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You are analyzing the after-tax cost of debt for a firm. You know that the firm’s...

You are analyzing the after-tax cost of debt for a firm. You know that the firm’s 12-year maturity, 15.50 percent semiannual coupon bonds are selling at a price of $1,117.25. These bonds are the only debt outstanding for the firm.

YTM?

After tax cost of debt at marginal 34% tax rate?



Then if selling at par YTM and after tax cost of debt?



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Calculation of Yield to maturity and after-tax cost of debt:Calculation of yield to maturity: Face value Coupon rate Current Price Maturity Semi-Annual Coupon Semi-annual Period $1,000 15.50% 1117.25 12 years 77.5 24 12 13 Cash flow to investor will be as follows: Semi-Annual Period Cash flow ($1,117.25 $78 $78 $78 $78 $78$1,078 13+D4 15 16 17 Yield to maturity is the rate at which if future NPV to Investor will be zero Let r be the yield to maturity then, S78 $78 S1,078 PV--$1175.. 19 21 $78 $78 $1,078 By solving above equation, yield to maturity r can be found Hit and trial method can be used to find the solution of above equation. 26 27 Rate(nper,pmt,PV, [fv],type) function of excel can be used to find the yield to maturity as follows: nper pmt PV 29 30 31 32 ($1,117.25) $1,000 6.75%-RATE(D28,D29,D30,D31) Semi annual Yield to maturity Yield to maturity -2* Semi-annual Yield to maturity 34 35 36 37 13.50%-o332 Hence yield to maturity is The yield to maturity will be the cost of debt. Tax rate 13.50% 39 34% After-tax cost of debt -Cost of Debt (1-Tax Rate) 996 -D37*(1-D39) 43 Hence after-tax cost of debt i 8.91% When bond is issued at par, Yield to maturity becomes equal to the coupon rate Thus Yield to maturity 47 15.50% 49 Tax rate 34% After-tax cost of debt 51 52 53 -Cost of Debt(1-Tax Rate) 10.23%-D4711-D49) Hence after-tax cost of debt i 10.23%

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