# Shapiro Chapter Solutions

Topics: Economics

Economic profit measures true increments to value, but is hard to assure. Accounting profit is correlated with economic profit, but not perfectly so. Accounting profit can be measured much more easily. B. What is the relationship between accounting rate of return and economic rate of return? Answer: The accounting rate of return is the ratio of after-tax profit to average book investment. Economic rate of return is the ratio of after-tax economic profit to the market value of the investment Economic profit equals cash accruals to the asset combined with changes in its market value.

2.

In 1991, AT&T laid a transatlantic fiber optic cable costing \$400 million that an handle 80,000 calls simultaneously. What is the payback on this investment if AT&T uses just half its capacity while netting one cent per minute on calls? Answer: 5210 Million per year assuming the half capacity is for 24 hours a day, 365 days per year. The annual payback is then 53%. 3. The satisfied owner off new \$15,000 car can be expected to buy another ten cars from the same company over the next 30 years (an average of one every three years) at an average price of \$15,000 (ignore the effects of inflation).

If the net profit margin on these cars is 20 percent, how much should an auto manufacturer be willing to spend to keep its customers satisfied? Assume a 9 percent discount rate. Answer: At a 20 percent profit margin, the auto company will earn an annuity to about \$3,000 every three years for the next 30 years. Discounted at 9 percent, this annuity is worth \$9,402, assuming that the tires new car is purchased three years from today.

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Hence, an investment to keep customers satisfied will have a positive NAP as long as the amount spent is less than \$9,402.

Thus, a car company should be willing to spend LIP to \$9,402 in present value terms to keep its customers satisfied. A trick is available to calculate the present value of this annuity)h Recognize that an annuity received every three years for 30 years and discounted at 9 percent is equivalent to a 10-year annuity discounted at 29. 5029 percent since each cash flow term is discounted at (I . 09)3 = 1295029. 4. Demonstrate that the following project has internal rates of return of O percent, 100 percent, and 200 percent.

Year \$1,200 12 13 I Cash flow +7,200 1-13,200 Answer: To demonstrate that an AIR calculation is valid, compute the net present value at the AIR. A valid AIR yields O. I Year | -400. 00 -488. 89 | +88. 9 10 Cash Flow 112 1 13 1 14 I I Total 1-1,200 I-I ,200 | -600 1-1,650 +450 5. During 1990, DOD Chemical generated the following returns on investment in its different business units: Business unit 116. 6 16. 7 Return on Investment (h) I Chemicals/Performance Products I I Consumer Specialties Plastics 12. 7 I Hydrocarbons/Energy Other 111. 15. 2 11. 6 I I DOD Chemical overall Given these returns, which of the business units should DOD invest additional capital in? What additional information would you need in order to make that decision? Answer: These figures tell you what DOD earned in 1990. In order to decide on future investments, you need the following information: 1. Whether these returns are representative of those expected to be earned in the future in these different divisions, What matters for investment decommissioning are projected future returns, not past returns.

To the extent that these returns vary widely from year to year-?which they do in the chemical business-?historical return data for one year are meaningless. One reason these data may be misleading is that they are based on historical cost figures for investment. You really want to calculate returns on the replacement cost of sets Inflation will cause asset values to be understated, which will lead the return on investment to be overstated. 2. The cost of capital for these divisions.

Each division is likely to have its own risk and, hence, its own cost Of capital. A high return could just indicate a high degree of risk and, therefore, a high required return. What matters is the projected return relative to the cost Of capital. A high projected return that is less than the risk-adjusted cost of capital will yield a negative NAP investment. Conversely, a low projected return that exceeds the cost Of capital Will yield a costive NAP investment. 3. The marginal return on investment in each division.

Even if the figures for, say, the plastics and chemical/performance products divisions exceed their cost of capital and are representative of those expected to be earned in the future, that does not automatically justify additional investment in those divisions. These figures tell us the average ROI; for investment purposes you need the marginal ROI. That is, what matters tort investment purposes is not the return on past investments but the return on future investments. As we have seen, many companies (e. G.

Monsanto, Philip Morris) have divisions that yield high returns on past investments but very low returns on incremental investments. 4, The extent to which these divisions sell to one another, DOD Chemical is a vertically-integrated company. Its hydrocarbons/energy unit sells to its downstream plastics unit, which in turn sells to its consumer specialties unit. Thus, the profitability of these units depends critically on the prices at which these internal transactions take place. Gore example, the hydrocarbons/energy unit may be showing a low ROI simply because it sells petroleum to the plastics unit at 3 below-market price.

That is, the hydrocarbons unit may be very profitable but its profits are showing up in the plastics unit in the form of a low price on raw materials. This is a form Of cross-subordination. Disentangling the true profitability of the different units of a vertically-integrated company like DOD turns out to be a very difficult task, but it is a necessary one for capital budgeting purposes. What matters is how profitable investments are from the standpoint of the overall company, not from the standpoint of the units undertaking those investments, 5, The returns associated with specific assets and activities within each vision.

What matters from an investment standpoint is not just how well each division can be expected to do in the future but hove well specific projects within each division can be expected to do. For example, certain products within the profitable plastics division may be earning a return while others are only earning a 2% return. Similarly, certain investments may be expected to yield a high return relative to their rockiness, whereas others have little chance of a significant payoff.

At the same time, the low-return hydrocarbons/newer division may have some very high-return projects, which are masked by a lot of value- storing activities elsewhere. Without detailed data on the returns associated with each division’s various activities, customers, and products, one can’t say where investment dollars would be best spent. CHAPTER 2: PROBLEMS 1. A firm is considering investing in a project with the following cash flows: I cash Flows 1 15 1 16 117 1 18 II I-I sass. O 2,000. 00 | 3,000. 00 4,000. 00 | 3,500. 00 13,000. 00 1 ,oho. O | 1,818. 18 12,479. 4 13,005. 26 12,390. 55 11,862. 76 11,128. 95 1513. 16 1466. 51 1,818. 18 4,297. 52 17,302. 78 9,693. 33 Ill 12,685. 04 | 13,664. 70 2. The pennon Oil Co. Just decide whether it is financially feasible to open an oil well off the coast of China. The drilling and rigging cost for the well is The well is expected to yield 585,000 barrels of oil a year at a net profit to pennon of \$5 a barrel for four years. The well will then be effectively depleted but must be capped and secured at a cost of Pennon requires an annual rate of return of 14 percent on its investment projects.

Should Pennon open the well? (Assume all Of a year’s production occurs at the end Of the year. ) Answer: Net annual profit = = \$2. MM. IV(Production) \$2_MM _ 2. MM _ 2. 9137 = 58. MM. IV(Capping) = SO. MOM _ = 4 _ 0. 5921 = \$2. MM. IV(Drilling) 55. MM. NAP = IV(Production) ? IV'(Capping) = 9. MM 2. MM 5. MM – \$1. MM. The well should be drilled, since the present value of the benefits exceeds the present value of the costs, The term NAP (Net Present Value) refers precisely to the difference in present value between the benefits and the costs of a project, 3.

Jack Nicolas, the golfing pro and real estate developer, is thinking Of acquiring an 800-acre property outside Atlanta that he intends to turn into an exclusive community for 600 families, The cost of this property and the necessary improvements is \$30 million. After setting aside a mandatory 25 percent of the property as green space, he figures he can sell the remaining lots for an average of \$90,000 an acre. By putting in a golf course on the 200 acres of green space, Nicolas believes he can instead sell the lots for an average of \$140,000 an acre.

The golf course, including clubhouse, has a projected price tag of \$6 million. In either event, the project is expected to take eight years to sell out at a rate of 75 lots per year. Jack Nicolas faces a marginal tax rate of 40 percent and can write off his land and development costs by prorating these costs against each lot old. A. If his required return is 14 percent, should Jack Nicolas go ahead with the initial project (i. E a community With no golf course)? Answer: The initial project, a community With no golf course, requires an initial outlay of \$MM, and reaps 6. MM per year for 8 years in the absence of taxes and depreciation. The present value of the decision at r 14% and t -40% can be determined from the following formula: b. Should he put in the golf course? Answer: With the golf course, the cost is MM, and pretax revenues are 10. MM per year. The same calculations as above can be made with the new data: NAP = + (1 -? Nicolas should build the golf course (exactly as we expected), a b, * An alternate display is illustrative: Tax ( @ 40%) Choosing Only Twit Golf Course I Annual Sales I Ann. Amortization I I Ann. Pretax Profit I I Ann.

After Profit 4. 638864 I cost I Present Value 37,574. 798 .NET Present Value 4. The Coin Coalition is trying to get the U. S. Government to replace the dollar bill with a gold-colored dollar coin. One argument is cost savings. A dollar bill costs 2. 6 cents to produce and lasts only about 17 months, A dollar coin, on the other hand, while costing 6 cents to produce, lasts for 30 years. About 1. 8 billion dollar bills must be replaced each year, The start-up costs of switching to a dollar coin are likely to be quite high, however. These costs have not been estimated. A.

What are the projected average annual cost savings associated with switching from the dollar bill to a dollar coin? Answer: Since each dollar bill in circulation lasts an average of I . 42 years (17/1 2), and 1. 8 billion are replaced each year, this must mean that there are about 2. 556 billion dollar bills in circulation. The cost of replacing I billion dollar bills each year at a cost per bill of 2. 5 cents is \$46. Million. Since the dollar coin lasts 30 years, only about 85. 2 million (2. 556 billion/30) coins must be replaced each year at an annual cost of \$5. 1 million.

Thus, the annual cost savings comes to approximately \$41. 7 million. B. Taking into account only the cost savings estimated in part a, how high can the start-up costs for this replacement project be and still yield a positive NAP for the LIST. Government? Else an 8 percent discount rate. Answer: The present value of the cost savings perpetuity estimated in part a, discounted at 8 percent, is \$41 or \$521. 25 million. Hence, the start- p costs for replacing the dollar bill with a dollar coin can be as high as \$521. 25 million in present value terms and this project will still yield a positive net present value. . Recent Census Bureau data show that the average income to a college- educated person was \$34,391 versus ASS,CLC for those without college. At the same time, the annual tuition at public universities was \$1,566 versus \$7,693 for private colleges. In the following questions, assume there is no difference in income between public and private university graduates. A. Based on these figures, what is the payback period for a college education, akin into account the four years of lost earnings while being in college? Do these calculations for both public and private colleges.

Answer: Based on the figures presented, the lost income during four years of college is 4 * 524,701 = 598,804 (if they don’t go to college they earn Nan-college incomes). The cost of the four years of college at a public (private) university is 56,264 (\$30,772). Combining these figures yields a total (undiscovered) cost for a public university of \$105,068. For a private college. This cost comes to \$129,576. The income advantage to a college education is 59,690 (534,391 . \$24,701). From radiation, it takes 105,068/3,690 = 10. 4 years to recover the cost of a public university education. The equivalent figure for a private college is 129,576/9,690 13. 37 years. B. Assuming college graduation at age 22 and retirement at age 65, what is the internal rate of return on a college degree from a public university? A private university? Answer: For a public university, the cash flows are four years of annual net cash outflows equal to \$26,267 (\$1 ,566 + \$24,701) and then 43 years of net cash inflows equal to \$9,690 annually, Whether all these cash flows occur at the beginning or end of the year, the AIR equals 7. Percent (the timing of the cash flows doesn’t matter because you are just multiplying the NAP-?which must equal zero-?by a constant). Poor a private university, the cash flows are four years of annual net cash outflows equal to \$32,394 (\$7,693 + \$24, 701) and then 43 years of net cash inflows equal to 59,690 annually. The AIR based on these numbers is 6. 32 percent. C. Assuming a 7 percent discount rate, and the same working life as in part b, what is the net present value of a college degree from a public university? A private university?

Answer: Assuming all cash flows occur at the end Of the year (here the timing goes matter), the NAP for a public university education is \$10,878. For a private college, the WV is . \$9,876. 6. The Fun Foods Corporation must decide on what new product lines to introduce next year, After-tax cash flows are listed below along with initial investments. The firm’s cost of capital is 12 percent and its target accounting rate of return is 20 percent, Assume straight-line depreciation and an asset life of five years. The corporate tax rate is 35 percent. All projects are independent.

I Project | \$1,250 | 1,200 I Yearly I Investment \$3,000 I s,coo 11,200 | 55,000 12,400 \$800 17,500 ,000 \$1,000 1,250 4,000 14 | 5350 | 600 a. Calculate the accounting rate of return on the project. Which projects are acceptable according to this criterion? (Note: Assume net income is equal to after-tax cash flow less depreciation. ) I Project A Total AT Cash Flow I Total Depreciation I Net Income Avgas Net Income | 5400 shoo 11400 1280 Project B 116750 7500 9250 Project C 18400 14000 | 4400 1880 Cacti Rate of return (Average Net Income “Average Book NV) ABA = Total depreciation/2. I 49. % Projects 8 and C are acceptable based on a 20% accounting rate of return. B. Calculate the payback period. All projects with a payback of fewer than four years are acceptable. Which are acceptable according to this criterion? Answer: Assuming depreciation effects are included in the cash flows: Payback A (years) 4. 53, Payback B Payback C 3,42_ Projects B and C are acceptable. Assuming depreciation has not been included: Payback A (years) = 4. 06, Payback B = 2. 73, Payback C = 3. 06. Projects B and C are c. Calculate the projects’ Naps. Which are acceptable according to this criterion?

Answer: NAP IV(After Tax Cash Flows) -? Initial Investment Assuming depreciation has already been incorporated: NAP A–?\$742. 2, NIB- 33801. 83, C – 51574. 01. Projects B and C are acceptable. If depreciation has not been incorporated, and all writers Gang be used: NAP = IV(After Tax Cash Flows)-? Nit NV IV(Deep Tax Shield) NAP A- \$518. 95, NAP B = ASSESS,34, NAP C = \$2583. 34, All projects are acceptable. D. Calculate the projects’ IR, Which are acceptable according to this Answer: AIR is the discount rate that makes NAP = 0. Depreciation included: AURA= 7. 0%, AIR 27. %, Projects B and C are acceptable. (AIR > 12%) Depreciation not included: AURA= 15. 43%, All projects are acceptable. (AIR > 12%) e. Which projects should be chosen? Answer: The firm should follow the guidelines of the NAP rule. 7. Aptest, Inc. , is negotiating with the U. S. Department of Housing and urban Development (HUT) to open a manufacturing plant in South Central L. A. , the scene of much of the rioting in April 1992. The proposed plant will cost \$3. 5 million and is projected to generate annual after-tax profits of \$550,000 million over its estimated tour-year elite.

Depreciation is straight-line over the tour-year period and Aptest;s tax rate is 35 percent, However, given the risks involved, Aptest is looking for a tax-exempt government subsidy. According to Aptest, the subsidy Just be able to achieve any of the following four objectives: (l) Provide a 2-year payback. (2) Provide an accounting rate of return of 35 percent. (3) Raise the plants AIR to 22 percent. (4) Provide an NAP of \$1 million when cash flows are discounted at 18 percent. A. Poor each alternative suggested by Aptest, develop a subsidy plan that minimizes the costs to HUT of achieving Pate’s objective.

You can schedule the subsidy payments at any time over the four-year period. Answer. Here are the alternatives With their costs: Payback. The annual cash flow,s are the sum of after-tax profits plus depreciation of \$306,250 or \$856,250. The sum of the first two years’ cash flows is \$1 , 712,500. To bring the payback to two years will require a subsidy of \$1 ; \$1 Since the computation of payback is insensitive to when the subsidy is paid, as long as it happens within the two-year period, the present value of its cost can be minimized by providing it at the end of year 2. AIR.

The accounting rate of return is 31. 43% In order to bring this up to 35%, it is necessary to bring average annual income up to \$612,500 , 750,000), an average annual increase of 62,500. The subsidy will equal \$250,000 Since the computation of AIR is insensitive to when the busily is received, its present value can be minimized by providing it at the end of the four years. AIR. With a subsidy of at time O, thereby lowering its net investment to Aptest will get its AIR up to 22%. Any delay will result in a correspondingly higher required subsidy (it will accrue at the rate of 22% annually. Or example, if the subsidy were to be provided at the end Of the first year, it would have to equal \$1 ? 1. 22) to get Aptest AIR up to 22%. Hence, HELD Will minimize its costs Of getting Pate’s AIR up to 22% by providing the subsidy immediately instead of waiting. NAP. The NAP of the project, discounted at 18%, is (1,196,635). Hence, a subsidy equal to \$1 , 196,635 that is paid up front will just provide a zero NAP when discounted at 18%. The subsidy will rise at the rate of 18% annually if it is paid in a future year. B.

Which of the four subsidy plans would you recommend to HUT if it uses a 15 percent discount rate? Answer. The winning subsidy plan is that associated with the AIR criterion, go paying \$250,000 at the end of the tour-year period, the present value of Hut’s cost when discounted at will be \$142,938. 8. The Fast Food chain is trying to introduce its new Hot and Spicy line of ambushers. One plan (S) will include a big media campaign but less in-house production capability. The other plan (L) will concentrate on a more gradual roll- out of the project but will involve more investment in personnel training and so forth.