Question

1. 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 = 0.25% + 1.25 RMarket R² = 0.60

The current one-year treasury bill rate is 4.8%, the current ten-year bond rate is 7.25% and the current thirty-year bond rate is 8%. 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?

ii. Would your expected return estimate change if the purpose was to get a discount rate to analyze a thirty-year capital budgeting project?

iii. An analyst has estimated, correctly, that the stock did 4.2% better than expected, annually, during the period of the regression. Can you estimate the annualized riskfree rate that he used for his estimate?

iv. The firm has a debt/equity ratio of 50% and faces a tax rate of 40%. 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?

Answer 1

i. What is the expected return on this stock over the next year?

Rstock = 0.25% + 1.25 RMarket    where R2 = 0.60

                        a).Lets find out Rmarket

                        Market returns of S&P 500 , last one year is 6.1 % (Google and get it)

                        Risk free rate = One year Treasury bill rate = 4.8 % (As its one year estimate)

                        Rmarket = 6.1 – 4.8 = 1.3 %

                        Hence Rstock = 0.25+1.25 x 1.3 = 1.875 %

                   ii.Would your expected return estimate change if the purpose was to get a discount rate to analyze a thirty-year capital budgeting project?

In that case we need to consider Market returns of S&P 500 for 30 years and risk free rate as 30 year bond rate is preferable.

iii.An analyst has estimated, correctly, that the stock did 4.2% better than expected, annually, during the period of the regression. Can you estimate the annualized risk free rate that he used for his estimate?

Revised Rstock = 4.2 % more than previously calculated Rstock

                         =     1.042 * 1.875 = 1.95375

Rstock = 0.25% + 1.25 RMarket    where R2 = 0.60

1.95375 = 0.25 + 1.25 x Rmarket

Revised Rmarket = 1.363

New annualized risk free rate = 6.1-1.363 = 4.737 %

              Market returns of S&P 500 , last one year is 6.1 % (Google and get it)

iv. The firm has a debt/equity ratio of 50% and faces a tax rate of 40%. 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?

                Unlevered Beta =Levered Beta /(1+[(1-tax)x(Debt/Equity)]

=1.25 /( 1+0.6x0.5)       [ 1.25 from regression equation]

=1.25/1.30

=0.97