Question

Shanken Corp. issued a 10-year, 8 percent semiannual bond 3 years ago. The bond currently sells for 96 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 10 years left to maturity; the book value of this issue is $30 million and the bonds sell for 55 percent of par. The company’s tax rate is 35 percent. What is the company's total book value of debt? What is the company's total market value of debt? What is your best estimate of the aftertax cost of debt? Show Steps please I got this wrong twice only have one more attempt

Answer 1

Note: for zero coupon bond it is not specified if there is semi annual compounding or not, so I have solved the last part with both with and without...so please confirm and use the correct part

Total book value of debt = FV debt 1 + FV debt 2 = 50+30=80m

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

MV of Bond1=1000*50000*0.96

=48000000

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

MV of Bond2=1000*30000*0.55

=16500000

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

=48000000+16500000

=64500000

Part 3

Using annual compounding for 0 coupon bond

Cost of debt

Bond1

K = Nx2

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

k=1

K =7x2

960 =∑ [(8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^7x2

k=1

YTM1 = 8.7769015569

Bond2

K = N

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

k=1

K =10

550 =∑ [(0*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^10

k=1

YTM2 = 6.16

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

Firm cost of debt=8.7769015569*(48000000)/(48000000+16500000)+6.16*(48000000)/(48000000+16500000)

Firm cost of debt=8.11%

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

After tax cost of debt = 8.11*(1-0.35)

= 5.27

Using semiannual compounding for 0 coupon bond

Cost of debt

Bond1

K = Nx2

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

k=1

K =7x2

960 =∑ [(8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^7x2

k=1

YTM1 = 8.7769015569

Bond2

K = Nx2

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

k=1

K =10x2

550 =∑ [(0*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM2 = 6.07

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

Firm cost of debt=8.7769015569*(48000000)/(48000000+16500000)+6.07*(48000000)/(48000000+16500000)

Firm cost of debt=8.08%

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

After tax cost of debt = 8.08*(1-0.35)

= 5.25