Question

Ying Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the following table. If the corporate tax rate is 32 percent, what is the aftertax cost of Ying's debt?

Bond	Coupon Rate	Price Quote	Maturity	Face Value
1	5.8%	107	7 years	$ 18,000,000
2	7.1	116	11 years	38,000,000
3	6.2	111	22 years	48,000,000
4	7.4	122	36 years	62,000,000

Multiple Choice

• 3.9%

• 3.53%

• 3.56%

• 5.46%

• 3.71%

Answer 1

Bond 1

Number of shares = Face value/par = 18000000/1000=18000

K = Nx2

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

k=1

K =7x2

1070 =∑ [(5.8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^7x2

k=1

YTM% = 4.62

Bond 2

Number of shares = Face value/par = 38000000/1000=38000

K = Nx2

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

k=1

K =11x2

1160 =∑ [(7.1*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^11x2

k=1

YTM% = 5.17

Bond 3

Number of shares = Face value/par = 48000000/1000=48000

K = Nx2

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

k=1

K =22x2

1110 =∑ [(6.2*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^22x2

k=1

YTM% = 5.34

Bond 4

Number of shares = Face value/par = 62000000/1000=62000

K = Nx2

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

k=1

K =36x2

1220 =∑ [(7.4*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^36x2

k=1

YTM = 5.915%

Total All debt value = price of Bond 1*No. of Bond 1 + price of Bond 2*No. of Bond 2 + price of Bond 3*No. of Bond 3 + price of Bond 4*No. of Bond 4

=1070*18000+1160*38000+1110*48000+1220*62000

=192260000

Weight of Bond 1 = price of Bond 1*No. of Bond 1/Total All debt Value

= 19260000/192260000

=0.1002

Weight of Bond 2 = price of Bond 2*No. of Bond 2/Total All debt Value

= 44080000/192260000

=0.2293

Weight of Bond 3 = price of Bond 3*No. of Bond 3/Total All debt Value

= 53280000/192260000

=0.2771

Weight of Bond 4 = price of Bond 4*No. of Bond 4/Total All debt Value

= 75640000/192260000

=0.3934

YTM of All debt = Weight of Bond 1*YTM of Bond 1+Weight of Bond 2*YTM of Bond 2+Weight of Bond 3*YTM of Bond 3+Weight of Bond 4*YTM of Bond 4

YTM of All debt = 4.62*0.1002+5.17*0.2293+5.34*0.2771+5.915*0.3934

YTM of All debt = 5.4551

After tax rate = YTM * (1-Tax rate)

After tax rate = 5.4551 * (1-0.32)

After tax rate = 3.71