Question

Corporation X common stock is trading at $200 a share and it has 1 million shares outstanding. The stock’s beta is 1.2, the risk-free rate 2%, and the market portfolio is expected to return 9%. Their debt consists of two issues of bonds:

Issue Maturity (years) Coupon (%) Market value (% of par) Amount outstanding (million $)

A 15 8% 101 50

B 25 10% 102 40

Assuming Corporation X is subject to a 21% corporate tax rate, please find its WACC.

Answer 1

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

MV of equity=200*1000000

=200000000

MV of Bond1=Par value*bonds outstanding*%age of par

MV of Bond1=1000*50000*1.01

=50500000

MV of Bond2=Par value*bonds outstanding*%age of par

MV of Bond2=1000*40000*1.02

=40800000

MV of firm = MV of Equity + MV of Bond1+ MV of Bond 2

=200000000+50500000+40800000

=291300000

Weight of equity = MV of Equity/MV of firm

Weight of equity = 200000000/291300000

W(E)=0.6866

Weight of debt = MV of Bond/MV of firm

Weight of debt = 91300000/291300000

W(D)=0.3134

Cost of equity

As per CAPM

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

Cost of equity% = 2 + 1.2 * (9 - 2)

Cost of equity% = 10.4

Cost of debt

Bond1

K = N

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

k=1

K =15

1010 =∑ [(8*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^15

k=1

YTM1 = 7.8839966649

Bond2

K = N

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

k=1

K =25

1020 =∑ [(10*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^25

k=1

YTM2 = 9.78

Firm cost of debt=YTM1*(MV bond1)/(MV bond1+MV bond2)+YTM2*(MV bond2)/(MV bond1+MV bond2)

Firm cost of debt=7.8839966649*(50500000)/(50500000+40800000)+9.78*(50500000)/(50500000+40800000)

Firm cost of debt=8.73%

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

After tax cost of debt = 8.73*(1-0.21)

= 6.8967

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

WACC=6.9*0.3134+10.4*0.6866

WACC =9.3%