Concept Questions◆What are the three difficulties in determining incremental cash flows?Sunk costs.Opportunity costsSide effects.◆Define sunk costs, opportunity costs, and side effects. Sunk costs are costs that have already been incurred and that will not be affected by the decision whether to undertake the investment.Opportunity costs are costs incurred by the firm because, if it decides to undertake a project, it will forego other opportunities for using the assets.Side effects appear when a project negatively affects cash flows from other parts of the firm.◆What are the items leading to cash flow in any year?Cash flow from operations (revenue-operating costs-taxes) plus cash flow of investment (cost of new machines + changes in net working capital + opportunity costs).◆Why did we determine income when NPV Analysis discounts cash flows, not income?Because we need to determine how much is paid out in taxes.◆Why is working capital viewed as a cash outflow?Because increases in working capital must be funded by cash generated elsewhere in the firm.◆What is the difference between the nominal and the real interest rate?The nominal interest rate is the real interest rate with a premium for inflation.◆What is the difference between nominal and real cash flows?Real cash flows are nominal cash flows adjusted for inflation.◆What is the equivalent annual cost method of capital budgeting?The decision as to which of various mutually exclusive machines to buy is based on the equivalent annual cost. The EAC is determined by dividing the net present value of costs by an annuity factor that has the same life as the machines. The machine with the lowest EAC should be acquired.◆Can you list the assumptions that we must to use EAC?All machines do the same job.They have different operating costs and livesThe machine will be indefinitely replaced.

Questions And ProblemsNPV and Capital Budgeting7.1 Which of the following cash flows should be treated as incremental cash flows when computing the NPV of an investment?a. The reduction in the sales of the company’s other products.b. The expenditure on plant and equipment.c. The cost of research and development undertaken in connection with the product during the past three years.d. The annual depreciation expense.e. Dividend payments.f. The resale value of plant and equipment at the end of the project’s life.g. Salary and medical costs for production employees on leave.Solutionsa.Yes, the reduction in the sales of the company’s other products is an incremental cash flow. Include these lost sales because they are a cost (a revenue reduction) which the firm must bear if it chooses to produce the new product.b.Yes, the expenditures on plant and equipment are incremental cash flows. These are direct costs of the new product line.c.No, the research and development costs are not included. The costs of research and development undertaken on the product during the past 3 years are sunk costs and should not be included in the evaluation of the project. The sunk costs must be borne whether or not the firm chooses to produce the new product; thus, they should have no bearing on the acceptability of the project.

d.Yes, the annual depreciation charge is part of the incremental cash flows. The depreciation charge is considered when computing the cash flows of the project. Remember, though, that it is the depreciation tax shield that is actually the cash flow.e.No, the dividend payments are not incremental cash flows. Dividend payments are not a cost of the project. The choice of whether or not to pay a dividend is a decision of the firm, which is separate from the decision of choosing investment projects. Dividend will be discussed thoroughly in a later chapter.f.Yes, the resale value is an important cash flow at the end of the life of a project. Yet, be careful with the resale value of plant and equipment. The price at which the firm sells the equipment is a cash inflow. If that price is different from the book value of the asset at the time of sale, tax consequence will arise. Remember that after an asset has been fully depreciated under current depreciation code, its book value is equal to zero. The difference between the book value and the sale price creates losses or gains which in turn create a tax credit or liability.g.Yes, salary and medical costs for production employees on leave are incremental cash flows of the project. The salaries of all personnel connected to the project must be included as costs of that project. Thus, the costs of employees who are on leave for a portion of the project life must be included as costs of that project.7.2 Your company currently produces and sells steel-shaft golf clubs. The Board of Directors wants you to look at introducing a new line of titanium bubble woods with graphite shaft. Which of the following costs are not relevant?I. Land you already own that will be used for the project and has a market value of $700,000.II. $300,000 drop in sales of steel-shaft clubs if titanium woods with graphite shaft are introduced.III. $200,000 spent on Research and Development last year on graphite shafts.a. I onlyb. II onlyc. III onlyd. I and III onlye. II and III only7.3 The Best Manufacturing Company is considering a new investment. Financial projections for the investment are tabulated below. (Cash flows are in $ thousands and the corporate tax rate is 34 percent.)Year 0 Year 1 Year 2 Year 3 Year 4Sales revenue 7,000 7,000 7,000 7,000Operating costs 2,000 2,000 2,000 2,000Investment 10,000Depreciation 2,500 2,500 2,500 2,500Net working capital 200 250 300 200 0(end of year)a. Compute the incremental net income of the investment.b. Compute the incremental cash flows of the investment.c. Suppose the appropriate discount rate is 12 percent. What is the NPV of the project?Solutions

Year 0 Year 1 Year 2 Year 3 Year 4(1) Sales revenue - $7,000 $7,000 $7,000 $7,000(2) Operating costs - 2,000 2,000 2,000 2,000(3) Depreciation - 2,500 2,500 2,500 2,500(4) Income before tax - 2,500 2,500 2,500 2,500(5) Taxes at 34% - 850 850 850 850(6) Net income 0 1,650 1,650 1,650 1,650(7) Cash flow from

operation [(1)-(2)-(5)]0 4,150 4,150 4,150 4,150

(8) Investment -10,000 - - - -(9) Changes in net working

capital-200 -50 -50 100 200

(10) Total cash flow from investment

-10,200 -50 -50 100 200

(11) Total cash flow -10,200 4,100 4,100 4,250 4,350a. Net income [from (6)]:

0 1,650 1,650 1,650 1,650b. Incremental cash flow [from (11)]:

-10,200 4,100 4,100 4,250 4,350c. NPV = -$10,200 + $4,100 / 1.12 + $4,100 / 1.122 + $4,250 / 1.123 + $4,350 / 1.124= $2,518.787.4 According to the February 7, 1983, issue of The Sporting News, the Kansas City Royals’designated hitter, Hal McRae, signed a three-year contract in January 1983 with the following provisions:• $400,000 signing bonus.• $250,000 salary per year for three years.• 10 years of deferred payments of $125,000 per year (these payments begin in year 4).• Several bonus provisions that total as much as $75,000 per year for the three years of the contract.Assume that McRae has a 60-percent probability of receiving the bonuses each year, and that he signed the contract on January 1, 1983. (Hint: Use the expected bonuses as incremental cash flows.) Assume an effective annual interest rate of 12.36 percent, and ignore taxes. McRae’s salary and bonus are paid at the end of the year. What was the present value of this contract in January when McRae signed it?SolutionsSince there is uncertainty surrounding the bonus payments, which McRae might receive, you must use the expected value of McRae’s salary in the computation of the PV of his contract. The expected value of McRae’s salary in years one through three is

$250,000 + 0.6 $75,000 + 0.4 $0 = $295,000.PV = $400,000 + $295,000 [(1 - 1 / 1.12363) / 0.1236]+ {$125,000 / 1.12363} [(1 - 1 / 1.123610 / 0.1236] = $1,594,825.68

7.5 Benson Enterprises, Inc., is evaluating alternative uses for a three-story manufacturing and warehousing building that it has purchased for $225,000. The company could continue to rent the building to the present occupants for $12,000 per year. The present occupants have indicated an interest in staying in the building for at least another 15 years. Alternatively, the company could modify the existing structure to use for its own manufacturing and warehousing needs. Benson’s production engineer feels the building could be adapted to handle one of two new product lines. The cost and revenue data for the two product alternatives follow.Product A Product BInitial cash outlay for building modifications $ 36,000 $ 54,000Initial cash outlay for equipment 144,000 162,000Annual pretax cash revenues (generated for 15 years) 105,000 127,500Annual pretax cash expenditures (generated for 15 years) 60,000 75,000The building will be used for only 15 years for either product A or product B. After 15 years, the building will be too small for efficient production of either product line. At that time, Benson plans to rent the building to firms similar to the current occupants. To rent the building again, Benson will need to restore the building to its present layout. The estimated cash cost of restoring the building if product A has been undertaken is $3,750; if product B has been produced, the cash cost will be $28,125. These cash costs can be deducted for tax purposes in the year the expenditures occur.Benson will depreciate the original building shell (purchased for $225,000) over a 30-year life to zero, regardless of which alternative it chooses. The building modifications and equipment purchases for either product are estimated to have a 15-year life; also, they can and will be depreciated on a straight-line basis. The firm’s tax rate is 34 percent, and its required rate of return on such investments is 12 percent.For simplicity, assume all cash flows for a given year occur at the end of the year. The initial outlays for modifications and equipment will occur at t _ 0, and the restoration outlays will occur at the end of year 15. Also, Benson has other profitable ongoing operations that are sufficient to cover any losses.Which use of the building would you recommend to management?SolutionsTo evaluate Benson’s alternatives, compute the after-tax net cash flows (A/T-NCF). First, note that the building left and depreciation are not incremental and should not be included in the analysis of these two alternatives.

Product A: t = 0 t = 1 - 14 t = 15Revenues $105,000 $105,000

-Foregone rent 12,000 12,000-Expenditures 60,000 63,750 **-Depreciation* 12,000 12,000Earnings before taxes $21,000 $17,250-Taxes (34%) 7,140 5,865Net income $13,860 $11,385+Depreciation 12,000 12,000Capital investment -$180,000A/T-NCF -$180,000 $25,860 $23,385

*Depreciation = ($144,000 + $36,000) / 15 = $12,000**Cash expenditures + Restoration costs

NPVA = -$180,000 + $25,860 14

12.0 + $23,385 / 1.1215

= -$180,000 + $25,860 (6.6282) + $23,385 / 1.1215= -$4,322.40

The cash flows in year 1 - 14 could have been computed using the simplification demonstrated in the text.A/T-NCF = Revenue (1 - T) - Expenses (1 - T) + Depreciation (T)= $105,000 (0.66) - $72,000 (0.66) + $12,000 (0.34)= $25,860The cash flows for the final year could have been computed by adjusting for the after-tax value of the restoration costs.

$25,860 - $3,750 (0.66) = $23,385

Product B: t = 0 t = 1 - 14 t = 15Revenues $127,500 $127,500-Foregone rent 12,000 12,000-Expenditures 75,000 103,125 **-Depreciation* 14,400 14,400Earnings before taxes $26,100 -$2,025-Taxes (34%) 8,874 -689Net income $17,226 -$1,336+Depreciation 14,400 14,400Capital investment -$216,000A/T-NCF -$216,000 $31,626 $13,064

*Depreciation = ($162,000 + $54,000) / 15 = $14,400**Cash expenditures + Restoration costs

NPVB = -$216,000 + $31,626 14

12.0 + $13,064 / 1.1215

= -$216,000 + $31,626 (6.6282) + $13,064 / 1.1215 = -$3,989.80

The cash flows in year 1 - 14 could have been computed using the simplification demonstrated the text. A/T-NCF = Revenue (1 - T) - Expenses (1 - T) + Depreciation (T)

= $127,500 (0.66) - $87,000 (0.66) + $14,400 (0.34)= $31,626

The cash flows for the final year could have been computed by adjusting for the after-tax value of the restoration costs.

$31,626 - $28,125 (0.66) = $13,064

Benson should continue to rent the building.

7.6 Samsung International has rice fields in California that are expected to produce average annual profits of $800,000 in real terms forever. Samsung has no depreciable assets and is an all-equity firm with 200,000 shares outstanding. The appropriate discount rate for its stock is 12 percent. Samsung has an investment opportunity with a gross present value of $1 million. The investment requires a $400,000 outlay now.

Samsung has no other investment opportunities. Assume that all cash flows are received at the end of each year. What is the price per share of Samsung?SolutionsEPS = $800,000 / 200,000 = $4

NPVGO = (-$400,000 + $1,000,000) / 200,000 = $3Price = EPS / r + NPVGO

= $4 / 0.12 + $3=$36.33

7.7 Dickinson Brothers, Inc., is considering investing in a machine to produce computer keyboards. The price of the machine will be $400,000 and its economic life five years. The machine will be fully depreciated by the straight-line method. The machine will produce 10,000 units of keyboards each year. The price of the keyboard will be $40 in the first year, and it will increase at 5 percent per year. The production cost per unit of the keyboard will be $20 in the first year, and it will increase at 10 percent per year. The corporate tax rate for the company is 34 percent. If the appropriate discount rate is 15 percent, what is the NPV of the investment?Solutions

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5Sales revenue $400,000 $420,000 $441,000 $463,050 $486,200Operating costs 200,000 220,000 242,000 266,200 292,820Depreciation 80,000 80,000 80,000 80,000 80,000Income before tax 120,000 120,000 119,000 116,850 113,380Taxes at 34% 40,800 40,800 40,460 39,729 38,549Net income 79,200 79,200 78,540 77,121 74,831Cash flow from operation (Sales Revenue – Operating Costs – Taxes)

159,200 159,200 158,540 157,121 154,831

Investment -$400,000NPV = -$400,000+ $159,200 / 1.15 + $159,200 / 1.152 + $158,540 / 1.153

+ $157,121 / 1.154 + $154,831 / 1.155= $129,868.29

7.8 Scott Investors, Inc., is considering the purchase of a $500,000 computer that has an economic life of five years. The computer will be depreciated based on the system enacted by the Tax Reform Act of 1986. (See Table 7.3 for the depreciation schedules.) The market value of the computer will be $100,000 in five years. The use of the computer will save five office employees whose annual salaries are $120,000. It also contributes to lower net working capital by $100,000 when they buy the computer. The net working capital will be recovered at the end of the period. The corporate tax rate is 34 percent. Is it worthwhile to buy the computer if the appropriate discount rate is 12 percent?Solutions

Year 0 Year 1 Year 2 Year 3 Year 4 Year 51. Annual Salary Savings $120,000 $120,000 $120,000 $120,000 $120,0002. Depreciation 100,000 160,000 96,000 57,600 57,6003. Taxable Income 20,000 -40,000 24,000 62,400 62,4004. Taxes 6,800 -13,600 8,160 21,216 21,2165. Operating Cash Flow

(line 1-4)113,200 133,600 111,840 98,784 98,784

6. Net working capital $100,000 -100,0007. Investment $500,000 75,792*8. Total Cash Flow -$400,000 $113,200 $133,600 $111,840 $98,784 $74,576

*75,792 = $100,000 - 0.34 ($100,000 - $28,800)NPV = -$400,000+ $113,200 / 1.12 + $133,600 / 1.122 + $111,840 / 1.123

+ $98,784 / 1.124 + $74,576 / 1.125= -$7,722.52

7.9 The Gap is considering buying an on-line cash register software from IBM so that it can effectively deal with its retail sales. The software package costs $750,000 and will be depreciated down to zero using the straight-line method over its five-year economic life. The marketing department predicts that sales will be $600,000 per year for the next three years, after which the market will cease to exist. Cost of goods sold and operating expenses are predicted to be 25 percent of sales. After three years the software can be sold for $40,000. The Gap also needs to add net working capital of $25,000 immediately. This additional net working capital will be recovered in full at the end of the project life. The corporate tax rate for Gap is 35 percent and the required rate of return on it is 17 percent. What is the NPV of the new software?Solutions

t = 0 t = 1- 2 t = 3 Revenues $600,000 $600,000- Expenses 150,000 150,000- Depreciation 150,000 150,000 Earnings Before Taxes $300,000 $300,000- Taxes (35%) 105,000 105,000 Net Income $195,000 $195,000+ Depreciation 150,000 150,000 Capital Investment - $750,000 + $40,000 Working Capital - 25,000 + $25,000 Capital Loss - $260,000 A / T - NCF - $775,000 $345,000 $150,000

The capital loss reflects $300,000 in book value of the asset less the sale of $ 40,000.The cash flows in year 1-2 could have been calculated byA/T - NCF = Revenue (1 - T) - Expenses (1 - T) + Depreciation (0.35)

= $600,000 (0.65) - $150,000 (0.65) + $150,000(0.35)= $345,000

NPV = - $775,000 + $345,000 2

17.0 + $150,000 / (1.17) 3

= - $134.445.457.10 Etonic Inc. is considering an investment of $250,000 in an asset with an economic life of five years. The firm estimates that the nominal annual cash revenues and expenses will be $200,000 and $50,000, respectively. Both revenues and expenses are expected to grow at 3 percent per year as that of the expected annual inflation. Etonic will use straight-line method to depreciate its asset to zero over the economic life. The salvage value of the asset is estimated to be $30,000 in nominal terms at the end of five years. The one-time NWC investment of $10,000 is required immediately. Further, the nominal discount rate for all cash flows is 15 percent. All corporate cash flows are subject to a 35 percent tax rate. All cash flows, except the initial investment and the NWC, occur at the end of the year. What is the project’s total nominal cash flow from assets in year 5?SolutionsA / T – NCF = $200,000 (1.03)5 (1 - 0.35) - $50,000 (1.03)5 (1 – 0.35) + $50,000 (0.35) +$30,000 (1 - 0.35) + $10,000 = $184,032.7

7.11 Commercial Real Estate, Inc., is considering the purchase of a $4 million building to lease. The economic life of the building will be 20 years. Assume that the building will be fully depreciated by the straight-line method and its market value in 20 years will be zero. The company expects that annual lease payments will increase at 3 percent per year. The appropriate discount rate for cash flows of lease payments is 13 percent, while the discount rate for depreciation is 9 percent. The corporate tax rate is 34 percent. What is the least Commercial Real Estate should ask for the first-year lease? Assume that the annual lease payment starts right after the signature of the lease contract.SolutionsThis is an annuity due (or annuity in advance) problem.PV of lease revenue after tax

= 0.66 L [1 / (0.13 - 0.03) - {1 / (0.13 - 0.03)} (1.03 / 1.13) 20](1.13)= 6.28904 LWhere L = the first year lease payment.

PV of depreciation tax shield for annual depreciation of $200,000= 0.34 $200,000 20

09.0 = $620,741.11

Solve the equation: NPV = -$4,000,000 + 6.28904 L + $620,741.11 = 0 L = $537,325.08

7.12 Royal Dutch Petroleum is considering going into a new project, which is typical for the firm. A capital tool required for the project costs $2 million. The marketing department predicts that sales will be $1.2 million per year for the next four years, after which the market will cease to exist. The tool, a five-year class capital tool, will be depreciated down to zero using the straight-line method. Cost of goods sold and operating expenses are predicted to be 25 percent of sales. After four years the tool can be sold for $150,000. Royal Dutch also needs to add net working capital of $100,000 immediately. This additional capital will be received in full at the end of the project life. The tax rate for Royal Dutch is 35 percent. The required rate of return on Royal Dutch is 16.55 percent.Solutions t = 0 t = 1 – 3 t = 4

Revenues $1,200,000 $1,200,000 - Expenses 300,000 300,000 - Depreciation 400,000 400,000 Earnings Before Taxes $500,000 $500,000 - Taxes (35%) 175,000 175,000 Net Income $325,000 $325,000 + Depreciation 400,000 400,000 Capital Investment - $2,000,000 +$150,000 NWC - 100,000 +$100,000 Capital Loss - $250,000 A / T – NCF -$2,100,000 $725,000 $725,000

NPV = - $2,100,000 + $725,000 4

1655.0 = - $93,391

Capital Budgeting with Inflation7.13 Consider the following cash flows on two mutually exclusive projects.Year Project A Project B0 _$40,000 _$50,0001 20,000 10,0002 15,000 20,0003 15,000 40,000Cash flows of project A are expressed in real terms while those of project B are expressed in nominal terms. The appropriate nominal discount rate is 15 percent, and the inflation is 4 percent. Which project should you choose?SolutionsReal interest rate = (1.15 / 1.04) - 1 = 10.58%NPVA = -$40,000+ $20,000 / 1.1058 + $15,000 / 1.10582 + $15,000 / 1.10583= $1,446.76NPVB = -$50,000+ $10,000 / 1.15 + $20,000 / 1.152 + $40,000 / 1.153= $119.17Choose project A.7.14 Sanders Enterprises, Inc., has been considering the purchase of a new manufacturing facility for $120,000. The facility is to be depreciated on a seven-year basis. It is expected to have no value after seven years. Operating revenues from the facility are expected to be $50,000 in the first year. The revenues are expected to increase at the inflation rate of 5 percent. Production costs in the first year are $20,000, and they are expected to increase at 7 percent per year. The real discount rate for risky cash flows is 14 percent, while the nominal riskless interest rate is 10 percent. The corporate tax rate is 34 percent. Should the company accept the suggestion?Solutions

After-tax revenues

= {$50,000 (1 - 0.34) / 1.05} 7

14.0 = $31,428.57

714.0

= $134,775.29

Assume production costs grow at a nominal rate of 7% a year, the real growth rate of the production costs = [(1 + 7%) / (1 + 5%)] - 1 = 1.905%

After-tax expenses= -{$20,000 (1 - 0.34) / 1.05} {1 / (0.14 - 0.01905)} [1 - (1.01905 / 1.14)7]= -$56,535.24Depreciation tax shield [from table 7.5]= $120,000 0.34 0.7214= $29,433.12NPV = -$120,000 + $134,775.29 - $56,535.24 + $29,433.12= -$12,326.83Do not accept the suggestion.

7.15 Phillips Industries runs a small manufacturing operation. For this year, it expects to have real net cash flows of $120,000. Phillips is an ongoing operation, but it expects competitive pressures to erode its (inflation-adjusted) net cash flows at 6 percent per year. The appropriate real discount rate for Phillips is 11 percent. All net cash flows are received at year-end. What is the present value of the net cash flows from Phillips’s operations?SolutionsPV = $120,000 / {0.11 - (-0.06)} = $705,882.357.16 Harry Gultekin, a small restaurant owner/manager, is contemplating the purchase of a larger restaurant from its owner who is retiring. Gultekin would finance the purchase by selling his existing small restaurant, taking a second mortgage on his house, selling the stocks and bonds that he owns, and, if necessary, taking out a bank loan. Because Gultekin would have almost all of his wealth in the restaurant, he wants a careful analysis of how much he should be willing to pay for the business. The present owner of the larger restaurant has supplied the following information about the restaurant from the past five years.Year Gross Revenue Profit_5 $875,000 $ 62,000_4 883,000 28,000_3 828,000 4,400_2 931,000 96,000Last 998,000 103,000As with many small businesses, the larger restaurant is structured as a Subchapter S corporation. This structure gives the owner the advantage of limited liability, but the pretax profits flow directly through to the owner, without any corporate tax deducted. The preceding figures have not been adjusted for changes in the price level. There is general agreement that the average profits for the past five years are representative of what can be expected in the future, after adjusting for inflation.Gultekin is of the opinion that he could earn at least $3,000 in current dollars per month as a hired manager. Gultekin feels he should subtract this amount from profits when analyzing the venture. Furthermore, he is aware of statistics showing that for restaurants of this size, approximately 6 percent of owners go out of business each year.Gultekin has done some preliminary work to value the business. His analysis is as follows:Price-Level Profits Imputed Managerial NetYear Profits Factor (current dollars) Wage Profits_5 $ 62,000 1.28 $ 79,400 $36,000 $ 43,400_4 28,000 1.18 33,000 36,000 _3,000_3 4,400 1.09 4,800 36,000 _31,200_2 96,000 1.04 99,800 36,000 63,800Last 103,000 1.00 103,000 36,000 67,000The average profits for the past five years, expressed in current dollars, are $28,000. Using this average profit figure, Gultekin produced the following figures. These figures are in current dollars.Expected Profits Risk- Realif Business Probability Adjusted Discount Present

Year Continues of Cont.* Profits Factor 2% ValueNext $28,000 1.000 $28,000 0.980 $27,400_2 28,000 0.940 26,300 0.961 25,300_3 28,000 0.884 24,700 0.942 23,300_4 28,000 0.831 23,300 0.924 21,500. . . . . .. . . . . .. . . . . .*Probability of the business continuing. The probability of failing in any year is 6 percent. That probability compounds over the years.Based on these calculations, Gultekin has calculated that the value of the restaurant is $350,000.a. Assume that there is indeed a 6 percent per year probability of going out of business.Do you agree with Gultekin’s assessment of the restaurant? In your answer, consider his treatment of inflation, his deduction of the managerial wage of $3,000 per month, and the manner in which he assessed risk.b. What present value would you place on the revenue stream; in other words, how much would you advise Gultekin that he should be willing to pay for the restaurant?7.16 a. The only mistake that Gultekin made was to discount at the risk-free rate of interest. The bankruptcy risk adjustment to the cash flows was correct, but these should have been discounted by a risk-adjusted rate. Given that Gultekin’s portfolio is un-diversified (all of his money would be in the restaurant), he should have used a higher discount rate. The deduction of the managerial wage was appropriate since the opportunity to earn that amount elsewhere is Gultekin’s opportunity cost of working in the restaurant.b. You should have chosen a higher discount rate and recomputed the value of the restaurant. For example, with a discount rate of 10%, the value is $28,000 / [0.10 - (-0.06)] = $175,000. Notice that the restaurant’s cash flows form a growing (actually declining) perpetuity.7.17 The Biological Insect Control Corporation (BICC) has hired you as a consultant to evaluate the NPV of their proposed toad ranch. BICC plans to breed toads and sell them as ecologically desirable insect-control mechanisms. They anticipate that the business will continue in perpetuity. Following negligible start-up costs, BICC will incur the following nominal cash flows at the end of the year.Revenues $150,000Labor costs 80,000Other costs 40,000The company will lease machinery from a firm for $20,000 per year. (The lease payment starts at the end of year 1.) The payments of the lease are fixed in nominal terms. Sales will increase at 5 percent per year in real terms. Labor costs will increase at 3 percent per year in real terms. Other costs will decrease at 1 percent per year in real terms. The rate of inflation is expected to be 6 percent per year. The real rate of discount for revenues and costs is 10 percent. The lease payments are risk-free; therefore, they must be discounted at the risk-free rate. The real risk-free rate is 7 percent. There are no taxes. All cash flows occur at year-end. What is the NPV of BICC’s proposed toad ranch today?SolutionsThe simplest approach to this problem is to discount the real cash flows. Since the revenues and costs are growing perpetuities, the formula for computing the PV of such a stream can be used. The first year amounts of the revenues and costs are stated in nominal terms. Since the growth rate and discount rate are real rates, adjust the initial amounts. For revenues, labor costs and the other costs, those amounts are $150,000 / 1.06, $80,000 / 1.06 and $40,000 / 1.06, respectively.

PV (revenue) = ($150,000 / 1.06) / (0.10 - 0.05) = $2,830,189PV (labor costs) = ($80,000 / 1.06) / (0.10 - 0.03) = $1,078,167PV (other costs) = ($40,000 / 1.06) / {0.10 - (-0.01)} = $343,053

The lease payment is given in nominal terms and it should be discounted by the nominal rate which is 0.1342 [= (1.07 1.06) - 1]. Thus, the present value of the lease payments is $20,000 / 0.1342 = $149,031. The lease payments are constant in nominal terms, but not in real terms. This can be seen that by computing the real value of the first few lease payments.

Year Nominal Real

1 $20,000 $20,000 / 1.06 = $18,8682 $20,000 $20,000 / 1.062 = $17,8003 $20,000 $20,000 / 1.063 = $16,792

The real payments form a declining perpetuity. You can apply the growing perpetuity formula to compute their PV in real terms, but be careful about which growth rate you use. The growth rate is not 6% as the inflation rate would imply. The growth rate is (1 / 1.06) - 1 = -0.0566. Using this growth rate, the PV of the real lease payments is $18,868 / [0.07 - (-0.0566)] = $149,036. You can use either method for computing the PV of the lease payments, but you are wise to use whichever method is easiest and most straight-forward. In this case, it would be easy to use the wrong growth rate or the wrong initial cash flow in the calculation of the real nominal flows. Note, both methods must give you the same amount in PV terms. (The difference in this case is due to rounding.) To find the NPV of BICC’s toad ranch, add the present values of the revenues and the costs. Recall, the start-up costs are negligible.NPV = $2,830,189 - $1,078,167 - $343,053 - $149,031= $1,259,938.7.18 Sony International has an investment opportunity to produce a new stereo color TV. The required investment on January 1 of this year is $32 million. The firm will depreciate the investment to zero using the straight-line method. The firm is in the 34-percent tax bracket. The price of the product on January 1 will be $400 per unit. That price will stay constant in real terms. Labor costs will be $15 per hour on January 1. They will increase at 2 percent per year in real terms. Energy costs will be $5 per physical unit on January 1; they will increase at 3 percent per year in real terms. The inflation rate is 5 percent. Revenues are received and costs are paid at year-end.Year 1 Year 2 Year 3 Year 4Physical production, in units 100,000 200,000 200,000 150,000Labor input, in hours 2,000,000 2,000,000 2,000,000 2,000,000Energy input, physical units 200,000 200,000 200,000 200,000The riskless nominal discount rate is 4 percent. The real discount rate for costs andrevenues is 8 percent. Calculate the NPV of this project.Solutions

Year 1 Year 2 Year 3 Year 4Revenues 40,000,000 80,000,000 80,000,000 60,000,000 Labor Costs 30,600,000 31,212,000 31,836,240 32,472,965 Energy Costs 1,030,000 1,060,900 1,092,727 1,125,509(Revenues-Costs) 8,370,000 47,727,100 47,071,033 26,401,526After-tax (Revenues-Costs) 5,524,200 31,499,886 31,066,882 17,425,007

NPV = -$32,000,000 + ($5,524,200/1.08 + $31,499,886/1.082 + $31,066,882/1.083

+ $17,425,007/1.084) + $8,000,000(34%)4

04.0= $43,464,183

where $8,000,000 is the amount of depreciation each year.7.19 Sparkling Water, Inc., sells 2 million bottles of drinking water each year. Each bottle sells at $2.5 in real terms and costs per bottle are $0.7 in real terms. Sales income and costs occur at year-end. Sales income is expected to rise at a real rate of 7 percent annually, while real costs are expected to rise at 5 percent annually. The relevant, real discount rate is 10 percent. The corporate tax rate is 34 percent. What is Sparkling worth today?SolutionsInitial revenues = $2.5 2,000,000= $5,000,000Initial expenses = $0.7 2,000,000= $1,400,000PV after tax = $5,000,000 (1 - 0.34) / (0.10 - 0.07) - $1,400,000 (1 - 0.34) / (0.10 - 0.05)= $110,000,000 - $18,480,000= $91,520,0007.20 International Buckeyes is building a factory that can make 1 million buckeyes a year for five years. The factory costs $6 million. In year 1, each buckeye will sell for $3.15 in nominal terms. The price will rise 5 percent each year in real terms. During the first year variable costs will be $0.2625 per buckeye in nominal terms and will rise by 2 percent each year in real terms. International Buckeyes will depreciate the value of the factory to zero over the five years by use of the straight-line method. International Buckeyes expects to be able to sell the factory for $638,140.78 at the end of year 5 (or $500,000 in real terms). The

nominal discount rate for risky cash flows is 20 percent. The nominal discount rate for riskless cash flows is 11 percent. The rate of inflation is 5 percent. Cash flows, except the initial investment, occur at the end of the year. The corporate tax rate is 34 percent; capital gains are also taxed at 34 percent. What is the net present value of this project?SolutionsThe analysis of the NPV of this project is most easily accomplished by separating the depreciation costs from the project’s other cash flows. Those costs should be discounted at a riskless rate. The riskless nominal rate is given. The revenues and variable costs are given in nominal terms, but their growth rates are real growth rates. Hence, they are most easily discounted using the real rate for risky cash flows. Remember that you can use different types of discount rates (real vs. nominal) in a problem as long as you are careful to discount real cash flows with the real rate and nominal cash flows with the nominal rate.First, determine the net income from the revenues and expenses not including depreciation.Note that the nominal price of a buckeye during the first year was $3.15. The inflation rate during the period was 5%. Therefore, the real price of a buckeye was $3.00 [= 3.15 / 1.05]. Similarly, the nominal variable cost for a buckeye was $0.2625; the real variable cost is $0.25 [= $0.2625 / 1.05].

t = 1 t = 2 t = 3 t = 4 t = 5Revenue $3,000,000 $3,150,000 $3,307,500 $3,472,875 $3,646,519- Variable cost 250,000 255,000 260,100 265,302 270,608Pre-tax earnings 2,750,000 2,895,000 3,047,400 3,207,573 3,375,911- Taxes (34%) 935,000 984,300 1,036,116 1,090,575 1,147,810Net income 1,815,000 1,910,700 2,011,284 2,116,998 2,228,101After-tax sale* 330,000

1,815,000 1,910,700 2,011,284 2,116,998 2,558,101

*After-tax proceeds = $500,000 0.66= $330,000Since these cash flows are in real terms, you must use the real discount rate to find the PV of the

flows.Real discount rate = 1.20 / 1.05 - 1 = 0.1429 = 14.29%The PV of the annual net incomes using the real discount rate of 14.29% is $6,950,673. (Note: Although the actual real discount rule is 14.2857143..., we round to 14.29 to computational conventional.)The NPV of the project is the present value of the net income in each year plus the present value of the depreciation tax shield.The depreciation per year: $6,000,000 / 5 = $1,200,000The depreciation tax shield per year: $1,200,000 0.34 = $408,000Again, the depreciation tax shield is in nominal terms, so discount it using the nominal riskless rate.

NPV = -$6,000,000 + $6,950,673 + $408,000 5

11.0= $2,458,600

7.21 Majestic Mining Company (MMC) is negotiating for the purchase of a new piece of equipment for their current operations. MMC wants to know the maximum price that it should be willing to pay for the equipment. That is, how high must the price be for the equipment to have an NPV of zero? You are given the following facts:a. The new equipment would replace existing equipment that has a current market value of $20,000.b. The new equipment would not affect revenues, but before-tax operating costs would be reduced by $10,000 per year for eight years. These savings in cost would occur at year-end.c. The old equipment is now five years old. It is expected to last for another eight years, and it is expected to have no resale value at the end of those eight years. It was purchased for $40,000 and is being depreciated to zero on a straight-line basis over 10 years.d. The new equipment will be depreciated to zero using straight-line depreciation over five years. MMC expects to be able to sell the equipment for $5,000 at the end of eight years. The proceeds from this sale would be subject to taxes at the ordinary corporate income tax rate of 34 percent.e. MMC has profitable ongoing operations.f. The appropriate discount rate is 8 percent.Solutions

Let I be the maximum price the Majestic Mining Company should be willing to pay for the equipment. Examine the incremental cash flows from purchasing the new equipment.

Incremental C0:Cost of the new equipment -ISale of the old equipment $20,000Tax effect of the sale* 0Total $20,000 - I

*Tax savings = T (Book value - Sale price)= 0.34 ($20,000 - $20,000)= $0

Book value = Cost - Accumulated depreciation= $40,000 - 5($40,000 / 10)= $20,000

Incremental C1 - C5 :After-tax savings: $10,000 0.66 = $6,600Depreciation tax shield: [I / 5 - $4,000] 0.34Incremental C6 - C8 :After-tax savings: $10,000 0.66 = $6,600Depreciation tax shield*: $0*At the end of year five, both pieces of equipment have been fully depreciated. Thus, Majestic Mining will no longer get a depreciation tax shield.Additional cash flows in t = 8:

Sale of equipment $5,000Tax effect* -1,700Total $3,300*Tax savings = T (Book value - Sale price)

= 0.34 ($0 - $5,000)= -$1,700

Book value: Since the equipment was depreciated to a zero value over five years, its book value is zero at the end of year eight.

NPV = -I + $20,000 + $6,600 8

08.0

+ [I / 5 - $4,000] (0.34) 5

08.0 + $3,300 / 1.088

= -I + $20,000 + $6,600 (5.7466) + [I / 5 - $4,000] (0.34) (3.9927) + $3,300 / 1.088= $0

0.7285 I = $54,280.3753I = $74,510

7.22 After extensive medical and marketing research, Pill, Inc., believes it can penetrate the pain reliever market. It can follow one of two strategies. The first is to manufacture a medication aimed at relieving headache pain. The second strategy is to make a pill designed to relieve headache and arthritis pain. Both products would be introduced at a price of $4 per package in real terms. The broader remedy would probably sell 10 million packages a year. This is twice the sales rate for the headache-only medication. Cash costs of production in the first year are expected to be $1.50 per package in real terms for the headache-only brand.Production costs are expected to be $1.70 in real terms for the more general pill. All prices and costs are expected to rise at the general inflation rate of 5 percent.Either strategy would require further investment in plant. The headache-only pill could be produced using equipment that would cost $10.2 million, last three years, and have no resale value. The machinery required to produce the broader remedy would cost $12 million and last three years. At this time the firm would be able to sell it for $1 million (in real terms). The production machinery would need to be replaced every three years, at constant real costs.Suppose that for both projects the firm will use straight-line depreciation. The firm faces a corporate tax rate of 34 percent. The firm believes the appropriate real discount rate is 13 percent. Capital gains are taxed at the ordinary corporate tax rate of 34 percent.Which pain reliever should the firm produce?

SolutionsHeadache onlyAfter-tax operating income= [($4 5,000,000) - ($1.50 5,000,000)] (1 - 0.34)= $8,250,000

Depreciation tax shield t = 1 t = 2 t = 3Nominal depreciation $3,400,000 $3,400,000 $3,400,000Real depreciation 3,238,095 3,083,900 2,937,048Tax shields (Real) 1,100,952 1,048,526 998,596

NPV = -$10,200,000 + $8,250,000 3

13.0 + $1,100,952 / 1.13

+ $1,048,526 / 1.132 + $998,596 / 1.133= $11,767,030Headache and ArthritisAfter-tax operating income= [($4 10,000,000) - ($1.70 10,000,000)] (1 - 0.34)= $15,180,000

Depreciation tax shield t = 1 t = 2 t = 3Nominal depreciation $4,000,000 $4,000,000 $4,000,000Real depreciation 3,809,524 3,628,118 3,455,350Tax shields (Real) 1,295,238 1,233,560 1,174,819

After-tax cash flow from sale of machinery = $1,000,000 (1-.34) = $660,000.

NPV = -$12,000,000 + $15,180,000 3

13.0 + $1,295,238 / 1.13

+ $1,233,560 / 1.132 + $1,174,819 / 1.133 + $660,000 / 1.133 = $27,226,204The firm should choose to manufacture Headache and Arthritis.7.23 A machine that lasts four years has the following net cash outflows. $12,000 is the cost of purchasing the machine, and $6,000 is the annual year-end operating cost. At the end of four years, the machine is sold for $2,000; thus, the cash flow at year 4, C4, is only $4,000.C0 C1 C2 C3 C4$12,000 $6,000 $6,000 $6,000 $4,000The cost of capital is 6 percent. What is the present value of the costs of operating a series of such machines in perpetuity?SolutionsAssume the tax rate is zero.

t = 0 t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 ...$12,000 $6,000 $6,000 $6,000 $4,000

$12,000 $6,000 $6,000 ...The present value of one cycle is:

PV = $12,000 + $6,000 3

06.0 + $4,000 / 1.064

= $12,000 + $6,000 (2.6730) + $4,000 / 1.064= $31,206.37The cycle is four years long, so use a four year annuity factor to compute the equivalent annual cost (EAC).

EAC = $31,206.37 / 4

06.0

= $31,206.37 / 3.4651= $9,006The present value of such a stream in perpetuity is$9,006 / 0.06 = $150,1007.24 A machine costs $60,000 and requires $5,000 maintenance for each year of its three-year life. After three years, this machine will be replaced. Assume a tax rate of 34 percent and a discount rate of 14 percent. If the machine is depreciated with a three-year straight-line without a salvage value, what is the equivalent annual cost (EAC)?Solutions PV of cash outflows

PV = $60,000 + (1 - 0.34) $5,000 3

14.0 - (0.34) $20,000

314.0

= $51,874.29

= EAC (3

14.0)

EAC = $22,343.89

7.25 United Healthcare, Inc. needs a new admitting system, which costs $60,000 and requires $2,000 in maintenance for each year of its five-year life. The system will be depreciated straight-line down to zero without salvage value at the end of five years. Assume a tax rate of 35 percent and an annual discount rate of 18 percent. What is the equivalent annual cost of this admitting system?SolutionsPV of cash outflows

PV = $60,000 + (1 - 0.35) $2,000 5

18.0 - (0.35) $12,000

518.0

= $50,931.20= EAC (5

18.0)

EAC= $16,286.677.26 Aviara Golf Academy is evaluating different golf practice equipment. The “easy as pie”equipment costs $45,000, has a three-year life, and costs $5,000 per year to operate. The relevant discount rate is 12 percent. Assume that the straight-line depreciation down to zero is used. Furthermore, it has a salvage value of $10,000. The relevant tax rate is 34 percent. What is the EAC of this equipment?Solutions PV of cash outflows

PV = $45,000 + (1 - 0.34) $5,000 3

12.0 - (0.34) $15,000

312.0

- $10,000 / (1.12) 3 = $22,030.11

= EAC (3

12.0)

EAC = $9,172.22Replacement with Unequal Lives7.27 Office Automation, Inc., is obliged to choose between two copiers, XX40 or RH45. XX40 costs less than RH45, but its economic life is shorter. The costs and maintenance expenses of these two copiers are given as follows. These cash flows are expressed in real terms.Copier Year 0 Year 1 Year 2 Year 3 Year 4 Year 5XX40 $700 $100 $100 $100RH45 900 110 110 110 $110 $110The inflation rate is 5 percent and the nominal discount rate is 14 percent. Assume that revenues are the same regardless of the copier, and that whichever copier the company chooses, it will buy the model forever. Which copier should the company choose? Ignore taxes and depreciation.SolutionsReal discount rate = (1.14 / 1.05) - 1 = 8.57%PV of cash outflow from XX40= $700 + $100 / 1.0857 + $100 / 1.08572 + $100 / 1.08573= $955.08

= EAC 3

0857.0 = (2.55082) EAC

EAC = $374.42

PV of cash outflow from RH45= $900 + $110 / 1.0857 + $110 / 1.08572 + $110 / 1.08573

+ $110 / 1.08574 + $110 / 1.08575= $1,332.68

= EAC (5

0857.0) = (3.93344) EAC

EAC = $338.81Choose RH45.7.28 Fiber Glasses must choose between two kinds of facilities. Facility I costs $2.1 million and its economic life is seven years. The maintenance costs for facility I are $60,000 per year.

Facility II costs $2.8 million and it lasts 10 years. The annual maintenance costs for facility II are $100,000 per year. Both facilities are fully depreciated by the straight-line method. The facilities will have no values after their economic lives. The corporate tax rate is 34 percent. Revenues from the facilities are the same. The company is assumed to earn a sufficient amount of revenues to generate tax shields from depreciation. If the appropriate discount rate is 10 percent, which facility should Fiber Glasses choose?SolutionsFacility I

After-tax maintenance costs

= (1 - 0.34) $60,0007

10.0 = $192,789.39

Depreciation tax shield

= (0.34) $300,000 7

10.0 = $496,578.72

PV of cash outflow= $2,100,000 + $192,789.39 - $496,578.72= $1,796,210.67

= EAC (7

10.0)

EAC = $368,951.55

Facility IIAfter-tax maintenance costs

= (1 - 0.34) $100,000 10

10.0 = $405,541.43

Depreciation tax shield

= (0.34) $280,000 10

10.0 = $584,962.79

PV of cash outflow= $2,800,000 + $405,541.43 - $584,962.79= $2,620,578.64

= EAC (10

10.0)

EAC = $426,487.11

Choose facility I.7.29 Pilot Plus Pens is considering when to replace its old machine. The replacement costs $3 million now and requires maintenance costs of $500,000 at the end of each year during the economic life of five years. At the end of five years the new machine would have a salvage value of $500,000. It will be fully depreciated by the straight-line method. The corporate tax rate is 34 percent and the appropriate discount rate is 12 percent. Maintenance cost, salvage value, depreciation, and book value of the existing machine are given as follows.Book ValueYear Maintenance Salvage Depreciation (end of year)0 $ 400,000 $2,000,000 $200,000 $1,000,0001 1,500,000 1,200,000 200,000 800,0002 1,500,000 800,000 200,000 600,0003 2,000,000 600,000 200,000 400,0004 2,000,000 400,000 200,000 200,000The company is assumed to earn a sufficient amount of revenues to generate tax shields from depreciation. When should the company replace the machine?SolutionsNew Machine

PV of cash outflow

= $3,000,000 + (1 - 0.34) $500,000 5

12.0

- (0.34) $600,000 5

12.0 - $500,000 (1 - 0.34) / 1.125

= $3,266,950.94

= EAC (5

12.0) = (3.60478) EAC

EAC = $906,283.98

Old Machine(1) If replace in year 1.

Opportunity cost of selling (after-tax)= $2,000,000 - 0.34 ($2,000,000 - $1,000,000)= $1,660,000

After-tax maintenance cost (Present value)= $400,000 (1 - 0.34) / 1.12= $235,714.29

PV of salvage value after tax= {$1,200,000 - 0.34 ($1,200,000 - $800,000)} / 1.12= $950,000

PV of depreciation tax shield= 0.34 $200,000 / 1.12 = $60,714.29

Thus, PV of cash outflow= $1,660,000 + $235,714.29 - $950,000 - $60,714.29= $885,000

Thus, PV in year 1 = $991,200 > EAC of new machine.Replace right now.

* We can check whether PV of old machine in year 2 has still higher cash outflow than EAC of new machine.

(2) Year 2PV in year 1

= {$1,200,000 - 0.34 ($1,200,000 - $800,000)} + $1,500,000 (1 - 0.34) / 1.12 - {$800,000 - 0.34 ($800,000 - $600,000)} / 1.12 - 0.34 $200,000 / 1.12= $1,233,642.85

Thus, PV in year 2= $1,233,642.85 1.12= $1,381,680.00

Even much greater than the cost in (1).Replace right now.

7.30 Gold Star Industries is in need of computers. They have narrowed the choices to the SAL 5000 and the DET 1000. They would need 10 SALs. Each SAL costs $3,750 and requires $500 of maintenance each year. At the end of the computer’s eight-year life Gold Star expects to be able to sell each one for $500. On the other hand, Gold Star could buy eight DETs. DETs cost $5,250 each and each machine requires $700 of maintenance every year.They last for six years and have a resale value of $600 for each one. Whichever model Gold Star chooses, it will buy that model forever. Ignore tax effects, and assume that maintenance costs occur at year-end. Which model should they buy if the appropriate discount rate is 11 percent?Solutions10 SALs

PV = $3,750 10 + ($500 10) 8

11.0 - ($500 10) / 1.118

= $61,060.98

= EAC (8

11.0)

EAC = $11,865.43

8 DETs

PV = $5,250 8 + ($700 8) 6

11.0 - ($600 8) / 1.116

= $63,124.74

= EAC (6

11.0)

EAC = $14,921.21

Gold star should buy 10 SALs.7.31 BYO University is faced with the decision of which word processor to purchase for its typing pool. It can buy 10 Bang word processors which cost $8,000 each and have estimated annual, year-end maintenance costs of $2,000 per machine. The Bang word processors will be replaced at the end of year 4 and have no value at that time. Alternatively, BYO could buy 11 IOU word processors to accomplish the same work. The IOU word processors would need to be replaced after three years. They cost only $5,000 each, but annual, year-end maintenance costs will be $2,500 per machine. A reasonable forecast is that each IOU word processor will have a resale value of $500 at the end of three years.The university’s opportunity cost of funds for this type of investment is 14 percent.Because the university is a nonprofit institution, it does not pay taxes. It is anticipated that whichever manufacturer is chosen now will be the supplier of future machines. Would you recommend purchasing 10 Bang word processors or 11 IOU machines?SolutionsTo evaluate the word processors, compute their equivalent annual costs (EAC).Bang

PV(costs) = (10 $8,000) + (10 $2,000) 4

14.0 = $80,000 + $20,000 (2.9137) = $138,274

EAC = $138,274 / 2.9137= $47,456

IOU

PV(costs) = (11 $5,000) + (11 $2,500) 3

14.0- (11 $500) / 1.143 = $55,000 + $27,500 (2.3216) - $5,500 / 1.143 = $115,132

EAC = $115,132 / 2.3216= $49,592

BYO should purchase the Bang word processors.7.32 Station WJXT is considering the replacement of its old, fully depreciated sound mixer. Two new models are available. Mixer X has a cost of $400,000, a five-year expected life, and after-tax cash flow savings of $120,000 per year. Mixer Y has a cost of $600,000, an eight-year life, and after-tax cash flow savings of $130,000 per year. No new technological developments are expected. The cost of capital is 11 percent. Should WJXT replace the old mixer with X or Y?SolutionsMixer X

NPV = -$400,000 + $120,000 5

11.0= $43,507.64

EAC = $43,507.64 / 5

11.0 = $11,771.88

Mixer Y

NPV = -$600,000 + $130,000 8

11.0= $68,995.96

EAC = $68,995.96 / 8

11.0 = $13,407.37

Choose Mixer Y.7.33 Kaul Construction must choose between two pieces of equipment. Tamper A costs $600,000 and it will last five years. This tamper will require $110,000 of maintenance each year. Tamper B costs $750,000, but it will last seven years. Maintenance costs for Tamper B are $90,000 per year. Kaul incurs all maintenance costs at the end of the year.The appropriate discount rate for Kaul Construction is 12 percent.a. Which machine should Kaul purchase?b. What assumptions are you making in your analysis for part (a)?Solutionsa. Tamper A

PV = $600,000 + $110,000 5

12.0= $996,525.38

EAC = $996,525.38 / 5

12.0= $276,445.84

Tamper B

PV = $750,000 + $90,000 7

12.0= $1,160,738.09

EAC = $1,160,738.09 / 7

12.0= $254,338.30

Choose Tamper B.b. The two assumptions behind replacement chains are:1. The time horizon is long.2. Replacement at the end of each cycle is possible.7.34 Philben Pharmaceutics must decide when to replace its autoclave. Philben’s current autoclave will require increasing amounts of maintenance each year. The resale value of the equipment falls every year. The following table presents this data.Year Maintenance Costs Resale ValueToday $ 0 $9001 200 8502 275 7753 325 7004 450 6005 500 500Philben can purchase a new autoclave for $3,000. The new equipment will have an economic life of six years. At the end of each of those years, the equipment will require $20 of maintenance. Philben expects to be able to sell the machine for $1,200 at the end of six years. Assume that Philben will pay no taxes. The appropriate discount rate for this decision is 10 percent. When should Philben replace its current machine?SolutionsFirst compute the equivalent annual cost (EAC) of the new machine.

PV(costs) = $3,000 + $20 6

10.0 - $1,200 / 1.106

= $3,000 + $20 (4.3553) - $1,200 / 1.106= $2,410EAC = $2,410 / 4.3553= $553Compute the cost of keeping the old autoclave for an additional year. Those costs include the foregone resale value for the previous year and maintenance for the current year. The costs are reduced by the resale value at the end of the current year.PV of keeping the old autoclave through year one:PV = $900 + $200 / 1.10 - $850 / 1.10= $309

The value of these costs at the end of year one is:$309 1.10 = $340It is cheaper to operate the old autoclave than to purchase the new one.Cost at the end of year one of keeping the old autoclave through year two:PV = $850 + $275 / 1.10 - $775 / 1.10= $395The value of these costs at the end of year two is:$395 1.10 = $435It is cheaper to operate the old autoclave than to purchase the new one.Cost at the end of year two of keeping the old autoclave through year three:PV = $775 + $325 / 1.10 - $700 / 1.10= $434The value of these costs at the end of year three is:$434 1.10 = $477It is cheaper to operate the old autoclave than to purchase the new one.Cost at the end of year three of keeping the old autoclave through year four:PV = $700 + $450 / 1.10 - $600 / 1.10= $564The value of these costs at the end of year four is:$564 1.10 = $620It would be cheaper to purchase the new autoclave than to operate the old one in year four. Hence, Philben should purchase the new machine at the end of year three.To be certain that future costs of the old autoclave do not make it more economical to operate, you should compute the annual cost of each of the additional years.Cost at the end of year four of keeping the old autoclave through year five:PV = $600 + $500 / 1.10 - $500 / 1.10= $600The value of these costs at the end of year five is:$600 1.10 = $660The decision to replace after year three was correct.7.35 (Challenge) A firm considers an investment of $28,000,000 (purchase price) in new equipment to replace old equipment that has a book value of $12,000,000 (market value of $20,000,000). If the firm replaces the old equipment with the new equipment, it expects to save $17,500,000 in pretax cash flow (net savings) savings the first year and an additional 12 percent (more than the previous year) per year for each of the following three years (total of four years). The old equipment has a four-year remaining life, being written off on a straight-line depreciation basis with no expected salvage value. The new equipment willbe depreciated under the MACRS system (which uses a double-declining balance approach, the half-year convention in year 1, and the option to switch to straight-line when it is beneficial) using a three-year life. In addition, it is assumed that replacement of the old equipment with the new equipment would require an increase in working capital of $5,000,000, which would not be recovered until the end of the four-year investment. If the relevant tax rates is 40 percent, find:a. The net investment (time 0 cash flow).b. The after-tax cash flow for each period.c. The internal rate of return, the net present value, and the profitability index.Solutions

Net Present Value

$3i,968,128

IRR 80% 76.94%PI 2.97

New Equipment Old EquipmentNew Equip. Value 28,000,000 Book Value 12,000,000Useful Life 3 Market Value 20,000,000

Increase in Working Cap

5,000,000

Year Depreciation Balance Growth 12%1 9,333,333 18,666,6672 12,444,444 6,222,222 Dep./yr (old) 3,000,000 3 4,148,148 2,074,074 Tax Rate 40%4 2,074,074 0 Discount rate 10%

Half-year convention in first year; switch to straight in year 3

0 1 2 3 4Purchase New Equip. (28,000,000)Sell Old Equip. 20,000,000 Tax on Old Equip. (3,200,000)Change in W/C (5,000,000) 5,000,000

Pre-tax CF Savings 17,500,000 19,600,000 21,952,000 24,586,240 Depreciation (old) 3,000,000 3,000,000 3,000,000 3,000,000 Depreciation (new) (9,333,333) (12,444,444) (4,148,148) (2,074,074)

Taxable Income 11,166,667 10,155,556 20,803,852 25,512,166Taxes (4,466,667) (4,062,222) (8,321,541) (10,204,866) Net Income 6,700,000 6,093,333 12,482,311 15,307,300Depreciation Add-back 6,333,333 9,444,444 1,148,148 (925,926)

Cash Flow (after-tax) -16,200,000 13,033,333 15,537,778 13,630,459 19,381,374

Mini Case: Goodweek Tires, Inc.Assumptions

PP&E Investment 120,000,000 Useful life of PP&E Investment (years) 7 Salvage Value of PP&E Investment 60,000,000 Annual Depreciation Expense (7 year MACRS)

Ending BookYear MACRS % Depreciation Value1 14.29% 17,148,000 102,852,000 2 24.49% 29,388,000 73,464,000

3 17.49% 20,988,000 52,476,000 Last year of project 4 12.49% 14,988,000 37,488,000 5 8.93% 10,716,000 26,772,000 6 8.93% 10,716,000 16,056,000 7 8.93% 10,716,000 5,340,000 8 4.45% 5,340,000 0

SuperTread price/unit in OEM market (year 1) 36.00 SuperTread price/unit in Replacement market (year 1) 59.00 SuperTread cost/unit (year 1) 18.00

Year 1 marketing and admin costs 25,000,000 Annual inflation rate 3.25%Corporate Tax rate 40.00%

Beta (1/24/97 Valueline) 1.30Rf (30 year U.S. Treasury Bond) 5.50%Rm (S&P 500 30 year average) 13.50%Re (from CAPM) Re= Rf+ e[ RM - Rf ] = 0.055 + 1.3[ 0.135 - 0.055 ] = 15.90% 15.90%

Year 1 OEM Market for SuperTread (2 million new cars x 4 tires/car) 8,000,000 OEM Market growth 2.50%SuperTread share of OEM market 11.00%

Year 1 Replacement Market for SuperTread 14,000,000 Replacement Market growth 2.00%SuperTread share of Replacement market 8.00%

Year 0 1 2 3 4Sales

OEM Market Units 880,000 902,000 924,550 947,664 Price 36.00 37.53 39.13 40.79 Total OEM Market 31,680,000 33,852,060 36,173,042 38,653,156

Replacement Market Units 1,120,000 1,142,400 1,165,248 1,188,553 Price 59.00 61.51 64.12 66.85 Total Replacement Market 66,080,000 70,266,168 74,717,530 79,450,885

Total Sales 97,760,000 104,118,228 110,890,572 118,104,041

Variable Costs Units (OEM + Replacement) 2,000,000 2,044,400 2,089,798 2,136,217 Cost 18.00 18.77 19.56 20.39 Total Variable Costs 36,000,000 38,363,166 40,881,699 43,565,831

SG&A 25,000,000 25,812,500 26,651,406 27,517,577

Depreciation 17,148,000 29,388,000 20,988,000 14,988,000

EBIT 19,612,000 10,554,562 22,369,466 32,032,633

Interest 0 0 0 0 Tax (40%) 7,844,800 4,221,825 8,947,786 12,813,053

Net Income 11,767,200 6,332,737 13,421,680 19,219,580

EBIT + Dep - Taxes 28,915,200 35,720,737 34,409,680 34,207,580 Less: Change in NWC 11,000,000 3,664,000 953,734 1,015,852 (16,633,586)Less: Captial Spending 120,000,000 (50,995,200)CF from Assets: (131,000,000) 25,251,200 34,767,003 33,393,828 101,836,366

Discounted CF from Assets 21,787,058 25,882,152 21,449,437 56,437,679

Total Discounted CF from Assets 125,556,326 Less: Investment (131,000,000)Net Present Value $( 5,443,674)

Results

Payback 3.37 yearsDiscounted Payback >4 never pays backAAR 16.42%IRR 14.22%NPV $ (5,443,674)PI 0.96