Question

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.

Answer 1

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.