Question

He stock is currently selling for $15.25 per share, and its noncallable $1,000 par value, 20-year, 7.25% bonds with semiannual payments are selling for $875.00. The beta is 1.25, the yield on a 6-month Treasury bill is 3.50%, and the yield on a 20-year Treasury bond is 5.50%. The required return on the stock market is 11.50%, but the market has had an average annual return of 14.50% during the past 5 years. The firm's tax rate is 40%. What is the best estimate of the after-tax cost of debt?

Answer 1

Answer: 5.14%

Explanation:

Best estimate of the after-tax cost of debt:

(1 - t) × kd is the yield on the bond which is calculated using the PV of annuity formula. So,equating the price & the PVs of coupons & PV of maturity value.

$875 = (1000\times 0.03625) \times(\frac{1- (1+r)^{-40}}{r}) + \frac{1,000}{(1+r)^{40} }$

$875 = 36.25 \times(\frac{1- (1+r)^{-40}}{r}) + \frac{1,000}{(1+r)^{40} }$

Therefore, the semi-annual (r) = 4.28%

Annual before tax cost of debt = 4.28 × 2

                                                    = 8.56%

So, after tax cost of debt = 8.56% × (1 - 40%)

                                          = 5.14%