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			5.5	%			105.26			5	years		$	55,000,000
2			7.1				114.02			8	years			50,000,000
3			7.0				112.57			15.5	years			70,000,000
4			6.3				101.81			25	years			77,000,000

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.)

	Cost of debt %

Answer 1

Number of bonds = FV/par value

Bond 1:=55000000/1000=55000

Bond 2:=50000000/1000=50000

Bond 3:=70000000/1000=70000

Bond 4:=77000000/1000=77000

Bond 1

K = Nx2

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

k=1

K =5x2

1052.6 =∑ [(5.5*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^5x2

k=1

YTM% = 4.32

Bond 2

K = Nx2

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

k=1

K =8x2

1140.2 =∑ [(7.1*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^8x2

k=1

YTM% = 4.96

Bond 3

K = Nx2

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

k=1

K =15.5x2

1125.7 =∑ [(7*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^15.5x2

k=1

YTM% = 5.76

Bond 4

K = Nx2

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

k=1

K =25x2

1018.1 =∑ [(6.3*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^25x2

k=1

YTM% = 6.16

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

=1052.6*55000+1140.2*50000+1125.7*70000+1018.1*77000

=272095700

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

=57893000/272095700

=0.21277

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

=57010000/272095700

=0.20952

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

=78799000/272095700

=0.2896

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

=78393700/272095700

=0.28811

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 = 0.21277*4.32+0.20952*4.96+0.2896*5.76+0.28811*6.16

YTM of all debt = 5.4012392

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

After tax rate = 5.4012392 * (1-0.25)

After tax rate = 4.05