C1. (Cost of borrowing) A firm issues a 10-year debt obligationthat bears a 12%

Question

C1. (Cost of borrowing) A firm issues a 10-year debt obligationthat bears a 12% coupon rate
and gives the investor the right to put the bond back to the issuerat the end of the fifth year
at 103% of its face amount. The issue has no sinking fund. Interestis paid semiannually.
The issuer’s tax rate is 34%.
a. Calculate the after-tax cost of debt, assuming the debt remainsoutstanding until
maturity.
b. Calculate the after-tax cost of debt, assuming investors put thebond back to the firm at
the end of the fifth year. (Note: Any unamortized issuance expensesand any redemption
premium can be deducted for tax purposes in the year ofredemption.)

Explanation / Answer

Kd = COupon rate when bond is sold at par T = Tax rate = 34% Assume Face value =$100 So Interest payment = PMT = 12%*FV = 12%*100=$12 As Interest is paid semiannually, PMT = $12/2= $6
Effective Interest Rate EAR for Semiannual payment= (1+Kd/2)^2 -1 = (1+12%/2)^2-1=12.36% pa So After Tax cost of Debt = 12.36*(1-34%) = 8.16%
b. When Bond is called at end of N=5 Yrs, Bond holder will get103% of Face value of $100 ie Bond holder will get $103=M. Interest rxd by Bond holder = 12% of 100 = $12. As it ispaidSemiannualy, INT = 12/2=6
We know that         2N Bond value Vb = SUm(INT/(1+Kd/2)^2N) + M/(1+Kd/2)^2N       t=1
Putting values & Solving for Kd, we will getKd=12.45% After Tax cost of Debt = Kd(1-T) = 12.45%(1-34%)=8.22%

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