Business 3019 Corporate Finance Lakehead University

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1 Business 3019 Corporate Finance Lakehead University Midterm Exam Suggested Answers Philippe Grégoire Winter (50 points) Weighted Average Cost of Capital Use the information in Table 1 to answer the following questions. Make sure that you carefully explain how each of your answers are obtained. Lassonde s short-term debt recorded as notes payable is expected to be a permanent feature of the firm s capital structure and the interest rate the company pays on this particular debt is 10% and is not expected to change. The expected growth rate of 5.00% that appears at the bottom of the dividend table is the expected growth rate of the company s annual dividend into the foreseeable future. (a) (5 points) Calculate Lassonde s pre-tax cost of debt. Answer: Short-term debt being a permanent feature of Lassonde s capital structure, it has to be included in the calculation. The pretax cost of short-term debt is 10% and the pretax cost of long-term debt is 6.56%, Lassonde s yield on longterm debt. The market value of short-term debt is equal to its book value, namely 8,000, and the market value of long-term debt is , 000 = 19, 440. The pretax cost of debt is then 8, 000 8, , % + 19, % = 7.56%. 8, , 440 (b) (10 points) Calculate Lassonde s cost of equity using the dividend discount model as well as the CAPM. Carefully explain your choice of parameters in each case. What do you think is a reasonable cost of equity for Lassonde? Explain. Answer: The last annual dividend paid was $0.40 and it is expected to grow at the rate of 5.00% into the foreseeable future. The stock price being $24, this gives us a required return of r DDM e = = 6.75%.

2 Using the CAPM with the 10-year government bonds as the risk-free rate and 1.11 as beta, we obtain r CAPM e = ( ) = 11.07%. The difference between the CAPM and the DDM is a bit large and the DDM discount rate is below the pretax cost of debt and very close to the yield on the company s long-term debt. It is therefore better to use the required return obtained with the CAPM. (c) (10 points) Compute the weighted average cost of capital (WACC) for Lassonde you would use to discount Lassonde s cash flows. Explain your answer. Answer: I would use the CAPM, the most recent beta and the yield on 10-year government bonds as the risk-free rate, which gives WACC = 27, , , (1.40) , = 8.49%. 27, , 750 (d) (10 points) Given the numbers in Table 1, provide what you consider to be a reasonable lower bound and a reasonable upper bound for Lassonde s WACC. Explain how you came up with these values. Answer: The highest reasonable beta I see is the average of the three betas given, i.e = I don t find reasonable to use 1.28 as beta. When using the yield on 10-year government bonds, we obtain a risk premium of = 5.2%. Alternatively, a risk premium of between 4% or 7% could be used, keeping the yield on 10-year government bonds as the risk-free rate (note that the difference between the TSX300 expected return and the yield on 3-month T-bills is = 7.0%). My acceptable maximum and minimum values for the cost of equity are then re MAX = = 13.61% re MIN = = 9.74% My acceptable maximum and minimum WACCs are then WACC MAX = WACC MIN = 27,440 27, , (1.40) ,750 27, , = 10.02% 27,440 27, , (1.40) ,750 27, , = 7.68% (e) (5 points) How would you justify the use of the CAPM to calculate the company s cost of equity? Why not use a more complex asset pricing model? 2

3 Answer: According to Bruner et al. (1998), 81% of corporations and 80% of financial advisers use the CAPM to calculate their cost of equity. In Graham and Harvey (2001) s survey, over 73% of the respondents answered that they always or almost always use the CAPM to calculate their cost of equity. (f) (5 points) Why do companies calculate their WACC? Is it important? Is it done frequently? Answer: Companies frequently calculate their WACC, the vast majority of them at least once a year. In Bruner et al. (1998), 78% of corporations surveyed answered that they were calculating their WACC at least once a year. (g) (5 points) Are there any methods that companies use to evaluate capital budgeting projects that do not require the use of a discount rate? Answer: Close to 57% of the respondents in Graham and Harvey (2001) answered that they always or almost always use the payback rule to evaluate capital budgeting projects. The payback rule does not involve the use of a discount rate. 2. (30 points) Capital Structure Use the information in Table 1 for this question also. Suppose now that Lassonde wants to issue $4 million in long-term debt and use the proceeds to repurchase common shares. There are no issuing costs. (a) (5 points) Calculate Lassonde s stock price once the new debt is issued. Answer: The new debt adds.4 4 = $1.6 million in tax shield to the firm, that is 1.6/1.750 = $.914 per share. The new stock price is then = $ (b) (5 points) How many shares will Lassonde be able to repurchase with $4 million? Answer: The firm will be able to repurchase 4, 000, 000/ = 160, 550 shares. (c) (5 points) Calculate Lassonde s beta under its new capital structure, i.e. after the share repurchase (use 1.11 as the original beta). Answer: Using β L β U = 1 + (1 t)d/e with β L = 1.11, E = 1, 750, = 42, 000, 000 and D = 27, 440, 000, we find β U = (1.4)27, 440/42, 000 = The number of shares remaining being 1,589,450, the new market value of equity is E = 1, 589, = 39, 600,

4 The new market value of debt is and thus D = 27, 440, , 000, 000 = 31, 440, 000 β L = β U (1 + (1 t)d /E ) =.7974 (1 + (1.4) 31, 440/39, 600) = Note that the new value of the firm is (in $000) V L = 31, , 600 = 71, 040, which is equal to the initial value of the firm, i.e. V L = E+D = 42, , 440 = 69, 440, plus the change in the debt tax shield: V L = V L + t D = 69, , 000 = 71, 040 (d) (5 points) Calculate Lassonde s cost of equity before and after the change in capital structure. Answer: Lassonde s initial cost of equity was and its new cost of equity is r e = ( ) = 11.07% r e = ( ) = 11.42%. (e) (5 points) Calculate Lassonde s WACC under the new capital structure, i.e. after the share repurchase. Answer: Here we need to use the equation WACC L = r 0 V U V U + td, where r 0 is the firm s WACC when it has no debt. Note that V L = 71, 040 = V U + td = V U , 440 V U = 71, , 440 = (f) (5 points) Should Lassonde consider bankrupcty costs when evaluating its value under the new capital structure? Do firms in general worry a lot about bankruptcy costs? Answer: According to the surveys reviewed in class, firms do not seem to be too preoccupied by bankruptcy costs. Moreover, Lassonde s level of debt does not seem too extreme. In order to answer this question, however, it would be better to have information about other firms in the same industry. 4

5 3. (20 points) The Binomial Model Consider a firm with an initial value V = 500 and which value in three years will be V 3 = { V u 3 = 800 with probability p = 0.7, V3 d = 250 with probability 1 p = 0.3. The firm has an original pure-discount debt with face value X = 300 due in three years and the risk-free rate is r f = 5%. (a) (10 points) Calculate (i) the firm s market value of debt, (ii) the firm s market value of equity, (iii) its return on assets, (iv) its return on debt and (v) its return on equity. Answer: δ = V 3 u V3 d = E3 u E3 d ( E = 1 V min { V3 d, X } ) δ (1 + r f ) T = D = V E = = 242. The firm s return on assets is = ( ) (1.05) 3 = 258 r a = ( ) 1/ = 8.29%, 500 its return on debt is r d = ( ) 1/ = 5.63% 242 and its return on equity is r e = ( ) 1/ = 10.67%. 258 (b) (5 points) Calculate the payoff to bondholders and shareholders if the firm uses $150 of idle cash to pay a dividend to shareholders. Answer: If the firm uses 150 units of its idle cash to pay dividends, its present value falls to V n = = 350 and its possible futures values are V u,n 3 = (1.05) 3 = 626, V d,n 3 = (1.05) 3 = 76. 5

6 This gives us δ n = V u,n 3 V d,n = = E u,n 3 E d,n { } E n = 1 min V d,n V n 3, X = 1 ( ) δ n (1 + r f ) T (1.05) 3 = 169 D n = V n E n = = 181. Changes in wealth are E n E = = 60 for shareholders, D n D = = 60 for bondholders. (The equations do not work exactly due to rounding.) (c) (5 points) Calculate the payoff to bondholders and shareholders if the firm uses $150 of idle cash to invest in a project that will pay $300 with certainty in three years. Which project of the two projects do shareholders prefer? Answer: Debt becomes risk-free in this case. Its present value is then and thus the new value of equity is Changes in wealth are D n = frac = 259 E n = = E n E = = 92 for shareholders, D n D = = 17 for bondholders. Shareholders thus prefer the second alternative. 6

7 Lassonde, Inc Balance Sheet ($000) Assets Current assets 24,000 Net fixed assets 46,000 Total assets 70,000 Liabilities and Owners Equity Notes payable 8,000 Accounts payable 12,000 Current liabilities 20,000 Long-term debt 18,000 Common stock 7,000 Retained earnings 25,000 Total liabilities and equity 70,000 Long-Term Debt (Average) Price Maturity 7 years Coupon rate 8.00% Yield 6.56% Market Data 3-month T-bill rate 3.50% 10-year gov. bonds yield 5.30% Expected TSX300 return 10.50% Lassonde, Inc Income Statement ($000) Sales 110,000 Cost of goods sold 92,500 Depreciation 9,200 EBIT 8,300 Interest 2,240 Taxable income 6,060 Taxes (40%) 2,424 Net income 3,636 Nb of common shares 1,750,000 Earnings/share $2.08 Dividend/share $0.40 Stock price $24.00 Lassonde s Beta Dividends March June September December March June September December Expected growth rate 5.00% Table 1: Data for questions 1 and 2. 7

Business Midterm Practice Questions

Business Midterm Practice Questions Business 3019 Midterm Practice Questions Here are some questions that you may find useful to review before the exam. You should also try the questions at the end of each chapter in the textbook. Answers