Yerba Industries is an all-equity firm whose stock has a beta of 1.10 and an expected return of 14.5 %. Suppose it issues new risk-free debt with a 5 % yield and repurchase 35 % of its stock. Assume perfect capital markets.
a. What is the beta of Yerba stock after this transaction?
b. What is the expected return of Yerba stock after this transaction?
Suppose that prior to this transaction, Yerba expected earnings per share this coming year of $ 5.00, with a forward P/E ratio (that is, the share price divided by the expected earnings for the coming year) of 9.
c. What is Yerba's expected earnings per share after this transaction? Does this change benefit the shareholder? Explain.
d. What is Yerba's forward P/E ratio after this transaction? Is this change in the P/E ratio reasonable? Explain.
a). D/E = 35/65 = 7/13
Levered beta = unlevered beta(1+D/E) = 1.10*(1+7/13) = 1.69
b). Expected return
rsU = rf + beta*(rm - rf) where risk-free rate (rf) = 5%; unlevered beta = 1.10; rsU = 14.5%
Solving for rm, rm = (rsU-rf)/beta +rf = (14.5%-5%)/1.10 + 5% = 13.64%
After the transaction, rsL = 5% + 1.69*(13.64%-5%) = 19.62%
c). Forward P/E = 9; EPS1 = 5, so current price = 9*5 = 45
Debt = 35%*45 = 15.75
Interest on debt = 5%*15.75 = 0.7875
New earnings = 5 - 0.7875 = 4.2125
New EPS = new earnings/%age of equity = 4.2125/65% = 6.48 per share
Risk increases as a result of this transaction.
d). New forward P/E = 45/6.48 = 6.94
P/E ratio falls as risk for the firm increases.
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