Alpha has an outstanding bond issue that has a 7% semiannual coupon, a current maturity of 20 years, a face value of $1000, and sells for $967.97. The firm's income tax rate is 40%. What should Alpha use as an after-tax cost of debt for cost of capital purposes? (Show calculations.)
Select one:
a. 4.42%
b. 8.15%
c. 4.38%
d. 5.26%
e. 4.85%
Ans:- In this question, we need to find the after-tax cost of debt. For that First, we need to find the YTM.we will use the Rate function of excel to find the YTM.
Nper = 20*2 = 40, Pmt = 7% * $1000 / 2 = $35, PV = -$967.97, FV = $1000
Note:- we have multiplied by 2 else it will return for semi-annually.
Therefore the YTM is 7.31%.
Now the After-Tax cost of debt for Alpha will be YTM * (1 - Tax Rate) = 7.31% * (1 - 0.40) = 4.38%.(approx)
Therefore the right option is (c).
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