Question

# Hi here's my question! You have just done a regression of monthly stock returns of Royal...

Hi here's my question!

You have just done a regression of monthly stock returns of Royal Inc., on monthly market returns

over the past five years and have come up with the following regression:

?" =0.03+1.4×?+

The variance of the stock is 50%, and the variance of the market is 20%. The current risk-free rate is 3% (it was 5% one year ago) and the market risk premium is 8.76%. The stock is currently selling for \$50, down \$4 over the past year; it has paid a dividend of \$2 during the past year and expects to pay a dividend of \$2.50 over the next year. Royal Inc. has a tax rate of 40%. Expected return is 15.26%

Question :
Royal Inc. has \$100 million in equity and \$70 million in debt. It plans to issue \$50 million in new equity and retire \$70 million in debt. Estimate the new beta

A. 0.88

B. 0.90

C. 0.92

D. 0.98

thank you :D

Using the equation given in the question:

Rn = 0.03 + 1.4 * Market return

Intercept given for the stock and market return = 0.03

Beta for stock return and Market returns = 1.40

Therefore,

Levered Beta = 1.40

Current Debt = \$70 million

Current Equity = \$100 million

Tax rate (TR) = 40%

Debt to Equity ratio (D/E Ratio) = Debt / Equity = 70 / 100 = 70%

Now we will Unlevered the Beta,

Unlevered Beta (UB) formula = Equity Beta / (1 + D/E ratio * (1 - TR))

UB = 1.40 / (1 + 70% * (1 - 40%)) = 1.40 / (1 + 70%*60%)

UB = 1.40 / 1.42

Unlevered Beta of the Firm = 0.9856

In New Capital Structure,

Debt = 0

Equity = Increased by \$ 50 million

Therefore, new capital structure has Zero D/E ratio.

Hence, The New Beta of Firm which is all equity financed is 0.9856. (Option D)