CORPORATE FINANCE 2 SESSION 9 EXERCISES & PROBLEMS
I. NET PRESENT VALUE & IRR 1. Calculate the NPV of the following project for discount rates of 0%, 50% and 100%.
Cash Flows (€) C1 +4,500
C0 -6,750
C2 +18,000
What is the IRR of the project?
2. Mary Lee owns a computer reselling business and is expanding her business. The estimated investment for the expansion project is €85,000 and it is expected to produce cash flows after taxes of €25,000 for each of the next 6 years. An alternate proposal involves an investment of €32,000 and after-tax cash flows of €10,000 for each of the next 6 years. The opportunity cost of capital is 13 percent. Calculate (a) IRR, and (b) NPV and advise Mary.
3. Refer to problem 2. Is there an opportunity cost of capital that would make Mary indifferent between the two projects? 4. For each of the following projects, calculate the IRR, and NPV. Assume the cost of capital to be 10 percent. Rank the projects using each criterion.
Projects Project A Project B Project C
Cash flow in € (1,000) Year Year 1 Year 2 Year 3 0 -100 145 -100 115 -45 20 20 20
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5. Plymouth and Company is considering the following mutually exclusive investments. Calculate the IRR, and the NPV for the two projects. Assume a cost of capital of 13 percent. Which project would you choose? Why do the rankings by the different methods differ?
Projects
Project A Project B
Project cash flows – (€1,000s) Year Year Year Year 0 1 2 3 -400 220 310 0 -400 130 190 260
6. Refer to problem 5. Compute and use the Modified Internal Rate of Return for project A to be able to compare it with project B.
7. You sell a flat valued at €300,000 for a down payment of €100,000 and 20 monthly payments of €11,000. Compute the monthly interest rate for this transaction. What is the yield to maturity?
8. Ruckhouser Corp. has an opportunity cost of capital of 10 percent and the following projects. Compute the NPV for each project. Assuming theses to be independent projects, select the best project(s) for the company. Explain why all the projects will not be selected even if their IRR is higher than the opportunity cost of capital. Projects
Cash flow in $ (1,000) Year 0 Year 1 Year 2 Year 3 IRR -%
Project A Project B Project C Project D Project E
-112 45 -100 146 -100
40 60 -26 -70 450
50 -70 80 -60 -550
60 -70 80 -50 175
15 16 11 12 29
9. Fingerhaus Inc. is considering a project with an investment of $300,000. The project is expected to generate annual cash flows of $85,000 in the first two years and $100,000 from years 3 to 7. At the end of year 8, the company will have to incur a cash flow of $250,000 to clean up the plant facility. Calculate the NPV and IRR for the project. Assume a cost of capital of 12 percent. Session 9 (FIN) – Exercises & Problems (2008)
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10. M & M Corp. has existing operations that will generate cash flows of $150,000 in year 1 and $200,000 in year 2. If the company makes an investment of $40,000 now, it can expect to receive $230,000 in year 1 and $180,000 in year 2. M & M’s cost of capital is 12 percent. Calculate the NPV and IRR of the project. Why is the IRR a poor measure of the project's profitability in this case? SOLUTIONS: NPV & IRR 1. Calculate the NPV of the following project for discount rates of 0, 50 and 100%.
C0 -6,750
Cash Flows (€) C1 +4,500
C2 +18,000
What is the IRR of the project?
€15,750; €4,250; €0 100% 2. Mary Lee owns a computer reselling business and is expanding her business. The estimated investment for the expansion project is €85,000 and it is expected to produce cash flows after taxes of €25,000 for each of the next 6 years. An alternate proposal involves an investment of €32,000 and after-tax cash flows of €10,000 for each of the next 6 years. The opportunity cost of capital is 13 percent. Calculate (a) IRR, and (b) NPV and advise Mary. Proposal 1: IRR = 19.1% (PV = -€85,000,FV = 0, PMT = €25,000, N = 6, I = IRR) NPV = present value of cash flows - €85,000 = €99,939 - €85,000 = €14,939 (PMT = €25,000, FV =0, N = 6, I = 13, PV = solve = €99,939) Proposal 2: IRR = 21.6 % - NPV = €7,975 Mary should choose proposal 1 as it has a higher NPV. IRR should not be used to choose among mutually exclusive projects. 3. Refer to problem 2. Is there an opportunity cost of capital that would make Mary indifferent between the two projects? Session 9 (FIN) – Exercises & Problems (2008)
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The cost of capital at which the two projects will produce the same NPV can be found by calculating the IRR of the difference in cash flows between the two projects. Proposal 1 requires an additional investment of €53,000 and generates extra cash flows of €15,000 for six years. The IRR for this set of cash flows is 17.6 % (PV = -53,000, PMT = 15,000, N = 6, I = IRR). This also means that for any cost of capital below 17.6%, proposal 1 will have a higher NPV.
4. For each of the following projects, calculate the IRR, and NPV. Assume the cost of capital to be 10 percent. Rank the projects using each criterion.
Projects Project A Project B Project C
Cash flow in € (1,000) Year 0 Year 1 Year 2 Year 3 -100 145 -100 115 -45 20 20 20
Project A: IRR = 13.2% (PV = -100, FV = 145, PMT = 0, N = 3, I = IRR) NPV = €8,940 (PV of €145 received 3 years from now is €108.94) Project B: IRR = 15%; NPV = €4,545; Project C: IRR = 15.9%; NPV = €4,737; Ranking of projects: IRR: 1. C 2. B NPV: 1. A 2. C
3. A 3. B
5. Plymouth and Company is considering the following mutually exclusive investments. Calculate the IRR, and the NPV for the two projects. Assume a cost of capital of 13 percent. Which project would you choose? Why do the rankings by the different methods differ?
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Projects
Project A Project B
Project cash flows – (€1,000s) Year Year Year Year 0 1 2 3 -400 220 310 0 -400 130 190 260
NPV for A = €37,466; NPV for B = €44,035 IRR for A = 19.7%; IRR for B = 18.7% Based on NPV, the company should choose project B. IRR ranks project A better because of the difference in cash flow patterns. Project A has more of its cash flow in the earlier years. 6. MIRR Terminal value \: 220 × (1.13) 2 + 310 × (1.13)1 = 631.218 Solve 631.218 = 400 × (1 + r ) 3 R= 16.4% 7. You sell a flat valued at €300,000 for a down payment of €100,000 and 20 monthly payments of €11,000. Use Excel to compute the monthly interest rate for this transaction. What is the yield to maturity?
Value V0 Monthly payment Number of monthly payment Date (months) 0 1 2 3 4 5 6 7 8 Session 9 (FIN) – Exercises & Problems (2008)
K€ 300 100 11 20
Flows 100 11 11 11 11 11 11 11 11 5 of 11
9 10 11 12 13 14 15 16 17 18 19 20
Monthly interest rate Yield to maturity (annual)
11 11 11 11 11 11 11 11 11 11 11 11
0.925% 11.69%
8. Ruckhouser Corp. has an opportunity cost of capital of 10 percent and the following projects. Compute the NPV for each project. Assuming theses to be independent projects, select the best project(s) for the company. Explain why all the projects will not be selected even if their IRR is higher than the opportunity cost of capital. Projects
Project A Project B Project C Project D Project E
Cash flow in $ (1,000) Year 0 Year 1 Year 2 Year 3 IRR % 15 60 50 -112 40 16 -70 -70 60 45 11 80 80 -100 -26 12 -50 -60 -70 146 29 -550 175 -100 450
The NPVs for the projects are as follows: Project A = $10,765 Project B = -$10,898 Project C = $2,585 Project D = -$4,789 Project E = -$13,974 Only projects A and C have positive NPVs. The others are really “borrowing” projects and should not be selected as the cost of borrowing (IRR) is higher than the opportunity cost of capital. Session 9 (FIN) – Exercises & Problems (2008)
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9. Fingerhaus Inc. is considering a project with an investment of $300,000. The project is expected to generate annual cash flows of $85,000 in the first two years and $100,000 from years 3 to 7. At the end of year 8, the company will have to incur a cash flow of $250,000 to clean up the plant facility. Use Excel to calculate the NPV and IRR for the project. Assume a cost of capital of 12 percent. Using the calculator: CF0 = -300,000, CO1 = 85,000, FO1 = 2, CO2 = 100,000, FO2 = 5 CO3 = -250,000, FO3 = 1, IRR = solve = 16.6%; NPV: I = 12%, NPV =30,054
10. M & M Corp. has existing operations that will generate cash flows of $150,000 in year 1 and $200,000 in year 2. If the company makes an investment of $40,000 now, it can expect to receive $230,000 in year 1 and $180,000 in year 2. M & M’s cost of capital is 12 percent. Use Excel to calculate the NPV and IRR of the project. Why is the IRR a poor measure of the project's profitability in this case? Incremental cash flows are: CF0 = -40,000, CO1 = 80,000, CO2 = -20,000; NPV: I = 12, NPV = $15,485; IRR = 70.71 %
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II. OTHER DECISION TOOLS 1. Black and Company is considering an investment in a new plant which will entail an immediate capital expenditure of €4,000,000. Operating income is expected to be €800,000 per year over the 10-year life of the plant. The opportunity cost of capital is 14 percent. Calculate: (a) The payback period, (b) NPV, (c) IRR, and (d) the profitability index (PVI).
2. Refer to Problem 4 (Part I) - For each of the following projects, calculate the present value index. Assume the cost of capital to be 10 percent. Rank the projects using each criterion (NPV, IRR and PI). Projects Year 0 Project A -100 Project B -100 Project C - 45
Cash flow in (€1,000) Year 1 Year 2 Year 3 145 115 20 20 20
NPV
IRR
8.94 4.54 4.7
13.2% 15% 15.9%
3. Refer to Problem 5 (Part I). Plymouth and Company is considering the following mutually exclusive investments. You already calculated the IRR and NPV for the two projects. Now, calculate the payback and rank the different projects, assuming that cost of capital is 13 percent. Which project would you choose? Why do the ranking by the different methods differ?
Projects Project A Project B
Project cash flows – (€1,000s) Year 0 Year 1 Year 2 Year 3 -400 220 310 0 -400
130
190
260
NPV
IRR
37.5
19.7%
44
18.7%
4. Mickey Minn Corp. is considering the following projects. The company is facing resource constraints and can invest only €800,000 this year. Advise the company.
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Projects A B C D E F
Investment NPV (€1,000s) (€1,000s) 100 8 400 43 300 25 200 23 200 21 200 19
IRR (%) 13.9 14.4 16.0 14.1 16.1 15.7
5. The Bluebird Company must choose between machines A and B, which perform exactly the same operations but have different lives of 2 and 3 years, respectively. Machine A costs €30,000 initially and has annual costs of €5,000. Machine B has an initial cost of €40,000 and annual costs of €7,000. If Bluebird’s cost of capital is 10 percent, which machine should it choose?
6. Bayerhouser Timber has vast tracts of timber land. One tract in the northwest region has timber ready for harvest and at current market prices will fetch a net revenue of $12 million. If the company waited for 1 year, 2 years, 3 years, and 4 years, the values would be $15 million, $17 million, $18 million, and $19 million respectively. What is the optimal harvesting point for the company if the cost of capital is 15 percent?
SOLUTIONS: Other decision tools
1.
(a) Annual cash flow = $800,000 Initial investment = $4,000,000 Payback period = $4,000,000/$800,000 = 5 years (b) Present value of cash flows = $800,000 x 5.216 = $4,172,800 NPV = $4,172,800 - $4,000,000 = $172,800 Alternately, using the calculator you can find the present value of the cash flows to equal $4,172,892. NPV = $172,892 (N = 10, I = 14, FV = 0, PMT = $800,000, PV = solve = $4,172,892) (c) IRR can be directly obtained by using the calculator: PV = -$4,000,000, PMT = $800,000, FV = 0, N = 10, I = solve = IRR = 15.1%
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(d) PV of cash inflows = $4,172,800 PV of cash outflows = Initial investment = $4,000,000 PVI = $4,172,800/$4,000,000 = 1.04 2.
Project A: IRR = 13.2% (PV = -100, FV = 145, PMT = 0, N = 3, I = IRR) NPV = $8,940 (PV of $145 received 3 years from now is $108.94) PVI = 108.94/100 = 1.0894 Project B: IRR = 15%; NPV = $4,545; PVI = 1.0455 Project C: IRR = -20% and 50%. The project has two IRRs because of the pattern of cash flows (two sign changes). NPV = -100 + 230/1.1 – 120/1.21 = 9.917 = $9,917 PVI = 1.0992 Project D: IRR = 15.9%; NPV = $4,737; PVI = 49.737/45 = 1.1053 Ranking of projects: IRR: NPV: PVI:
3.
1. C 1. C 1. D
2. D 2. A 2. C
3. B 3. D 3. A
4. A (also C) 4. B 4. B
Payback for A = 1 + 180/310 = 1.58 years. Payback for B = 2 + 80/260 = 2.31 NPV for A = $37,466; NPV for B = $44,035 IRR for A = 19.7%; IRR for B = 18.7% Based on NPV, the company should choose project B. Payback and IRR rank project A better because of the difference in cash flow patterns. Project A has more of its cash flow in the earlier years.
4.
The profitability index and ranking based on PI for the different projects are: Project Project A Project B
PVI 1.080 (108/100) 0.108 (443/400)
Session 9 (FIN) – Exercises & Problems (2008)
Ranking 6 2 10 of 11
Project C Project D Project E Project F
1.083 (325/300) 1.115 (223/200) 1.105 (221/200) 1.095 (219/200)
5 1 3 4
Projects D, B, and E should be selected to invest the $800,000
5. Present value of costs for A = $38,678, EAC = $22,286 Present value of costs for B = $57,408, EAC = $23,085 A is cheaper.
6. The table below gives the present values of harvesting at different years.
Years 0 1 2 12,000 15,000 Net revenue 17,000 Present value at 12,854 12,000 13,040 15 % The optimal timing will be to harvest at the end of year 1.
Session 9 (FIN) – Exercises & Problems (2008)
Dollars in 1000s 3 4 18,000 19,000 11,835 10,863
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