Exam (Correction) Exercise 1: Market efficiency

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1 Executive MA Program Pr. Eric Jondeau orporate Finance Exam (orrection) Exercise 1: Market efficiency (10 points) Answer the following questions in a few lines. a) TransTrust orp. has changed how it accounts for inventory. Taxes are unaffected, although the resulting earnings report released this quarter is 20% higher than what it would have been under the old accounting system. There is no other surprise in the earnings report and the change in the accounting treatment was publicly announced. Assume market efficiency. Will the stock price be higher when the market learns that the reported earnings are higher? Given that semi-strong form of market efficiency holds approximately in the real world, the stock price should stay the same. The accounting system changes are publicly available information. The investors would know that in essence, there is no change in the operational and financial state of the firm's current and future cash flows. o the stock price will not change after the announcement of increased earnings. b) Newtech orp. is going to adopt a new chip-testing device that can greatly improve its production efficiently. Do you think the lead engineer can profit from purchasing the firm's stock before the news release on the device? After reading the announcement in the Wall treet Journal, should you be able to earn an abnormal return from purchasing the stock? Assume market efficiency. The market is generally considered to be efficient up to the semi-strong form, which means that no systematic profit can be made by trading on publicly available information. The lead engineer of the device can profit from purchasing the firm s stock before the news release on the implementation of the new technology because she can trade on insider information. As the information on the new technology becomes publicly available, nobody can profit from rushing into the stock market based on Wall treet Journal articles. c) A hypothetical study has documented that firms usually experience a period of price runup before their public stock offerings. After reading this study, Alex Johnson invests in firms that have just carried out new stock offerings. ased on the study's conclusion that these firms have generally performed very well before the stock offering, can Alex make money using this strategy if market efficiency holds?

2 No, Alex cannot make money by investing in firms that just issued public stock based on the fact that these firms performed better than others. If they are considered better performing firms, the market s expectation of their current and future cash flows would already have been raised to a higher level and reflected in the current stock prices. No abnormal profit can be made since the purchasing prices of the stocks would have already been commensurate with the higher expected earning powers. Exercise 2: Valuation of a project (25 points) You are a successful financial analyst in a well-known investment bank. You are asked to evaluate the investment project of Veblen Inc., a client of the bank. This project has the following characteristics: The project is expected to have an infinite life. The initial investment is $16 million. Any depreciation on the project will be reinvested into the project as capital maintenance expenditure. There will be no working capital investment. Earnings before interest and taxes are expected to be $8 million per year. The corporate tax rate is τ = 35%. The project is financed for 50% by perpetual debt at interest rate r = 8%. a) In order to estimate the discount rate relevant for the evaluation of the project, you have identified two firms in the same business. The characteristics of the two firms are the following: Firm A Firm eta of equity Debt interest rate 7% 10% /(+) The risk free rate is 5% and the market risk premium is 8%. alculate the cost of equity of the two firms. To calculate the cost of equity, we use the market model r = r + β ( r r ) = = 11.4% for firm A f m f r = r + β ( r r ) = = 13.8% for firm f m f 2

3 b) Given the cost of equity and the cost of debt, give the expression for the discount rate of a firm if it were all-equity financed ( r 0 ). alculate the discount rate of the two firms if they were all-equity financed. What may explain the difference between the r 0 of the two firms? Finally, compute the relevant discount rate for Veblen, if it were all-equity financed, assuming that it is a simple average of the estimates for these two firms. The debt-to-equity ratio for the two firms is / = 0.25 and 1.5 respectively for firm A and firm. In order to estimate the cost of capital of a firm if it were all-equity financed, when we know the cost of equity and the cost of debt, we solve the relation r = r0 + (1 τ )( r0 r ) for r 0. This gives (1 τ ) 1 1 r0 = r + r = r + 1 (1 ) (1 ) 1 r τ (1 ) τ + τ (1 τ ) + o that we have 1 1 r0 = = 10.8% (1 0.35) (1 0.35) 1 1 r0 = = 11.9% (1 0.35) (1 0.35) for firm A for firm We computed the cost of equity of the two firms in the same business. In principle, the two costs of equity should be equal, since we corrected for both the industry and the leverage effect. The remaining difference may be explained by the size of the two companies, by the quality of the management, by the ability to invest in a niche. Last, since we assume that the discount rate of the all-equity financed Veblen is the simple average of the two firms, we have r 0 = (10.8% %) / 2 = 11.35% c) Given the debt-to-equity ratio adopted for the project, calculate the cost of equity capital of the project ( r ). Then, calculate the WA relevant for the project and the NPV of the project. 3

4 The debt-to-equity ratio for the project is / = 1, or equivalently the ratio /(+) = 0.5. We then use the result from MM Proposition II with taxes once again to obtain r = r0 + (1 τ )( r0 r ) = (1 0.35) ( ) = 13.5% The WA relevant for the project is rwa = r + (1 τ ) r = (1 0.35) 0.08 = 9.37% + + The initial investment is $16 million. The after-tax cash flows are 8 (1 0.35) = $5.2 million. The NPV of the project is therefore given by NPV t t t= 0 rwa t= = = 16 + = $39.51 million t (1 + ) ( ) d) We now focus on the Adjusted NPV of the project. ompute the tax shield and deduce the APV of the project. ompare with the result obtained by the WA approach. ince we consider a perpetual debt, the tax shield is just given by τ r = = $0.22 million per year. The tax shield is discounted at the r rate. The PV of the tax shield is therefore 0.22 PV ( T) = = 2.8. ( ) t t= 1 With the Adjusted NPV approach, the NPV should be discounted at the cost of capital of the all-equity financed firm r 0. We obtain NPV t t t= 0 r0 t= = = 16 + = $29.8 million t (1 + ) ( ) Finally the Adjusted NPV is equal to APV = NPV + PV ( T) = =$32.6 million The NPV obtained using both WA and APV approaches are positive, indicating that Veblen should invest in the project. 4

5 Exercise 3: hange in the capital structure (20 points) You are asked to evaluate the capital structure of the company GoHome. The board of the company would like to know if it should buy some own shares back by issuing additional debt. You are given the following information: Earnings before taxes $ million Number of shares outstanding 100 million shares urrent debt 0 eta of equity ( β ) 1.2 Expected market return ( r m ) 17.5% Risk free rate ( r f ) 5% orporate tax ( τ ) 35% As you know, increasing leverage may affect the rating of the firm and consequently the interest rate on the debt. GoHome is currently rated AAA. It considers that an increase in the debt level would have the following consequences on its rating and its interest rate: Additional debt Rating Interest rate $200 million A- 7 % $400 million + 8 % a) alculate the cost of equity of the company GoHome, the cost of capital and the value of the assets of the company under the current situation. ompute the price of the shares of the company. The cost of equity is computed using the market model r = r + β ( r r ) = ( ) = 20% f m f ince the firm is unlevered, the cost of capital is given by the cost of equity, so that r0 = r = 20%. The value of the unlevered firm is V U (1 τ ) EIT (1 0.35) = = = $500 million r

6 Given the number of shares outstanding, the price per share is simply $500 million / 100 million shares = $5. b) For both levels of debt under consideration, compute the value of the corresponding tax shield, the value of the company as well as the value of the equity (market capitalization). alculate the return on equity and the WA for each debt level. The tax shield is given by τ, the value of the assets of the firm by VL = VU + τ, and the value of the equity by = VL. Then, we obtain the return on equity as r = r0 + (1 τ )( r0 r ) or and the WA is given by r = r + (1 τ ) r + + WA r ( EIT r )(1 τ ) = 0 T V L r WA urrent structure 0 0% 20% New structure 200 7% 20% % 20% c) For both levels of debt under consideration, calculate the expected price of the shares of the company and the number of shares the company may buy back. The price per share is obtained by P = / N, where N is the number of shares outstanding, and the number of shares the company can buy back is NR = / P. Price per Number of T V L share shares urrent structure 0 0% New structure 200 7% % Interestingly, the firm would have the opportunity to buy back all its stocks! 6