per bottle, or:Aftertax revenue in year 1 in real terms = (2,100,000 × $1.25)(1 – 0.34) = $1,732,500 Revenues will grow at six percent per year in real terms forever. Apply the growing perpetuity formula, we find the present value of the revenues is:PV of revenues = C1 / (R –g)PV of revenues = $1,732,500 / (0.10 – 0.06) = $43,312,500The real aftertax costs in year 1 will be:Aftertax costs in year 1 in real terms = (2,100,000 × $0.75)(1 – 0.34) = $1,039,500Costs will grow at five percent per year in real terms forever. Applying the growing perpetuity formula, we find the present value of the costs is:PV of costs = C1 / (R –g)PV of costs = $1,039,500 / (0.10 – 0.05) = $20,790,000Now we can find the value of the firm, which is:Value of the firm = PV of revenues – PV of costsValue of the firm = $43,312,500 – 20,790,000 = $22,522,50020. （1）Purchase new machine:总成本：–$12,000,000Purchase newmachineNet working capital –250,000Total –$12,250,000经营性现金流：Operating expense $4,500,000Depreciation 3,000,000EBT $1,500,000Taxes 585,000Net income $915,000OCF $3,915,000NPV = –$12,250,000 + $3,915,000(PVIFA10%,4) + $500,000 / 1.10⌒4 = $330,776.59And the IRR is:0 = –$12,250,000 + $3,915,000(PVIFA IRR,4) + $250,000 / (1 + IRR)⌒4 IRR = 11.23% （2）Keep old machine:总成本：Keep machine –$3,000,000Taxes –390,000Total –$3,390,000经营性现金流：Depreciation $1,000,000EBT –$1,000,000Taxes –390,000Net income –$610,000OCF $390,000So, the NPV of the decision to keep the old machine will be:NPV = –$3,390,000 + $390,000(PVIFA10%,4) = –$2,153,752.48And the IRR is:0 = –$3,390,000 + $390,000(PVIFA IRR,4)Using a spreadsheet or financial calculator, we find the IRR is: IRR = –25.15%（3）Purchase new machine and Sell old machinePurchase new machine –$12,000,00Net working capital –250,000Sell old machine 3,000,000Taxes on old machine 390,000Total –$8,860,000经营性现金流：Operating expense savings $4,500,000Depreciation 2,000,000EBT $2,500,000Taxes 975,000Net income $1,525,000OCF $3,525,000The NPV under this method is:NPV = –$8,860,000 + $3,525,000(PVIFA10%,4) + $250,000 / 1.104 = $2,484,529.06And the IRR is:0 = –$8,860,000 + $3,525,000(PVIFA IRR,4) + $250,000 / (1 + IRR)4Using a spreadsheet or financial calculator, we find the IRR is: IRR = 22.26%So, this analysis still tells us the company should purchase the new machine. This is really the same type of analysis we originally did. Consider this: Subtract the NPV of the decision to keep the old machine from the NPV of the decision to purchase the new machine. You will get:Differential NPV = $330,776.59 – (–$2,153,752.48) = $2,484,529.06This is the exact same NPV we calculated when using the second analysis method21. Purchase new machine:The initial cash outlay for the new machine is the cost of the new machine. We can calculate the operating cash flow created if the company purchases the new machine. The maintenance cost is an incremental cash flow, so using the pro forma income statement, and adding depreciation to net income, the operating cash flow created by purchasing the new machine each year will be:Maintenance cost $350,000Depreciation 600,000EBT –$950,000Taxes –323,000Net income –$627,000OCF –$27,000Notice the taxes are negative, implying a tax credit. The new machine also has a salvage value at the end of five years, so we need to include this in the cash flows analysis. The aftertax salvage value will be:Sell machine $500,000Taxes –170,000Total $330,000The NPV of purchasing the new machine is:NPV = –$3,000,000 – $27,000(PVIFA12%,5) + $330,000 / 1.12⌒5 = –$2,910,078.10Keep old machine:The initial cash outlay for the keeping the old machine is the market value of the old machine, including any potential tax. The decision to keep the old machine has an opportunity cost, namely, the company could sell the old machine. Also, if the company sells the old machine at its current value, it will incur taxes. Both of these cash flows need to be included in the analysis. So, the initial cash flow of keeping the old machine will be:Keep machine –$1,800,000Taxes 204,000Total –$1,596 ,000Next, we can calculate the operating cash flow created if the company keeps the old machine. We need to account for the cost of maintenance, as well as the cash flow effects of depreciation. The pro forma income statement, adding depreciation to net income to calculate the operating cash flow will be:Maintenance cost $520,000Depreciation 240,000EBT –$760,000Taxes –258,400Net income –$501,600OCF –$261,600The old machine also has a salvage value at the end of five years, so we need to include this in the cash flows analysis. The aftertax salvage value will be:Sell machine $200,000Taxes –68,000Total $132,000So, the NPV of the decision to keep the old machine will be:NPV = –$1,596,000 – $261,600(PVIFA12%,5) + $132,000 / 1.125 = –$2,464,109.11The company should keep the old machine since it has a greater NPVThere is another way to analyze a replacement decision that is often used. It is an incremental cash flow analysis of the change in cash flows from the existing machine to the new machine, assuming the new machine is purchased. In this type of analysis, the initial cash outlay would be the cost of the new machine, and the cash inflow (including any applicable taxes) of selling the old machine. In this case, the initial cash flow under this method would be:Purchase new machine –$3,000,000Sell old machine 1,800,000Taxes on old machine –204,000Total –$1,404,000The cash flows from purchasing the new machine would be the difference in the operating expenses. We would also need to include the change in depreciation. The old machine has a depreciation of $240,000 per year, and the new machine has a depreciation of $600,000 per year, so the increased depreciation will be $360,000 per year. The pro forma income statement and operating cash flow under this approach will be:Maintenance cost –$170,000Depreciation 360,000EBT –$190,000Taxes –64,600Net income –$125,400OCF $234,600The salvage value of the differential cash flow approach is more complicated. The company will sell the new machine, and incur taxes on the sale in five years. However, we must also include the lost sale of the old machine. Since we assumed we sold the old machine in the initial cash outlay, we lose the ability to sell the machine in five years. This is an opportunity loss that must be accounted for. So, the salvage value is:Sell machine $500,000Taxes –170,000Lost sale of old –200,000Taxes on lost sale of68,000oldTotal $198,000The NPV under this method is:NPV = –$1,404,000 + $234,600(PVIFA12%,5) + $198,000 / 1.12⌒5 = –$445,968.99So, this analysis still tells us the company should not purchase the new machine. This is really the same type of analysis we originally did. Consider this: Subtract the NPV of the decision to keep the old machine from the NPV of the decision to purchase the new machine. You will get:Differential NPV = –$2,910,078.10 – (–2,464,109.11) = –$445,968.99This is the exact same NPV we calculated when using the second analysis method22. The project has a sales price that increases at 5 percent per year, and a variable cost per unit that increases at 6 percent per year. First, we need to find the sales price and variable cost for each year. The table below shows the price per unit and the variable cost per unit each year.Year 1 Year 2 Year 3 Year 4 Year 5Sales price $40.00 $42.00 $44.10 $46.31 $48.62Cost per unit $20.00 $21.20 $22.47 $23.82 $25.25Using the sales price and variable cost, we can now construct the pro forma income statement for each year. We can use this income statement to calculate the cash flow each year. We must also make sure to include the net working capital outlay at the beginning of the project,and the recovery of the net working capital at the end of the project. The pro forma income statement and cash flows for each year will be:Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Revenues $600,000.00 $630,000.00 $661,500.00 $694,575.00 $729,303.75 Fixed costs 75,000.00 75,000.00 75,000.00 75,000.00 75,000.00 Variable costs 300,000.00 318,000.00 337,080.00 357,304.80 378,743.09 Depreciation 106,000.00 106,000.00 106,000.00 106,000.00 106,000.00 EBT $119,000.00 $131,000.00 $143,420.00 $156,270.20 $169,560.66 Taxes 40,460.00 44,540.00 48,762.80 53,131.87 57,650.63 Net income $78,540.00 $86,460.00 $94,657.20 $103,138.33 $111,910.04 OCF $184,540.00 $192,460.00 $200,657.20 $209,138.33 $217,910.04 Capital spending –$530,000NWC 25,000 25,000Total cash flow –$555,000 $184,540.0$192,460.0$200,657.2$209,138.33$242,910.04With these cash flows, the NPV of the project is:NPV = –$555,000 + $184,540 / 1.15 + $192,460 / 1.15⌒2 + $200,657.20 / 1.15⌒3 + $209,138.33 / 1.15⌒4 +$242,910.04 / 1.15⌒5 = $123,277.08We could also answer this problem using the depreciation tax shield approach. The revenues and variable costs are growing annuities, growing at different rates. The fixed costs and depreciation are ordinary annuities. Using the growing annuity equation, the present value of the revenues is:PV of revenues = C {[1/(r –g)] – [1/(r –g)] × [(1 + g)/(1 + r)]⌒t}(1 – t C)PV of revenues = $600,000{[1/(.15 – .05)] – [1/(.15 – .05)] × [(1 + .05)/(1 + .15)]⌒5}PV of revenues = $2,192,775.00And the present value of the variable costs will be:PV of variable costs = C {[1/(r –g)] – [1/(r –g)] × [(1 + g)/(1 + r)]⌒t}(1 – t C)PV of variable costs = $300,000{[1/(.15 – .06)] – [1/(.15 – .06)] × [(1 + .06)/(1 + .15)]⌒5} PV of variable costs = $1,115,551.25The fixed costs and depreciation are both ordinary annuities. The present value of each is: PV of fixed costs = C({1 – [1/(1 + r)]⌒t } / r )PV of fixed costs = $75,000({1 – [1/(1 + .15)]⌒5 } / .15)PV of fixed costs = $251,411.63PV of depreciation = C({1 – [1/(1 + r)]⌒t } / r )PV of depreciation = $106,000({1 – [1/(1 + .15)]⌒5 } / .15) = $355,328.4423. To find the bid price, we need to calculate all other cash flows for the project, and then solve for the bid price. The aftertax salvage value of the equipment is:Aftertax salvage value = $60,000(1 – 0.35) = $39,000Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for the NPV of the project is:NPV = 0 = – $830,000 – 75,000 + OCF(PVIFA14%,5) + [($75,000 + 39,000) / 1.14⌒5] Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:OCF = $845,791.97 / PVIFA14%,5 = $246,365.29The easiest way to calculate the bid price is the tax shield approach, so:OCF = $246,365.29 = [(P – v)Q – FC ](1 – tc) + tcD$246,365.29 = [(P – $8.50)(130,000) – $210,000 ](1 – 0.35) + 0.35($830,000/5) P = $12.34。