Please explain

Where does the FV $1,000 come from?

Where does $47.50 come from?

Cost of debt for a company: You are analysing the after-tax cost of debt for a company. You know that the companys 12-year maturity, 9.5 per cent coupon bonds are selling at a price of $1,200. 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 rate is 30 per cent? What if the bonds are selling at par?

Maturity 12

Rate 9.5%

Current Bond $1,200

Tax 30%

Solution:

The current YTM for the bonds can be calculated as follows.

$1,200 = $47.50 x PVIFA(24, YTM/2) + $1,000 x PVIF(24, YTM/2) Solving, we find that YTM = 0.07008 and therefore the after-tax cost of debt is equal to 0.07008 x (1 .30) = 0.049056, or 4.906%

If the bonds are priced at par, then the YTM on the bonds is 9.5 per cent and then the after-tax cost of debt would be 6.65%