Chapter 9. Ross, Westerfield and Jordan, ECF 4 th ed 2004 Solutions. Answers to Concepts Review and Critical Thinking Questions

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1 Ross, Westerfield and Jordan, ECF 4 th ed 2004 Solutions Chapter 9. Answers to Concepts Review and Critical Thinking Questions 1. In this context, an opportunity cost refers to the value of an asset or other input that will be used in a project. The relevant cost is what the asset or input is actually worth today, not, for example, what it cost to acquire. 2. For tax purposes, a firm would choose MACRS because it provides for larger depreciation deductions earlier. These larger deductions reduce taxes, but have no other cash consequences. Notice that the choice between MACRS and straight-line is purely a time value issue; the total depreciation is the same, only the timing differs. 3. It s probably only a mild over-simplification. Current liabilities will all be paid presumably. The cash portion of current assets will be retrieved. Some receivables won t be collected, and some inventory will not be sold, of course. Counterbalancing these losses is the fact that inventory sold above cost (and not replaced at the end of the project s life) acts to increase working capital. These effects tend to offset. 4. Management s discretion to set the firm s capital structure is applicable at the firm level. Since any one particular project could be financed entirely with equity, another project could be financed with debt, and the firm s overall capital structure remain unchanged, financing costs are not relevant in the analysis of a project s incremental cash flows according to the stand-alone principle. 5. Depreciation is a non-cash expense, but it is tax-deductible on the income statement. Thus deprecia-tion causes taxes paid, an actual cash outflow, to be reduced by an amount equal to the depreciation tax shield t C D. A reduction in taxes that would otherwise be paid is the same thing as a cash inflow, so the effects of the depreciation tax shield must be added in to get the total incremental aftertax cash flows. 6. There are two particularly important considerations. The first is erosion. Will the essentialized book simply displace copies of the existing book that would have otherwise been sold? This is of special concern given the lower price. The second consideration is competition. Will other publishers step in and produce such a product? If so, then any erosion is much less relevant. A particular concern to book publishers (and producers of a variety of other product types) is that the publisher only makes money from the sale of new books. Thus, it is important to examine whether the new book would displace sales of used books (good from the publisher s perspective) or new books (not good). The concern arises any time there is an active market for used product. 7. This market was heating up rapidly, and a number of other manufacturers were planning competing products.

2 8. One company may be able to produce at lower incremental cost or market better. For example, GM may have been able to retool existing production more cheaply, and GM also has a larger dealer network. Also, of course, one of the two may have made a mistake! 9. GM would recognize that the outsized profits would dwindle as more products come to market and competition becomes more intense. 10. With a sensitivity analysis, one variable is examined over a broad range of values. With a scenario analysis, all variables are examined for a limited range of values. 11. It is true that if average revenue is less than average cost, the firm is losing money. This much of the statement is therefore correct. At the margin, however, accepting a project with a marginal revenue in excess of its marginal cost clearly acts to increase operating cash flow. 12. The implication is that they will face hard capital rationing. 13. Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows. The danger is greatest with a new project because the cash flows are probably harder to predict. 14. The option to abandon reflects our ability to reallocate assets if we find our initial estimates were too optimistic. The option to expand reflects our ability to increase cash flows from a project if we find our initial estimates were too pessimistic. Since the option to expand can increase cash flows and the option to abandon reduces losses, failing to consider these two options will generally lead us to underestimate a project s NPV. Solutions to Questions and Problems Basic 1. The $6 million acquisition cost of the land six years ago is a sunk cost. The $6.8 million current appraisal of the land is an opportunity cost if the land is used rather than sold off, therefore it represents part of the project s initial investment. The $10 million cash outlay and $500,000 grading expenses are the initial fixed asset investments needed to get the project going. Therefore, the proper year zero cash flow to use in evaluating this project is $6,800, ,000, ,000 = $17.3 million. 2. Sales due solely to the new product line are 12,000($15,000) = $180 million. Increased sales of the motor home line occur because of the new product line introduction; thus 2,000($50,000) = $100 million in new sales is relevant. Erosion of luxury motor coach sales is also due to the new mid-size campers; thus 1,000($90,000) = $90 million loss in sales is relevant. The net sales figure to use in evaluating the new line is thus $180 million million 90 million = $190 million.

3 3. Sales $ 800,000 Variable costs 480,000 Fixed costs 190,000 Depreciation 95,000 EBIT $ 35,000 Taxes@35% 12,250 Net income $ 22, Sales $ 612,800 OCF = EBIT + D T Variable costs 321,680 = $186, ,000 65,142 = $225,978 Depreciation 105,000 Depreciation tax shield = t c D EBIT $ 186,120 =.35($105,000) = $36,750 Taxes@35% 65,142 Net income $ 120, Beginnin g Beginning Book Value Depreciatio n Depreciatio n Ending Book Value 1 $861, $123,036.9 $737, , , , , , , , , , , , , , , , , , , , , BV 5 = $520, ,000( 5 / 8 ) = $195,000 The asset is sold at a loss to book value, so the depreciation tax shield of the loss is recaptured. Aftertax salvage value = $125,000 + ($195, ,000)(0.35) = $149, BV 4 = $6.4M 6.4M( ) = $1,105,920 The asset is sold at a gain to book value, so this gain is taxable. Aftertax salvage value = $1,500,000 + ($1,105,920 1,500,000)(0.34) = $1,366, A/R fell by $6,720, and inventory increased by $4,484, so net current assets fell by $2,236 NWC = (CA CL) = $2,236 7,720 = $9,956 Net cash flow = S C NWC = $116,400 45,400 ( 9,956) = $80,956

4 9. Sales $1,920,000 Costs 985,000 Depreciation 600,000 EBIT 335,000 Taxes 117,250 Net income $ 217,750 OCF = EBIT + D T = $335, , ,250 = $817, NPV = $1.8M + 817,750(PVIFA 15%,3 ) = $67, Year Cash Flow 0 = $1.8M 250,000 $2,050, , , ,262,750 = $817, K + 300K(1 0.35) NPV = $2.05M + 817,750(PVIFA 15%,2 ) + ($1,262,750 / ) = $109, D 1 = $1.8M(0.3333) = $599,940 D 2 = $1.8M(0.4444) = $799,920 D 3 = $1.8M(0.1482) = $266,760 BV 3 = $1.8M (599, , ,760) = $133,380 The asset is sold at a gain to book value, so this gain is taxable. Aftertax salvage value = $300,000 + (133, ,000)(0.35) = $241,683 OCF t = (S C)(1 t c ) + t c D t, so: Year Cash Flow 0 = $1.8M 250,000 $2,050, ,729 = ($1.92M 985K)(0.65) ($599,940) 2 887,722 = ($1.92M 985K)(0.65) ($799,920) 3 1,192,799 = ($1.92M 985K)(0.65) ($266,760) + 250, ,683 NPV = $2.05M + ($817,729/1.15) + ($887,722/ ) + ($1,192,799/ ) = $116, Annual depreciation charge = $460,000/5 = $92,000 Aftertax salvage value = $40,000(1 0.34) = $26,400 OCF = $118,000(1 0.34) ($92,000) = $109,160 NPV = $460,000 27, ,160(PVIFA 10%,5 ) + [($26, ,000) / ] = $14, Annual depreciation charge = $700,000/5 = $140,000 Aftertax salvage value = $160,000(1 0.35) = $104,000 OCF = $300,000(1 0.35) ($140,000) = $244,000 NPV = 0 = $700, ,000 + $244,000(PVIFA IRR%,5 ) + [($104,000 70,000) / (1+IRR) 5 ] IRR = 27.82%

5 15. $250K cost savings case: OCF = $250,000(1 0.35) ($140,000) = $211,500 NPV = $700, ,000 + $211,500(PVIFA 20%,5 ) + [($104,000 70,000) / (1.20) 5 ] = $16, $200K cost savings case: OCF = $200,000(1 0.35) ($140,000) = $179,000 NPV = $700, ,000 + $179,000(PVIFA 20%,5 ) + [($104,000 70,000) / (1.20) 5 ] = $81, Base Case Best Case Worst Case Unit sales 80,000 92,000 68,000 Price/unit $1,380 $1,587 $1,173 Variable cost/unit $140 $119 $161 Fixed costs $7,000,000 $5,950,000 $8,050, An estimate for the impact of changes in price on the profitability of the project can be found from the sensitivity of NPV with respect to price; NPV/ P. This measure can be calculated by finding the NPV at any two different price levels and forming the ratio of the changes in these parameters. Whenever a sensitivity analysis is performed, all other variables are held constant at their basecase values. 18. a. D = $1,260,000/6 = $210,000 per year OCF base = [(P v)q FC](1 t c ) + t c D = [($35 19)(105K) 950K](0.65) ($210K) = $548,000 NPV base = $1,260,000 + $548,000(PVIFA 15%,6 ) = $813, Say Q = 100,000: OCF new = [($35 19)(100K) 950K](0.65) ($210K) = $496,000 NPV base = $1,260,000 + $496,000(PVIFA 15%,6 ) = $617, NPV/ S = ($813, ,103.42)/(105, ,000) = +$ If sales were to drop by 500 units then, NPV would drop by $39.359(500) = $19,679 b. Say v = $17: OCF new = [($35 18)(105K) 950K](0.65) ($210K) = $616,5250 OCF/ v = ($548, ,250)/($19 18) = $68,250 If variable costs fell by $1 then, OCF would rise by $68, OCF best = {[($35)(1.1) (19)(0.9)](105K)(1.1) 950K(0.9)}(0.65) ($210K) = $1,124,355 NPV best = $1,260,000 + $1,124,355(PVIFA 15%,6 ) = $2,995, OCF worst = {[($35)(0.9) (19)(1.1)](105K)(0.9) 950K(1.1)}(0.65) ($210K) = $45,355 NPV worst = $1,260,000 + $45,355(PVIFA 15%,6 ) = $1,088, The marketing study is a sunk cost and should be ignored. Sales $380,000 OCF = EBIT + D T = $99, ,000 39,600 Variable 76,000 = $119,400 costs Costs 145,000 Payback Period = $240,000/$119,400 = 2.01 years Depreciation 60,000 NPV = $240K + $119,400(PVIFA 13%,4 ) = $115, EBIT 99,000 IRR = $240K = $119,400(PVIFA R%,4 ) = 34.59% Taxes 39,600 Net income $ 59,400

6 Intermediate 21. D 1 = $500,000(0.2000) = $100,000; D 2 = $500,000(0.3200) = $160,000 D 3 = $500,000(0.1920) = $96,000; D 4 = $500,000(0.1152) = $57,600 BV 4 = $500,000 ($100, , , ,600) = $86,400 The asset is sold at a gain to book value, so this gain is taxable. After-tax salvage value = $80,000 + ($86,400 80,000)(0.34) = $82,176 OCF 1 = $200,000(1 0.34) ($100,000) = $166,000 OCF 2 = $200,000(1 0.34) ($160,000) = $186,400 OCF 3 = $200,000(1 0.34) ($96,000) = $164,640 OCF 4 = $200,000(1 0.34) ($57,600) = $151,584 NPV = $500,000 18,000 + ($166,000 3,000)/ ($186,400 3,000)/ ($164,640 3,000)/ ($151, , ,176)/ = $17, ,000 units = [($28 16)(110,000) $170,000](0.66) ($390,000/3) = $803, ,000 units = [($28 16)(111,000) $170,000](0.66) ($390,000/3) = $811,120 Sensitivity = OCF/ Q = ($803, ,120)/(110, ,000) = +$7.92 OCF will increase by $7.92 for every additional unit sold. 23. a. Base Case Lower Bound Upper Bound Unit sales Variable cost/unit $13,500 $12,150 $14,850 Fixed costs $160,000 $144,000 $176,000 OCF base = [($18,000 13,500)(150) $160,000](0.65) ($820K/4) = $406,500 NPV base = $820, ,500(PVIFA 15%,4 ) = $340, OCF worst = [($18,000 14,850)(135) $176,000](0.65) ($820K/4) = $233, NPV worst = $820, ,762.50(PVIFA 15%,4 ) = $152, OCF best = [($18,000 12,150)(165) $144,000](0.65) ($820K/4) = $605, NPV best = $820, , (PVIFA 15%,4 ) = $908, b. Say FC are $150K: OCF = [($18,000 13,500)(150) $150,000](0.65) ($820K/4) = $413,000 NPV = $820,000 + $413,000(PVIFA 15%,4 ) = $359, NPV/ FC = ($340, ,106.06)/($160,000 $150,000) = $1.856 For every dollar FC increase, NPV falls by $ The marketing study and the research and development are both sunk costs and should be ignored. Sales New clubs $700 46,000 = $32,200,000 Exp. clubs $1,100 ( 12,000) = 13,200,000 Cheap clubs $300 20,000 = 6,000,000 $25,000,000

7 Var. costs New clubs $340 46,000 = $15,640,000 Exp. clubs $550 ( 12,000) = 6,600,000 Cheap clubs $100 20,000 = 2,000,000 $11,040,000 Sales $25,000,00 0 Variable costs 11,040,000 Costs 8,000,000 Depreciation 2,300,000 EBIT 3,660,000 Taxes 1,464,000 Net income $ 2,196,000 OCF = EBIT + D Taxes = $3,660, ,300,000 1,464,000 = $4,496,000 Payback period = 3 + $3.512M/$4.496M = 3.78 years NPV = $16.1M $0.9M + $4.496M(PVIFA 14%,7 ) + $0.9/ = $2,639, IRR = $16.1M $0.9M + $4.496M(PVIFA IRR%,7 ) + $0.9/IRR 7 = 18.85% 25. Base Case Lower Bound Upper Bound Unit sales (new) 46,000 41,400 50,600 Price (new) $700 $630 $770 VC (new) $340 $306 $374 Fixed costs $8,000,000 $7,200,000 $8,800,000 Sales lost (expensive) 12,000 10,800 13,200 Sales gained (cheap) 20,000 18,000 22,000 Best case Sales New clubs $770 50,600 = $38,962,000 Exp. clubs $1,100 ( 10,800) = 11,880,000 Cheap clubs $300 22,000 = 6,600,000 $33,682,000 Var. costs New clubs $306 50,600 = $15,483,600 Exp. clubs $550 ( 10,800) = 5,940,000 Cheap clubs $100 22,000 = 2,200,000 $11,743,600

8 Sales $33,682,00 0 Variable costs 11,743,600 Costs 7,200,000 Depreciation 2,300,000 EBIT 12,438,400 Taxes 4,975,360 Net income $ 7,463,040 OCF = EBIT + D Taxes = $12,438, ,300,000 4,975,360 = $9,763,040 NPV = $16.1M $0.9M + $9,763,040(PVIFA 14%,7 ) + $0.9/ = $25,226, Worst case Sales New clubs $630 41,400 = $26,082,000 Exp. clubs $1,100 ( 13,200) = 14,520,000 Cheap clubs $300 18,000 = 5,400,000 $16,962,000 Var. costs New clubs $374 41,400 = $15,483,600 Exp. clubs $550 ( 13,200) = 7,260,000 Cheap clubs $100 18,000 = 1,800,000 $10,023,600 Sales $16,962,00 0 Variable costs 10,023,600 Costs 8,800,000 Depreciation 2,300,000 EBIT 4,161,600 Taxes 1,664,640 Net income $2,496,960 *assumes a tax credit OCF = EBIT + D Taxes = $4,161, ,300, ,664,640 = $196,960 NPV = $16.1M $0.9M + ( $196,960)(PVIFA 14%,7 ) + $0.9/ = $17,484,950.93

CHAPTER 6 MAKING CAPITAL INVESTMENT DECISIONS

CHAPTER 6 MAKING CAPITAL INVESTMENT DECISIONS Answers to Concepts Review and Critical Thinking Questions 1. In this context, an opportunity cost refers to the value of an asset or other input that will