Corporate Finance Core Principles and Applications Chapter 8 Essay - Part 8

CHAPTER 8 MAKING CAPITAL INVESTMENT DECISIONS Answers to Concept Questions 1 - Corporate Finance Core Principles and Applications Chapter 8 Essay introduction. In this context, an opportunity cost refers to the value of an asset or other input that will be used in a project. The relevant cost is what the asset or input is actually worth today, not, for example, what it cost to acquire. 2. a. Yes, the reduction in the sales of the company’s other products, referred to as erosion, should be treated as an incremental cash flow. These lost sales are included because they are a cost (a revenue reduction) that the firm must bear if it chooses to produce the new product. . Yes, expenditures on plant and equipment should be treated as incremental cash flows. These are costs of the new product line. However, if these expenditures have already occurred (and cannot be recaptured through a sale of the plant and equipment), they are sunk costs and are not included as incremental cash flows. c. No, the research and development costs should not be treated as incremental cash flows. The costs of research and development undertaken on the product during the past three years are sunk costs and should not be included in the evaluation of the project.

Decisions made and costs incurred in the past cannot be changed. They should not affect the decision to accept or reject the project. d. Yes, the annual depreciation expense must be taken into account when calculating the cash flows related to a given project. While depreciation is not a cash expense that directly affects cash flow, it decreases a firm’s net income and hence, lowers its tax bill for the year. Because of this depreciation tax shield, the firm has more cash on hand at the end of the year than it would have had without expensing depreciation. . No, dividend payments should not be treated as incremental cash flows. A firm’s decision to pay or not pay dividends is independent of the decision to accept or reject any given investment project. For this reason, dividends are not an incremental cash flow to a given project. Dividend policy is discussed in more detail in later chapters. f. Yes, the resale value of plant and equipment at the end of a project’s life should be treated as an incremental cash flow.

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The price at which the firm sells the equipment is a cash inflow, and any difference between the book value of the equipment and its sale price will create accounting gains or losses that result in either a tax credit or liability. g. Yes, salary and medical costs for production employees hired for a project should be treated as incremental cash flows. The salaries of all personnel connected to the project must be included as costs of that project. 3. Item I is a relevant cost because the opportunity to sell the land is lost if the new golf club is produced.

Item II is also relevant because the firm must take into account the erosion of sales of existing products when a new product is introduced. If the firm produces the new club, the earnings from the existing clubs will decrease, effectively creating a cost that must be included in the decision. Item III is not relevant because the costs of research and development are sunk costs. Decisions made in the past cannot be changed. They are not relevant to the production of the new clubs. 4. For tax purposes, a firm would choose MACRS because it provides for larger depreciation deductions earlier.

These larger deductions reduce taxes, but have no other cash consequences. Notice that the choice between MACRS and straight-line is purely a time value issue; the total depreciation is the same; only the timing differs. 5. It’s probably only a mild over-simplification. Current liabilities will all be paid, presumably. The cash portion of current assets will be retrieved. Some receivables won’t be collected, and some inventory will not be sold, of course. Counterbalancing these losses is the fact that inventory old above cost (and not replaced at the end of the project’s life) acts to increase working capital. These effects tend to offset one another. 6. Management’s discretion to set the firm’s capital structure is applicable at the firm level. Since any one particular project could be financed entirely with equity, another project could be financed with debt, and the firm’s overall capital structure would remain unchanged, financing costs are not relevant in the analysis of a project’s incremental cash flows according to the stand-alone principle. . The EAC approach is appropriate when comparing mutually exclusive projects with different lives that will be replaced when they wear out. This type of analysis is necessary so that the projects have a common life span over which they can be compared. For example, if one project has a three-year life and the other has a five-year life, then a 15-year horizon is the minimum necessary to place the two projects on an equal footing, implying that one project will be repeated five times and the other will be repeated three times.

Note the shortest common life may be quite long when there are more than two alternatives and/or the individual project lives are relatively long. Assuming this type of analysis is valid implies that the project cash flows remain the same over the common life, thus ignoring the possible effects of, among other things: (1) inflation, (2) changing economic conditions, (3) the increasing unreliability of cash flow estimates that occur far into the future, and (4) the possible effects of future technology improvement that could alter the project cash flows. . Depreciation is a non-cash expense, but it is tax-deductible on the income statement. Thus depreciation causes taxes paid, an actual cash outflow, to be reduced by an amount equal to the depreciation tax shield, tcD. A reduction in taxes that would otherwise be paid is the same thing as a cash inflow, so the effects of the depreciation tax shield must be added in to get the total incremental aftertax cash flows. 9. There are two particularly important considerations.

The first is erosion. Will the “essentialized” book simply displace copies of the existing book that would have otherwise been sold? This is of special concern given the lower price. The second consideration is competition. Will other publishers step in and produce such a product? If so, then any erosion is much less relevant. A particular concern to book publishers (and producers of a variety of other product types) is that the publisher only makes money from the sale of new books.

Thus, it is important to examine whether the new book would displace sales of used books (good from the publisher’s perspective) or new books (not good). The concern arises any time there is an active market for used product. 10. Definitely. The damage to Porsche’s reputation is a factor the company needed to consider. If the reputation was damaged, the company would have lost sales of its existing car lines. 11. One company may be able to produce at lower incremental cost or market better. Also, of course, one of the two may have made a mistake! 2. Porsche would recognize that the outsized profits would dwindle as more products come to market and competition becomes more intense. Solutions to Questions and Problems NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1.

Using the tax shield approach to calculating OCF, we get: OCF = (Sales – Costs)(1 – tC) + tCDepreciation OCF = [($7 ? 2,000) – ($2 ? 2,000)](1 – 0. 34) + 0. 34($27,000/6) OCF = $8,130 So, the NPV of the project is: NPV = –$27,000 + $8,140(PVIFA14%,6) NPV = $4,614. 87 Since the NPV is positive, the company should accept the project. 2. 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 total cash flow each year will be: | | |Year 1 |Year 2 |Year 3 |Year 4 | | |Sales | |$7,500 |$7,500 |$7,500 |$7,500 | |  |Costs | |2,000 |2,000 |2,000 |2,000 | |  |Depreciation | | 4,000 | 4,000 | 4,000 | 4,000 | |  |EBT | |$1,500 |$1,500 |$1,500 |$1,500 | |  |Tax | | 510 | 510 | 510 | 510 | |  |Net income | |$ 990 |$ 990 |$ 990 |$ 990 | |  |  | | | | | | |  |OCF |0 |$4,990 |$4,990 |$4,990 |$4,990 | |  |Capital spending |–$16,000 |0 |0 |0 |0 | |  |NWC | –300 | –350 | –300 | –250 | 1,200 | |  |Incremental cash flow |–$16,300 |$4,640 |$4,690 |$4,740 |$6,190 | The NPV for the project is: NPV = –$16,300 + $4,640 / 1. 12 + $4,690 / 1. 122 + $4,740 / 1. 123 + $6,190 / 1. 124 NPV = –$1,110. 61 3.

Using the tax shield approach to calculating OCF, we get: OCF = (Sales – Costs)(1 – tC) + tCDepreciation OCF = ($2,600,000 – 1,125,000)(1 – 0. 35) + 0. 35($3,400,000/3) OCF = $1,355,416. 67 So, the NPV of the project is: NPV = –$3,400,000 + $1,355,416. 67(PVIFA10%,3) NPV = –$29,279. 36 4. The cash outflow at the beginning of the project will increase because of the spending on NWC. At the end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of the equipment will result in a cash inflow, but we also must account for the taxes which will be paid on this sale. So, the cash flows for each year of the project will be: |Year |Cash Flow | | | | |0 |–$3,700,000 | | = –$3,400,000 – 300,000 | | |1 |1,355,417 | | | | |2 |1,355,417 | | | | |3 |1,947,917 | | = $1,355,417 + 300,000 + 450,000 + (0 – 450,000)(. 35) | And the NPV of the project is: NPV = –$3,700,000 + $1,355,417(PVIFA10%,2) + ($1,94,917 / 1. 103) NPV = $115,874. 66 5. First we will calculate the annual depreciation for the equipment necessary for the project. The depreciation amount each year will be: Year 1 depreciation = $3,400,000(0. 3330) = $1,133,220

Year 2 depreciation = $3,400,000(0. 4440) = $1,511,300 Year 3 depreciation = $3,400,000(0. 1480) = $503,540 So, the book value of the equipment at the end of three years, which will be the initial investment minus the accumulated depreciation, is: Book value in 3 years = $3,400,000 – ($1,133,220 + 1,511,300 + 503,540) Book value in 3 years = $251,940 The asset is sold at a gain to book value, so this gain is taxable. Aftertax salvage value = $251,940 + ($251,940 – 450,000)(0. 35) Aftertax salvage value = $380,679 To calculate the OCF, we will use the tax shield approach, so the cash flow each year is: OCF = (Sales – Costs)(1 – tC) + tCDepreciation |Year |Cash Flow | | | | |0 |– $3,700,000 | | = –$3,400,000 – 300,000 | | |1 |1,355,377 | | = $1,475,000(. 65) + 0. 35($1,133,220) | | |2 |1,487,705 | | = $1,475,000(. 65) + 0. 35($1,511,300) | | |3 |1,815,668 | | = $1,475,000(. 65) + 0. 35($503,540) + $300,000 + 380,679 | Remember to include the NWC cost in Year 0, and the recovery of the NWC at the end of the project. The NPV of the project with these assumptions is: NPV = –$3,700,000 + ($1,355,377/1. 10) + ($1,487,705/1. 102) + ($1,815,668/1. 103) NPV = $125,807. 42 6.

First, we will calculate the annual depreciation of the new equipment. It will be: Annual depreciation charge = $860,000/5 Annual depreciation charge = $172,000 The aftertax salvage value of the equipment is: Aftertax salvage value = $95,000(1 – 0. 35) Aftertax salvage value = $61,750 Using the tax shield approach, the OCF is: OCF = $350,000(1 – 0. 35) + 0. 35($172,000) OCF = $287,700 Now 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 Year 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 = –$860,000 + 110,000 + $287,700(PVIFAIRR%,5) + [($61,750 – 110,000) / (1+IRR)5] IRR = 25. 52% 7. First, we will calculate the annual depreciation of the new equipment. It will be: Annual depreciation = $430,000/5 Annual depreciation = $86,000 Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so: Aftertax salvage value = MV + (BV – MV)tc

Very often, the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes: Aftertax salvage value = MV + (0 – MV)tc Aftertax salvage value = MV(1 – tc) We will use this equation to find the aftertax salvage value since we know the book value is zero. So, the aftertax salvage value is: Aftertax salvage value = $40,000(1 – 0. 34) Aftertax salvage value = $26,400 Using the tax shield approach, we find the OCF for the project is: OCF = $130,000(1 – 0. 34) + 0. 34($86,000) OCF = $115,040 Now we can find the project NPV. Notice that we include the NWC in the initial cash outlay.

The recovery of the NWC occurs in Year 5, along with the aftertax salvage value. NPV = –$430,000 – 15,000 + $115,040(PVIFA10%,5) + [($26,400 + 15,000) / 1. 105] NPV = $16,798. 25 8. To find the BV at the end of four years, we need to find the accumulated depreciation for the first four years. We could calculate a table with the depreciation each year, but an easier way is to add the MACRS depreciation amounts for each of the first four years and multiply this percentage times the cost of the asset. We can then subtract this from the asset cost. Doing so, we get: BV4 = $8,600,000 – 8,600,000(0. 2000 + 0. 3200 + 0. 1920 + 0. 1152) BV4 = $1,486,080 The asset is sold at a gain to book value, so this gain is taxable.

Aftertax salvage value = $1,950,000 + ($1,486,900 – 1,950,000)(. 35) Aftertax salvage value = $1,787,628 9. 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 capital. So, the cash outlay today for the project will be: |  |Equipment |–$2,800,000 | |  |NWC | –100,000 | |  |Total |–$2,900,000 | Using the bottom-up approach to calculating the operating cash flow, we find the operating cash flow each year will be:   |Sales |$1,500,000 | |  |Costs |450,000 | |  |Depreciation | 700,000 | |  |EBT |$350,000 | |  |Tax | 122,500 | |  |Net income |$227,500 | The operating cash flow is: OCF = Net income + Depreciation OCF = $227,500 + 700,000 OCF = $927,500 To 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 are assuming the net working capital will be recovered. So, the project NPV is: NPV = –$2,900,000 + $927,500(PVIFA14%,4) + $100,000 / 1. 44 NPV = –$138,323. 81 10. 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 = $65,000(1 – 0. 35) = $42,250 To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I are: OCF = –$78,000(1 – 0. 35) + 0. 35($375,000/3) = –$6,950 NPV = –$375,000 – $6,950(PVIFA14%,3) + ($42,250/1. 143) = –$362,617. 80 EAC = –$362,617. 80 / (PVIFA14%,3) = –$156,190. 90 And the OCF and NPV for Techron II are: OCF = –$73,000(1 – 0. 35) + 0. 5($510,000/5) = –$11,750 NPV = –$510,000 – $11,750(PVIFA14%,5) + ($42,250/1. 145) = –$528,395. 38 EAC = –$528,395. 38 / (PVIFA14%,5) = –$153,912. 88 The 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. Intermediate 11. First, we will calculate the depreciation each year, which will be: D1 = $520,000(0. 2000) = $104,000 D2 = $520,000(0. 3200) = $166,400 D3 = $520,000(0. 1920) = $99,840 D4 = $520,000(0. 1152) = $59,904 The book value of the equipment at the end of the project is:

BV4 = $520,000 – ($104,000 + 166,400 + 99,840 + 59,904) = $89,856 The asset is sold at a loss to book value, so this creates a tax refund. After-tax salvage value = $70,000 + ($89,856 – 70,000)(0. 35) = $76,949. 60 So, the OCF for each year will be: OCF1 = $185,000(1 – 0. 35) + 0. 35($104,000) = $152,650 OCF2 = $185,000(1 – 0. 35) + 0. 35($166,400) = $174,490 OCF3 = $185,000(1 – 0. 35) + 0. 35($99,840) = $151,194 OCF4 = $185,000(1 – 0. 35) + 0. 35($59,904) = $141,216 Now we have all the necessary information to calculate the project NPV. We need to be careful with the NWC in this project. Notice the project requires $20,000 of NWC at the beginning, and $4,000 more in NWC each successive year.

We will subtract the $20,000 from the initial cash flow, and subtract $4,000 each year from the OCF to account for this spending. In Year 4, we will add back the total spent on NWC, which is $32,000. The $4,000 spent on NWC capital during Year 4 is irrelevant. Why? Well, during this year the project required an additional $4,000, but we would get the money back immediately. So, the net cash flow for additional NWC would be zero. With all this, the equation for the NPV of the project is: NPV = – $520,000 – 20,000 + ($152,650 – 4,000)/1. 09 + ($174,490 – 4,000)/1. 092 + ($151,194 – 4,000)/1. 093 + ($141,216 + 32,000 + 76,949. 60)1. 094 NPV = $40,884. 02 12.

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: OCFA = –$130,000(1 – 0. 34) + 0. 34($485,000/4) OCFA = –$44,575 NPVA = –$430,000 – $44,575(PVIFA11%,4) NPVA = –$680,217. 28 And the NPV of System B is: OCFB = –$115,000(1 – 0. 34) + 0. 34($650,000/6) OCFB = –$39,067 NPVB = –$650,000 – $39,067(PVIFA11%,7) NPVB = –$815,273. 01 If the system will not be replaced when it wears out, then System A should be chosen, because it has the more positive NPV. 13.

If the equipment will be replaced at the end of its useful life, the correct capital budgeting technique is EAC. Using the NPVs we calculated in the previous problem, the EAC for each system is: EACA = – $680,217. 28 / (PVIFA11%,5) EACA = –$184,046. 60 EACB = – $858,884. 93 / (PVIFA11%,7) EACB = –$182,268. 50 If the conveyor belt system will be continually replaced, we should choose System B since it has the more positive NPV. 14. Since we need to calculate the EAC for each machine, revenue is irrelevant. The sales figure is only used to calculate the variable costs since EAC only uses the costs of operating the equipment, not the sales. Using the bottom up approach, or net income plus depreciation, method to calculate OCF, we get:   |  |Machine A | |Machine B | |  |Variable costs |–$3,500,000 | |–$3,000,000 | |  |Fixed costs |–2,300,000 | |–2,600,000 | |  |Depreciation | –566,667 | | –544,444 | |  |EBT |–$6,366,667 | |–$6,144,444 | |  |Tax | 2,228,333 | | 2,150,556 | |  |Net income |–$4,138,333 | |–$3,993,889 | |  |+ Depreciation | 566,667 | | 544,444 | |  |OCF |–$3,571,667 | |–$3,449,444 | The NPV and EAC for Machine A is: NPVA = –$3,400,000 – $3,571,667(PVIFA10%,6) NPVA = –$18,955,539. 46 EACA = –$18,955,539. 46 / (PVIFA10%,6) EACA = –$4,352,331. 76 And the NPV and EAC for Machine B is: NPVB = –$4,900,000 – 3,449,444(PVIFA10%,9)

NPVB = –$24,765,432. 71 EACB = – $24,765,432. 71 / (PVIFA10%,9) EACB = –$4,300,283. 09 You should choose Machine B since it has a more positive EAC. 15. 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. 11 = (1 + r)(1 + . 04) r = . 0673 or 6. 73% So, the NPV of Project A’s real cash flows, discounting at the real interest rate, is: NPV = –$35,000 + $18,000 / 1. 673 + $17,000 / 1. 06732 + $16,000 / 1. 06733 NPV = $9,948. 18 Project B’s cash flow are in nominal terms, so the NPV discount at the nominal interest rate is: NPV = –$45,000 + $22,000 / 1. 11 + $34,000 / 1. 112 + $12,000 / 1. 113 NPV = $11,189. 28 We should accept Project B if the projects are mutually exclusive since it has the highest NPV. 16. To determine the value of a firm, we can simply 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 = (2,000,000 ? $1. 05)(1 – 0. 34) Aftertax revenue in year 1 in real terms = $1,386,000 Revenues will grow at 5 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 = $1,386,000 / (0. 08 – 0. 05) PV of revenues = $46,200,000 The real aftertax costs in year 1 will be: Aftertax costs in year 1 in real terms = (2,000,000 ? $0. 85)(1 – 0. 34) Aftertax costs in year 1 in real terms = $1,122,000 Costs will grow at 4 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 = $1,122,000 / (0. 08 – 0. 04) PV of costs = $28,050,000 Now we can find the value of the firm, which is: Value of the firm = PV of revenues – PV of costs Value of the firm = $46,200,000 – 28,050,000 Value of the firm = $18,150,000 17.

To calculate the nominal cash flows, we simple increase each item in the income statement by the inflation rate, except for depreciation. Depreciation is a nominal cash flow, so it does not need to be adjusted for inflation in nominal cash flow analysis. Since the resale value is given in nominal terms as of the end of year 5, it does not need to be adjusted for inflation. Also, no inflation adjustment is needed for either the depreciation charge or the recovery of net working capital since these items are already expressed in nominal terms. Note that an increase in required net working capital is a negative cash flow whereas a decrease in required net working capital is a positive cash flow. The nominal aftertax salvage value is:   |Market price |$40,000 | |  |Tax on sale |–13,600 | |  |Aftertax salvage value |$26,400 | Remember, to calculate the taxes paid (or tax credit) on the salvage value, we take the book value minus the market value, times the tax rate, which, in this case, would be: Taxes on salvage value = (BV – MV)tC Taxes on salvage value = ($0 – 40,000)(. 34) Taxes on salvage value = –$13,600 Now we can find the nominal cash flows each year using the income statement. Doing so, we find: |  |  |Year 0 |Year 1 |Year 2 |Year 3 |Year 4 |Year 5 | | Sales | |$210,000 |$216,300 |$222,789 |$229,473 |$236,357 | |  |Expenses | |68,000 |70,040 |72,141 |74,305 |76,535 | |  |Depreciation | |75,000 |75,000 |75,000 |75,000 |75,000 | |  |EBT | |$67,000 |$71,260 |$75,648 |$80,167 |$84,822 | |  |Tax | |22,780 |24,228 |25,720 |27,257 |28,840 | |  |Net income | |$44,220 |$47,032 |$49,928 |$52,910 |$55,983 | |  |OCF | |$119,220 |$122,032 |$124,928 |$127,910 |$130,983 | |  |  | | | | | | | |  |Capital spending |–$375,000 | | | | |$26,400 | |  |NWC |–19,000 | | | | |19,000 | |  |Total cash flow |–$394,000 |$119,220 |$122,032 |$124,928 |$127,910 |$176,383 | 18.

The present value of the company is the present value of the future cash flows generated by the company. Here we have real cash flows, a real interest rate, and a real growth rate. The cash flows are a growing perpetuity, with a negative growth rate. Using the growing perpetuity equation, the present value of the cash flows are: PV = C1 / (R – g) PV = $190,000 / [. 09 – (–. 04)] PV = $1,461,538. 46 19. To find the EAC, we first need to calculate the NPV of the incremental cash flows. We will begin with the aftertax salvage value, which is: Taxes on salvage value = (BV – MV)tC Taxes on salvage value = ($0 – 16,000)(. 34) Taxes on salvage value = –$5,440   |Market price |$16,000 | |  |Tax on sale | –5,440 | |  |Aftertax salvage value |$10,560 | Now we can find the operating cash flows. Using the tax shield approach, the operating cash flow each year will be: OCF = –$8,000(1 – 0. 34) + 0. 34($57,000/3) OCF = $1,180 So, the NPV of the cost of the decision to buy is: NPV = –$57,000 + $1,180(PVIFA12%,3) + ($10,560/1. 123) NPV = –$46,649. 44 In order to calculate the equivalent annual cost, set the NPV of the equipment equal to an annuity with the same economic life. Since the project has an economic life of three years and is discounted at 12 percent, set the NPV equal to a three-year annuity, discounted at 12 percent.

EAC = –$46,649. 44 / (PVIFA12%,3) EAC = –$19,422. 45 20. We will find the EAC of the EVF first. There are no taxes since the university is tax-exempt, so the maintenance costs are the operating cash flows. The NPV of the decision to buy one EVF is: NPV = –$7,500 – $2,000(PVIFA9%,4) NPV = –$13,979. 44 In order to calculate the equivalent annual cost, set the NPV of the equipment equal to an annuity with the same economic life. Since the project has an economic life of four years and is discounted at 9 percent, set the NPV equal to a three-year annuity, discounted at 9 percent. So, the EAC per unit is: EAC = –$13,979. 44 / (PVIFA9%,4) EAC = –$4,315. 01

Since the university must buy 10 of the mowers, the total EAC of the decision to buy the EVF mower is: Total EAC = 10(–$4,315. 01) Total EAC = –$43,150. 15 Note, we could have found the total EAC for this decision by multiplying the initial cost by the number of mowers needed, and multiplying the annual maintenance cost of each by the same number. We would have arrived at the same EAC. We can find the EAC of the AEH mowers using the same method, but we need to include the salvage value as well. There are no taxes on the salvage value since the university is tax-exempt, so the NPV of buying one AEH will be: NPV = –$4,800 – $2,400(PVIFA9%,3) + ($900/1. 93) NPV = –$10,180. 14

So, the EAC per machine is: EAC = –$10,180. 14 / (PVIFA9%,3) EAC = –$4,021. 71 Since the university must buy 11 of the mowers, the total EAC of the decision to buy the AEH mowers is: Total EAC = 11(–$4,021. 71) Total EAC = –$44,238. 85 The university should buy the EVF mowers since the EAC is lower. Notice that the EAC of the AEH is lower on a per machine basis, but because the university needs more of these mowers, the total EAC is higher. 21. We will calculate the aftertax salvage value first. The aftertax salvage value of the equipment will be: Taxes on salvage value = (BV – MV)tC Taxes on salvage value = ($0 – 75,000)(. 34) Taxes on salvage value = –$25,500   |Market price |$75,000 | |  |Tax on sale | –25,500 | |  |Aftertax salvage value |$49,500 | Next, we will calculate the initial cash outlay, that is, the cash flow at Time 0. To undertake the project, we will have to purchase the equipment. The new project will decrease the net working capital, so this is a cash inflow at the beginning of the project. So, the cash outlay today for the project will be: |  |Equipment |–$530,000 | |  |NWC | 68,000 | |  |Total |–$462,000 |

Now we can calculate the operating cash flow each year for the project. Using the bottom up approach, the operating cash flow will be: |  |Saved salaries |$125,000 | |  |Depreciation | 106,000 | |  |EBT |$ 19,000 | |  |Taxes | 6,460 | |  |Net income |$ 12,540 | And the OCF will be: OCF = $12,540 + 106,000 OCF = $118,540 Now we can find the NPV of the project, which is: NPV = –$462,000 + $118,540(PVIFA9%,5) + ($49,500 – 68,000) / 1. 095 NPV = –$24,127. 18 22.

Replacement decision analysis is the same as the analysis of two competing projects, in this case, keep the current equipment, or purchase the new equipment. We will consider the purchase of the new machine first. Purchase new machine: The initial cash outlay for the new machine is the cost of the new machine, plus the increased net working capital. So, the initial cash outlay will be: |  |Purchase new machine |–$23,000,000 | |  |Net working capital | –400,000 | |  |Total |–$23,400,000 | Next, we can calculate the operating cash flow created if the company purchases the new machine. The saved operating expense is an incremental cash flow.

Additionally, the reduced operating expense is a cash inflow, so it should be treated as such in the income statement. 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: |  |Operating expense |$5,000,000 | |  |Depreciation |5,750,000 | |  |EBT |–$750,000 | |  |Taxes |– 300,000 | |  |Net income |–$450,000 | |  |OCF |$5,300,000 |

So, the NPV of purchasing the new machine, including the recovery of the net working capital, is: NPV = –$23,400,000 + $5,300,000(PVIFA10%,4) + $400,000 / 1. 104 NPV = –$6,326,507. 75 And the IRR is: 0 = –$23,400,000 + $5,300,000(PVIFAIRR,4) + $400,000 / (1 + IRR)4 Using a spreadsheet or financial calculator, we find the IRR is: IRR = –3. 09% Now we can calculate the decision to keep the old machine: Keep old machine: The initial cash outlay for the new 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 |–$10,500,000 | |  |Taxes | 1,800,000 | |  |Total |–$8,700,000 | Next, we can calculate the operating cash flow created if the company keeps the old machine. There are no incremental cash flows from keeping the old machine, but we need to account for the cash flow effects of depreciation. The income statement, adding depreciation to net income to calculate the operating cash flow will be:   |Depreciation |$1,500,000 | |  |EBT |–$1,500,000 | |  |Taxes |– 600,000 | |  |Net income |–$900,000 | |  |OCF |$600,000 | So, the NPV of the decision to keep the old machine will be: NPV = –$8,700,000 + $900,000(PVIFA10%,4) NPV = –$6,798,080. 73 And the IRR is: 0 = –$8,700,000 + $600,000(PVIFAIRR,4) Using a spreadsheet or financial calculator, we find the IRR is: IRR = –37. 07% The company should buy the new machine since it has a greater NPV. There 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, the increased inventory, 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 |–$23,000,000 | |  |Net working capital |–400,000 | | |Sell old machine |10,500,000 | |  |Taxes on old machine | –1,800,000 | |  |Total |–$14,700,000 | The cash flows from purchasing the new machine would be the saved operating expenses. We would also need to include only the change in depreciation.

The new machine has a depreciation of $5,750,000 per year, and the new machine has a depreciation of $8 million per year, so the increased depreciation will be $4,250,000 per year. The pro forma income statement and operating cash flow under this approach will be: |  |Operating expense |$5,000,000 | |  |Depreciation |–4,250,000 | |  |EBT |$750,000 | |  |Taxes | 300,000 | |  |Net income |$450,000 | |  |OCF |$4,700,000 | The NPV under this method is:

NPV = –$14,700,000 + $4,700,000(PVIFA10%,4) + $400,000 / 1. 104 NPV = $471,572. 98 And the IRR is: 0 = –$14,700,000 + $4,700,000(PVIFAIRR,4) + $400,000 / (1 + IRR)4 Using a spreadsheet or financial calculator, we find the IRR is: IRR = 11. 46% 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 = –$6,326,507. 75 – (–6,798,080. 73) = $471,572. 98 This is the exact same NPV we calculated when using the second analysis method. b.

Even though the saved expenses are less than the cost of the machine, the cash flows are also increased because of the higher depreciation of the new machine. The depreciation tax shield increases the cash flows enough to make the NPV positive. 23. We can find the NPV of a project using nominal cash flows or real cash flows. Either method will result in the same NPV. For this problem, we will calculate the NPV using both nominal and real cash flows. The initial investment in either case is $780,000 since it will be spent today. We will begin with the nominal cash flows. The revenues and production costs increase at different rates, so we must be careful to increase each at the appropriate growth rate. The nominal cash flows for each year will be: | |Year 0 |Year 1 |Year 2 |Year 3 | | |Revenues | |$320,000. 00 |$336,000. 00 |$352,800. 00 | | |Costs | |$125,000. 00 |130,000. 00 |135,200. 00 | | |Depreciation | |111,428. 57 |111,428. 57 |111,428. 57 | | |EBT | |$83,571. 43 |$94,571. 43 |$106,171. 43 | | |Taxes | |28,414. 9 |32,154. 29 |36,098. 29 | | |Net income | |$55,157. 14 |$62,417. 14 |$70,073. 14 | | |OCF | |$166,585. 71 |$173,845. 71 |$181,501. 71 | | |  | | | | | | |Capital spending |–$780,000 | | | | | |Total cash flow |–$780,000 |$166,585. 71 |$173,845. 71 |$181,501. 71 | | |Year 4 |Year 5 |Year 6 |Year 7 | | |Revenues |$370,440. 00 |$388,962. 00 |$408,410. 10 |$428,830. 61 | | |Costs |140,608. 00 |146,232. 32 |152,081. 61 |158,164. 88 | | |Depreciation |111,428. 57 |111,428. 57 |111,428. 57 |111,428. 57 | | |EBT |$118,403. 43 |$131,301. 11 |$144,899. 92 |$159,237. 16 | | |Taxes |40,257. 17 |44,642. 38 |49,265. 97 |54,140. 63 | | |Net income |$78,146. 6 |$86,658. 73 |$95,633. 94 |$105,096. 52 | | |OCF |$189,574. 83 |$198,087. 30 |$207,062. 52 |$216,525. 09 | | |  | | | | | | |Total cash flow |$189,574. 83 |$198,087. 30 |$207,062. 52 |$216,525. 09 | Now that we have the nominal cash flows, we can find the NPV. We must use the nominal required return with nominal cash flows. Using the Fisher equation to find the nominal required return, we get: 1 + R) = (1 + r)(1 + h) (1 + R) = (1 + . 11)(1 + . 05) R = . 1655 or 16. 55% So, the NPV of the project using nominal cash flows is: NPV = –$780,000 + $166,585. 71 / 1. 1655 + $173,845. 71 / 1. 16552 + $181,501. 71 / 1. 16553 + $189,574. 83 / 1. 16554 + $198,087. 30 / 1. 16555 + $207,062. 52 / 1. 16556 + $216,525. 09 / 1. 16557 NPV = –$42,875. 55 We can also find the NPV using real cash flows and the real required return. This will allow us to find the operating cash flow using the tax shield approach. Both the revenues and expenses are growing annuities, but growing at different rates. This means we must find the present value of each separately.

We also need to account for the effect of taxes, so we will multiply by one minus the tax rate. So, the present value of the aftertax revenues using the growing annuity equation is: PV of aftertax revenues = C {[1/(r – g)] – [1/(r – g)] ? [(1 + g)/(1 + r)]t}(1 – tC) PV of aftertax revenues = $320,000{[1/(. 11 – . 05)] – [1/(. 11 – . 05)] ? [(1 + . 05)/(1+. 11)]7}(1–. 34) PV of aftertax revenues = $947,824. 62 And the present value of the aftertax costs will be: PV of aftertax costs = C {[1/(r – g)] – [1/(r – g)] ? [(1 + g)/(1 + r)]t}(1 – tC) PV of aftertax costs = $125,000{[1/(. 11 – . 04)] – [1/(. 11 – . 04)] ? [(1 + . 04)/(1 + . 11)]7}(1 – . 34) PV of aftertax costs = $361,257. 0 Now we need to find the present value of the depreciation tax shield. The depreciation amount in the first year is a real value, so we can find the present value of the depreciation tax shield as an ordinary annuity using the real required return. So, the present value of the depreciation tax shield will be: PV of depreciation tax shield = ($780,000/7)(. 34)(PVIFA11%,7) PV of depreciation tax shield = $150,557. 22 Using the present value of the real cash flows to find the NPV, we get: NPV = Initial cost + PV of revenues – PV of costs + PV of depreciation tax shield NPV = –$780,000 + 947,824. 62 – 361,257. 40 + 150,557. 22 NPV = –$42,875. 55

Notice, the NPV using nominal cash flows or real cash flows is identical, which is what we would expect. 24. Here we have a project in which the quantity sold each year increases. First, we need to calculate the quantity sold each year by increasing the current year’s quantity by the growth rate. So, the quantity sold each year will be: Year 1 quantity = 5,000 Year 2 quantity = 5,000(1 + . 10) = 5,500 Year 3 quantity = 5,500(1 + . 10) = 6,050 Year 4 quantity = 6,050(1 + . 10) = 6,655 Year 5 quantity = 6,655(1 + . 10) = 7,321 Now we can calculate the sales revenue and variable costs each year. The pro forma income statements and operating cash flow each year will be: |  |Year 0 |Year 1 |Year 2 |Year 3 |Year 4 |Year 5 | | |Revenues | |$275,000. 00 |$302,500. 00 |$332,750. 00 |$366,025. 00 |$402,627. 50 | | |Fixed costs | |120,000. 00 |120,000. 00 |120,000. 00 |120,000. 00 |120,000. 00 | | |Variable costs | |115,000. 00 |126,500. 00 |139,150. 00 |153,065. 00 |168,371. 50 | | |Depreciation | |42,000. 00 |42,000. 00 |42,000. 0 |42,000. 00 |42,000. 00 | | |EBT | |–$2,000. 00 |$14,000. 00 |$31,600. 00 |$50,960. 00 |$72,256. 00 | | |Taxes | |–680. 00 |4,760. 00 |10,744. 00 |17,326. 40 |24,567. 04 | | |Net income | |–$1,320. 00 |$9,240. 00 |$20,856. 00 |$33,633. 60 |$47,688. 96 | | |OCF | |$40,680. 00 |$51,240. 00 |$62,856. 00 |$75,633. 60 |$89,688. 6 | | |  | | | | | | | | |Equipment |–$210,000 | | | | | | | |NWC |–$34,000 | | | | |$34,000 | | |  | | | | | | | | |Total CF |–$244,000 |$40,680. 00 |$51,240. 00 |$62,856. 00 |$75,633. 60 |$123,688. 96 | So, the NPV of the project is: NPV = –$244,000 + $40,680 / 1. 17 + $51,240 / 1. 172 + $62,856 / 1. 173 + $75,633. 60 / 1. 174 + $123,688. 96 / 1. 175 NPV = –$35,776. 03

We could also have calculated the cash flows using the tax shield approach, with growing annuities and ordinary annuities. The sales and variable costs increase at the same rate as sales, so both are growing annuities. The fixed costs and depreciation are both 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 – tC) PV of revenues = $275,000{[1/(. 17 – . 10)] – [1/(. 17 – . 10)] ? [(1 + . 10)/(1 + . 17)]5} PV of revenues = $1,042,754. 54 And 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 – tC) PV of variable costs = $115,000{[1/(. 17 – . 10)] – [1/(. 17 – . 10)] ? (1 + . 10)/(1 + . 17)]5} PV of variable costs = $436,060. 99 The 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 = $120,000({1 – [1/(1 + . 17)]5 } / . 17) PV of fixed costs = $383,921. 54 PV of depreciation = C({1 – [1/(1 + r)]t } / r ) PV of depreciation = $42,000({1 – [1/(1 + . 17)]5 } / . 17) PV of depreciation = $134,372. 54 Now, we can use the depreciation tax shield approach to find the NPV of the project, which is: NPV = –$244,000 + ($1,042,754. 54 – 383,921. 54 – 436,060. 99)(1 – . 34) + ($134,372. 54)(. 34) NPV = –$35,776. 03 25.

We will begin by calculating the aftertax salvage value of the equipment at the end of the project’s life. The aftertax salvage value is the market value of the equipment minus any taxes paid (or refunded), so the aftertax salvage value in four years will be: Taxes on salvage value = (BV – MV)tC Taxes on salvage value = ($0 – 300,000)(. 38) Taxes on salvage value = –$114,000 |  |Market price |$300,000 | |  |Tax on sale | –114,000 | | |Aftertax salvage value |$186,000 | Now we need to calculate the operating cash flow each year. Using the bottom up approach to calculating operating cash flow, we find:   |  |Year 0 |Year 1 |Year 2 |Year 3 |Year 4 | |  |Revenues | |$2,508,000 |$4,560,000 |$3,240,000 |$2,280,000 | |  |Fixed costs | |680,000 |680,000 |680,000 |680,000 | |  |Variable costs | |376,200 |684,000 |486,000 |342,000 | |  |Depreciation |  |1,366,530 |1,822,450 |607,210 |303,810 | |  |EBT |  |$85,270 |$1,373,550 |$1,466,790 |$954,190 | |  |Taxes |  |32,403 |521,949 |557,380 |362,592 | |  |Net income |  |$52,867 |$851,601 |$909,410 |$591,598 | |  |OCF |  |$1,419,397 |$2,674,051 |$1,516,620 |$895,408 | |  |  | | | | | | |  |Capital spending |–$4,100,000 | | | |$186,000 | |  |Land |–950,000 | | | |975,000 | |  |NWC |–150,000 | | | |150,000 | |  |  | | | | | | |  |Total cash flow |–$5,200,000 |$1,419,397. 40 |$2,674,051. 00 |$1,516,619. 80 |$2,206,407. 80 | Notice the calculation of the cash flow at time 0. The capital spending on equipment and investment in net working capital are cash outflows are both cash outflows. The aftertax selling price of the land is also a cash outflow.

Even though no cash is actually spent on the land because the company already owns it, the aftertax cash flow from selling the land is an opportunity cost, so we need to include it in the analysis. Additionally, at the end of the project, the land can be sold. With all the project cash flows, we can calculate the NPV, which is: NPV = –$5,200,000 + $1,419,397. 40 / 1. 13 + $2,674,051 / 1. 132 + $1,516,619. 80 / 1. 133 + $2,206,407. 80 / 1. 134 NPV = $554,602. 89 The company should proceed with the manufacture of the zithers. 26. Replacement decision analysis is the same as the analysis of two competing projects, in this case, keep the current equipment, or purchase the new equipment. We will consider the purchase of the new machine first. 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 |–$305,000 | |  |Depreciation |– 900,000 | |  |EBT |–$1,205,000 | |  |Taxes |– 409,700 | |  |Net income |–$795,300 |   |OCF |$104,700 | Notice 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 |$500,000 | |  |Taxes |–170,000 | |  |Total |$330,000 | The NPV of purchasing the new machine is: NPV = –$4,500,000 – $104,700(PVIFA12%,5) + $330,000 / 1. 125 NPV = –$3,935,329. 07

Notice the NPV is negative. This does not necessarily mean we should not purchase the new machine. In this analysis, we are only dealing with costs, so we would expect a negative NPV. The revenue is not included in the analysis since it is not incremental to the machine. Similar to an EAC analysis, we will use the machine with the least negative NPV. Now we can calculate the decision to keep the old machine: Keep old machine: The initial cash outlay for 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 |–$2,500,000 | |  |Taxes | 442,000 | |  |Total |–$2,058,000 | Next, 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 incomes statement, adding depreciation to net income to calculate the operating cash flow will be:   |Maintenance cost |–$550,000 | |  |Depreciation |–240,000 | |  |EBT |–$790,000 | |  |Taxes |–268,600 | |  |Net income |–$521,400 | |  |OCF |–$281,400 | The 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 |$280,000 | |  |Taxes |–95,200 | |  |Total |$184,800 |

So, the NPV of the decision to keep the old machine will be: NPV = –$2,058,000 – $281,400(PVIFA12%,5) + $184,800 / 1. 125 NPV = –$2,967,523. 54 The company should keep the old machine since it has a greater (less negative) NPV. There 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 |–$4,500,000 | |  |Sell old machine |2,500,000 | |  |Taxes on old machine |– 442,000 | |  |Total |–$2,442,000 | The cash flows from purchasing the new machine would be the difference in the operating expenses. We would also need to include only the change in depreciation. The old machine has a depreciation of $240,000 per year, and the new machine has a depreciation of $900,000 per year, so the increased depreciation will be $660,000 per year. The pro forma income statement and operating cash flow under this approach will be:   |Maintenance cost |$245,000 | |  |Depreciation |–660,000 | |  |EBT |–$415,000 | |  |Taxes |–141,100 | |  |Net income |–$273,900 | |  |OCF |$386,100 | The 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 |$500,000 | |  |Taxes |–170,000 | |  |Lost sale of old |–280,000 | |  |Taxes on lost sale of old | 95,200 | |  |Total |$145,200 | The NPV under this method is: NPV = –$2,442,000 + $386,100(PVIFA12%,5) + $145,200 / 1. 125 NPV = –$967,805. 53 So, this analysis still tells us the company should not purchase the new machine. This is really the same type of analysis as we did considering the replacement decision as mutually exclusive projects. 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 = –$3,935,329. 07 – (–2,967,523. 54) = –$967,805. 53 This is the exact same NPV we calculated when using the second analysis method. 27.

A kilowatt hour is 1,000 watts for 1 hour. A 60-watt bulb burning for 500 hours per year uses 30,000 watts, or 30 kilowatts. Since the cost of a kilowatt hour is $0. 101, the cost per year is: Cost per year = 30($0. 101) Cost per year = $3. 03 The 60-watt bulb will last for 1,000 hours, which is 2 years of use at 500 hours per year. So, the NPV of the 60-watt bulb is: NPV = –$0. 50 – $3. 03(PVIFA10%,2) NPV = –$5. 76 And the EAC is: EAC = –$5. 76 / (PVIFA10%,2) EAC = –$3. 3181 Now we can find the EAC for the 15-watt CFL. A 15-watt bulb burning for 500 hours per year uses 7,500 watts, or 7. 5 kilowatts. And, since the cost of a kilowatt hour is $0. 101, the cost per year is:

Cost per year = 7. 5($0. 101) Cost per year = $0. 7575 The 15-watt CFL will last for 12,000 hours, which is 24 years of use at 500 hours per year. So, the NPV of the CFL is: NPV = –$3. 50 – $0. 7575(PVIFA10%,24) NPV = –$10. 31 And the EAC is: EAC = –$10. 31 / (PVIFA10%,24) EAC = –$1. 1470 Thus, the CFL is much cheaper. But: see our next two questions. 28. To solve the EAC algebraically for each bulb, we can set up the variables as follows: W = light bulb wattage C = cost per kilowatt hour H = hours burned per year P = price the light bulb The number of watts use by the bulb per hour is: WPH = W / 1,000 And the kilowatt hours used per year is: KPY = WPH ? H

The electricity cost per year is therefore: ECY = KPY ? C The NPV of the decision to but the light bulb is: NPV = – P – ECY(PVIFAR%,t) And the EAC is: EAC = NPV / (PVIFAR%,t) Substituting, we get: EAC = [–P – (W / 1,000 ? H ? C)PVIFAR%,t] / PFIVAR%,t We need to set the EAC of the two light bulbs equal to each other and solve for C, the cost per kilowatt hour. Doing so, we find: [–$0. 50 – (60 / 1,000 ? 500 ? C)PVIFA10%,2] / PVIFA10%,2 = [–$3. 50 – (15 / 1,000 ? 500 ? C)PVIFA10%,24] / PVIFA10%,24 C = $0. 004509 So, unless the cost per kilowatt hour is extremely low, it makes sense to use the CFL. But when should you replace the incandescent bulb? See the next question. 29.

We are again solving for the breakeven kilowatt hour cost, but now the incandescent bulb has only 500 hours of useful life. In this case, the incandescent bulb has only one year of life left. The breakeven electricity cost under these circumstances is: [–$0. 50 – (60 / 1,000 ? 500 ? C)PVIFA10%,1] / PVIFA10%,1 = [–$3. 50 – (15 / 1,000 ? 500 ? C)PVIFA10%,24] / PVIFA10%,24 C = –$0. 007131 Unless the electricity cost is negative (Not very likely! ), it does not make financial sense to replace the incandescent bulb until it burns out. 30. The debate between incandescent bulbs and CFLs is not just a financial debate, but an environmental one as well. The numbers below correspond to the numbered items in the question: 1.

The extra heat generated by an incandescent bulb is waste, but not necessarily in a heated structure, especially in northern climates. 2. Since CFLs last so long, from a financial viewpoint, it might make sense to wait if prices are declining. 3. Because of the nontrivial health and disposal issues, CFLs are not as attractive as our previous analysis suggests. 4. From a company’s perspective, the cost of replacing working incandescent bulbs may outweigh the financial benefit. However, since CFLs last longer, the cost of replacing the bulbs will be lower in the long run. 5. Because incandescent bulbs use more power, more coal has to be burned, which generates more mercury in the environment, potentially offsetting the mercury concern with CFLs. 6.

As in the previous question, if CO2 production is an environmental concern, the the lower power consumption from CFLs is a benefit. 7. CFLs require more energy to make, potentially offsetting (at least partially) the energy savings from their use. Worker safety and site contamination are also negatives for CFLs. 8. This fact favors the incandescent bulb because the purchasers will only receive part of the benefit from the CFL. 9. This fact favors waiting for new technology. 10. This fact also favors waiting for new technology. While there is always a “best” answer, this question shows that the analysis of the “best” answer is not always easy and may not be completely possible because of incomplete data.

As for how to better legislate the use of incandescent bulbs, our analysis suggests that requiring them in new construction might make sense. Rental properties in general should probably be required to use CFLs (why rentals? ). Another piece of legislation that makes sense is requiring the producers of CFLs to supply a disposal kit and proper disposal instructions with each one sold. Finally, we need much better research on the hazards associated with broken bulbs in the home and workplace and proper procedures for dealing with broken bulbs. 31. Here we have a situation where a company is going to buy one of two assets, so we need to calculate the EAC of each asset.

To calculate the EAC, we can calculate the EAC of the combined costs of each computer, or calculate the EAC of an individual computer, then multiply by the number of computers the company is purchasing. In this instance, we will calculate the EAC of each individual computer. For the SAL 5000, we will begin by calculating the aftertax salvage value, then the operating cash flows. So: SAL 5000: Taxes on salvage value = (BV – MV)tC Taxes on salvage value = ($0 – 400)(. 34) Taxes on salvage value = –$136 |  |Market price |$400 | |  |Tax on sale | –136 | | |Aftertax salvage value |$264 |

The incremental costs will include the maintenance costs, depreciation, and taxes. Notice the taxes are negative, signifying a lower tax bill. So, the incremental cash flows will be: |  |Maintenance cost |–$500. 00 | |  |Depreciation | –525. 00 | |  |EBT |–$1,025. 00 | |  |Tax |–348. 50 | |  |Net income |–$676. 50 | |  |OCF |–$151. 50 | So, the NPV of the decision to buy one unit is: NPV = –$4,200 – $151. 50(PVIFA11%,8) + $264 / 1. 118 NPV = –$4,865. 08 And the EAC on a per unit basis is: –$4,865. 8 = EAC(PVIFA11%,8) EAC = –$945. 39 Since the company must buy 9 units, the total EAC of the decision is: Total EAC = 9(–$945. 39) Total EAC = –$8,508. 49 And the EAC for the DET 1000: Taxes on salvage value = (BV – MV)tC Taxes on salvage value = ($0 – 500)(. 34) Taxes on salvage value = –$170 |  |Market price |$500 | | |Tax on sale | –170 | |  |Aftertax salvage value |$330 | The incremental costs will include the maintenance costs, depreciation, and taxes. Notice the taxes are negative, signifying a lower tax bill.

So, the incremental cash flows will be: |  |Maintenance cost |–$600. 00 | |  |Depreciation | –850. 00 | |  |EBT |–$1,450. 00 | |  |Tax | –493. 00 | |  |Net income |–$957. 00 | |  |OCF |–$107. 00 | So, the NPV of the decision to buy one unit is: NPV = –$5,100 – $107(PVIFA11%,6) + $330 / 1. 116 NPV = –$5,376. 24 And the EAC on a per unit basis is: –$5,376. 24 = EAC(PVIFA11%,6) EAC = –$1,270. 82 Since the company must buy 7 units, the total EAC of the decision is: Total EAC = 7(–$1,270. 82)

Total EAC = –$8,895. 71 The company should choose the SAL 5000 since the total EAC is lower. 32. Here we are comparing two mutually exclusive projects with inflation. Since each will be replaced when it wears out, we need to calculate the EAC for each. We have real cash flows. Similar to other capital budgeting projects, when calculating the EAC, we can use real cash flows with the real interest rate, or nominal cash flows and the nominal interest rate. Using the Fisher equation to find the real required return, we get: (1 + R) = (1 + r)(1 + h) (1 + . 16) = (1 + r)(1 + . 05) r = . 0667 or 6. 67% This is the interest rate we need to use with real cash flows.

We are given the real aftertax cash flows for each asset, so the NPV for the XX40 is: NPV = –$1,500 – $125(PVIFA6. 67%,3) NPV = –$1,803. 05 So, the EAC for the XX40 is: –$1,803. 05 = EAC(PVIFA6. 67%,3) EAC = –$693. 10 And the EAC for the RH45 is: NPV = –$1,900 – $175(PVIFA6. 67%,5) NPV = –$2,623. 98 –$2,623. 98 = EAC(PVIFA6. 67%,5) EAC = –$634. 26 The company should choose the RH45 because it has the lower (less negative) EAC. 33. The project has a sales price that increases at five percent per year, and a variable cost per unit that increases at 7 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 5 | |  |Sales price |$75. 00 |$78. 75 |$82. 69 |$86. 82 |$91. 16 | |  |Cost per unit |$20. 00 |$21. 40 |$22. 90 |$24. 50 |$26. 22 | Using 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 | |$1,125,000. 00 |$1,181,250. 00 |$1,240,312. 50 |$1,302,328. 13 |$1,367,444. 53 | |  |Fixed costs | |325,000. 00 |325,000. 00 |325,000. 00 |325,000. 00 |325,000. 00 | |  |VC | |300,000. 00 |321,000. 00 |343,470. 00 |367,512. 90 |393,238. 80 | |  |Dep. | |190,000. 00 |190,000. 0 |190,000. 00 |190,000. 00 |190,000. 00 | |  |EBT | |$310,000. 00 |$345,250. 00 |$381,842. 50 |$419,815. 23 |$459,205. 73 | |  |Taxes | |105,400. 00 |117,385. 00 |129,826. 45 |142,737. 18 |156,129. 95 | |  |Net income | |$204,600. 00 |$227,865. 00 |$252,016. 05 |$277,078. 05 |$303,075. 78 | |  |OCF | |$394,600. 00 |$417,865. 00 |$442,016. 05 |$467,078. 05 |$493,075. 8 | |  |  | | | | | | | |  |Equipment |–$950,000 | | | | | | |  |NWC |–180,000 | | | | |$180,000 | |  |  | | | | | | | |  |Total CF |–$1,130,000 |$394,600. 00 |$417,865. 00 |$442,016. 05 |$467,078. 05 |$673,075. 78 |

With these cash flows, the NPV of the project is: NPV = –$1,131,000 + $394,600 / 1. 11 + $417,865 / 1. 112 + $442,016. 05 / 1. 113 + $467,078. 05 / 1. 114 + $673,075. 08 / 1. 115 NPV = $594,958. 92 We 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} PV of revenues = $1,125,000{[1/(. 11 – . 05)] – [1/(. 11 – . 05)] ? [(1 + . 05)/(1 + . 11)]5}

PV of revenues = $4,548,543. 97 And 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} PV of variable costs = $300,000{[1/(. 11 – . 07)] – [1/(. 11 – . 07)] ? [(1 + . 10)/(1 + . 07)]5} PV of variable costs = $1,257,403. 60 The 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 = $325,000({1 – [1/(1 + . 11)]5 } / . 11) PV of fixed costs = $1,201,166. 53 PV of depreciation = C({1 – [1/(1 + r)]t } / r ) PV of depreciation = $190,000({1 – [1/(1 + . 11)]5 } / . 11) PV of depreciation = $702,220. 3 Now, we can use the depreciation tax shield approach to find the NPV of the project, which is: NPV = –$1,130,000 + ($4,548,543. 97 – 1,257,403. 60 – 1,201,166. 53)(1 – . 34) + ($702,220. 43)(. 34) + $180,000 / 1. 115 NPV = $594,958. 92 Challenge 34. This is an in-depth capital budgeting problem. Probably the easiest OCF calculation for this problem is the bottom up approach, so we will construct an income statement for each year. Beginning with the initial cash flow at time zero, the project will require an investment in equipment. The project will also require an investment in NWC. So, the cash flow required for the project today will be:   |Capital spending | –$21,000,000 | |  |Change in NWC | –1,750,000 | |  |Total cash flow |–$22,750,000 | Now we can begin the remaining calculations. Sales figures are given for each year, along with the price per unit. The variable costs per unit are used to calculate total variable costs, and fixed costs are given at $900,000 per year. To calculate depreciation each year, we use the initial equipment cost of $21 million, times the appropriate MACRS depreciation each year. The remainder of each income statement is calculated below.

Notice at the bottom of the income statement we added back depreciation to get the OCF for each year. The section labeled “Net cash flows” will be discussed below: |Year |0 |Year 1 |Year 2 |Year 3 |Year 4 |Year 5 | |  |Ending book value | |$17,999,100 |$12,856,200 |$9,183,300 |$6,560,400 |$4,685,100 | |  |  | | | | | | | |  |Sales | |$31,155,000 |$35,510,000 |$47,905,000 |$42,210,000 |$32,495,000 | |  |Variable costs | |22,320,000 |25,440,000 |34,320,000 |30,240,000 |23,280,000 | |  |Fixed costs | |950,000 |950,000 |950,000 |950,000 |950,000 | |  |Depreciation | |3,000,900 |5,142,900 |3,672,900 |2,622,900 |1,875,300 | |  |EBIT | |4,884,100 |3,977,100 |8,962,100 |8,397,100 |6,389,700 | |  |Taxes | |1,709,435 |1,391,985 |3,136,735 |2,938,985 |2,236,395 | |  |Net income | |3,174,665 |2,585,115 |5,825,365 |5,458,115 |4,153,305 | |  |Depreciation | |3,000,900 |5,142,900 |3,672,900 |2,622,900 |1,875,300 | |  |OCF | |$6,175,565 |$7,728,015 |$9,498,265 |$8,081,015 |$6,028,605 | |  |  | | | | | | | |  |Net cash flows | | | | | | | |  |OCF | |$6,175,565 |$7,728,015 |$9,498,265 |$8,081,015 |$6,028,605 | |  |Change in NWC |–$1,750,000 |–653,250 |–1,859,250 |854,250 |1,457,250 |1,951,000 | |  |Capital spending |–21,000,000 | | | | |4,369,785 | |  |Total cash flow |–$22,750,000 |$5,522,315 |$5,868,765 $10,352,515 |$9,538,265 |$12,349,390 | After we calculate the OCF for each year, we need to account for any other cash flows. The other cash flows in this case are NWC cash flows and capital spending, which is the aftertax salvage of the equipment. The required NWC capital is 15 percent of the sales change. We will work through the NWC cash flow for Year 1. The total NWC in Year 1 will be 15 percent of sales increase from Year 1 to Year 2, or: Increase in NWC for Year 1 = . 15($35,510,000 – 31,155,000) Increase in NWC for Year 1 = $653,250 Notice that the NWC cash flow is negative. Since the sales are increasing, we will have to spend more money to increase NWC.

In Year 3 and Year 4, the NWC cash flow is positive since sales are declining. And, in Year 5, the NWC cash flow is the recovery of all NWC the company still has in the project. To calculate the aftertax salvage value, we first need the book value of the equipment. The book value at the end of the five years will be the purchase price, minus the total depreciation. So, the ending book value is: Ending book value = $21,000,000 – ($3,000,900 + 5,142,900 + 3,672,900 + 2,622,900 + 1,875,300) Ending book value = $4,685,100 The market value of the used equipment is 20 percent of the purchase price, or $4. 2 million, so the aftertax salvage value will be: Aftertax salvage value = $4,200,000 + ($4,685,100 – 4,200,000)(. 5) Aftertax salvage value = $4,369,785 The aftertax salvage value is included in the total cash flows are capital spending. Now we have all of the cash flows for the project. The NPV of the project is: NPV = –$22,750,000 + $5,522,315/1. 17 + $5,868,765/1. 172 + $10,352,515/1. 173 + $9,538,265/1. 174 + $12,349,390/1. 175 NPV = $3,443,735. 34 And the IRR is: NPV = 0 = –$22,750,000 + $5,522,315/(1 + IRR) + $5,868,765/(1 + IRR)2 + $10,352,515/(1 + IRR)3 + $9,538,265/(1 + IRR)4 + $12,349,390/(1 + IRR)5 IRR = 22. 52% We should accept the project. 35. To find the initial pretax cost savings necessary to buy the new machine, we should use the tax shield approach to find the OCF.

We begin by calculating the depreciation each year using the MACRS depreciation schedule. The depreciation each year is: D1 = $625,000(0. 3333) = $208,312. 50 D2 = $625,000(0. 4445) = $277,812. 50 D3 = $625,000(0. 1481) = $92,562. 50 D4 = $625,000(0. 0741) = $46,312. 50 Using the tax shield approach, the OCF each year is: OCF1 = (S – C)(1 – 0. 35) + 0. 35($208,312. 50) OCF2 = (S – C)(1 – 0. 35) + 0. 35($277,812. 50) OCF3 = (S – C)(1 – 0. 35) + 0. 35($92,562. 50) OCF4 = (S – C)(1 – 0. 35) + 0. 35($46,312. 50) OCF5 = (S – C)(1 – 0. 35) Now we need the aftertax salvage value of the equipment. The aftertax salvage value is: After-tax salvage value = $60,000(1 – 0. 35) = $39,000

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