Question

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%

Answer 1

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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