Question

medicom co. has 6,500 bonds outstanding that are selling at 96.5% of par, paying semiannual coupon of 4.8% with 2 years remaining to maturity. the company also have 48,000 shares of 5.5% preferred stock at 75,000 shares of common stock outstanding .the preferred stock sells for $64 a share. the common stock has a beta of 1.32 and sells for $41 a share.the preferred stock has a stated value of $100. the risk free rate is 2.2% and the market risk premium is 8.4%. the corporate tax rate is 21 percent. a. what is the weighted average cost of capital ?

Answer 1

a) Cost of bond (YTM after tax)

YTM = (Coupon + ((F - P)/n)) / ((F + P) /2)

Here,

F (Face value) = $100

P (Price) = $96.50 ($100 * 96.50%)

Coupon = Face value * Coupon rate

Coupon = $100 * 4.8% * 6/12 months

Coupon = $2.4

n (period) = 2 years * 2 = 4

Tax rate = 21% or 0.21

YTM calculation,

YTM = ($2.4 + (($100 - $96.50) / 4)) / (($100 + 96.50)/2)

YTM = ($2.4 + $0.875) / $98.25

YTM = $3.275 / $98.25

YTM (semi annually) = 0.0333

Now

YTM (annually) = ((1 + YTM semi annually)^n) - 1

n (no. Of compounding per year) = 2

YTM (annually) = ((1 + 0.0333)^2) - 1

YTM (annually) = 1.0677 - 1 = 0.0677

Cost of debt after tax = YTM annually*(1 - tax rate)

Cost of debt after tax = 0.0677 * (1 - 0.21)

Cost of debt after tax = 0.0535 or 5.35%

b) Cost of preferred stock = Dividend / Price

Here,

Dividend = Par value * Rate of preferred stock

Dividend = $100 * 5.5% = $5.50

Price = $64

Now,

Cost of preferred stock = $5.50 / $64

Cost of preferred stock = 0.0859 or 8.59%

c) Cost of equity using CAPM

Cost of equity = Rf + Beta * (Rm - Rf)

Here,

Rf (Risk free rate) = 2.2% or 0.022

Rm - Rf (Risk premium) = 8.4% or 0.084

Beta = 1.32

Now,

Cost of equity = 0.022 + (1.32 * 0.084)

Cost of equity = 0.0220 + 0.1110

Cost of equity = 0.1330 or 13.30%

d) Weight of capital :

Bond = 6,500 Bonds * $100 = $6,50,000

Preferred stock = 48,000 shares * $64 = $30,72,000

Equity = 75,000 shares * $41 = $30,75,000

Total capital = $6,50,000 + $30,72,000 + $30,75,000

Total capital = $67,97,000

Weight of debt = Bond / Total capital

Weight of debt = $6,50,000 / $67,97,000 = 0.0956

Weight of preferred stock = Preferred stock / Total capital

Weight of preferred stock = $30,72,000 / $67,97,000 = 0.4520

Weight of equity = Equity / Total capital

Weight of equity = $30,75,000 / $67,97,000 = 0.4524

e) Weighted average cost of capital (WACC) = (Wieght of debt * Cost of debt) + (Weight of preferred stock * Cost of preferred stock) + (Weight of equity * Cost of equity)

Using above data,

WACC = (0.0956 * 0.0535) + (0.4520 * 0.0859) + (0.4524 * 0.1330)

WACC = 0.0051 + 0.0388 + 0.0602

WACC = 0.1041 or 10.41%