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. The mean market return is 8.5% and the ERP is 5.5%.

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

Given

Rstock = 0.25% + 1.25 RMarket

Implies beta = 1.25

Risk free rate = 4.8%

Ten year bond rate = 7.25%

Thirty year bond rate = 8%

Number of shares outstanding = 10 million

Selling price of share = $10

Mean market return = 8.5% = mean market return

ERP = 5.5% = equity risk premium

i.

Expected return of stock next year

=Risk free rate + 1.25 *market premium

= 4.8% + 1.25 * 8.5% = 15.425%

Expected return of stock next year = 15.425%

ii.

Yes, we would use the long term bond rate as riskless rate

Expected return on stock = Thirty year bond rate + 1.25 * ERP = 8% + 1.25 *5.5 %= 14.875 %

Expected return on stock = 14.875 %

iii.

monthly Jensen’s Alpha = (1+ 0.042)^ 1/12 -1 = 0.003434 = 0.34%

0.34% = 0.25% - risk free rate (1-1.25)

Monthly risk free rate =( 0.25-0.34)/ (1-1.25) = 0.36%

Annualized risk free rate = (1+ 0.0036)^12 -1 = 0.044065 = 4.41%

Annualized risk free rate =4.41%

iv.

debt to equity ratio = 50%

tax rate = 40%

$50 million new debt to be issued

Unlevered beta = 1.25/ [1+ (1-tax rate) (debt equity ratio)]

= 1.25/ [1+ (1-0.4)*0.5] = 1.25/1/3 = 0.9615

Market value of equity = Number of shares outstanding * Selling price of share = = = 10 million *$10 = 100 million

Existing debt = 0.5 * 100 million = 50 million

New debt = 50 million + $50 million new = $100 million debt

New Levered beta = unlevered beta * [1+ (1- tax rate)* (new debt/ equity)]

= 0.9615 *[1+ (1-0.4)*(100 million/100 million)]

= 0.9615 * [1+ 0.6]

New beta = 1.5384