13 CHAPTER CAPITAL INVESTMENT DECISIONS
QUESTIONS FOR WRITING AND DISCUSSION
1. Independent projects are such that the acceptance of one does not preclude the acceptance of another. With mutually exclusive projects, acceptance of one precludes the acceptance of others. 2. The timing and quantity of cash flows determine the present value of a project. The present value is critical for assessing whether a project is acceptable or not. 3. By ignoring the time value of money, good projects can be rejected and bad projects accepted. 4. The payback period is the time required to recover the initial investment. Payback = $80,000/$30,000 = 2.67 years 5. (a) A measure of risk. Roughly, projects with shorter paybacks are less risky. (b) Obsolescence. If the risk of obsolescence is high, firms will want to recover funds quickly. (c) Self-interest. Managers want quick paybacks so that short-run performance measures are affected positively, enhancing chances for bonuses and promotion. Also, this method is easy to calculate. 6. The accounting rate of return is the average income divided by original or average investment. ARR = $100,000/$300,000 = 33.33% 7. Agree. Essentially, net present value is a measure of the return in excess of the investment and its cost of capital. 8. NPV measures the increase in firm value from a project. 9. The cost of capital is the cost of investment funds and is usually viewed as the weighted average of the costs of funds from all sources. It should serve as the discount rate for calculating net present value or the benchmark for IRR analysis. 10. For NPV, the required rate of return is the discount rate. For IRR, the required rate of return is the benchmark against which the IRR is compared to determine whether an investment is acceptable or not. 11. If NPV > 0, then the investment is accept able. If NPV < 0, then the investment should be rejected. Disagree. Only if the funds received each period from the investment are reinvested to earn the IRR will the IRR be the actual rate of return. Postaudits help managers determine if resources are being used wisely. Additional resources or corrective action may be needed. Postaudits also serve to encourage managers to make good capital investment decisions. They also provide feedback that may help improve future decisions. NPV signals which investment maximizes firm value; IRR may provide misleading signals. IRR may be popular because it provides the correct signal most of the time and managers are accustomed to working with rates of return. Often, investments must be made in assets that do not directly produce revenues. In this case, choosing the asset with the least cost (as measured by NPV) makes sense. NPV analysis is only as good as the accuracy of the cash flows. If projections of cash flows are not accurate, then incorrect investment decisions may be made. The quality and reliability of the cash flow projections are directly related to the assumptions and methods used for forecasting. If the assumptions and methods are faulty, then the forecasts will be wrong, and incorrect decisions may be made. The principal tax implications that should be considered in Year 0 are gains and losses on the sale of existing assets. The MACRS method provides more shielding effect in earlier years than the straightline method does. As a consequence, the present value of the shielding benefit is greater for the MACRS method. The half-year convention assumes that an asset is in service for only a half year in the
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year of acquisition. Thus, only half of the first years depreciation can be claimed, regardless of the date on which use of the asset actually began. It increases the length of time depreciation is recognized by one year over the indicated class life. 21. Intangible and indirect benefits are of much greater importance in the advanced manufacturing environment. Greater quality, more reliability, improved delivery, and the ability to maintain or increase market share are ex-
amples of intangible benefits. Reduction in support labor in such areas as scheduling and stores are indirect benefits. 22. Sensitivity analysis changes the assumptions on which the capital investment analysis is based. Even with sound assumptions, there is still the element of uncertainty. No one can predict the future with certainty. By changing the assumptions, managers can gain insight into the effects of uncertain future events.
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EXERCISES 131 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. a e c a d e c b d e 11. b 12. 13. 14. 15. 16. 17. 18. 19. 20. c a e c a e b e c
132 1. 2. Payback period = $200,000/$60,000 = 3.33 years Payback period: $125,000 1.0 year 175,000 1.0 year 200,000 0.8 year
$500,000 2.8 years 3. Investment = annual cash flow payback period = $120,000 3 = $360,000
4. Annual cash flow = Investment/payback period = $250,000/2.5 = $100,000 per year
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133 1. Initial investment(Average depreciation = 300,000): Accounting rate of return = Average accounting income/Investment
= ($2,500,000 $2,000,000 - $300,000)/$1,500,000 = 13.3%
2. Accounting rate of return (ARR): Project A:ARR = ($12,800 $4,000)/$20,000 = 44% Project B:ARR = ($7,600 $2,000)/$20,000 = 18% Project A should be chosen. 3. ARR = Average Net Income/Average Investment 0.25 = $100,000/Average Investment Average Investment = $100,000/0.25 = $400,000 Thus, Investment = 2 $400,000 = $800,000 4. ARR = Average Net Income/Investment
0.50 = Average Net Income/$200,000 Average Net Income = 0.50 $200,000 = $100,000
134 1. NPV = P I = (5.650 $240,000) $1,360,000 = $(4,000) The system should not be purchased. 2. NPV = P I = (4.623 $9,000) $30,000 = $11,607 Yes, he should make the investment.
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3. NPV = P - I I = P NPV I = 4.355 $10,000 - $3,550 = $40,000 135 P 1. = CF(df) = I for the IRR, thus, df = Investment/Annual cash flow = $1,563,500/$500,000 = 3.127 For five years and a discount factor of 3.127, the IRR is 18%. 2. P = CF(df) = I for the IRR, thus, df = $521,600/$100,000 = 5.216 For ten years, and a discount factor of 5.216, IRR = 14% Yes, the investment should be made. 3. CF(df) = I for the IRR, thus, CF = I/df = $2,400,000/4.001 =$599,850.
13-6
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Larson Blood Analysis Equipment: Year 0 1 2 3 4 5 NPV Cash Flow $(200,000) 120,000 100,000 80,000 40,000 20,000 Discount Factor 1.000 0.893 0.797 0.712 0.636 0.567 Present Value $(200,000) 107,160 79,700 56,960 25,440 11,340 $ 80,600
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13-6 Concluded Lawton Blood Analysis Equipment: Year 0 1 2 3 4 5 NPV Cash Flow $(200,000) 20,000 20,000 120,000 160,000 180,000 Discount Factor 1.000 0.893 0.797 0.712 0.636 0.567 Present Value $(200,000) 17,860 15,940 85,440 101,760 102,060 $ 123,060
2. CF(df) I = NPV CF(3.605) - $200,000 = $123,060 (3.605)CF = $323,060 CF = $323,060/3.605 CF = $89,614 per year Thus, the annual cash flow must exceed $89,614 to be selected. 137 1. Payback period = Original investment/Annual cash inflow = $800,000/($1,300,000 $1,000,000) = $800,000/$300,000 = 2.67 years a. Initial investment(Average depreciation = 160,000): Accounting rate of return = Average accounting income/Investment = ($300,000 $160,000)/$800,000 = 17.5%
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13-7 Concluded
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3.
Year 0 1 2 3 4 5 NPV
Cash Flow $(800,000) 300,000 300,000 300,000 300,000 300,000
Discount Factor 1.000 0.909 0.826 0.751 0.683 0.621
Present Value $(800,000) 272,700 247,800 225,300 204,900 186,300 $ 337,000
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P = CF(df) = I for the IRR, thus, df = Investment/Annual cash flow = $800,000/$300,000 = 2.67 For five years and a discount factor of 2.67, the IRR is between 24 and 26%.
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PROBLEMS 1322
1. The IRR using the best estimates: Selling price Unit variable cost Unit contribution margin Per unit $10 4 $6 $ 6,000,000 2,000,000 $ 4,000,000
Total contribution margin ($6 1,000,000 annual sales volume) Less: Fixed costs Annual cash flow Discount factor = $12,000,000/$4,000,000 = 3.00
Five years and a discount factor of 3.00 implies a rate of approximately 20 percent. 2. a. If the per-unit selling price is reduced 10 percent, the adjusted IRR is 8 percent, as calculated below: Per unit 90% of selling price $9 Unit variable cost 4 Contribution margin $5 Total contribution margin ($5 1,000,000 annual sales volume) $5,000,000 Less: Fixed costs 2,000,000 Annual cash flow $3,000,000 Discount factor = $12,000,000/$3,000,000 = 4.00, which implies an IRR that is approximately 8 percent. b. If the per-unit sales volume is reduced 10 percent, the adjusted IRR is 13 percent, as calculated below: Per unit Selling price $10 Unit variable cost 4 Contribution margin $6 Total contribution margin ($6 900,000 annual sales volume) Less: Fixed costs Annual cash flow $5,400,000 2,000,000 $3,400,000
Discount factor = $12,000,000/$3,400,000 = 3.53, which implies an IRR that is approximately 13 percent (IRR between 12 and 14 percent).
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c. If the per-unit variable cost is reduced 10 percent, the adjusted IRR is 24 percent, as calculated below: Per unit Selling price $10.00 Unit variable cost 3.60 Contribution margin $ 6.40 Total contribution margin ($6.40 1,000,000 annual sales volume) Less: Fixed costs Annual cash flow $6,400,000 2,000,000 $4,400,000
Discount factor = $12,000,000/$4,400,000 = 2.73, which implies an IRR that is approximately 24 percent. 3. Sensitivity analysis determines the impact that certain changes in assumptions have on IRR or NPV as appropriate. It helps management to identify key variables and to know whether additional information is needed. It also helps determine the volatility of the project. Sensitivity analysis is limited because it provides no information about probability and uncertainty. The range of values possible with their probability of occurrence are important information. It also ignores the fact that assumptions are dynamic and can interact with each other.
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1324 1. 1.00 year 1.00 year 1.00 year 0.13 year* 3.13 years *$3,800/$29,400
$16,800 24,000 29,400 3,800 $74,000
Note: Cash flow = Increased revenue less cash expenses of $3,000 2. Accounting rate of return using original investment: Average cash flow = ($16,800 + $24,000 + $29,400 + $29,400)/4 = $24,900 Average depreciation = ($74,000 $6,000)/4 = $17,000 Accounting rate of return = ($24,900 $17,000)/$74,000 = $7,900/$74,000 = 10.7% Accounting rate of return using average investment: Accounting rate of return = $7,900/$40,000* = 19.8% *Average investment = (Investment + Salvage)/2 = ($74,000 + $6,000)/2
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1324 Concluded
3. Year 0 1 2 3 4 NPV Cash Flow $(74,000) 16,800 24,000 29,400 35,400* Discount Factor 1.000 0.893 0.797 0.712 0.636 Present Value $(74,000) 15,002 19,128 20,933 22,514 $ 3,577
*Includes $6,000 salvage value IRR (by trial and error): Using 14 percent as the first guess: Year Cash Flow 0 $(74,000) 1 16,800 2 24,000 3 29,400 4 35,400 NPV The IRR is about 14 percent. The equipment should be purchased. (The NPV is positive and the IRR is larger than the cost of capital.) Dr. Avard should not be concerned about the accounting rate of return in making this decision. The payback, however, may be of some interest, particularly if cash flow is of concern to Dr. Avard. 4. Year 0 1 2 3 4 NPV Cash Flow $(74,000) 11,200 16,000 19,600 25,600 Discount Factor 1.000 0.893 0.797 0.712 0.636 Present Value $(74,000) 10,002 12,752 13,955 16,282 $(21,009) Discount Factor 1.000 0.877 0.769 0.675 0.592 Present Value $(74,000) 14,734 18,456 19,845 20,957 $ (8)
For Years 14, the cash flows are 2/3 of the original cash flow increases. Year 4 also includes $6,000 salvage value. Given the new information, Dr. Avard should not buy the equipment.
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