Question

# You are analysing the cost of debt for a company. You know that the company’s 14-year...

1. You are analysing the cost of debt for a company. You know that the company’s 14-year maturity, 10.55 per cent coupon bonds are selling at a price of \$1050.24. The bonds pay interest semi-annually and have a face value of \$1000. If these bonds are the only debt outstanding for the company, what is the after-tax cost of debt for this company if the corporate tax is 30 per cent?

Face Value = \$1,000
Current Price = \$1,050.24

Annual Coupon Rate = 10.55%
Semiannual Coupon Rate = 5.275%
Semiannual Coupon = 5.275%*\$1,000 = \$52.75

Time to Maturity = 14 years
Semiannual Period to Maturity = 28

Let semiannual YTM be i%

\$1,050.24 = \$52.75 * PVIFA(i%, 28) + \$1,000 * PVIF(i%, 28)

Using financial calculator:
N = 28
PV = -1,050.24
PMT = 52.75
FV = 1000

I = 4.94%

Semiannual YTM = 4.94%
Annual YTM = 2 * 4.94%
Annual YTM = 9.88%

Before-tax Cost of Debt = 9.88%
After-tax Cost of Debt = 9.88% * (1 - 0.30)
After-tax Cost of Debt = 6.92%

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