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 33 percent, what is the aftertax cost of Ying's debt?

  

Bond	Coupon Rate	Price Quote	Maturity	Face Value
1	5.9%	108	3 years	$ 19,000,000
2	6.5	116	6 years	37,000,000
3	5.7	111	16 years	40,000,000
4	6.6	126	30 years	56,000,000

Answer 1

Number of bonds = FV/par value

Bond 1:=19000000/1000=19000

Bond 2:=37000000/1000=37000

Bond 3:=40000000/1000=40000

Bond 4:=56000000/1000=56000

Bond 1

K = Nx2

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

k=1

K =3x2

1080 =∑ [(5.9*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^3x2

k=1

YTM% = 3.09

Bond 2

K = Nx2

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

k=1

K =6x2

1160 =∑ [(6.5*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^6x2

k=1

YTM% = 3.52

Bond 3

K = Nx2

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

k=1

K =16x2

1110 =∑ [(5.7*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^16x2

k=1

YTM% = 4.71

Bond 4

K = Nx2

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

k=1

K =30x2

1260 =∑ [(6.6*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^30x2

k=1

YTM% = 4.93

Weighted Average YTM

Total All debt value = price of Bond 1*Shares of Bond 1 + price of Bond 2*Shares of Bond 2 + price of Bond 3*Shares of Bond 3 + price of Bond 4*Shares of Bond 4

=1080*19000+1160*37000+1110*40000+1260*56000

=178400000

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

=20520000/178400000

=0.11502

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

=42920000/178400000

=0.24058

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

=44400000/178400000

=0.24888

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

=70560000/178400000

=0.39552

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 = 0.11502*3.09+0.24058*3.52+0.24888*4.71+0.39552*4.93

YTM of all debt = 4.3243918

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

After tax rate = 4.3243918 * (1-0.33)

After tax rate = 2.9