Question

Ying Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the following table.

Bond		Coupon Rate				Price Quote				Maturity			Face Value
1			7.0	%			105.76			6	years		$	50,000,000
2			8.5				115.52			9	years			45,000,000
3			8.2				114.07			16.5	years			65,000,000
4			7.8				103.31			26	years			72,000,000

If the corporate tax rate is 25 percent, what is the aftertax cost of the company’s debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Number of bonds = FV/par value

Bond 1:=50000000/1000=50000

Bond 2:=45000000/1000=45000

Bond 3:=65000000/1000=65000

Bond 4:=72000000/1000=72000

Bond 1

K = Nx2

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

k=1

K =6x2

1057.6 =∑ [(7*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^6x2

k=1

YTM% = 5.85

Bond 2

K = Nx2

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

k=1

K =9x2

1155.2 =∑ [(8.5*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^9x2

k=1

YTM% = 6.22

Bond 3

K = Nx2

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

k=1

K =16.5x2

1140.7 =∑ [(8.2*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^16.5x2

k=1

YTM% = 6.77

Bond 4

K = Nx2

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

k=1

K =26x2

1033.1 =∑ [(7.8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^26x2

k=1

YTM% = 7.51

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

=1057.6*50000+1155.2*45000+1140.7*65000+1033.1*72000

=253392700

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

=52880000/253392700

=0.20869

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

=51984000/253392700

=0.20515

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

=74145500/253392700

=0.29261

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

=74383200/253392700

=0.29355

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 = 0.20869*5.85+0.20515*6.22+0.29261*6.77+0.29355*7.51

YTM of all debt = 6.6823997

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

After tax rate = 6.6823997 * (1-0.25)

After tax rate = 5.01