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

Answer 1

Using the regression equation given in the question: Rⁿ = 0.03 + 1.4 * Market return

Intercept of Stock's returns with respect to Market returns = 0.03

Beta or Slope of Stock's returns with respect to Market returns = 1.40

Therefore, Current Equity or Levered Beta = 1.40

Current Debt = $70 million | Current Equity = $100 million | Tax rate = 40%

Debt to Equity ratio = Debt / Equity = 70 / 100 = 70%

Now we will Unlever the Beta and remove current Debt to equity's impact from the Beta.

Unlevered or Asset Beta formula = Equity Beta / (1 + Debt to Equity ratio * (1 - Tax rate))

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

Unlevered Beta = 1.40 / 1.42

Unlevered or Asset Beta of the firm = 0.9856

In New Capital Structure: Debt = 0 | Equity = Increased by $ 50 million

Therefore, New capital structure has Zero Debt to equity ratio.

Hence, The New Beta of Firm which is all equity financed is 0.9856. Therefore, Option D is the correct answer among the given choices.