Question

Shanken Corp. issued a 20-year, 5.1 percent semiannual bond 2 years ago. The bond currently sells for 97 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 15 years left to maturity; the book value of this issue is $40 million and the bonds sell for 52 percent of par. The company’s tax rate is 25 percent. a. 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.) b. 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.) c. 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.)

Answer 1

a

Total debt BV = debt 1 BV + debt 2 BV = 50+40 = 90 m

b

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

MV of Bond1=1000*50000*0.97

=48500000

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

MV of Bond2=1000*40000*0.52

=20800000

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

=48500000+20800000

=69300000

c

Cost of debt

Bond1

K = N

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

k=1

K =18

970 =∑ [(5.1*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^18

k=1

YTM1 = 5.3639876886

Bond2

K = N

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

k=1

K =15

520 =∑ [(0*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^15

k=1

YTM2 = 4.46

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

Firm cost of debt=5.3639876886*(48500000)/(48500000+20800000)+4.46*(48500000)/(48500000+20800000)

Firm cost of debt=5.09%

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

After tax cost of debt = 5.09*(1-0.25)

= 3.82%