Question

Titas Mining Corporation has 6.4 million shares of common stock outstanding and 175,000 6.2% semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $53 per share and has a beta of 1.15; the bonds have 25 years to maturity and sell for 106% of par. The market risk premium is 6.8%, T-bills are yielding 3.1% and the company’s tax rate is 22%.

            a. What is the firm’s market value capital structure?

            b. If the company is evaluating a new investment project that has the same risk as the firm’s typical project, what rate should the firm use to discount the project’s cash flows?

Answer 1

a

MV of equity=Price of equity*number of shares outstanding

MV of equity=53*6400000

=339200000

MV of Bond=Par value*bonds outstanding*%age of par

MV of Bond=1000*175000*1.06

=185500000

MV of firm = MV of Equity + MV of Bond

=339200000+185500000

=524700000

Weight of equity = MV of Equity/MV of firm

Weight of equity = 339200000/524700000

W(E)=0.6465

Weight of debt = MV of Bond/MV of firm

Weight of debt = 185500000/524700000

W(D)=0.3535

b

Cost of equity

As per CAPM

Cost of equity = risk-free rate + beta * (Market risk premium)

Cost of equity% = 3.1 + 1.15 * (6.8)

Cost of equity% = 10.92

Cost of debt

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =25x2

1060 =∑ [(6.2*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^25x2

k=1

YTM = 5.7448485317

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

After tax cost of debt = 5.7448485317*(1-0.22)

= 4.480981854726

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

WACC=4.48*0.3535+10.92*0.6465

WACC =8.64%