BIA Leuphana Problem Set 01 Discount Rates PDF

Problem Set #1 - Solution Problems You are an investor who is interested in the emerging markets of Asia. You are trying to value some stocks in Malaysia, which does not have a long history of financial markets. During the last two years, the stock market has gone up 60% a year, while the g...

Problem Set #1 - Solution Problems You are an investor who is interested in the emerging markets of Asia. You are trying to value some stocks in Malaysia, which does not have a long history of financial markets. During the last two years, the stock market has gone up 60% a year, while the government borrowing rate has been 15%, yielding an historical premium of 45%. Would you use this as your risk premium, looking into the future? If not, what would you base your estimate of the premium on? When equity is valued, the cash flows to equity investors are discounted at their cost (the cost of equity) to arrive at a present value, which is the value of the equity stake in the business. When the firm is valued, the cash flows to all investors in the firm (including equity investors, lenders and preferred stockholders) are discounted at the weighted average cost of capital to arrive at a present value, which equals the value of the entire firm (generally much higher than the value of just the equity stake.) The distinction matters for two reasons: (1) Mismatching cash flows and discount rates can cause significant errors in valuation. (2) Not recognizing what the present value of the cash flows measures can also lead to misinterpretations. For instance, if the present value of cash flows to the firm is treated as the value of equity, there is an obvious problem. The beta for Eastman Kodak is 1.10. The current six-month treasury bill rate is 3.25%, while the thirty-year bond rate is 6.25%. Estimate the cost of equity for Eastman Kodak, based upon a) using the treasury bill rate as your risk-free rate. b) using the treasury bond rate as your risk-free rate. Use the premiums provided on the slides, if necessary. Which one of these estimates would you use in valuation? Why? CAPM: using T.Bill rate = 3.25% + 1.10 (8.41%) = 12.50% CAPM: using T.Bond rate = 6.25% + 1.10 (5.50%) = 12.30% The long-term bond rate should be used as the risk-free rate, because valuation is based upon a long time horizon. * 8.41% is the arithmetic mean average premium earned by stocks over treasury bills between 1926 and 1990. 1  ** 5.50% is the geometric mean average premium earned by stocks over treasury bonds between 1926 and 1990. You are trying to estimate the cost of equity to use in valuing BMW, and a data service reports a beta estimate of 0.90. However, the beta is estimated relative to the Frankfurt Stock Exchange (DAX). If you were an international portfolio manager with holdings across many markets, would you use this beta estimate? How would you estimate beta to meet your needs? An international portfolio manager would prefer a beta estimated relative to an international index. Stock returns would be regressed against returns on such an index to estimate its beta. You have been asked to estimate the beta of a high-technology firm which has three divisions with the following characteristics Division: Personal Computers; Beta:1.60 Market Value: $100 million Division: Software; Beta:2.00 Market Value: $150 million Division: Computer Mainframes; Beta:1.20 Market Value: $250 million a) What is the beta of the equity of the firm? b) What would happen to the beta of equity if the firm divested itself of its software business? c) If you were asked to value the software business for the divestiture, which beta would you use in your valuation? A. Beta = 1.60 * 100/500 + 2.00 * 150/500 + 1.20 * 250/500 = 1.52 B. If they pay the cash out as a dividend: Beta = 1.60 * 100/350 + 1.20 * 250/350 = 1.31 If they keep the cash in the firm: Beta = 1.60*100/500 + 0*150/500 + 1.20*250/500 = 0.92 C. Use 2.00, the beta for the software division. 2  The following are the betas of the equity of four forestry/paper product companies, and their debt/equity ratios. Company: Weyerhauser; Beta:1.15 Debt/Equity Ratio: 33.91% Company: Champion International; Beta:1.18 Debt/Equity Ratio: 54.14% Company: Intenational Paper; Beta:1.05 Debt/Equity Ratio: 45.50% Company: Kimberly-Clark; Beta:0.91 Debt/Equity Ratio: 11.29% All the firms face a corporate tax rate of 40%. a) Estimate the unlevered beta of each firm. What do the unlevered betas tell you about these firms? b) Assume now that Kimberly Clark is planning to increase its debt/equity ratio to 30%. What will its new beta be? c) If you were valuing an initial public offering in the paper products area, what beta would you use in the valuation? (Assume that the firm going public plans to have a debt/equity ratio of 40%.) A. Beta D/E Unlevered Beta Weyerhauser 1.15 33.91% 0.95557808 Champion 1.18 54.14% 0.89067359 International Intenational 1.05 45.50% 0.82482325 Paper Kimberly- 0.91 11.29% 0.85226741 Clark The unlevered betas measure the business and operating leverage risk associated with each of these firms. B. New beta for Kimberly Clark = 0.85 * (1 + (1-0.4) (0.30)) = 1.00 C. The average unlevered beta of these comparable firms should be relevered using the debt equity ratio of the initial public offering. Average Unlevered Beta = 0.88 Beta of the Initial Public Offering = 0.88 (1 + (1-0.4) (0.40)) = 1.09 3  The following is a description of the cost structure and betas of five firms in the food production industry: Company: CPC International; Fixed costs:62% ; Variable costs:38% ; Beta:1.23; Debt Ratio: 18.83% Company: Ralston Purina; Fixed costs:47% ; Variable costs:53% ; Beta:0.81; Debt Ratio: 38.32% Company: Quaker Oats; Fixed costs:45% ; Variable costs:55% ; Beta:0.75; Debt Ratio: 13.28% Company: Chiquita; Fixed costs:50% ; Variable costs:50% ; Beta:0.88; Debt Ratio: 75.35% Company: Kellogg’s; Fixed costs:40% ; Variable costs:60% ; Beta:0.76; Debt Ratio: 5.57% All the firms face a corporate tax rate of 40%. a) Based upon just the operating leverage, which firms would you expect to have the highest and lowest betas (assuming that they are in the same business)? b) Chiquita’s beta is believed to be misleading because its financial leverage has increased dramatically since the period when the beta was estimated. If the average D/(D+E) ratio during the period of the regression (to estimate the betas) was only 30%, what would your new estimate of Chiquita’s beta be? A. CPC should have the highest beta (because of its high fixed costs) and Kellogg's should have the lowest beta (because of its low fixed costs). B. Old Debt/Equity Ratio = D/(D+E)/( 1 - D/(D+E)) = 0.3/ (1-0.3) = 0.4286 Unlevered Beta (using D/E ratio of 30%) = 0.88/(1 + (1 - 0.4) * 0.4286) = 0.70 New Debt/Equity Ratio = 0.7535/(1 - 0.7535) = 3.06 New Levered Beta = 0.70 (1 + (1 - 0.4) * (3.06)) = 1.985 4  The following is a list of companies, with prices, dividends per share and expected growth rates in dividends (from analyst projections) for each company: Company: Merck; Market price:$32.00 ; Current DPS:$1.06 ; Growth rate in DPS:15.0% ; Beta:1.10 Company: Ogden Co.; Market price:$25.00 ; Current DPS:$1.25 ; Growth rate in DPS:4.0% ; Beta:1.30 Company: Honda (ADR); Market price:$25.00 ; Current DPS:$0.27 ; Growth rate in DPS:10.0% ; Beta:0.75 Company: Microsoft; Market price:$84.00 ; Current DPS:$0.00 ; Growth rate in DPS:NMF ; Beta:1.30 Microsoft has an expected growth rate in earnings of 24% for the next five years. a) Estimate the cost of equity using the dividend growth model. Which, if any, of these firms may be reasonable candidates for using this model? Why? b) Estimate the cost of equity using the CAPM. (The thirty-year bond rate is 6.25%.) c) Which estimate will you use in valuation and why? A. See second-to-last column below. B. See last column below. Cost of Equity Price DPS g Beta DDM CAPM Merck $32.00 $1.06 15.00% 1.10 18.81% 12.30% Ogden $25.00 $1.25 4.00% 1.30 9.20% 13.40% Co. Honda $25.00 $0.27 10.00% 0.75 11.19% 10.38% (ADR) Microsoft $84.00 $0.00 NMF 1.30 NMF 13.40% C. Use the CAPM estimate, because (1) the DDM cost of equity cannot be calculated for many firms, with no dividends and/or no record of growth in the same; and (2) the CAPM cost of equity has logical constraints. The DDM cost of equity does not. 5  Merck & Company has 1.13 billion shares traded at a market value of $32 per share, and $1.918 billion in book value of outstanding debt (with an estimated market value of $2 billion). The equity has a book value of $5.5 billion, and the stock has a beta of 1.10. The firm paid interest expenses of $160 million in the most recent financial year, is rated AAA and paid 35% of its income as taxes. The thirty-year government bond rate is 6.25%, and AAA bonds trade at a spread of twenty basis points (0.2%) over the treasury bond rate. a) What are the market value and book value weights on debt and equity? b) What is the cost of equity? c) What is the after-tax cost of debt? d) What is the cost of capital? A. Market Weights Book Weights Value Value Debt $2,000.00 5.24% $1918 25.86% m Equity $36,160.00 94.76% $5500 74.14% m B. Cost of Equity = 6.25% + 1.10 * 5.50% = 12.30% C. After-tax Cost of Debt = 6.45% (1 - 0.35) = 4.19% D. Cost of Capital = 12.30% * (36160/38160) + 4.19% * (2000/38160) = 11.87% General Motors has 710 million shares trading at $55 per share and $69 billion in debt outstand- ing (with a market value of $65 billion), on which it incurred an interest expense of $5 billion in the most recent year. It also has $4 billion in preferred stock outstanding, trading at par, on which it paid a dividend of $365 million. The stock has a beta of 1.10 and is rated A (which com- mands a spread of 1.25% over the treasury bond rate of 6.25%). The company faced a corporate tax rate of 40%. a) What is the cost of equity for GM? b) What is the after-tax cost of debt for GM? c) What is the cost of preferred stock? d) What is the cost of capital? 6 A. Cost of Equity = 6.25% + 1.10 * 5.50% = 12.30% B. After-tax Cost of Debt = 7.50% * (1 - 0.4) = 4.50% C. Cost of Preferred Stock = 365/4000 = 9.125% D. Cost of Capital = 12.30% * (710 * 55)/[(710 * 55)+ 65000 + 4000] + 4.50% * 65000/[(710 * 55) + 65000 + 4000] + 9.125% * 4000/[(710 * 55)+ 65000 + 4000] = 7.49% 7