Finance 402: Problem Set 6 1. Halflever, Inc. is financed half by debt and half by equity. You have the following data: Please fill in the blanks. r E =?? r D = 12% r A =?? β E = 1.5 β D =?? β A =?? r f = 10% r M = 18% D/E = 1 2. Company Upstart goes public. In order to value the company the investment bank that underwrites the offering needs to value Upstart. An important part of this is to determine the cost of capital at which they should discount Upstart s future cash flows. The investment bank looks at the data of the industry at the time and finds the following three companies: Company Equity beta Debt beta Debt/Equity ratio A 1.2 0.0 20% B 1.0 0.1 25% C 1.8 0.3 50% When Upstart goes public, they will also take on debt to make up 20% of their capital structure. This debt would have a beta of 0.1. The market risk premium is 8% and the risk free rate of interest is 5%. 2.a What is a good estimate for Upstart s cost of capital? 1
2.b What is the expected return on Upstart s equity after they go public? 3. The chairman of Slack decides that the company should increase the proportion of debt in its capital structure. Currently the company has 10% debt in its capital structure, and an equity beta of 0.8. The debt is considered risk free and yields an expected return of 5%, whereas the stock market expected return is 13%. The market capitalization of the company is currently $360 million. The chairman of Slack thinks that she can increase the proportion of debt to 60% by paying a one-time special dividend and issuing debt for the amount of this dividend. Then debt would have an expected return of 6%. 3.a What is the debt beta, the asset beta, and the cost of capital of the company before the refinancing? What is the risk premium on the stock market? 3.b What is the total value of the company before the recapitalization? What is the amount of debt issued and the dividend paid? 3.c What is the beta of the common stock after the refinancing? What is the required rate of return on the common stock after the refinancing? 3.d How has the wealth of each individual shareholder changed? Assume that the debt is privately placed, so shareholders do not buy the debt issued. 3.e Using the same assumptions as in 3.d, how has the beta of the portfolio of the holders of common stock changed as a result of the refinancing? How could the shareholders invest in the market portfolio to restore the risk of their portfolio to what it was before the refinancing? 2
4. Suppose two companies X and Z have exactly the same operating characteristics and their business risks are perfectly correlated (i.e., exactly the same cashflows). They differ only in the way they finance their operations. Both companies will be liquidated exactly one year from now and shareholders will receive a liquidating dividend at the end of the year. Company X is expected to pay a liquidating dividend of $55 million, but this is uncertain, so shareholders discount this dividend at a rate of 10%. Z has issued bond to finance its operations. Currently Z s securities are trading as follows: Bonds Shares $10 million $42 million The bonds are AAA rated and the expected return is the same as on the risk free asset which is 5%. 4.a Suppose company X has 2,500,000 shares outstanding. What is the current share price of X? 4.b What is the total valuation of company Z s assets today? 4.c Show how you can set up an arbitrage portfolio in order to benefit from any mispricing of companies X and Z relative to each other. 5. Savvy Supermarkets is a chain of grocery stores that is currently financed with 12.5% debt. The CEO of Savvy decides that the proportion of debt in the current capital structure is too low because investors in Savvy s stock demand a higher rate of return. Savvy issues debt and pays out all proceeds as a special dividend to shareholders. The current rate of return on Savvy s equity is 16%, only slightly higher than the 14% currently expected on the stock market index. Suppose the risk free rate is 6% and Savvy has 10 million shares outstanding for a price of $18 per share. 3
For answering the following questions, assume all assets are priced on the SML. 5.a What is the equity beta of Savvy if the debt has an expected return of 6%? 5.b What is the cost of capital of Savvy? Answer this question by using both methods, namely unlevering betas and the weighted average cost of capital. 5.c Suppose the CEO wishes to realize a target expected return on equity of 20% through leveraging and paying the proceeds as a special dividend. How much debt should the company issue, assuming that all debt can be issued at an expected return equal to the risk-free rate? What is the cost of capital now? 6. Use the dividend growth model in order to determine the growth rate of a company with the following data: Current stock price: $50.00 Expected end of period dividend $3.75 Equity beta: 0.75 Market risk premium 8% Risk free rate 5% 6.a What is the weighted average cost of capital of this company if the debt/equity ratio is 0.25 and the debt is considered to be risk-free? 6.b What is the expected end of period price? capital gain? Hence, what is the expected 4
6.c Suppose an analyst agrees with all the data given above, but expects an end of period price for this stock of $53 (excluding the dividend payment). Show that this stock does not lie on the security market line. If the market as a whole would adopt the view of this analyst, then how does the stock price have to move so that expected returns are consistent with the CAPM again? 6.d Suppose that at the end of the period the company pays a dividend of only $2.50. How does the stock price react when the dividend announcement is made and the market had no prior knowledge of the dividend cut? Assume that on the dividend announcement day the market expects that the reduced dividend reflects a temporary problem, so that dividends will bounce back to $3.75 1.035 one year after the cut and resume growing at the original rate after that. 6.e How does your answer change if the dividend cut reflects a permanent reduction in earnings prospects, so that the dividends resume growth at the rate you computed above immediately after the dividend payment of $2.50? 7. Consider a company with the following balance sheet: Assets Liabilities Total Assets = 200 Equity = 120 Long Term Debt = 60 Short Term Debt = 20 Assume that the debt betas are zero, and that the coupons are 9% for long term debt and 8% for short term debt. The risk free rate of interest is 5% and the expected return on the market as a whole is 15%. The beta of the equity of the company is 1.5. The company has an environmentally hazardous project that costs $2 million in capital outlays now, lasts for 10 years. At the end of each of these 10 years the project generates net operating cash flows of $450,000. At the 5
end of year 10 the company also has to pay for some clean-up connected with this project of $1 million. 7.a Determine the company s required rate of return on equity. 7.b Determine the company s cost of capital using the method of unlevering betas as well as weighted average cost of capital. 7.c What is the NPV of the project? Should the company take it? 7.d Suppose the company could lease rather than buy the equipment connected with this project. This would reduce capital expenditure on outlay to $500,000 today, but the company would still be responsible for the clean-up costs. The lease payments are certain to be $200,000 per year. Should the company lease? 6