Question

Bank of America has 14 million common shares outstanding with current price of $50 and book value of $18 a share and a beta of 1.88. They also have two bond issues outstanding. The first bond issue has book value of $100 million, coupon rate of 11% and currently sells at 125.678% of par. The second bond issue is a zero coupon bond with book value of $50 million and currently sells at 43%. Maturity of both bonds is 15 years. The tax rate is 45%. Market return is 8% and the T. bill rate is 3.5%. (step-by-step, pls)

1. What are capital structure weights on a book value basis?

2. What are capital structure weights on a market value basis?

3. What is the Weighted Average Cost of Capital (WACC)?

Answer 1

1

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

BV of equity=18*14000000

=252000000

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

BV of Bond1=1000*100000*1

=100000000

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

BV of Bond2=1000*50000*1

=50000000

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

=252000000+100000000+50000000

=402000000

Weight of equity = BV of Equity/BV of firm

Weight of equity = 252000000/402000000

W(E)=0.6269

Weight of debt = BV of Bond/BV of firm

Weight of debt = 150000000/402000000

W(D)=0.3731

2

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

MV of equity=50*14000000

=700000000

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

MV of Bond1=1000*100000*1.25678

=125678000

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

MV of Bond2=1000*50000*0.43

=21500000

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

=700000000+125678000+21500000

=847178000

Weight of equity = MV of Equity/MV of firm

Weight of equity = 700000000/847178000

W(E)=0.8263

Weight of debt = MV of Bond/MV of firm

Weight of debt = 147178000/847178000

W(D)=0.1737

3

Cost of equity

As per CAPM

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

Cost of equity% = 3.5 + 1.88 * (8 - 3.5)

Cost of equity% = 11.96

Cost of debt

Bond1

K = N

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

k=1

K =15

1256.78 =∑ [(11*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^15

k=1

YTM1 = 8.0000430579

Bond2

K = N

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

k=1

K =15

430 =∑ [(0*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^15

k=1

YTM2 = 5.79

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

Firm cost of debt=8.0000430579*(125678000)/(125678000+21500000)+5.79*(125678000)/(125678000+21500000)

Firm cost of debt=7.68%

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

After tax cost of debt = 7.68*(1-0.45)

= 4.224

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

WACC=4.22*0.1737+11.96*0.8263

WACC =10.62%