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)
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