Homework #2 Suggested Solutions

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Kathryn Shields
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1 JEM034 Corporate Finance Winter Semester 017/018 Instructor: Olga Bychkova Homework # Suggested Solutions Problem 1. (4.1) Consider the following three stocks: (a) Stock A is expected to provide a dividend of $10 a share forever. (b) Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 4% a year forever. (c) Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 0% a year for five years (i.e., until year ) and zero thereafter. If the market capitalization rate for each stock is 10%, which stock is the most valuable? What if the capitalization rate is 7%? = $ P A = DIV 1 r = $ = $100, P B = DIV 1 r g = $ = $83.33, P C = DIV ) 1 (1 + g) (1 + r g (1 + r) ( ) (1 + 0.) ( ) (1 + r) DIV 1(1 + g) 5 r 1 $5(1 + 0.)5 ( ) 0.1 At a capitalization rate of 10%, Stock C is the most valuable. For a capitalization rate of 7%, the calculations are similar. The results are: Therefore, Stock B is the most valuable. P A = $14.8, P B = $1.7, P C = $ = = $ Problem. (4.19) Mexican Motors stock sells for 00 pesos per share and next year s dividend is 8.5 pesos. Security analysts are forecasting earnings growth of 7.5% per year for the next five years. (a) Assume that earnings and dividends are expected to grow at 7.5% in perpetuity. What rate of return are investors expecting? (b) Mexican Motors has generally earned about 1% on book equity (ROE = 0.1) and paid out 50% of earnings as dividends. Suppose it maintains the same ROE and payout ratio in the long run future. What is the implication for g? For r? Should you revise your answer to part (a) of this question? 1

(a) r = DIV 1 + g = $8.5 + 0.075 = 0.1175 or 11.75%. P 0 $00 (b) g = plowback ratio ROE = (1 0.5) 0.1 = 0.0 or %. The stated payout ratio and ROE are inconsistent with the security analysts forecasts.

2 (a) r = DIV 1 + g = $ = or 11.75%. P 0 $00 (b) g = plowback ratio ROE = (1 0.5) 0.1 = 0.0 or %. The stated payout ratio and ROE are inconsistent with the security analysts forecasts. With g = %, r = DIV 1 + g = $ = or 10.5%. P 0 $00 Problem 3. (4.3) Look at the financial forecasts for Growth Tech given in the following table: Assume that the opportunity cost of capital is r = 0.1 and a dividend s perpetual constant growth rate of 8% starting from year 4. (a) Calculate the value of Growth Tech stock. (b) What part of that value reflects the discounted value of P 3, the price forecasted for year 3? (c) What part of P 3 reflects the present value of growth opportunities (PVGO) after year 3? (d) Suppose that competition will catch up with Growth Tech by year 4, so that it can earn only its cost of capital on any investments made in year 4 or subsequently. What is Growth Tech stock worth now under this assumption? (Make additional assumptions if necessary.) (a) Growth Tech s stock price is: P 0 = $ $ $ $ = $3.81. (b) The horizon value contributes: P V (P 3 ) = $ = $.07.

(c) Without PVGO, P 3 would equal earnings for year 4 capitalized at 1 percent: Therefore, P V GO = P 3 = $.49 0.1 = 0.75. $1.4 $0.75 = $31 $0.75 = $10.5. 0.1 0.08 (d) The PVGO of $10.

3 (c) Without PVGO, P 3 would equal earnings for year 4 capitalized at 1 percent: Therefore, P V GO = P 3 = $ = $1.4 $0.75 = $31 $0.75 = $ (d) The PVGO of $10.5 is lost at year 3. Therefore, the current stock price of $3.81 will decrease by: $ = $7.3. The new stock price will be: $3.81 $7.3 = $1.51. Problem 4. (5.1) (a) What is the payback period on each of the following projects? (b) Given that you wish to use the payback rule with a cutoff period of two years, which projects would you accept? (c) If you use a cutoff period of three years, which projects would you accept? (d) If the opportunity cost of capital is 10%, which projects have positive NPVs? (e) If a firm uses a single cutoff period for all projects, it is likely to accept too many short lived projects. True or false? (f) If the firm uses the discounted payback rule, will it accept any negative NPV projects? Will it turn down positive NPV projects? Explain. (a) P ayback A = 3 years, P ayback B = years, P ayback C = 3 years. (b) B. (c) A, B, and C. $1, 000 $1, 000 $3, 000 (d) NP V A = $5, = $1, 011; $1, 000 $, 000 $3, 000 NP V B = $1, = $3, 378; $1, 000 $1, 000 $3, $5, = $, 405. NP V C = $5, Projects B and C have positive NPVs. (e) True. (f) It will accept no negative NPV projects but will turn down some with positive NPVs. A project can have positive NPV if all future cash flows are considered but still do not meet the stated cutoff period. 3

5) Consider a project with the following cash flows: (a) How many internal rates of return does this project have?

4 Problem 5. (5.4) You have the chance to participate in a project that produces the following cash flows: The internal rate of return is 13%. If the opportunity cost of capital is 10%, would you accept the offer? No (you are effectively borrowing at a rate of interest higher than the opportunity cost of capital). Problem. (5.5) Consider a project with the following cash flows: (a) How many internal rates of return does this project have? (b) Which of the following numbers is the project IRR: (i) 50%; (ii) 1%; (iii) +5%; (iv) +50%? (c) The opportunity cost of capital is 0%. Is this an attractive project? Briefly explain. (Hint: Compute NPV of the project.) (a) Two. (b) NP V = IRR 75 = 0 IRR = 50% and IRR = +50%. (1 + IRR) (c) Yes, NP V = = 14.. Problem 7. (5.1) Mr. Cyrus Clops, the president of Giant Enterprises, has to make a choice between two possible investments: The opportunity cost of capital is 9%. Mr. Clops is tempted to take B, which has the higher IRR. (a) Explain to Mr. Clops why this is not the correct procedure. (b) Show him how to adapt the IRR rule to choose the best project. 4

(c) Show him that this project also has the higher NP V. (a) Because Project A requires a larger capital outlay, it is possible that Project A has both a lower IRR and a higher NPV than Project B.

5 (c) Show him that this project also has the higher NP V. (a) Because Project A requires a larger capital outlay, it is possible that Project A has both a lower IRR and a higher NPV than Project B. (In fact, NP V A is greater than NP V B for all discount rates less than 10 percent.) Because the goal is to maximize shareholder wealth, NPV is the correct criterion. (b) To use the IRR criterion for mutually exclusive projects, calculate the IRR for the incremental cash flows: C 0 C 1 C IRR A B % IRR + 11 = 0 IRR = 0.1 or 10%. (1 + IRR) Because the IRR for the incremental cash flows exceeds the cost of capital, the additional investment in A is worthwhile. (c) NP V A = $400 + $ $ = $81.8. NP V B = $00 + $ $ = $79.1. Problem 8. (5.15) Borghia Pharmaceuticals has $1 million allocated for capital expenditures. Which of the following projects should the company accept to stay within the $1 million budget? How much does the budget limit cost the company in terms of its market value? The opportunity cost of capital for each project is 11%. (Hint: How much does the company loose in terms of NPV?) W AP I 1,3,4, = W AP I 1,,4,7 = $, 000 $43, 000 $14, 000 $3, $1, 000, 000 $1, 000, 000 $1, 000, 000 $1, 000, 000 = 0.18; $, 000 $4, 000 $14, 000 $48, $1, 000, 000 $1, 000, 000 $1, 000, 000 $1, 000, 000 = 0.14; 5

6 W AP I 1,,5,7 = W AP I 1,4,5,7 = W AP I 3,,7 = $, 000 $4, 000 $7, 000 $48, $1, 000, 000 $1, 000, 000 $1, 000, 000 $1, 000, 000 = 0.117; $, 000 $14, 000 $7, 000 $48, $1, 000, 000 $1, 000, 000 $1, 000, 000 $1, 000, 000 = 0.135; $43, 000 $3, 000 $48, $1, 000, 000 $1, 000, 000 $1, 000, 000 = Thus, given the budget of $1 million, the best the company can do is to accept projects 1, 3, 4, and. If the company accepted all positive NPV projects, the market value (compared to the market value under the budget limitation) would increase by the NPV of project 5 plus the NPV of project 7: $7, $48, 000 = $55, 000. Thus, the budget limit costs the company $55,000 in terms of its market value. Problem 9. (5.17) Calculate the modified IRR for the following project: Assume the cost of capital is 1%. C 0 = 3, 000, C 1 = +3, 500, C + P V (C 3 ) = +4, , , 500 3, MIRR = 0 MIRR = 7.84%. MIRR =

Midterm Review. P resent value = P V =

Midterm Review. P resent value = P V = JEM034 Corporate Finance Winter Semester 2018/2019 Instructor: Olga Bychkova Midterm Review F uture value of $100 = $100 (1 + r) t Suppose that you will receive a cash flow of C t dollars at the end of