Question

You are eyeing an investment in a corporate bond which has a YTM of 14.95%, and a stated rate of interest of 13.04% paid semi-annually, with a maturity of 20 years, and a PAR value of $1,000. What is the price of this bond?

Multiple Choice

• $1,702.84

• $470.87

• $879.39

• $880.12

Answer 1

Given the current market rate of 14.950% for a similar bond, a bond with a face value of $1,000.00 and paying a coupon rate of 13.040% (compounding semi-annually), should be selling for $879.39

C = coupon payment = $130.40 (Par Value * Coupon Rate)

n = number of years = 20

i = market rate, or required yield = 14.950% = 0.15

k = number of coupon payments in 1 year = 2

P = value at maturity, or par value = 1000

Present Value of Ordinary Annuity Formula

BP = C/k * [ 1 - [ 1 ] ] (1 + i/k)nk i/k + P (1 + i/k)nk

Plug In The Variables and Solve

BP = 130/2 * [ 1 - [ 1 ] ] (1 + 0.1495/2)20*2 0.1495/2 + 1000 (1 + 0.1495/2)20*2

BP = 65.20 * [ 1 - [ 1 ] ] (1 + 0.0748)40 0.0748 + 1000 (1 + 0.0748)40

BP = 65.20 * [ 1 - [ 1 ] ] 17.877 0.0748 + 1000 17.877

BP = 65.20 * 1 - 0.0559 0.0748 + 1000 17.877

BP = 65.20 * 0.9441 0.0748 + 55.94

BP = 65.20 * 12.63 + 55.94

BP = 823.45 + 55.94

BP = $879.39