Question

Titan Mining Corporation has 9 million shares of common stock outstanding and 340,000 5.7 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $38 per share and has a beta of 1.2; the bonds have 20 years to maturity and sell for 119 percent of par. The market risk premium is 7.8 percent, T-bills are yielding 3 percent, and the company’s tax rate is 25 percent.

  

a.	What is the firm's market value capital structure? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .3216.)
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? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

   

Answer 1

What is the firm's market value capital structure?

Market value of equity E = Number of shares * stock price = 9 million *$38 = $342 million

Market value of debt D = number of bonds outstanding * face value * selling at % of par

= 340,000 * $1000 * 119% = $404.60 million

Firm’s market value capital structure = Market value of equity E + Market value of debt D

(D +E)= $342 million +$404.60 million

= $746.60 million

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?

We need to find the YTM on bond issues

Before tax cost of debt is bond’s yield; we have following formula for calculation of bond’s yield

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where

Price of the bond P0 = $404.60 million

M = value at maturity, or par value = 340,000 * $1000 = $340 million

C = coupon payment = 5.7%/2 of $404.60 million = $9,690,000 semiannual coupon

n = number of payments = 20 years *2 = 40

i = interest rate, or yield to maturity =?

Now we have,

$404.60 million = $9,690,000 * [1 – 1 / (1+i) ^20] /i + $340 million / (1+i) ^20

We got the value of i = 1.72%

Therefore YTM of bond = 2 *1.72 = 3.44%

Tax rate = 25%

Therefore After tax cost of debt rd = 3.44% *(1-0.25) = 2.58%

re= the firm's cost of equity = risk free rate (rf) + β of stock * risk premium on the market

= 3% + 1.2 * 7.8% = 12.36%

Weighted Average Cost of Capital (WACC)

WACC = [E/ (E+D)] * re + [D/ (E+D)] * rd

Where, re is the cost of equity

rd is the after tax cost of debt

E is the value of common equity

D is the value of debt

WACC = ($ 342 million / $746.60 million) * 12.36% + ($404.60 million / $746.60 million) * 2.58%

= 5.66% + 1.40%

=7.06%

Therefore firm can use Weighted Average Cost of Capital (WACC) as discount rate of firm; which is 7.06%