Question

Shanken Corp. issued a 30-year, 10 percent semiannual bond 4 years ago. The bond currently sells for 94 percent of its face value. The book value of the debt issue is $50 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 14 years left to maturity; the book value of this issue is $50 million and the bonds sell for 54 percent of par. The company’s tax rate is 38 percent.

What is the company's total book value of debt? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, e.g., 1,234,567.)

Total book value

$

What is the company's total market value of debt? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, e.g., 1,234,567.)

Total market value

$

What is your best estimate of the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Cost of debt

%

Answer 1

Total book value = BV debt 1 + BV debt 2

=50+50=100m = 100000000

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

MV of Bond1=1000*50000*0.94

=47000000

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

MV of Bond2=1000*50000*0.54

=27000000

MV of total debt= MV of Bond1+ MV of Bond 2

=47000000+27000000

=74000000

Cost of debt

Bond1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =26x2

940 =∑ [(10*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^26x2

k=1

YTM1 = 10.687

Bond2

K = N

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

k=1

K =14

540 =∑ [(0*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^14

k=1

YTM2 = 4.5

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

Firm cost of debt=10.687*(47000000)/(47000000+27000000)+4.5*(47000000)/(47000000+27000000)

Firm cost of debt=8.43%

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

After tax cost of debt = 8.43*(1-0.38)

= 5.23%