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			5.9	%			105.66			5	years		$	51,000,000
2			7.5				114.42			8	years			46,000,000
3			7.4				112.97			15.5	years			66,000,000
4			6.7				102.21			25	years			73,000,000

If the corporate tax rate is 21 percent, what is the aftertax cost of the company’s debt?

Answer 1

Solution:
	After-tax cost of the company’s debt	4.53	%
Working Notes:
	Calculation of market value of debt and its weight in the total debt
			[(Quote/Face value per bond) x total face value]	[Market value / total market value 255,693,300]
Bond	Price Quote	Face value	Market value	Weight
1	105.66	51,000,000	53,886,600	0.210747016
			[(105.66/100) x 51,000,000]	[53,886,600/255,693,300]
2	114.42	46,000,000	52,633,200	0.20584505
3	112.97	66,000,000	74,560,200	0.291600132
4	102.21	73,000,000	74,613,300	0.291807803
		Total	255,693,300	1
	Since these bond are paying semi annual coupon , means twice a year. Its YTM can be exactly calculated by financial calculator or excel method here we use excel method.
BOND 1
	No. of period = years to maturity x no. of coupon in a year = 5 x 2 =nper = N = 10
	Face value of bond = FV= $51000000
	Price of the bond =Market value of bond= PV = -$53886600
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 5.9% x 51,000,000/2= $1,504,500
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(10,1504500,-53886600,51000000)
	0.023096405
	=2.30964046%
	The YTM calculated is semi annual
	Annual YTM Bond 1 = Semi annual YTM x 2
	Annual YTM Bond 1 = 2.30964046% x 2
	Annual YTM Bond 1 = 4.61928092%
BOND 2
	No. of period = years to maturity x no. of coupon in a year = 8 x 2 =nper = N = 16
	Face value of bond = FV= $46000000
	Price of the bond =Market value of bond= PV = -$52633200
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 7.5% x 46,000,000/2=$1725000
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(16,1725000,-52633200,46000000)
	0.026339003
	=2.633900285%
	The YTM calculated is semi annual
	Annual YTM Bond 2 = Semi annual YTM x 2
	Annual YTM Bond 2 = 2.633900285% x 2
	Annual YTM Bond 2 = 5.2678006%
BOND 3
	No. of period = years to maturity x no. of coupon in a year = 15.5 x 2 =nper = N = 31
	Face value of bond = FV= $66000000
	Price of the bond =Market value of bond= PV = -$
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 7.4% x 66,000,000/2=$2442000
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(31,2442000,-74560200,66000000)
	0.030474262
	=3.047426156%
	The YTM calculated is semi annual
	Annual YTM Bond 3 = Semi annual YTM x 2
	Annual YTM Bond 3 = 3.047426156%x 2
	Annual YTM Bond 3 = 6.0948523%
BOND 4
	No. of period = years to maturity x no. of coupon in a year = 25 x 2 =nper = N = 50
	Face value of bond = FV= $73000000
	Price of the bond =Market value of bond= PV = -$
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 6.7% x 73,000,000/2=$2445500
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(50,2445500,-74613300,73000000)
	0.032598224
	=3.259822408%
	The YTM calculated is semi annual
	Annual YTM Bond 4 = Semi annual YTM x 2
	Annual YTM Bond 4 =3.259822408%x 2
	Annual YTM Bond 4 = 6.5196448%
Now	We calculate pre tax cost of debt
	Pre tax cost of debt = Sum of (weight x Annual YTM)
	A = Calculated above	B= see above	C= A x B
Bond	Annual YTM	Weight	Pre tax cost of Bond
1	4.6192809%	0.210747016	0.97349967%	D
2	5.2678006%	0.205845050	1.08435068%	E
3	6.0948523%	0.291600132	1.77725973%	F
4	6.5196448%	0.291807803	1.90248322%	G
		Pre tax cost of debt	5.73759330%	H= D+E+F+G
	Aftertax cost of the company’s debt
	=Pre tax cost of debt x (1- tax rate)
	=5.7375933% x (1-0.21)
	=4.5326987%
	=4.53%
Please feel free to ask if anything about above solution in comment section of the question.