4. You have run a regression of monthly returns on a stock against monthly retur

Question

4. You have run a regression of monthly returns on a stock against monthly returns on the S&P; 500 index, and come up with the following output Rstock:0.26% + 1.74 * RMarket R2-0.69 The current one-year treasury bill rate is 2%, the current ten-year bond rate is 3.7% and the current thirty-year bond rate is 5.2%. The firm has 10 million shares outstanding, selling for $10 per share. i. What is the expected return on this stock over the next year? (1 point) Assume a 1 year MRP of 3.8%, and a 30 year MRP of 7%. ii. Would your expected return estimate change if the purpose was to get a discount rate to analyze a thirty-year capital budgeting project? (1 point) iii. An analyst has estimated, correctly, that the stock did 4.1% better than expected, annually, during the period of the regression. Estimate the annualized riskfree rate that he used for his estimate? (2 points) iv. The firm has a debt/equity ratio of 50%, and faces a tax rate of 38%. It is planning to issue $50 million in new debt and acquire a new business for that amount, with the same risk level as the firm's existing business. What will the beta be after the acquisition? (2 points)

Explanation / Answer

(i). Expected return = Rf + beta*MRP =2+1.74*3.8% = 8.612%

(ii) Expected discount rate (30 -year) = Rf (30 year) + beta*MRP(30-year) = 5.2+1.74*7 = 17.38%

(iii) If the stock did 4.1% better than expected, it mean the stock gave a return of 17.38*1.041 = 18.09258%

Risk free rate he assumed = 18.09258 - 1.74*7 = 5.91%

Risk free rate he assumed = 5.91%

(iv) Beta Unlevered = Beta levered/(1+(1-T)*D/E) as per Hamada equation

Beta Unlevered = 1.74/(1+(1-0.38)*0.5) =1.74/1.31 = 1.328

Therefore, Unlebered beta = 1.328

Now, Orginal Debt/Equity = 0.5. Equity =10 Million *10 = 100 Million

Since total equity = 100 Million, Debt = 0.5*100 = 50 Million

With additional 50 Million debt, the total debt = 50+50 = 100 Million.

Now Debt to equity = D/E = 100/100 = 1

As per Hamada equation , new beta = Beta Unlevered *(1+(1-T)*D/E) = 1.328*(1+(1-0.38)*1) = 2.15

New Beta after acquisition = 2.15

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