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You are analyzing the after-tax cost of debt for a firm. You know that the firm’s 12-year maturity, 15.50 percent semiannual coupon bonds are selling at a price of $1,117.25. These bonds are the only debt outstanding for the firm. What is the current YTM of the bonds and after-tax cost of debt for this firm if the bonds are selling at par?

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Answer:

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Nper = 12*2 = 24

PMT = $77.50 (1000*0.0155*1/2)

Pv = 1.117.25

Fv = 1,000

1. Pretax cost of debt = Rate(nper, pmt, -pv, fv) * 2

Pretax cost of debt = Rate(24, 77.5, -1117.25, 1000) * 2

Pretax cost of debt = 0.0675 * 2

Pretax cost of debt = 0.135

Pretax cost of debt = 13.5%

2. After tax cost of debt = Pretax cost of debt * (1 - tax rate)

After tax cost of debt = 0.1350*(1-0.34)

After tax cost of debt = 0.0891

After tax cost of debt = 8.91%

3. Nper = 12*2 = 24

PMT = $77.50 (1000*0.0155*1/2)

Pv = 1,000

Fv = 1,000

Pretax cost of debt = Rate(nper, pmt, -pv, fv) * 2

Pretax cost of debt = Rate(24, 77.5, -1000, 1000)

Pretax cost of debt = 0.0775 * 2

Pretax cost of debt = 0.1550

Pretax cost of debt = 15.50%

After tax cost of debt = Pretax cost of debt * (1-tax rate)

After tax cost of debt = 0.1550*(1-0.34)

After tax cost of debt = 0.1023

After tax cost of debt = 10.23%

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