Question

Zeta Ltd. has the following book value capital structure at the present time:

                                                                                                                ($Million)

Bonds (remaining maturity = 20 years)  

Coupon rate= 10%    .......................................... $30 million

Coupon payment= semi-annual

   Number outstanding = 30,000

Common stock (Number outstanding = 1.5 million)...................................$25 million

Retained earnings......................................................................................$10 million

______________

$65 million          

New debt financing is available in the form of bonds, with the face value of $1000, the annual coupon of 8%, term = 20 years, coupon payments semi-annual and these bonds can be sold at face value. Common shares can be sold to the public at $30 per share. The firm has a beta of its common stock equal to 2.5, the current yield on the risk-free asset is 3% and the yield on the market portfolio is expected to be 10%. The expected earnings per share at the end of the year are $4.5. The firm's tax rate is 40 percent. Assume that the current market values of the firm's bonds and common stock provide the firm's desired capital structure over time.

Compute Zeta's weighted average cost of capital.          

Answer 1

K = Nx2

MV of bond =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Bond book value/(1 + YTM/2)^Nx2

k=1

K =20x2

=∑ [(10*30000000/200)/(1 + 8/200)^k]     +   30000000/(1 + 8/200)^20x2

k=1

MV of bond = 35937832.17

MV of equity = price*shares outstanding = 30*1500000=45000000

D/E = MV of bond/MV of equity = 35937832.17/45000000=0.7986

D/A = D/(E+D)

D/A = 0.7986/(1+0.7986)

=0.444

Cost of equity

As per CAPM

Cost of equity = risk-free rate + beta * (expected return on the market - risk-free rate)

Cost of equity% = 3 + 2.5 * (10 - 3)

Cost of equity% = 20.5

After tax cost of debt = cost of debt*(1-tax rate)

After tax cost of debt = 8*(1-0.4)

= 4.8

Weight of equity = 1-D/A

Weight of equity = 1-0.444

W(E)=0.556

Weight of debt = D/A

Weight of debt = 0.444

W(D)=0.444

WACC=after tax cost of debt*W(D)+cost of equity*W(E)

WACC=4.8*0.444+20.5*0.556

WACC% = 13.53