Question

Avicorp has a $ 13.8 million debt issue​ outstanding, with a 5.8 % coupon rate. The debt has​ semi-annual coupons, the next coupon is due in six​ months, and the debt matures in five years. It is currently priced at 96 % of par value. a. What is​ Avicorp's pre-tax cost of​ debt? Note: Compute the effective annual return. b. If Avicorp faces a 40 % tax​ rate, what is its​ after-tax cost of​ debt? ​Note: Assume that the firm will always be able to utilize its full interest tax shield.

a. The cost of debt is _____% per year.  ​(Round to four decimal​ places.)

b. If Avicorp faces a 40 % tax​ rate, the​ after-tax cost of debt is ____?

Answer 1

(a) Face Value of Debt Issue = $ 13.8 million, Coupon Rate = 5.8% payable semi-annually, Tenure = 5 years or (5 x 2) = 10 half-years, Current Price = 96 % of Par Value = 0.96 x 13.8 = $ 13.248 million

Semi-Annual Coupon = 13.248 x 0.5 x 0.058 = $ 0.3842 million

Let the YTM be 2R

Therefore, 13.248 = 0.3842 x (1/R) x [1-{1/(1+R)^(10)}] + 13.8 / (1+R)^(10)

Using hit and trial method/ EXCEL's Goal Seek Function/ an electronic calculator to solve the above equation, we get:

R = 0.032592 or 3.2592 %

Pre-Tax Cost of Debt = YTM = 2 x R = 2 x 3.2592 = 6.5184 %

(b) Tax Rate - 40 % , After-Tax Cost of Debt = 6.5184 x (1-0.4) = 3.91104 %