Question

You are analyzing the after-tax cost of debt for a firm. You know that the firm’s 12-year maturity, 10.25 percent semiannual coupon bonds are selling at a price of $1,028.51. If these bonds are the only debt outstanding for the firm. What is the current YTM of the bonds?

Answer 1

YTM calculation can be done manually (approximate value) or through Excel or Financial Calculator (Exact).

For approximate manual calculations:

where Approx YTM is periodic for periodic coupon C, Face value F, Price P and n periods to maturity.

For C = 10.25%/2 * 100 0 = $51.25 --> semi-annual coupon

F = $1000

P = $1,028.51

n = 12 * 2 = 24 semi-annual periods

Approx YTM = 50.0621/1014.255

Approx YTM = 4.94% --> Semi-annual YTM

Approx YTM = 2 * 4.94% = 9.87% --> Annual YTM

For Financial Calculator:

use inputs - PMT = 51.25, N = 24, PV = -1028.51, FV = 1000, compute i/Y.

i/Y = 4.92% --> Semi-annual. Multiply this by 2 for Annual YTM = 9.84%