A company is considering issuing long-term debt. The debt would have a thirty-year maturity and a ten percent coupon rate. In order to sell the issue, the bonds must be underpriced at a discount of five percent of face value. In addition, the company would have to pay flotation costs of five percent of face value. The firm's tax rate is 21 percent. Given this information, the annualized after-tax cost of debt for the company would be .

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Explanation:

First and foremost, the issue price of the bond is the face value minus adjustments for discount and flotation costs

issue price=$1000*(1-5%-5%)

issue price=$900

semiannual coupon=face value*coupon rate/2

semiannual coupon=$1000*10%/2

semiannual coupon=$50

number of semiannual coupons in 30 years=30*2=60

Using a financial calculator, pretax cost of debt is computed thus:

N=60(number of semiannual coupons)

PMT=50(semiannual coupon)

PV=-900(price)

FV=1000(face value)

CPT

I/Y=5.58%(semiannual yield)

annual yield=5.58%*2=11.16%

after-tax cost of debt=annual yield*(1-tax rate)

tax rate=21%

after-tax cost of debt=11.16%*(1-21%)

after-tax cost of debt=8.82%

Alternative approach

Yield to Maturity [YTM] = Coupon Amount + [(Par Value – Bond Price) / Maturity Years] / [(Par Value + Bond Price)/2]

semiannual YTM=50+(1000-900)/30/(1000+900)/2

semiannual YTM=(50+3.33)/950

semiannual YTM=5.61%

annual YTM=5.61%*2=11.22%

after-tax cost of debt=11.22%*(1-21%)

after-tax cost of debt=8.86%