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CHAPTER 8 CAPITAL BUDGETING DECISIONSPART II 81 Kinds of Capital Budgeting Merck can use the same techniques to some extent. Theoretically, it should evaluate all R&D projects as if they were ordinary capital expenditures. They are certainly capital expenditures in the sense that the company expects future returns from current expenditures. The problem is that estimates of returns for new projects are extremely speculative. As projects move toward fruition, estimates of returns become more solid and at some point DCF techniques make sense. But a company that thrives on new products, especially products with enormous R&D expenditures, must make the investments based on the best scientific judgment. The following continuum might be helpful in explaining the point | | Basic Applied P&E for New research research Development product Replacements As you move from left to right, estimates of returns, and of required investments, become less speculative. With the routine decisions to replace existing plant assets, DCF techniques shine. However, to the left of the spectrum, other factors become more important 82 Macroeconomic Events and Capital Budgeting Note to the Instructor: The questions posed by this problem are designed to encourage students to think about the interrelationships in the economy and the factors that can affect the attitudes and plans of a given industry or firm. The depth of the discussion will be affected by the students' backgrounds in economics and the instructor's inclination to encourage students to exercise their reasoning powers. We've provided a minimum in response to each question. The instructor may want to explore the trickledown effects of each factor. 1. Many industries will be affected by such a law. The law would reduce the investment spending of companies involved with gasolinerelated products, including (but not limited to) companies making gasoline engines. Manufacturers of electrical charging units would be more inclined to invest. Further, the law is likely to affect the inclination of a given company to invest in different kinds of projects. For example, an oil company would shift its interest from one type of project to another, being more inclined to invest in a project related to alternative uses of oil. 2. The demand for cotton would increase and for other fibers would decrease Companies involved in the processing of raw cotton would increase capital spending; those of companies using primarily cotton to produce other products would also increase. Companies using other fibers would reduce their spending. Companies producing cotton, including cotton farmers, will reduce their expected investments in production equipment. 3. Capital spending plans of domestic auto makers would probably increase. Prices of substitute products (foreign autos) are likely to rise unless foreign manufacturers are willing to bear the increased cost. Domestic autos would become relatively lowerpriced, which would increase demand. Of course. a tariff could prompt domestic makers to increase their prices and try to maintain unit volume at previous levels. Thus, we cannot be certain that domestic firms would increase capital spending to increase production, but it is a likely action. If domestic auto makers do increase their capital spending, their suppliers are likely to do so also. Increases in unit volume of domestic autos would spur increases in purchases of steel, glass, vinyl, and other components. 4. The expected effect of an increase in corporate income taxes is a reduced inclination to invest by all firms because of the reduction in future cash flows associated with any proposed project. (The subject of the incidence of corporate taxes can be raised if the students want to pursue this point.) 5. Capital spending plans for colleges and universities would be directly affected, with a general increase in inclination to invest. To a lesser extent, the plans of textbook publishers and other organizations that provide school supplies would be affected. 6. Capital spending would fall because the present value of depreciation tax shields would fall because the flows would come in later 83 Capital Budgeting Effects of Events 1. A property tax increase reduces the acceptability of proposals requiring some investment in real property. A project considered acceptable before the tax increase might become unacceptable because of the increased future taxes 2. Introduction of a tax credit reduces the cash investment required for any project qualifying for the credit. This should not affect projects already acceptable. It could, however, make some projects advisable that were unacceptable under the old tax environment. 3. It seems likely that the expected future cash flows from the project would be decreased because of either a lower price (to maintain the expected sales volume) or a lower volume to be expected at the same price. Hence, the present value of the future returns would decline, and a project heretofore acceptable might no longer be so. Note to the Instructor: A change in ranking of acceptable investments could result in each of the above cases. Projects not involving real estate investments could rise in rank; projects qualifying for the investment credit, projects involving new products, or projects involving new products other than that for which a substitute has been found could also rise in rank. 84 Choosing Depreciation Methods The general answer is that a company should postpone taking tax deductions when doing so increases the amounts of the tax savings sufficiently to offset the delay in their receipt. An expected increase in the tax rate is the most obvious case. Other possibilities, not all of which all students will have reason to know, include (a) The company has operating losses and expects continuing losses (or only small operating profits) for several years. It might then be unable to take advantage of the higher deductions now (b) The company is unincorporated, and expected incomes of its owner(s) from other sources (and the likely marginal tax rates) will increase. The additional tax savings from straightline depreciation could then exceed the penalty for delaying those deductions. Note to the Instructor: A factor common to some of the circumstances mentioned in requirement 2 is an understanding that straightline depreciation for tax purposes uses ADR lives, which are almost always longer than the number of years for deductions using MACRS. Instructors with particular competence in taxation might wish to discuss the influence of the alternative minimum tax on a decision to forgo the benefits of accelerated depreciation. (We thank Professor Will Yancey for bringing the last point to our attention.) 85 Comparison of Methods (Extension of 715) (510 minutes) Total Present Profitability Project Value Investment Index Rank A $58,935 $70,000 .842 3 B 77,485 70,000 1.107 1 C 69,898 70,000 .999 2 In this case, the rankings are the same as when the projects were analyzed using the net present value method. 86 Basic Investment Analysis (20 minutes) 1. Negative $2,150 Tax Cash Flows Annual savings ($600,000 x .10) $60,000 $ 60,000 Depreciation ($240,000/10) 24,000 Increase in taxable income $36,000 Increase in taxes at 40% 14,400 14,400 Net cash savings $ 45,600 Present value factor, 10 years, 14% 5.216 Present value of future flows $237,850 Cost of project, investment 240,000 Net present value ($ 2,150) 2. $60,687 Net present value, from requirement 1 ($ 2,150) Divided by present value factor, 10 years, 14% 5.216 Required increase in aftertax annual flows $ 412 Divided by (1 40% tax rate) 60% Equals required increase in beforetax cash savings $ 687 Plus expected savings 60,000 Equals required savings $60,687 A small increase in savings makes the investment worthwhile on a quantitative basis. If the company has other reasons for making the investment, it should go ahead even if the expected NPV is negative 3. Yes, the advantage is $17,679. Tax Cash Flow Savings with new machine $ 60,000 $ 60,000 Extra depreciation: New machine $24,000 Old machine ($66,000/10) 6,600 17,400 Increase in taxable income $ 42,600 Increase in taxes at 40% 17,040 17,040 Aftertax cash flow increase $ 42,960 Present value factor, 14%, 10 years 5.216 Present value of future flows $224,079 Cost of new machine: Cost of machine $240,000 Less proceeds from sale of old machine 12,000 $228,000 Less tax saving, loss on sale of old machine [($66,000 $12,000) x 40%] 21,600 Net cost of new machine 206,400 Difference, in favor of new machine $ 17,679 87 Basic Replacement Decision (1520 minutes) 1. $84,800 Tax Cash Flow Cost of new lathe $100,000 Resale price of existing lathe $12,000 (12,000) Book value 20,000 Loss for tax purposes $ 8,000 Tax saving at 40% ( 3,200) Net required investment $ 84,800 2. $91,215 present value, for an NPV of $6,415 Tax Cash Flow Savings in cash costs ($63,000 $22,000) $41,000 $ 41,000 Additional depreciation ($25,000 $5,000) 20,000 Increase in taxable income $21,000 Increased income taxes at 40% 8,400 8,400 Net cash flow $ 32,600 Present value factor, 4 years, 16% 2.798 Present value of future cash flows $ 91,215 Cost of new investment (requirement 1) 84,800 Net present value $ 6,415 The net present value is positive and reasonably high. The company should accept the investment on economic grounds. 3. NPV increases by $1,656, to $8,071. Because salvage value is ignored for depreciation purposes, nothing changes until the last flow. Salvage value net of tax ($5,000 x 60%) $ 3,000 Present value factor, single payment, 4 years, 16% .552 Present value of recovery $ 1,656 88 Relationships (25 minutes) 1. $65,946 ($250,000/3.791) 2. $76,577. The easiest approach is to recognize, as the chapter shows, that the $65,946 aftertax cash flow is the result of two things: the tax saving from depreciation and the operating cash flow after taxes. Aftertax cash flow $65,946 Less cash flow from tax shield [40% x ($250,000/5)] 20,000 Aftertax cash flow from operations 45,946 Divided by (1 40% tax rate) 60% Equals pretax cash flow from operations $76,577 89 Working Capital Investment (20 minutes) $46,262 Tax Cash Flow Contribution margin [60,000 x ($9 $4)] $300,000 $300,000 Cash fixed costs 140,000 140,000 Pretax cash flow 160,000 160,000 Depreciation ($300,000/4) 75,000 Increase in taxable income $ 85,000 Increased income taxes at 40% 34,000 34,000 Net cash flow 126,000 Present value factor, 4 years, 12% 3.037 Present value of operating flows $382,662 Present value of return on working capital* 63,600 Total present value 446,262 Investment ($300,000 + $80,000 + $20,000) 400,000 Net present value $ 46,262 * ($80,000 + $20,000) x .636 810 Replacement Decision Working Capital (1520 minutes) $1,632, not a huge margin, so the company might not make the investment if its managers are uncertain about their estimates Investment: Tax Cash Flow Purchase price $200,000 Sale price of existing machine $50,000 (50,000) Tax basis 80,000 Loss 30,000 Tax benefit at 40% (12,000) (12,000) Net investment in machinery $138,000 Working capital investment 80,000 Recovery ($80,000 x .769) ( 61,520) Total investment $156,480 Annual savings: Tax Cash Flow Cash savings ($180,000 $60,000) $120,000 $120,000 Increased depreciation ($100,000 $40,000) 60,000 Increase in taxable income 60,000 Increased tax at 40% 24,000 24,000 Annual net cash flow $ 96,000 Present value factor, 2 years, 14% 1.647 Present value of flows 158,112 Investment 156,480 Net present value $ 1,632 811 Basic MACRS (1015 minutes) Aftertax cash flow ($400,000 x .60) $ 240,000 Present value factor, 10 years, 14% 5.216 Present value of operating flows $1,251,840 MACRS shield ($1,500,000 x .40 x .706) 423,600 Total present value 1,675,440 Less investment 1,500,000 Net present value $ 175,440 812 Mutually Exclusive Alternatives (Extension of 721) (1015 minutes) 1. 1.330 for the handfed machine and 1.228 for the semiautomatic machine HandFed Semiautomatic Total present value of future cash flows (from 722) $1,063,610 $1,719,260 Divided by investment $ 800,000 $1,400,000 Equals PI 1.330 1.228 2. The memo should include (a) reference to the results of analyzing the alternatives using discounted cash flow techniques, and (b) a recommendation that the choice depends on the projected returns for opportunities available for investing the $600,000 incremental outlay for the semiautomatic machine. Note to the Instructor: Class coverage of this assignment can be expanded by determining the return on the incremental outlay, and students' memos might include such an analysis. As shown below, the IRR on the $600,000 incremental outlay is over 18%, well above the 14% cost of capital Incremental investment $600,000 Divided by incremental cash flow $225,000 Equals present value factor for 4 years 2.667 Factor for 18% 2.690 If expected returns from other available uses of the $600,000 approximate the cost of capital, investing in the handfed machine plus those other projects would produce the same total NPV available by acquiring the semiautomatic machine but with the additional risk accompanying reliance on more estimates In an undergraduate introductory course, we try to avoid extended discussions of the concept of cost of capital and the conceptual issues differentiating the NPV and IRR approaches to evaluating investments. Some instructors might, however, choose to introduce reinvestment assumptions and other issues relating to these approaches 813 Investing to Reduce Inventory, JIT (1520 minutes) About $24.2 million, so the investment is desirable (in millions) Tax Cash Flow Additional cash operating costs $1.50 $ 1.50 Plus depreciation ($8.5/5) 1.70 Decrease in taxable income $3.20 Reduced income tax at 40% 1.28 1.28 Net cash outflow $ 0.22 Present value factor, 5 years, 12% 3.605 Present value of future outflows $ 0.793 Investment, net inflow, $8.5 $43.7 + $10.2 25.000 Net present value $24.207 Note to the Instructor: You might wish to point out how the cash operating costs and depreciation tax shield nearly offset one another. This result is purely a function of the numbers we used, not a generalizable conclusion 814 New Product Decision Sensitivity Analysis (2025 minutes) Note to the Instructor: You might want to ask the class whether Minnie’s might suffer losses in sales of its other doughnuts. We deem this likely because people probably don’t increase their doughnut consumption every time a new product comes out. We deliberately did not mention this possibility in the text so that you could ignore it or deal with it as you choose 1. $65,250 Tax Cash Flow Additional contribution margin (50,000 x $3) $150,000 $150,000 New cash fixed costs 60,000 60,000 Increase in income before depreciation $ 90,000 90,000 New depreciation (210,000/6) 35,000 Increase in taxable income $ 55,000 Increase in taxes, at 45% 24,750 24,750 Increase in annual aftertax cash flow $ 65,250 2. (a) $43,757 Increase in annual aftertax cash flow (from requirement 1) $ 65,250 Present value factor, 14%, 6 years 3.889 Total present value of future cash flows $253,757 Less investment 210,000 NPV $ 43,757 (b) About 21.3%. Students using tables will find Investment $210,000 Divided by annual cash flow $ 65,250 Equals present value factor for 6 years 3.218 Closest factors: For 20% 3.326 For 22% 3.167 (c) 1.208 ($253,757/$210,000) 3. $80,457 NPV (from 2a) $ 43,757 Divided by present value factor, 14%, 6 years 3.889 Allowable decrease in annual aftertax cash flows $ 11,251 Divided by (1 45% tax rate) 55% Equals allowable decrease in beforetax cash flows $ 20,457 Cash fixed operating costs 60,000 Allowable total cash fixed operating costs $ 80,457 4. More than 4 but less than 5 years Present value factor (computed in 2b) Closest factors for 16%: For 4 years 3.218 2.798 For 5 years 3.274 5. 43,181 units Estimated sales, in cases 50,000 Allowable decrease in annual beforetax cash flows (from req 3) $ 20,457 Divided by perunit contribution margin $3 Allowable decline in number of units sold 6,819 Case sales to achieve 14% IRR 43,181 6. Variable cost could increase about $0.41, to $5.41 Allowable decrease in annual beforetax cash flows (from req 3) $ 20,457 Divided by expected volume in cases 50,000 Allowable decrease in contribution margin per unit $ 0.41 Note to the Instructor: To remind students of the components of contribution margin, you might ask the class how much the expected selling price could fall and the project still return 14%. Of course, the answer is the same as for requirement 6, $0.41, because a lower selling price has the same effect on contribution margin as an increase in percase variable cost. 815 Working Capital (15 minutes) General Note to the Instructor: This exercise illustrates the principle that any delay in receiving cash flows involves the opportunity cost on the investment, whether or not there are capital expenditures. The exercise is simple enough that students should have little problem determining that there is a negative NPV. Some students might inquire as to the difference between this exercise and the principles in Chapter 5. Here we have a full year, just at the cutoff we mentioned in Chapter 5. More importantly, here the time value of money is significant. Present value of inflow (30,000 x $20 x .862) $517,200 Investment 540,000 NPV ($ 22,800) 816 Mutually Exclusive Investments (20 minutes) 1. (a) $351,900 for the handfed machine, $408,840 for the semiautomatic machine. Handfed machine Tax Cash Flows Revenue $1,750,000 $1,750,000 Cash operating costs 1,450,000 1,450,000 Pretax cash flow 300,000 300,000 Depreciation ($1,000,000/10) 100,000 Increase in taxable income $ 200,000 Increase in taxes at 40% 80,000 80,000 Net cash flow $ 220,000 Present value factor, 10 years, 10% 6.145 Present value of future flows $1,351,900 Less investment 1,000,000 Net present value $ 351,900 Semiautomatic machine Tax Cash Flows Revenue $1,750,000 $1,750,000 Cash operating costs 1,230,000 1,230,000 Pretax cash flow 520,000 520,000 Depreciation ($2,000,000/10) 200,000 Increase in taxable income $ 320,000 Increase in taxes at 40% 128,000 128,000 Net cash flow $ 392,000 Present value factor, 10 years, 10% 6.145 Present value of future flows $2,408,840 Less investment 2,000,000 Net present value $ 408,840 (b) About 18% for the handfed, 14% for the semiautomatic Handfed: $1,000,000/$220,000 = 4.545, which is close to the factor for 18% Semiautomatic: $2,000,000/$392,000 = 5.102, which is close to the factor for 14% (c) 1.352 for the handfed and 1.204 for the semiautomatic Handfed: $1,351,900/$1,000,000 = 1.352 Semiautomatic: $2,408,840/$2,000,000 = 1.204 2. The semiautomatic machine is the better choice because its NPV is higher than that of the handfed machine. Note to the Instructor: One way to illustrate the acceptability of the incremental investment in the semiautomatic machine is to demonstrate, as below, the NPV (at cost of capital) for the incremental investment. Net cash flow, semiautomatic $ 392,000 Net cash flow, handfed 220,000 Incremental net cash flow from semiautomatic $ 172,000 Present value factor, 10%, 10 years 6.145 Present value of incremental flows $1,056,940 Incremental investment ($2,000,000 $1,000,000) 1,000,000 Net present value of incremental investment $ 56,940 The depth of the discussion depends on how deeply you wish to explore the concepts underlying the decision criteria, particularly their assumptions about reinvestment of cash flows. The only clue students have from the text is that the project with the higher NPV should be accepted unless doing so would force rejection of other projects returning more than cost of capital. 817 Sensitivity Analysis (Extension of 816) (20 minutes) The sales volumes needed to provide a 10% return are $1,431,857 for the handfed machine and $1,565,188 for the semiautomatic model. HandFed Semiautomatic Net present value, from previous assignment $ 351,900 $ 408,840 Divided by present value factor, 10 years, 10% 6.145 6.145 Equals allowable decline in net cash flow $ 57,266 $ 66,532 Divided by (1 the 40% tax rate) .60 .60 Equals allowable decline in pretax cash flow and contribution margin $ 95,443 $ 110,887 Divided by contribution margin percentages* 30% 60% Equals allowable decline in sales volume $ 318,143 $ 184,812 Expected sales $1,750,000 $1,750,000 Minus allowable decline, above 318,143 184,812 Sales to yield 10% $1,431,857 $1,565,188 * 100% minus 70%, and minus 40%. The decision to acquire the semiautomatic machine appears somewhat less desirable because breakeven volume, based on NPV's, is higher for that machine. Thus, the semiautomatic machine is riskier than the handfed one. However, both breakeven volumes are well below the $1,750,000 anticipated, so the difference is probably not large enough to change the decision. 818 Basic MACRS (15 minutes) 1. NPV is a negative $20,040 Present value of operating flows ($160,000 x 60% x 4.833) $463,968 Present value of tax shield ($600,000/10 x 40% x 4.833) 115,992 Total present value 579,960 Less investment 600,000 Net present value ($ 20,040) 2. NPV becomes positive by $25,968 Present value of operating flows, above $463,968 Present value of tax shield ($600,000 x 40% x .675) 162,000 Total present value 625,968 Less investment 600,000 Net present value $ 25,968 Using 7year MACRS is worth $46,008 present value ($20,040 + $25,968, or $162,000 $115,992 819 Review of Chapters 7 and 8 (2540 minutes) 1. $68,000 Tax Cash Flow Contribution margin [60,000 x ($11 $8)] $180,000 $180,000 Less cash fixed costs 90,000 90,000 Increased income before depreciation 90,000 90,000 Less depreciation ($210,000/6) 35,000 Increase in taxable income $ 55,000 Increased taxes at 40% 22,000 22,000 Increase in annual aftertax cash flows $ 68,000 a net present value per dollar spent, three persons could be saved from kidney disease or two from heart disease. Kidney Heart Disease Disease Present values of: 3 lives saved ($141,405 x 3) $424,215 2 lives saved ($212,850 x 2) $425,700 Less cost 300,000 300,000 Net present value $124,215 $125,700 Note to the Instructor: Students' answers to requirement 2 will depend on their experiences and personal views. Scores of nonquantifiable factors are involved in a decision such as this, and there are other quantifiable issues as well. Personal views and experiences notwithstanding, the goal of improving students' analytical skills is served if class discussion includes coverage of the relatively simple analysis shown above as well as the matters covered in the analytical comments that follow. The NPV analysis is conceptually weak because it relates the cost to the communitytreatment cost of the department, paid for by taxes, to the incomes of individuals treated, rather than to the benefits to the community. Individual incomes influence community benefits in some ways (e.g., receipts from local income taxes, contributions to charitable and cultural activities). But individual incomes are not a particularly good measure of benefits to the community and the issue here is use of community finances. For example, being younger, victims of kidney disease probably have more dependents than do the heartdisease victims whose children are more likely to be selfsupporting. Thus, treating kidney disease might produce greater savings to the community (in social security, welfare, and other payments to dependents). Evaluation of community benefits must also consider that (a) more lives can be saved if kidney disease is treated, because of the lower cost to save one life; and that (b) treatment of kidney disease will add more years of life to community members because persons saved from that disease have ten more years of life than those saved from heart disease. (An important point to remember is that a decision such as the one in this problem does not consider the lives of any particular individuals.) As with any benefit/cost situation under conditions of resource scarcity, a decision must be made as to who is to benefit from the use of those resources. This sociopolitical problem can't be resolved with quantifiable factors alone. That this particular decision involves human lives does not negate the need for a decision about what the community is to do with its limited resources. The community can choose to increase the available resources, but it is still likely to set some limit short of taxing its members to a subsistence level. 835 WhentoSell Decisions (20 minutes) 1. About 14%. The choice is between $700 now and $1,170 in four years. The present value factor is .598 ($700/$1,170), which is closest to .592 for four years and 14%. 2. About $1,100, which is $700/.636, the present value divided by the factor for four years and 12%. 3. Nine years gives the highest IRR Price for Expected Additional SixYearOld Future PV Discount Rate for Holding Period Scotch / Price = Factor Closest Factor 1 (sell at 7) $700 $ 800 .875 14% (.877) 2 700 950 .737 16% (.743) 3 700 1,200 .583 20% (.579) 4 700 1,400 .500 18% (.516) 4. Ten years gives the highest present value and highest net present value because the investment is $700 under all choices Additional Expected PV Holding Future Factor Present Period Price x at 12% = Value 1 $ 800 .893 $714 2 950 .797 757 3 1,200 .712 854 4 1,400 .636 890 Note to the Instructor: Requirements 3 and 4 are contrived to give different decisions under the two criteria, IRR and NPV. As discussed in the chapter, in most cases the NPV criterion will give the better decision where mutually exclusive investments are under consideration. That conclusion is not always correct, because it depends on the assumed rate of return earned by the incoming cash flows. In this particular case, if the proceeds from sale after nine years could be reinvested at 20%, the IRR earned if the Scotch is held until it is nine years old, the company would have at the end of the fourth year $1,440 ($1,200 x 1.20), which is more than it would have if it held the Scotch until the end of year four. If the company could earn only the cost of capital of 9%, it would have $1,308 at the end of year four, which is less than it would have if it held the Scotch until it was ten years old ($1,400). 836 Increased Sales and Working Capital (2530 minutes) The decision is a tossup. The NPV is a negative $437, $160,000 $159,563, which is within rounding errors Investment required: Outlay for the machine $ 80,000 Increase in working capital 80,000 Total current outlay $160,000 Present value of cash flows: Annual returns of $26,450 for 10 years at 14% $26,450 (from below) x 5.216 $137,963 Return of the investment in working capital, at the end of the 10th year ($80,000 x .270) 21,600 Total present value $159,563 Computation of Cash Flows for 10 Years Existing Proposed Conditions Conditions Revenues: 80,000 x $8 $640,000 105,000 x $7 $735,000 Variable costs: Labor: Currently ($2.25 x 80,000 units) 180,000 Future (labor force constant) 180,000 Other: 80,000 x $2.25 180,000 105,000 x $2.25 236,250 Total variable costs 360,000 416,250 Contribution margin $280,000 $318,750 Increase in contribution margin $38,750 Depreciation ($80,000/10) 8,000 Increase in taxable income $30,750 Tax on above increase (40%) 12,300 Net increase in aftertax cash flow $26,450 837 Sensitivity Analysis (Extension of 733) (20 minutes) 1. 207,527 units, a drop of 42,473 Net present value, from 834 $262,458 Divided by present value factor, 5 years, 14% 3.433 Equals allowable decrease in net cash flow $ 76,452 Divided by (1 40% tax rate) 60% Equals allowable decrease in pretax cash flow and income $127,420 Divided by contribution margin per unit ($4 $1) $3 Equals allowable decrease in unit volume 42,473 Expected unit volume 250,000 Less allowable decrease in unit volume 42,473 Equals unit volume required to earn 14% IRR 207,527 2. Pitcairn's managers might be more inclined to make the investment after seeing that it would take a drop of 42,473 units in volume to bring the net present value to zero. The required volume is about 17% below the expected level of 250,000 units, which is a fairly large decrease. 838 Backing a Play (30 minutes) 1. The play appears to be a good investment, with a $325,851 NPV. Tax Cash Flow Annual gross receipts $1,500,000 $1,500,000 Cash expenses: Salaries 600,000 600,000 Rent [$20,000 + (5% x $1,500,000)] 95,000 95,000 Royalties (10% x $1,500,000) 150,000 150,000 Other cash expenses 140,000 140,000 Total cash expenses 985,000 985,000 Pretax cash flow 515,000 515,000 Depreciation ($500,000/4) 125,000 Taxable income $ 390,000 Tax at 40% 156,000 Annual cash flow $ 359,000 Present value factor, 20%, 4 years 2.589 Total present value of future annual returns $ 929,451 Present value of return of working capital investment $200,000 x 0.482 96,400 Total present value 1,025,851 Less investment 700,000 Net present value $ 325,851 2. $1,253,215 Net present value, computed in requirement 1 $ 325,851 Divided by present value factor for 4 years at 20% 2.589 Equals allowable decline in net cash flow $ 125,860 Divided by (1 40% tax rate) 60% Equals allowable decline in pretax income and revenue $ 209,767 Divided by contribution margin (100% less variable costs of 5% for rent and 10% for royalty) 85% Equals allowable decline in gross receipts $ 246,785 Expected revenue $1,500,000 Less allowable decline 246,785 Equals revenue needed for 20% IRR $1,253,215 The decline is 16.5% of revenue, so the decision is not extremely sensitive to the estimate of revenue. You might very well elect not to back the play for that reason, given that plays are probably riskier investments than most. 839 Replacement Decision (25 minutes) 1. $19,900 Purchase price, outflow $37,300 Tax saving from loss on sale of old machine: Sale of old machine, a cash inflow $12,000 (12,000) Book value of old machine 18,000 Tax loss $ 6,000 Tax saving at 40%, a cash inflow ( 2,400) Saved cost of repairs, net of tax ($5,000 x 60%) ( 3,000) Net cost $19,900 2. The new machine should be a wise investment because it involves a cash outlay of $19,900 with anticipated returns of $26,866 computed as below. Tax Cash Flow Cash savings due to greater speed $ 6,000 $ 6,000 Change in depreciation: Depreciation on new asset ($37,300/10) $3,730 Depreciation on old asset 1,800 Additional depreciation from new asset 1,930 Increase in taxable income $ 4,070 Tax on increased income, at 40% 1,628 1,628 Increase in net cash flow $ 4,372 Present value factor, 10 years, 10% 6.145 Total present value of savings $ 26,866 840 Valuing a Football Team (2535 minutes) 1. $17,591,288 calculated as follows Aftertax operating cash flow ($4,000,000 x .72) $ 2,880,000 Present value factor, 10 years, 14% 5.216 Present value of operating flows $15,022,080 Let M = the maximum investment. The amortization tax shield is [(M/10) x .28 x 5.216], which is subtracted from M along with the present value of the operating flows. Thus, M = $15,022,080 + [(M/10) x .28 x 5.216] M = $15,022,080 + .14605M .85395M = $15,022,080 M = $17,591,288 As proof, Tax Cash Flows Operating $4,000,000 $ 4,000,000 Amortization ($17,591,288/10) 1,759,129 Pretax profit $2,240,871 Tax at 28% 627,444 Net cash flow $ 3,372,556 Present value factor 5.216 Present value $17,591,252 The difference between the $17,591,252 and the $17,591,288 is from rounding. 2. $16,250,627. The tax shield here is a lump sum at the end of 10 years, so the shield = M x .28 x .270. (The .270 is the present value of a single payment in 10 years.) Thus, M = $15,022,080 + (M x .28 x .27) M = $15,022,080 + .0756M .9244M = $15,022,080 M = $16,250,627 As proof, Present value of operating flows, above $15,022,080 Present value of writeoff ($16,250,627 x .28 x .27) 1,228,547 Equals investment $16,250,627 841 Investing in Quality, JIT, Declining Base (1520 minutes) About $1,221 thousand dollars. Tax Cash Flow Saved contribution margin ($1,500.0 x 60%) $ 900.0 $ 900.0 Less additional cash fixed costs 700.0 700.0 Pretax cash inflow 200.0 200.0 Depreciation ($5,500.0/10) 550.0 Decrease in taxable income $ 350.0 Reduced income tax at 40%, a cash inflow 140.0 Net cash inflow $ 340.0 Present value factor, 10 years, 12% 5.650 Present value of future flows $1,921.0 Less investment ($5,500.0 $4,800.0) 700.0 Net present value $1,221.0 Note to the Instructor: The solution follows the position in the chapter of assuming that there is no negative effect on inventory at some future date. This assignment also involves no additional cash inflows from sales but rather a halt in the decline of sales. Some students will not see this point and will wonder what the benefits are. If the point hasn't been made in connection with other assignments, it's worth pointing out here that some benefits of JIT operations are not easily quantified, particularly those having to do with increased quality of product and additional manufacturing flexibility. 842 Attracting Industry (2025 minutes) 1. Looking only at the receipts and costs for the town, the investment will not return enough to meet the 9% required rate of return. Receipts: Rent $ 150,000 Sales tax ($6,000,000 x 1%) 60,000 Property taxes [($4,400,000/$1,000) x $80] 352,000 Total receipts 562,000 Additional costs 105,000 Annual net cash inflow $ 457,000 Present value factor, 9%, 20 years 9.129 Present value of future cash inflows $4,171,953 Less investment 4,300,000 Net present value ($ 128,047) 2. The above analysis considers only the receipts and costs of the town itself. The state, as well as the town, would benefit from the new plant, because the state would save some of the money it now spends on unemployed people. Hence, it's possible the state might be willing to share some of the cost of this project. If the interest rate for the state is also 9%, it would be worth $27,387,000 ($2,000 x 1,500 reduced unemployment x 9.129, the present value factor) to the state if the 1,500 people were taken off the unemployment rolls. Of course, that figure assumes the level of unemployment would stay at about the same level for the next 20 years if the factory were not built. At least some of the unemployed are likely to become discouraged and move away. The town council and mayor might accept the project if they think it worthwhile to increase taxes somewhat to cover the required investment. They might consider it worthwhile to do so if they believe the town would benefit in noneconomic ways from having fewer unemployed persons. For example, they might consider the positive effects on the unemployed of being given jobs. 843 Dropping a Product (30 minutes) 1. Quickclean should not be dropped Tax Cash Flow Present value of future cash flows: Contribution margin $700,000 $700,000 Avoidable fixed costs 580,000 580,000 Cash flow before taxes 120,000 120,000 Less depreciation 100,000 Increase in taxable income 20,000 Tax at 40% 8,000 8,000 Net cash flow $112,000 Present value factor, 14%, 5 years 3.433 Present value of future cash flows $384,496 Present value of disposal of equipment: Book value and loss for tax purposes $500,000 Tax savings at 40%, and present value of inflow 200,000 Net present value in favor of keeping Quickclean $184,496 2. Quickclean should be dropped. Tax Cash Flow Selling price of machinery $350,000 $350,000 Book value 500,000 Loss for tax purposes 150,000 Tax saving at 40% rate 60,000 60,000 Total present value of disposal $410,000 Present value of future inflows, requirement 1 384,496 Net present value of dropping Quickclean $ 25,504 844 New Product Complementary Effects (35 minutes) 1. The product should not be introduced. The NPV is a negative $155,160. Investment required: Machinery $2,000,000 Inventories 500,000 Receivables (10,000 units per month x 2 x $20) 400,000 Total investment $2,900,000 Tax Cash Flows Present value of future cash flows: Contribution margin [120,000 x ($20 $9)] $1,320,000 $1,320,000 Less: Additional fixed costs $300,000 Forgone rent of space 120,000 420,000 420,000 Cash flow before taxes 900,000 900,000 Depreciation ($2,000,000/10) 200,000 Taxable income $ 700,000 Income tax at 40% 280,000 Net operating cash flow, years 110 $ 620,000 Present value factor, 10 years, 20% 4.192 Present value of future operating cash flows $2,599,040 Recovery of working capital investment (computed above) in year 10 $ 900,000 Present value factor, single payment in 10 years at 20% .162 145,800 Total present value of future cash flows $2,744,840 Less investment required, above 2,900,000 Net present value ($ 155,160) 2. The complementary effects make the new product desirable. The positive present value of the future flows from increased sales of the existing product, less the additional investment in inventory and receivables, is $251,544, which is more than enough to offset the $155,160 deficiency in NPV considering the new product by itself as in requirement 1. Contribution margin [30,000 x ($10 $6)] $ 120,000 Less additional income tax at 40% 48,000 Cash flow 72,000 Present value factor, 10 years, 20% 4.192 Present value of future operating flows $ 301,824 Recovery of additional investment in working capital $60,000 Single payment factor, 10 years, 20% .162 9,720 Total present value of future inflows 311,544 Less additional investment in receivables and inventory 60,000 Net present value of increased sales $ 251,544 845 Closing a Plant Externalities (35 minutes) 1. A $268,800 difference in present values favors closing the plant Total Project Approach Close plant: Increased shipping costs $ 900,000 Tax at 40% 360,000 Net cash outflow 540,000 Present value factor, 10 years, 14% 5.216 Present value of increased shipping costs 2,816,640 Severance pay, net of tax, $800,000 $320,000 480,000 Subtotal 3,296,640 Less selling price of plant 400,000 Present value of future cash flows $2,896,640 Keep plant open: Investment required $4,000,000 Depreciation tax shield, $4,000,000/10 x 40% $ 160,000 Present value factor, 10 years, 14% 5.216 Present value of future cash inflows 834,560 Present value of future cash outflows $3,165,440 Difference favoring closing plant, $3,165,440 $2,896,640 $ 268,800 The investment in equipment produces a net annual cash inflow from tax savings from the depreciation deduction. Some of the flows could be treated differently. For example, the severance pay and sale price of the plant could be treated as savings (avoided costs) under the alternative of keeping the plant open. Incremental Approach Tax Cash Flows Annual savings from keeping open: Shipping costs saved $900,000 $ 900,000 Less depreciation expense 400,000 Difference in taxable income 500,000 Difference in taxes at 40% 200,000 200,000 Net annual savings $ 700,000 Present value factor, 10 years, 14% 5.216 Present value of future savings $3,651,200 Net investment required: Equipment $4,000,000 Foregone selling price 400,000 Avoided severance pay, net of tax (480,000) Net amount of investment 3,920,000 Net present value favoring closing ($ 268,800) 2. Some of the factors also to be considered follow (a) Both the company's managers and city officials must consider the impact of the closing on the city of Vesalia. Nearly 400 people will be put out of work. How many of those people will find other employment is influenced by the availability of other employment locally. Some may leave the area; some of those who stay may require additional assistance from the city. Offering employees the opportunity to move to the new location might help those employees but could still have negative effects on the city. (b) The company's managers should assess the likelihood of reaching some type of compromise if the relevant information is shared with city officials and possibly with persons representing the company's employees. Managers could try to negotiate some assistance from the city, perhaps in the form of lower property taxes. Managers could also try to negotiate wage concessions from employees. (As an example, consider the wage concessions negotiated by troubled airlines in the early 1990s.) If the pollution standards were established locally, city officials might not have considered the costs to the city of the increase in unemployed citizens or the potential for reduced propertytax revenues. As interested parties, city officials might reconsider the standards when better informed of the company's situation. If the pollution standards were established at the national level, concessions on property taxes and/or wages might still be negotiated to offset the monetary advantage of closing the plant. (c) The company's managers might not have considered whether the Montclair area has the additional workers needed to handle the increase in production at the Montclair plant. Note to the Instructor: Apart from the difficulties presented by the qualitative issues in it, this problem is difficult for many students because of the number of cash flow items involved. We've assumed the company considered all the discernible monetary aspects of the situation. As examples, we assumed that (1) the company's calculations include any changes in selling and administrative costs that would result from eliminating one of its locations; (2) no opportunities exist for reducing operating costs at the Vesalia plant other than the tax and wage concessions mentioned in requirement 2; (3) transferring production from the Vesalia to the Montclair plant would not affect any company plans for future use of the currently unused capacity at the Montclair plant; and (4) closing the Montclair plant and transferring its production to the Vesalia plant is financially unwise. An interesting aspect of this problem is that the analysis does not involve contribution margin. The inability to change selling price is a reasonable assumption in a competitive industry. The cost structures and relative sizes of the two plants are unknown. If the Montclair plant can handle the increased production, one must wonder about the implications of the assertion that cash production costs at the two plants are equal. 846 Modification of Equipment (35 minutes) The memo should recommend that the new equipment be purchased and the old equipment sold. The computations submitted in support of the recommendation could be either of the two approaches shown below. Totalproject approach The present value of the future outflows of buying new equipment is $96,080 less than that of modifying the existing equipment ($284,160 $188,080). Tax Cash Flow Modify existing equipment: Annual cash OUTFLOW, excess of operating costs over new equipment* ($ 50,000) ( 50,000) Depreciation [$100,000 + ($300,000/4)] 175,000 Total tax deductible expense 225,000 Tax saving at 40% 90,000 90,000 Net aftertax cash flow (inflow) ($ 40,000) Present value factor, 16%, 4 years 2.798 Present value of future cash savings ($111,920) Less investment required 300,000 Present value of future cash inflows $188,080 * This amount could also be shown as a reduction under the "buy new equipment" alternative. Tax Cash Flow Buy new equipment: Depreciation ($800,000/4) $200,000 Tax savings at 40% 80,000 ($ 80,000) Present value factor, 16%, 4 years 2.798 Present value of tax shield ($223,840) Investment: Price of new equipment $800,000 Less proceeds on sale of existing equipment $220,000 (220,000) Book value of equipment 400,000 Loss for tax purposes $180,000 Tax saving at 40% ( 72,000) Net investment 508,000 Less present value of depreciation tax shield, above 223,840 Present value of future cash outflows $284,160 Incremental approachbuy rather than modify Tax Cash Flow Operating savings, a cash inflow $ 50,000 $ 50,000 Increased depreciation ($200,000 $175,000) 25,000 Reduction in tax deductible expenses 25,000 Lost tax savings at 40%, an outflow 10,000 10,000 Net cash inflow favoring modification $ 40,000 Times relevant present value factor 2.798 Present value of future savings $111,920 Net investment required: Net purchase price (above) $508,000 Modifications avoided 300,000 Net outlay 208,000 Difference in favor of buying $ 96,080 847 Mutually Exclusive Investments (50 minutes) The company should buy the Rapidgo 350 and replace it in five years. Rapidgo 600 Present Values Original cost $ 90,000 Annual operating costs $15,000 Plus depreciation ($90,000/10) 9,000 Total expenses $24,000 Tax saving at 40% rate $ 9,600 Net cash outflows ($15,000 $9,600) $ 5,400 Present value factor, 10 years, 16% 4.833 Present value of future annual cash flows 26,098 Total present value $116,098 Rapidgo 350 Present Values Original cost $ 50,000 Annual operating costs, first 5 years $12,000 Depreciation ($50,000/5) 10,000 Total expenses $22,000 Tax saving at 40% $ 8,800 Net cash outflows ($12,000 $8,800) $ 3,200 Present value factor, 5 years, 16% 3.274 Present value of flows for first 5 years 10,477 Purchase price of replacement machine $60,000 Present value factor, 5 years, 16% .476 Present value of replacement cost 28,560 Annual operating costs, second 5 years $12,000 Depreciation ($60,000/5) 12,000 Total expense $24,000 Tax saving at 40% $ 9,600 Net cash outflows ($12,000 $9,600) $ 2,400 Present value of flows* 3,742 Total present value $ 92,779 * $2,400 x 1.559, which is the sum of the present value factors for single payments 6, 7, 8, 9, and 10 years hence (.410 + .354 + .305 + .263 + 227) Cash flow $2,400 Times present value annuity factor, 5 years, 16% 3.274 Equals present value of annuity at beginning of 6th year (5 years from now) $7,858 Present value factor, single payment 5 years, 16% .476 Present value of delayed annuity $3,740 848 Replacement Decision, MACRS (30 minutes) 1. Buy Purchase cost (80,000 x $20) $1,600,000 Less tax saving at 40% 640,000 Net cash outflow $ 960,000 Present value factor, 12%, 8 years 4.968 Present value of buying $4,769,280 Make Variable costs (80,000 x $9.30*) $ 744,000 Cash fixed costs 100,000 Total cash costs 844,000 Less tax savings at 40% 337,600 Net cash flow $ 506,400 Present value factor, 12%, 8 years 4.968 Present value of operating flows $2,515,795 Present value of MACRS ($2,500,000 x .40 x .738) ( 738,000) Present value of salvage value ($100,000 x 60% x .404) ( 24,240) Less investment 2,500,000 Total present value of making $4,253,555 * $9.30 = $4.50 + $3.00 + $1.80 2. About 63,831 units (80,000 16,169) Advantage to making ($4,769,280 $4,253,555) $515,725 Divided by relevant present value factor 4.968 Equals allowable decline in annual net cash flow $103,809 Divided by (1 40% tax rate) 60% Equals allowable decline in annual pretax cash flow $173,015 Divided by difference in variable cost ($20.00 $9.30) $ 10.70 Equals allowable decline in unit volume 16,170 849 Evaluating an Investment Proposal (40 minutes) The assistant is incorrect; the project should be accepted. The assistant has made the following errors. 1. The research and development costs and administrative time have already been incurred and so are sunk costs 2. Interest on debt specific to this particular project should not be a component of the cash flow analysis. 3. The tax saving from scrapping the existing equipment has been ignored 4. The treatment of depreciation is incorrect. The analysis should use the difference between depreciation on the existing machinery and that on the new machinery, not the depreciation on the new machinery. 5. The annual cash flow calculation is incorrect because the calculation included a deduction for depreciation, which is not a current cash flow. Depreciation should be added to the $75,000 to arrive at cash flow. The following analysis corrects the above errors Investment required: Purchase price of machinery $350,000 Tax savings on scrapping old machinery ($110,000 loss x 40%) 44,000 Net investment required $306,000 Tax Cash Flows Annual cash flows: Labor $ 75,000 $ 75,000 Materials 80,000 80,000 Variable overhead 40,000 40,000 $ 195,000 $ 195,000 Less tax at 40% of savings 78,000 78,000 Net saving before tax effect of depreciation $ 117,000 Tax savings from increase in depreciation ($35,000 $11,000*) x 40% 9,600 Net increase in cash flow $ 126,600 Present value factor, 10 years, 16% 4.833 Present value of future cash flows $ 611,858 Net investment required, from above 306,000 Net present value $ 305,858 * $110,000 book value divided by remaining life of 10 years 850 Expanding a Factory (60 minutes) The smaller expansion, Plan A, should be accepted. The first step is to determine how to use the additional capacity. The products produce contribution margin per machinehour as follows: 101X, $9; 201X, $6; 305X, $8. Therefore, 101X should be made first, until its sales potential is reached, then 305X, and finally, 201X. The NPV of Plan A is $497,400. The NPV of Plan B is $353,400, or $144,000 less than that of Plan A. Plan B can be analyzed in total or incrementally. Both approaches are shown below. Analysis of Plan A Computation of product quantities and contribution margin: Available machinehours 200,000 Less production of 30,000 101Xs (2 x 30,000) 60,000 Hours remaining 140,000 Divided by hours required for 305X 5 Equals number of 305Xs to be made 28,000 Contribution margin: 101X (30,000 x $18) 540,000 305X (28,000 x $40) 1,120,000 Total contribution margin $1,660,000 Tax Cash Flows Computation of NPV: Contribution margin $1,660,000 $1,660,000 Less additional fixed costs requiring cash 600,000 600,000 Cash flow before taxes 1,060,000 1,060,000 Less depreciation ($4,000,000/10) 400,000 Increased taxable income 660,000 Increase in income taxes (40%) 264,000 264,000 Net cash flow $ 796,000 Present value factor, 12%, 10 years 5.650 Present value of future flows $4,497,400 Investment required 4,000.000 Net present value $ 497,400 Analysis of Plan B Available machinehours 280,000 Less hours devoted To 101X ( 60,000) To 305X (140,000) Hours available in excess of Plan A 80,000 Less hours used for additional production of 305X (30,000 28,000) x 5 ( 10,000) Hours remaining for production of 201X 70,000 Divided by hours required to produce 201X 4 Equals number of 201Xs to be made 17,500 Contribution margin: 101X (30,000 x $18) $ 540,000 305X (30,000 x $40) 1,200,000 201X (17,500 x $24) 420,000 Total contribution margin $2,160,000 Annual cash flows: Tax Cash Flows Contribution margin $2,160,000 $2,160,000 Less additional fixed costs requiring cash 800,000 800,000 Cash flow before taxes 1,360,000 1,360,000 Less depreciation ($5,500,000/10) 550,000 Increased taxable income $ 810,000 Increase in income tax, at 40% 324,000 324,000 Net cash flow $1,036,000 Present value factor, 12%, 10 years 5.650 Present value of future flows $5,853,400 Less investment required 5,500,000 Net present value $ 353,400 Incremental analysis Tax Cash Flows Increased contribution margin $2,160,000 $1,660,000 $ 500,000 $ 500,000 Increased fixed cash costs ($800,000 $600,000) 200,000 200,000 Increased pretax cash flow 300,000 300,000 Increased depreciation ($550,000 $400,000) 150,000 Increased taxable income $ 150,000 Increased income tax at 40% 60,000 60,000 Increased net cash flow $ 240,000 Present value factor, 12%, 10 years 5.650 Present value of incremental cash flows $1,356,000 Incremental investment 1,500,000 Net present value of incremental investment ($ 144,000) The $144,000 is also the difference between the two net present values ($497,400 $353,400). Note to the Instructor: As always, the validity of the analysis depends on the validity of the estimates. An additional factor some students might discuss is how pattern of demand might affect production scheduling and, hence, the decision on the magnitude of the expansion. For example, if demand is seasonal and inventory carrying costs high, the company might believe the benefits of volume flexibility with Plan B exceed the benefits of the stable production needed to meet demand with the smaller facility. Some students may pursue a point raised in the problem, the production manager's comment that the cost per machine hour and investment per machine hour figures were lower for Plan B than for Plan A. As shown below, the production manager is correct; but the point is irrelevant to the decision. Plan A Plan B Fixed cost per machinehour ($600,000 + $400,000)/200,000 $ 5.00 ($800,000 + $550,000)/280,000 $ 4.82 Investment per machinehour $4,000,000/200,000 $20.00 $5,500,000/280,000 $19.64 ... The NPV analysis is conceptually weak because it relates the cost to the communitytreatment cost of the department, paid for by taxes, to the incomes of individuals treated, rather than to the benefits to the community. ... is to work with the advantage of Machine B over Machine A and determine if the additional cost of the former is justified. Savings in operating cost of B over A ($12,000 $3,000) $ 9,000 Tax on cost savings (40%) 3,600 ... Present value of aftertax savings from Machine B $43,015 Since the cost of this advantage is $40,000 ($80,000 cost of B vs. $40,000 cost of A), purchase of Machine B is wise. We can also approach the problem