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Answers to Warm-Up Exercises
E12-1. Sensitivity analysis
Answer: Using the 12% cost of capital to discount all of the cash flows for each scenario to yield the following NPVs, resulting in a NPV range of $19,109.78:
Pessimistic Most Likely Optimistic $3,283.48 $6,516.99 $15,826.
E12-2. Using IRR selection criteria
Answer: The minimum amount of annual cash inflow needed to earn 8% is $11,270.
N 5, I 8%, PV $45, Solve for PMT $11,270. The IRR of the project is 12.05%. N 5, PV $45,000, PMT $12, Solve for I $12.05% The project is acceptable since its IRR exceeds the firm’s 8% cost of capital. Since the required cash flow is much less than the anticipated cash flow, one would expect the IRR to exceed the required rate of return.
E12-3. Risk-adjusted discount rates
Answer: Project Sourdough RADR 7.0%
N 7, I 7%, PMT $5, Solve for PV $29,641. NPV PVn Initial investment NPV $29,641.09 $12, NPV $17,141.
Project Greek Salad RADR 8.0% N 7, I 8%, PMT $4, Solve for PV $20,825. NPV PVn Initial investment NPV $20,825.48 $7, NPV $13,325.
Yeastime should select Project Sourdough.
E12-4. ANPV
Answer: You may use a financial calculator to determine the IRR of each project. Choose the project with the higher IRR. Project M Step 1: Find the NPV of the project
NPVM Key strokes CF 0 -$35,000, CF 1 $12,000, CF 2 $25,000, CF 3 $30, Set I 8% Solve for NPV $21,359. Step 2: Find the ANPV N 3, I 8, PV $21,359. Solve for PMT $8,288. Project N Step 1: Find the NPV of the project NPVM Key strokes CF 0 -$55,000, CF 1 $18,000, CF 2 $15,000, CF 3 $25, CF 4 $10,000, CF 5 $8,000, CF 6 $5,000, CF 7 $5, Set I 8% Solve for NPV $13,235. Step 2: Find the ANPV N 7, I 8, PV $13,235. Solve for PMT $2,542. Based on ANPV, you should advise Outcast, Inc. to choose Project M.
E12-5. NPV profiles
Answer: The investment opportunity schedule (IOS) in this problem does not allow us to determine the maximum NPV allowed by the budget constraint. In order to determine whether the IOS maximizes the NPV for Longchamps Electric, we will need to know the NPV for each of the six projects. However, it does appear likely that Longchamps Electric will maximize firm value by selecting Project 4 (IRR 11%), Project 2 (IRR 10%), and Project 5 (IRR 9%). The total investment in these three projects will be $135,000, leaving $15,000 excess cash for future investment opportunities.
P12-2. Breakeven cash flows
LG 2; Intermediate a. N 12, I 14%, PV $35, Solve for PMT $6,183. b. N 12, I 10%, PV $35, Solve for PMT $5,136. The required cash flow per year would decrease by $1,047.27.
P12-3. Breakeven cash inflows and risk
LG 2; Intermediate a. Project X Project Y N 5, I 15%, PMT $10,000 N 5, I 15%, PMT $15, Solve for PV 33,521.55 Solve for PV $50,282. NPV PV initial investment NPV PV initial investment NPV $33,521.55 $30,000 NPV $50,282.33 $40, NPV $3,521.55 NPV $10,282. b. Project X Project Y N 5, I 15%, PV $30,000 N 5, I 15%, PV $40, Solve for PMT $8,949.47 Solve for PMT $11,932. c. Project X Project Y Probability 60% Probability 25% d. Project Y is more risky and has a higher potential NPV. Project X has less risk and less return while Project Y has more risk and more return, thus the risk-return tradeoff. e. Choose Project X to minimize losses; to achieve higher NPV, choose Project Y.
P12-4. Basic scenario analysis
LG 2; Intermediate a. Range A $1,800 $200 $1,600 Range B $1,100 $900 $ b.
NPVs
Outcome Project A Project B
Pessimistic (^) $ 6,297.29 $ 337. Most likely 513.56 513. Optimistic 7,324.41 1,364. Range $13,621.70 $1,702.
c. Although the ―most likely‖ outcome is identical for Project A and B, the NPV range varies considerably. d. Project selection would depend upon the risk disposition of the management. (A is more risky than B but also has the possibility of a greater return.)
P12-5. Scenario analysis
LG 2; Intermediate a. Range P $1,000 $500 $ Range Q $1,200 $400 $ b.
NPVs
Outcome Project P Project Q
Pessimistic $72.28 $542. Most likely 1,608.43 1,608. Optimistic 3,144.57 4,373.
c. Range P $3,144.57 $72.28 $3,072. Range Q $4,373.48 ( $542.17) $4,915. Each computer has the same most likely result. Computer Q has both a greater potential loss and a greater potential return. Therefore, the decision will depend on the risk disposition of management.
P12-6. Personal Finance: Impact of inflation on investments
LG 2; Easy a. c.
Year
Investment Cash Flows
Current NPV (a)
Higher Inflation NPV (b)
Lower Inflation NPV (c)
0 1 2 3 4 5 (7,500) 2, 2, 2, 1, 1,
Total NPV $ 58 $ (131) $ 254
d. As the inflation rate rises the NPV of a given set of cash flows declines.
P12-7. Simulation
LG 2; Intermediate a. Ogden Corporation could use a computer simulation to generate the respective profitability distributions through the generation of random numbers. By tying various cash flow assumptions together into a mathematical model and repeating the process numerous times, a probability distribution of project returns can be developed. The process of generating random numbers and using the probability distributions for cash inflows and outflows allows values for each of the variables to be determined. The use of the computer also allows for more sophisticated
d. After adjusting the discount rate, even though all projects are still acceptable, the ranking changes. Project G has the highest NPV and should be chosen.
P12-9. Risk-adjusted discount rates—Tabular
LG 4; Intermediate a. Project A N 5, I 8%, PMT $7, Solve for PV $27,948. NPV $27,948.97 $20, NPV $7,948. Project B N 5, I 14%, PMT $10, Solve for PV $34,330. NPV $34,330.81 $30, NPV $4,330. Project A, with the higher NPV, should be chosen. b. Project A is preferable to Project B, since the NPV of A is greater than the NPV of B.
P12-10. Personal Finance: Mutually exclusive investment and risk
LG 4; Intermediate a. N 6, I 8.5%, PMT $3, Solve for PV 13,660. NPV $13,660.76 $10, NPV $3,660. b. N 6, I 10.5%, PMT $3, Solve for PV $16,310. NPV $16,31.28 $12, NPV $4,310. c. Using NPV as her guide, Lara should select the second investment. It has a higher NPV. d. The second investment is riskier. The higher required return implies a higher risk factor.
P12-11. Risk-adjusted rates of return using CAPM
LG 4; Challenge a. rX 7% 1.2(12% 7%) 7% 6% 13% rY 7% 1.4(12% 7%) 7% 7% 14% NPV calculation for X: N 4, I 13%, PMT $30, Solve for PV 89,234. NPV $89,234.14 $70, NPV $19,234. NPV calculation for Y: CF 0 -$78,000, CF 1 $22,000, CF 2 $32,000, CF 3 $38,000, CF 4 $46, Set I 14% Solve for NPV $18,805.
b. The RADR approach prefers Project Y over Project X. The RADR approach combines the risk adjustment and the time adjustment in a single value. The RADR approach is most often used in business.
P12-12. Risk classes and RADR
LG 4; Basic a. Project X
CF 0 -$180,000, CF 1 $80,000, CF 2 $70,000, CF 3 $60,000, CF 4 $60,000, CF 5 $60, Set I 22% Solve for NPV $14.930.
Project Y
CF 0 -$235,000, CF 1 $50,000, CF 2 $60,000, CF 3 $70,000, CF 4 $80,000, CF 5 $90, Set I 13% Solve for NPV $2,663.
Project Z CF 0 -$310,000, CF 1 $90,000, CF 2 $90,000, CF 3 $90,000, CF 4 $90,000, CF 5 $90, [or, CF 0 -$310,000, CF 1 $90,000, F 1 5] Set I 15% Solve for NPV -$8,306.
b. Projects X and Y are acceptable with positive NPVs, while Project Z with a negative NPV is not. Project X, with the highest NPV, should be undertaken.
P12-13. Unequal lives—ANPV approach
LG 5; Intermediate a. Machine A CF 0 -$92,000, CF 1 $12,000, CF 2 $12,000, CF 3 $12,000, CF 4 $12,000, CF 5 $12,000, CF 6 $12, [or, CF 0 -$92,000, CF 1 $12,000, F 1 6] Set I 12% Solve for NPV -$42,663.
Machine B CF 0 -$65,000, CF 1 $10,000, CF 2 $20,000, CF 3 $30,000, CF 4 $40, Set I 12% Solve for NPV $6,646.
Machine C CF 0 -$100,500, CF 1 $30,000, CF 2 $30,000, CF 3 $30,000, CF 4 $30,000, CF 5 $30, [or, CF 0 -$105,000, CF 1 $30,000, F 1 5]
Rank Project 1 Z 2 X 3 Y
b. Project X N 4, I 14%, PV $ Solve for ANPV (PMT) – $9,260. Project Y N 2, I 14%, PV $1801. Solve for ANPV (PMT) $1,093. Project Z N 5, I 14%, PV $3582. Solve for ANPV (PMT) $1,043.
Rank Project 1 X 2 Y 3 Z
c. Project Y should be acquired since it offers the highest ANPV. Not considering the difference in project lives resulted in a different ranking based primarily on the unequal lives of the projects.
P12-15. Unequal lives—ANPV approach
LG 5; Intermediate a. Sell
CF 0 -$200,000, CF 1 $200,000, CF 2 $250, Set I 12% Solve for NPV $177,869.
License CF 0 -$200,000, CF 1 $250,000, CF 2 $100, CF 3 $80,000, CF 4 $60,000, CF 5 $40, Set I 12% Solve for NPV $220,704.
Manufacture CF 0 -$450,000, CF 1 $200,000, CF 2 $250,000, CF 3 $200,000, CF 4 $200,000, CF 5 $200,000, CF 6 $200, [or, CF 0 -$450,000, CF 1 $200,000, F 1 1, CF 2 $250,000, F 2 1, CF 3 $200,000, F 3 4] Set I 12% Solve for NPV $412,141.
Rank Alternative 1 Manufacture 2 License 3 Sell
b. Sell N 2, I 12%, PV $ Solve for ANPV (PMT) $105,245. License N 5, I 12%, PV $220,704. Solve for ANPV (PMT) $61,225. Manufacture N 6, I 12%, PV $412,141. Solve for ANPV (PMT) $100,243.
Rank Alternative 1 Sell 2 Manufacture 3 License
c. Comparing the NPVs of projects with unequal lives gives an advantage to those projects that generate cash flows over the longer period. ANPV adjusts for the differences in the length of the projects and allows selection of the optimal project. This technique implicitly assumes that all projects can be selected again at their conclusion an infinite number of times.
P12-16. NPV and ANPV decisions
LG 5; Challenge
a. – b. (^) Unequal-Life Decisions Annualized Net Present Value (ANPV)
Samsung Sony Cost Annual Benefits Life Terminal value Required rate of return
3 years $ 9.0%
4 years $ 9.0%
a. CF 0 -$2,350, CF 1 $900, CF 2 $900, CF 3 $900 + $400 $1, Set I 9% Solve for NPV $237.
b. N 3, I 9%, PV $237. Solve for ANPV (PMT) $93.
c. CF 0 -$2,700, CF 1 $1,000, CF 2 $1,000, CF 3 $1,000, CF 4 $1,000 + $350 $1, Set I 9%
the best option is to choose Projects B, F, and G, which also use the entire capital budget and provide an NPV of $900,000. c. The internal rate of return approach uses the entire $4,500,000 capital budget but provides $200,000 less present value ($5,400,000 – $5,200,000) than the NPV approach. Since the NPV approach maximizes shareholder wealth, it is the superior method. d. The firm should implement Projects B, F, and G, as explained in part c.
P12-19. Capital Rationing—NPV Approach
LG 6; Intermediate
a. (^) Project PV Initial Investment Total Investment A $384, B 210, C 125,000 $100,000 $100, D 990, E 570, F 150,000 $100,000 $200, G 960,000 $800,000 $1,000,
b. The optimal group of projects is Projects C, F, and G, resulting in a total net present value of $235,000. Project G would be accepted first because it has the highest NPV. Its selection leaves enough of the capital budget to also accept Project C and Project F.
P12-20. Ethics problem
LG 4; Challenge Student answers will vary. Some students might argue that companies should be held accountable for any and all pollution that they cause. Other students may take the larger view that the appropriate goal should be the reduction of overall pollution levels, and that carbon credits are a way to achieve that goal. From an investor standpoint, carbon credits allow the polluting firm to meet legal obligations in the most cost-effective manner, thus improving the bottom line for the company and investor.
