Question

Finding the WACC [LO3] Titan Mining Corporation has 7.5 million shares of common stock outstanding, 250,000 shares of 4.2 percent preferred stock outstand- ing, and 140,000 bonds with a semiannual coupon of 5.1 percent outstanding, par value $1,000 each. The common stock currently sells for $51 per share and has a beta of 1.15, the preferred stock currently sells for $103 per share, and the bonds have 15 years to maturity and sell for 107 percent of par. The market risk premium is 7.5 percent, T-bills are yielding 2.4 percent, and the company's tax rate is 22 percent. 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]

market value of common stock  = shares outstanding * price per share

market value of common stock  = 7,500,000 * $51

market value of common stock  = $382,500,000

market value of preferred stock  = shares outstanding * price per share

market value of preferred stock  = 250,000 * $103

market value of preferred stock  = $25,750,000

market value of debt = bonds outstanding * price per bond

market value of debt = 140,000 * ($1,000 * 107%)  

market value of debt = $149,800,000

total market value = $382,500,000 + $25,750,000 + $149,800,000

total market value = $558,050,000

weight of common stock = market value of common stock / total market value

weight of common stock = $382,500,000 / $558,050,000

weight of common stock = 0.685

weight of preferred stock = market value of preferred stock / total market value

weight of preferred stock = $25,750,000 / $558,050,000

weight of preferred stock = 0.046

weight of debt = market value of debt / total market value

weight of debt = $149,800,000 / $558,050,000

weight of debt = 0.268

b]

WACC = (weight of common stock * cost of common stock) + (weight of preferred stock * cost of preferred stock) + (weight of debt * cost of debt)

cost of common stock = risk free rate + (beta * market risk premium)

cost of common stock = 2.4% + (1.15 * 7.5%)  

cost of common stock = 11.03%

cost of preferred stock = annual dividend / price per share

cost of preferred stock = ($100 * 4.2%) / $103

cost of preferred stock = 4.08%

cost of debt = YTM of bond * (1 - tax rate)

YTM is calculated using RATE function in Excel with these inputs :

nper = 15*2 (15 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 5.1% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -1000 * 107% (current bond price = face value * 107%. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 2.23%. This is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 4.46%

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

cost of debt = 4.46% * (1 - 22%) ==> 3.48%

A1 fc =RATE(15*2, 1000*5.1%/2,-1000*107%, 1000) D E F G B C 1 2.23%

WACC = (weight of common stock * cost of common stock) + (weight of preferred stock * cost of preferred stock) + (weight of debt * cost of debt)

WACC = (0.685 * 11.03%) + (0.046 * 4.08%) + (0.268 * 3.48%)

WACC = 8.68%