5 years ago, Barton Industries issued 25-year noncallable, semiannual bonds with a $900 face value and a 12% coupon, semiannual payment ($54 payment every 6 months). The bonds currently sell for $845.87. If the firm's marginal tax rate is 40%, what is the firm's after-tax cost of debt?

7.85%

Explanation:

Yield to maturity is considered as the cost of debt.

The actual return that an investor earn on a bond until its maturity is called the Yield to maturity. It is a long term return which is expressed in annual rate.

According to given data

Face Value = $900

Coupon Payment = C = $54 every six months

Price of the Bond = P = $845.87

Numbers of period = n = (25-5) years x 2 = 40 periods

Use Following Formula to calculate YTM

Yield to maturity = [ C + (F - P) / n ] / [ (F + P) / 2 ]

Yield to maturity = [ $54 + ($900 - $845.87) / 40 ] / [ ($900 + 845.87) / 2 ]

Yield to maturity = $55.35 / 872.94

Yield to maturity = 0.0634 = 6.34% per six months

Now find the annual rate by following compounding factor.

YTM = [ (1 + 6.34%) ^2 ] - 1 = 13.1% per year

Now we will deduct the tax from the rate.

After tax cost of Debt = 13.1 x (1 - 0.4) = 7.85%