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Answers to Warm-Up Exercises
E10-1. Payback period Answer: The payback period for Project Hydrogen is 4.29 years. The payback period for Project Helium is 5.75 years. Both projects are acceptable because their payback periods are less than Elysian Fields’ maximum payback period criterion of 6 years.
E10-2. NPV Answer:
Year Cash Inflow Present Value 1 $400,000 $ 377,358. 2 375,000 333,748. 3 300,000 251,885. 4 350,000 277,232. 5 200,000 149,451. Total $1,389,677.
NPV $1,389,677.35 $1,250,000 $139,677. Herky Foods should acquire the new wrapping machine.
E10-3: NPV comparison of two projects Answer:
Project Kelvin Present value of expenses – $45, Present value of cash inflows 51,542 (PMT $20,000, N 3, I 8, Solve for PV) NPV $ 6, Project Thompson Present value of expenses $275, Present value of cash inflows 277,373 (PMT $60,000, N 6, I 8, Solve for PV) NPV $ 2, Based on NPV analysis, Axis Corporation should choose an overhaul of the existing system.
E10-4: IRR Answer: You may use a financial calculator to determine the IRR of each project. Choose the project with the higher IRR.
Project T-Shirt PV 15,000, N 4, PMT 8, Solve for I IRR 39.08% Project Board Shorts PV 25,000, N 5, PMT 12, Solve for I IRR 38.62% Based on IRR analysis, Billabong Tech should choose project T-Shirt.
E10-5: NPV Answer:
Note: The IRR for Project Terra is 10.68% while that of Project Firma is 10.21%. Furthermore, when the discount rate is zero, the sum of Project Terra’s cash flows exceed that of Project Firma. Hence, at any discount rate that produces a positive NPV, Project Terra provides the higher net present value.
P10-3. Choosing between two projects with acceptable payback periods LG 2; Intermediate a.
Project A Project B
Year
Cash Inflows
Investment Balance Year
Cash Inflows
Investment Balance (^0) $100,000 0 $100, 1 $10,000 (^) 90,000 1 40,000 (^) 60, 2 20,000 (^) 70,000 2 30,000 (^) 30, 3 30,000 (^) 40,000 3 20,000 (^) 10, 4 40,000 0 4 10,000 0 5 20,000 5 20,
Both Project A and Project B have payback periods of exactly 4 years. b. Based on the minimum payback acceptance criteria of 4 years set by John Shell, both projects should be accepted. However, since they are mutually exclusive projects, John should accept Project B. c. Project B is preferred over A because the larger cash flows are in the early years of the project. The quicker cash inflows occur, the greater their value.
P10-4. Personal finance: Long-term investment decisions, payback period LG 4 a. and b.
Project A Project B
Year
Annual Cash Flow
Cumulative Cash Flow
Annual Cash Flow
Cumulative Cash Flow 0 $(9,000) $(9,000) $(9,000) $(9,000) 1 2,00 (6,800) 1,500 (7,500) 2 2,500 (4,300) 1,500 (6,000) 3 2,500 (1,800) 1,500 (4,500) 4 2,000 3,500 (1,000) 5 1,800 4, Total Cash Flow 11,000 12, Payback Period (^3) 1,800/2,000 3.9 years 4 1,000/4,000 4.25 years
c. The payback method would select Project A since its payback of 3.9 years is lower than Project B’s payback of 4.25 years.
d. One weakness of the payback method is that it disregards expected future cash flows as in the case of Project B.
P10-5. NPV
LG 3; Basic NPV PVn Initial investment a. N 20, I 14%, PMT $2, Solve for PV $13,246. NPV $13,246.26 $10, NPV $3,246. Accept project b. N 20, I 14%, PMT $3, Solve for PV 19,869. NPV $19,869.39 $25, NPV $5,130. Reject c. N 20, I 14%, PMT $5, Solve for PV $33,115. NPV $33,115.65 $30, NPV $33,115. NPV $3, Accept
P10-6. NPV for varying cost of capital LG 3; Basic a. 10% N 8, I 10%, PMT $ Solve for PV $26,674. NPV PVn Initial investment NPV $26,674.63 $24, NPV $2,674. Accept; positive NPV b. 12% N 8, I 12%, PMT $5, Solve for PV $24,838. NPV PVn Initial investment NPV $24,838.20 $24, NPV $838. Accept; positive NPV
P10-8. NPV
LG 3; Challenge a. N 5, I 9%, PMT $385, Solve for PV $1,497,515. The immediate payment of $1,500,000 is not preferred because it has a higher present value than does the annuity. b. N 5, I 9%, PV $1,500, Solve for PMT $385,638. c. Present valueAnnuity Due PVordinary annuity (1 discount rate) $1,497,515.74 (1.09) $1,632, Calculator solution: $1,632, Changing the annuity to a beginning-of-the-period annuity due would cause Simes Innovations to prefer to make a $1,500,000 one-time payment because the present value of the annuity due is greater than the $1,500,000 lump-sum option. d. No, the cash flows from the project will not influence the decision on how to fund the project. The investment and financing decisions are separate.
P10-9. NPV and maximum return LG 3; Challenge a. N 4, I 10%, PMT $4, Solve for PV $12,679. NPV PV Initial investment NPV $12,679.46 $13, NPV – $320. Reject this project due to its negative NPV. b. N 4, PV -$13,000, PMT $4, Solve for I 8.86% 8.86% is the maximum required return that the firm could have for the project to be acceptable. Since the firm’s required return is 10% the cost of capital is greater than the expected return and the project is rejected.
P10-10. NPV—mutually exclusive projects LG 3; Intermediate a. and b. Press A CF 0 -$85,000; CF 1 $18,000; F1 8 Set I 15% Solve for NPV -$4,228. Reject
Press B CF 0 -$60,000; CF 1 $12,000; CF 2 $14,000; CF 3 $16,000; CF 4 $18,000; CF 5 $20,000; CF 6 $25, Set I 15% Solve for NPV $2,584. Accept Press C CF 0 -$130,000; CF 1 $50,000; CF 2 $30,000; CF 3 $20,000; CF 4 $20,000; CF 5 $20,000; CF 6 $30,000; CF 7 $40,000; CF 8 $50, Set I 15% Solve for NPV $15,043. Accept c. Ranking—using NPV as criterion
Rank Press NPV 1 C $15,043. 2 B 2,584. 3 A 4,228.
d. Profitability Indexes Profitability Index Present Value Cash Inflows Investment Press A: $80,771 $85,000 0. Press B: $62,588 $60,000 1. Press C: $145,070 $130,000 1. e. The profitability index measure indicates that Press C is the best, then Press B, then Press A (which is unacceptable). This is the same ranking as was generated by the NPV rule.
P10-11. Personal finance: Long-term investment decisions, NPV method LG 3 Key information: Cost of MBA program $100, Annual incremental benefit $ 20, Time frame (years) 40 Opportunity cost 6.0% Calculator Worksheet Keystrokes: CF 0 100, CF 1 20, F 1 40 Set I 6% Solve for NPV $200, The financial benefits outweigh the cost of the MBA program.
P10-14. IRR—Mutually exclusive projects LG 4; Intermediate IRR is found by solving:
1
$0 initial investment (1 IRR)
n (^) t t t
CF
Most financial calculators have an ―IRR‖ key, allowing easy computation of the internal rate of return. The numerical inputs are described below for each project. Project A CF 0 $90,000; CF 1 $20,000; CF 2 $25,000; CF 3 $30,000; CF 4 $35,000; CF 5 $40, Solve for IRR 17.43% If the firm’s cost of capital is below 17%, the project would be acceptable. Project B CF 0 $490,000; CF 1 $150,000; CF 2 $150,000; CF 3 $150,000; CF 4 $150, [or, CF 0 $490,000; CF 1 $150,000, F 1 4] Solve for IRR 8.62% The firm’s maximum cost of capital for project acceptability would be 8.62%. Project C CF 0 $20,000; CF 1 $7500; CF 2 $7500; CF 3 $7500; CF 4 $7500; CF 5 $ [or, CF 0 $20,000; CF 1 $7500; F 1 5] Solve for IRR 25.41% The firm’s maximum cost of capital for project acceptability would be 25.41%. Project D CF 0 $240,000; CF 1 $120,000; CF 2 $100,000; CF 3 $80,000; CF 4 $60, Solve for IRR 21.16% The firm’s maximum cost of capital for project acceptability would be 21% (21.16%).
P10-15. IRR—Mutually exclusive projects LG 4; Intermediate a. and b. Project X
1 2 3 4 5
$0 $100,000^ $120,000^ $150,000^ $190,000^ $250,000 $500,
(1 IRR) (1 IRR) (1 IRR) (1 IRR) (1 IRR)
CF 0 -$500,000; CF 1 $100,000; CF 2 $120,000; CF 3 $150,000; CF 4 $190,
CF 5 $250,
Solve for IRR 15.67; since IRR^ cost of capital, accept. Project Y
1 2 3 4 5
$0 $140,000^ $120,000^ $95,000^ $70,000^ $50,000 $325,
(1 IRR) (1 IRR) (1 IRR) (1 IRR) (1 IRR)
CF 0 $325,000; CF 1 $140,000; CF 2 $120,000; CF 3 $95,000; CF 4 $70,
CF 5 $50,
Solve for IRR 17.29%; since IRR cost of capital, accept. c. Project Y, with the higher IRR, is preferred, although both are acceptable.
P10-16. Personal Finance: Long-term investment decisions, IRR method LG 4; Intermediate IRR is the rate of return at which NPV equals zero
Computer inputs and output: N 5, PV $25,000, PMT $6, Solve for IRR 6.40%
Required rate of return: 7.5% Decision: Reject investment opportunity
P10-17. IRR, investment life, and cash inflows LG 4; Challenge a. N 10, PV -$61,450, PMT $10, Solve for I 10.0% The IRR cost of capital; reject the project. b. I 15%, PV $61,450, PMT $10, Solve for N 18.23 years The project would have to run a little over 8 more years to make the project acceptable with the 15% cost of capital. c. N 10, I 15%, PV $61, Solve for PMT $12,244.
P10-18. NPV and IRR LG 3, 4; Intermediate a. N 7, I 10%, PMT $4, Solve for PV $19,473. NPV PV Initial investment NPV $19,472 $18, NPV $1,223. b. N 7, PV $18,250, PMT $4, Solve for I 12.01% c. The project should be accepted since the NPV 0 and the IRR the cost of capital.
P10-20. All techniques, conflicting rankings LG 2, 3, 4: Intermediate a.
Project A Project B
Year
Cash Inflows
Investment Balance Year
Cash Inflows
Investment Balance 0 $150,000 0 $150, 1 $45,000 105,000 1 $75,000 75, 2 45,000 60,000 2 60,000 15, 3 45,000 15,000 3 30,000 15, 4 45,000 30,000 4 30,000 0 5 45,000 30, 6 45,000 30,
Payback $150,000 3.33 years 3 years 4 months A $45,
Payback 2 years $15,000years 2.5 years 2 years 6 months B $30,
b. At a discount rate of zero, dollars have the same value through time and all that is needed is a summation of the cash flows across time. NPV A ($45,000 6) - $150,000 $270,000 $150,000 $120, NPV B $75,000 $60,000 $120,000 $150,000 $105, c. NPVA: CF 0 $150,000; CF 1 $45,000; F 1 6 Set I 9% Solve for NPVA $51,886. NPVB: CF 0 $150,000; CF 1 $75,000; CF 2 $60,000; CF 3 $120, Set I 9% Solve for NPV $51,112. Accept d. IRRA: CF 0 $150,000; CF 1 $45,000; F 1 6 Solve for IRR 19.91% IRRB: CF 0 $150,000; CF 1 $75,000; CF 2 $60,000; CF 3 $120, Solve for IRR 22.71%
e.
Rank Project Payback NPV IRR A 2 1 2 B 1 2 1
The project that should be selected is A. The conflict between NPV and IRR is due partially to the reinvestment rate assumption. The assumed reinvestment rate of Project B is 22.71%, the project’s IRR. The reinvestment rate assumption of A is 9%, the firm’s cost of capital. On a practical level Project B may be selected due to management’s preference for making decisions based on percentage returns and their desire to receive a return of cash quickly.
P10-21. Payback, NPV, and IRR LG 2, 3, 4; Intermediate a. Payback period Balance after 3 years: $95,000 $20,000 $25,000 $30,000 $20, 3 ($20,000 $35,000) 3.57 years b. NPV computation CF 0 $95,000; CF 1 $20,000; CF 2 $25,000; CF 3 $30,000; CF 4 $35, CF 5 $40, Set I 12% Solve for NPV $9,080.
c. $0 $20,000 1 $25,000 2 $30,000 3 $35,000 4 $40,000 5 $95, (1 IRR) (1 IRR) (1 IRR) (1 IRR) (1 IRR) CF 0 $95,000; CF 1 $20,000; CF 2 $25,000; CF 3 $30,000; CF 4 $35, CF 5 $40, Solve for IRR 15.36% d. NPV $9,080; since NPV 0; accept IRR 15%; since IRR 12% cost of capital; accept The project should be implemented since it meets the decision criteria for both NPV and IRR.
P10-22. NPV, IRR, and NPV profiles LG 3, 4, 5; Challenge a. and b. Project A CF 0 $130,000; CF 1 $25,000; CF 2 $35,000; CF 3 $45, CF 4 $50,000; CF 5 $55, Set I 12% NPVA $15,237. Based on the NPV the project is acceptable since the NPV is greater than zero. Solve for IRRA 16.06%
Project B CF 0 $85,000; CF 1 $40,000; CF 2 $35,000; CF 3 $30, CF 4 $10,000; CF 5 $5, Set I 12% NPVB $9,161. Based on the NPV the project is acceptable since the NPV is greater than zero. Solve for IRRB 17.75% Based on the IRR the project is acceptable since the IRR of 17.75% is greater than the 12% cost of capital.
c.
Data for NPV Profiles NPV Discount Rate A B 0% $80,000 $35, 12% $15,238 $9, 15% — $ 4, 16% 0 — 18% — 0
d. The net present value profile indicates that there are conflicting rankings at a discount rate less than the intersection point of the two profiles (approximately 15%). The conflict in rankings is caused by the relative cash flow pattern of the two projects. At discount rates above approximately 15%, Project B is preferable; below approximately 15%, Project A is better. Based on Thomas Company’s 12% cost of capital, Project A should be chosen. e. Project A has an increasing cash flow from Year 1 through Year 5, whereas Project B has a decreasing cash flow from Year 1 through Year 5. Cash flows moving in opposite directions often cause conflicting rankings. The IRR method reinvests Project B’s larger early cash flows at the higher IRR rate, not the 12% cost of capital.
P10-23. All techniques—decision among mutually exclusive investments LG 2, 3, 4, 5, 6; Challenge
Project A B C Cash inflows (years 1 5) $20,000 $ 31,500 $ 32, a. Payback^ 3 years 3.2 years 3.4 years b. NPV^ $10,345 $ 10,793 $ 4, c. IRR*^ 19.86% 17.33% 14.59% *Supporting calculations shown below: a. Payback Period: Project A: $60,000 $20,000 3 years Project B: $100,000 $31,500 3.2 years Project C: $110,000 $32,500 3.4 years b. NPV Project A CF 0 $60,000; CF 1 $20,000; F 1 5 Set I 13% Solve for NPVA $10,344. Project B CF 0 $100,000; CF 1 $31,500; F 1 5 Set I 13% Solve for NPVB $10,792. Project C CF 0 $110,000; CF 1 $32,500; F 1 5 Set I 13% Solve for NPVC $4,310. c. IRR Project A CF 0 $60,000; CF 1 $20,000; F 1 5 Solve for IRRA 19.86% Project B CF 0 $100,000; CF 1 $31,500; F 1 5 Solve for IRRB 17.34% Project C CF 0 $110,000; CF 1 $32,500; F 1 5 Solve for IRRC 14.59%
Project B Payback period $50,000 $15,000 3.33 years
b. Project A CF 0 $80,000; CF 1 $15,000; CF 2 $20,000; CF 3 $25,000; CF 4 $30,000; CF 5 $35, Set I 13% Solve for NPVA $3,659. Project B CF 0 $50,000; CF 1 $15,000; F 1 5 Set I 13% Solve for NPVB $2,758.
c. Project A CF 0 $80,000; CF 1 $15,000; CF 2 $20,000; CF 3 $25,000; CF 4 $30,000; CF 5 $35, Solve for IRRA 14.61% Project B CF 0 $50,000; CF 1 $15,000; F 1 5 Solve for IRRB 15.24% d.
Data for NPV Profiles NPV Discount Rate A B 0% $45,000 $25, 13% $3,655 2, 14.6% 0 — 15.2% — 0
Intersection—approximately 14% If cost of capital is above 14%, conflicting rankings occur. The calculator solution is 13.87%. e. Both projects are acceptable. Both have similar payback periods, positive NPVs, and equivalent IRRs that are greater than the cost of capital. Although Project B has a slightly higher IRR, the rates are very close. Since Project A has a higher NPV, accept Project A.
P10-25. Integrative—Multiple IRRs LG 6; Basic a. First the project does not have an initial cash outflow. It has an inflow, so the payback is immediate. However, there are cash outflows in later years. After 2 years, the project’s outflows are greater than its inflows, but that reverses in year 3. The oscillating cash flows (positive-negative-positive-negative-positive) make it difficult to even think about how the payback period should be defined. b. CF 0 $200,000, CF 1 920,000, CF 2 $1,592,000, CF 3 $1,205,200, CF 4 $343, Set I 0%; Solve for NPV $0. Set I 5%; Solve for NPV $15. Set I 10%; Solve for NPV $0. Set I 15%; Solve for NPV $6. Set I 20%; Solve for NPV $0. Set I 25%; Solve for NPV $7. Set I 30%; Solve for NPV $0. Set I 35%, Solve for NPV $39. c. There are multiple IRRs because there are several discount rates at which the NPV is zero. d. It would be difficult to use the IRR approach to answer this question because it is not clear which IRR should be compared to each cost of capital. For instance, at 5%, the NPV is negative, so the project would be rejected. However, at a higher 15% discount rate the NPV is positive and the project would be accepted. e. It is best simply to use NPV in a case where there are multiple IRRs due to the changing signs of the cash flows.
