Filer Manufacturing has 8757596 shares of common stock outstanding. The current share price is $56.37, and the book value per share is $9.59. Filer Manufacturing also has two bond issues outstanding. The first bond issue has a face value of $49755532, has a 0.05 coupon, matures in 10 years and sells for 83 percent of par. The second issue has a face value of $52381094, has a 0.06 coupon, matures in 20 years, and sells for 92 percent of par.
The most recent dividend was $2.94 and the dividend growth rate is 0.04. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 0.34. What is Filer's aftertax cost of debt?
Step 1: Calculate After-Tax Yield to Maturity of First Bond
The yield to maturity can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Payment (here, Coupon Payment), PV = Present Value (here, Current Bond Price) and FV = Future Value (here, Face Value/Par Value).
Here, Nper = 10*2 = 20, PMT = 49,755,532*5%*1/2 = $1,243,888.30, PV = 49,755,532*83% = $41,297,091.56 and FV = $49,755,532 [we use 2 since the bond is semi-annual]
Substituting these values in the above formula, we get,
After-Tax Yield to Maturity of First Bond = Rate(20,1243888.30,-41297091.56,49755532)*2*(1-.34) = 4.91%
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Step 2: Calculate After-Tax Yield to Maturity of Second Bond
The yield to maturity can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Payment (here, Coupon Payment), PV = Present Value (here, Current Bond Price) and FV = Future Value (here, Face Value/Par Value).
Here, Nper = 20*2 = 40, PMT = 52,381,094*6%*1/2 = 1,571,432.82, PV = 52,381,094*92% = $48,190,606.48 and FV = $52,381,094 [we use 2 since the bond is semi-annual]
Substituting these values in the above formula, we get,
After-Tax Yield to Maturity of Second Bond = Rate(40,1571432.82,-48190606.48,52381094)*2*(1-.34) = 4.44%
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Step 3: Calculate Filer's After-Tax Cost of Debt
The value of Filer's after-tax cost of debt is determined as below:
Filer's After-Tax Cost of debt = Market Value of First Bond/(Market Value of First Bond + Market Value of Second Bond)*After-Tax Yield to Maturity of First Bond + Market Value of Second Bond/(Market Value of First Bond + Market Value of Second Bond)*After-Tax Yield to Maturity of Second Bond
Substituting these values in the above formula, we get,
Filer's After-Tax Cost of Debt = 41,297,091.56/(41,297,091.56 + 48,190,606.48)*4.91% + 48,190,606.48/(41,297,091.56 + 48,190,606.48)*4.44% = 4.66% (answer)
The Filer's After-Tax Cost of Debt is 4.66%.
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Notes:
1) There can be a slight difference in final answer on account of rounding off values.
2) Market value of bonds is same as current selling price (Present Value) of bonds.
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