Question

You are analyzing the after-tax cost of debt for a firm. You know that the firm’s 12-year maturity, 18.00 percent semiannual coupon bonds are selling at a price of $1,551.95. These bonds are the only debt outstanding for the firm.

What is the current YTM of the bonds? (Round final answer to 2 decimal places, e.g. 15.25%.)

YTM

%

What is the after-tax cost of debt for this firm if it has a marginal tax rate of 34 percent? (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25%.)

After-tax cost of debt

%

What is the current YTM of the bonds and after-tax cost of debt for this firm if the bonds are selling at par? (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answers to 2 decimal places, e.g. 15.25%.)

YTM		%
After-tax cost of debt		%

Answer 1

Solution:
a.	Current YTM of the bonds
	YTM              10.00   %
Working Notes:
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	First we get the semi annual YTM
	No. of period = years to maturity x no. of coupon in a year = 12 x 2 =nper = N = 24
	Face value of bond = FV= $1,000     as normal if par value details are not given
	Price of the bond = PV = -$1551.95
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 18% x $1,000 /2= $90
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(24,90,-1551.95,1000)
	4.9999774%
	=4.9999774%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 4.9999774% x 2
	YTM annual = 10.0000%
	YTM annual bond =10.00%
	Current YTM of the bond is 10.00%
b.	After-tax cost of debt     6.60 %
Working Notes:
	After-tax cost of debt
	=Current YTM of the bond x ( 1 - tax rate)
	=10.0000 % x ( 1 - 34%)
	=10.0000 % x 0.66
	=6.60%
c.	YTM                                                 18.00 %
	After-tax cost of debt                    11.88 %
Working Notes:
	Since the bond is selling at par , it current YTM must be equals to is coupon rate that is 18% lets check it.
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	First we get the semi annual YTM
	No. of period = years to maturity x no. of coupon in a year = 12 x 2 =nper = N = 24
	Face value of bond = FV= $1,000     as normal if par value details are not given
	Price of the bond = PV = -$1000
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 18% x $1,000 /2= $90
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(24,90,-1000,1000)
	9.0000000%
	=9.00000%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 9.0000% x 2
	YTM annual = 18.0000%
	YTM annual bond =18.00%
	Current YTM of the bond is 18.00%
	After-tax cost of debt
	=Current YTM of the bond x ( 1 - tax rate)
	=18.0000 % x ( 1 - 34%)
	=18.0000 % x 0.66
	=11.88%
Please feel free to ask if anything about above solution in comment section of the question.