Question

Yerba Industries is an​ all-equity firm whose stock has a beta of 0.60 and an expected return of 13 %. Suppose it issues new​risk-free debt with a 6 % yield and repurchase 10 % 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 $ 0.50​, with a forward​ P/E ratio​ (that is, the share price divided by the expected earnings for the coming​ year) of 14.

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. beta of Yerba stock = Unlevered beta*[1+(1 - tax rate)*(debt/equity)

Tax rate is not given.

beta of Yerba stock = 0.60*[1+(1-0)*(0.10/0.90)] = 0.60*(1+0.10/.90) = 0.60*(1+0.11) = 0.60*1.11 = 0.67

b. We can use capital asset pricing model for calculation of expected return.

expected return = risk-free rate + beta*market risk premium

first we calculate market risk premium before the transaction.

market risk premium = (expected return - risk-free rate)/beta = (13% - 6%)/0.60 = 7%/0.60 = 11.67%

expected return of Yerba stock after the transaction = 6% + 0.67*11.67% = 6% + 7.8189% = 13.82%

c. share price before transaction = expected earning per share*forward P/E ratio = $0.50*14 = $7

value per share of the firm is also $7 because it was all equity financed.

value of debt = value per share of firm*weight of debt = $7*0.10 = $0.7

interest on debt = value of debt*debt interest rate = $0.7*6% = $0.042

expected earnings per share after the transaction = ($0.50 - $0.042)/0.90 = $0.51

This change does not benefit the shareholder because stock price does not change..

d. Yerba's forward​ P/E ratio after this​ transaction = $7/$0.51 = 13.72

Due to higher risk forward​ P/E ratio will fall which has happened after the transaction.