Question

An all-equity firm has 100,000 shares of common stock outstanding. Investors require a 25% return on the firm’s equity. The firm is expected to live for one year. Its end-of-year cash flows can be $1M, $2M, $3M, $4M, and $5M with equal probabilities. There are no corporate or personal taxes, and no bankruptcy costs.

a) What is the value of the firm

b) Suppose the firm issues debt with face value of $1M maturing in a year with no coupons, and uses the proceeds to repurchase some of its equity. The required return on debt is 10%. Assume that the equity is repurchased at the market price. How many shares does the firm repurchase?

c) What is the value of the remaining shares?

d) What is the expected return on the levered firm’s equity?

Answer 1

a) Expected cash flow= 0.2(1+2+3+4+5)=$3mn

At 25% discount rate the value of firm = 3/(1+25%) or $2.4mn

So, value of the firm is $2.4mn

b) The share price of the firm =2,400,000/100000 or $24/share

The value of debt fund raised= 1,000,000/1.1=909090.9

So, the firm would be able to repurchase=909090.9/24=37878.8 or 37878 number of share

c) Remaining share outstanding =(100000-37878)=62122

So, the value of remaining share=62122*24=$1,490,928

d) The expected return on levered equity= ReU+D/E*(ReU-Rf) (Where ReU= Required rate of unlevered equity, Rf= Risk Free Rate, D= Debt, E= Equity)

=25%+(909090.9/1,490,928)*(25%-Rf)=25%+0.609*(25%-Rf)

If Rf=0%, the expected return on levered equity= 40.24%