Question

Waller, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 16 years to maturity that is quoted at 92 percent of face value. The issue makes semiannual payments and has an embedded cost of 10 percent annually. 1) What is the company's pretax cost of debt? 2) If the tax rate is 38%, what is the after tax cost of debt?

Answer 1

Value of Debt can be calculated as follows:

Let us assume that the company has an outstanding debt of $100.

Present Value of Debt PV: $92

Interest/Coupon Payments PMT= (10%*100)/2= 5

No. of Periods for Debt to mature (semiannual) N= 16*2= 32

Future Value of Debt= $100

Pre-Tax cost of Debt (Yield to maturity) can be given by this equation:

Or this formula:

92= 5* [(1- {1/(1+YTM)³²})/YTM] + 100* 1/(1+YTM)³²

Since the debt's current value is lower than face value, it implies that the yield or cost of debt is higher than the coupon payments. Using hit and trial, we can compute YTM manually.

Or the numbers can be plugged in the financial calculator to obtain YTM of 11.078%

Pre Tax cost of Debt= 11.078%

After Tax cost of Debt= 11.078*(1-0.38)= 7%

Coupon 1 , Coupon 2 (1 +YTM)1 (1+YTM)2 Bond Price_ Coupon n Face Value

(1 + YTM)n Bond Price = Coupon x +(Face Value x (. YTM + YTM)