Question

Yerba Industries is an​ all-equity firm whose stock has a beta of 0.60 and an expected return of 11%. Suppose it issues new​ risk-free debt with a 4.5% 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 $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. Levered Beta = Unlevered Beta * (1 + Debt-Equity ratio)

β_e        = β_u (1+ d/e)

β_e        = 0.60 (1+35/65)

β_e        = 0.60 (1.59)

β_e        = 0.92

Beta of Yerba Stock after transaction is 0.92

b. Unlevered Expected Return = Risk free debt + Levered Beta (Levered Expected Return - Risk free debt)/ Unlevered Beta

r_e         = r_f + β_e (r_m – r_f)/ β_u

r_e         = 4.5 + 0.92 (11 – 4.5)/0.60

r_e         = 4.5 + 0.92 (10.83)

r_e         = 4.5 + 9.97

r_e         = 14.47

Expected Return of Yerba Stock after transaction is 14.47

c.

Profit = Forward P/E Ratio*expected earning per share= 14 (0.50) = 7

Borrowing = Repurchases*Profit = 35% (7) = 2.45

Interest = Risk free debt*Borrowing = 4.5% (2.45) = 0.11

Earnings = Expected earning per share - Interest = 0.50 – 0.11 = 0.39

Earning per share = Earnings/ Outstanding shares = 0.39/0.65 = 0.6

Beneficial stock as less risk is involved.

d. Profit- Earning Ratio = Profit/ Earning per share

Profit- Earning Ratio = 7/0.6

Profit- Earning Ratio   = 11.66

It will rise due to less risk and high profit.