Question

ABC, Inc. offers a bond with a coupon of 9 percent with semiannual payments and a yield to maturity of 7.75 percent. The bonds mature in 14 years. What is the market price of a $1,000 face value bond?

Answer 1

The formula for calculating Coupon bond price or the Market price is mentioned below:

Where, C = Coupon payment for per period, YTM = Yield to maturity, P = Face value of bond, and n = Number of periods.

Since Coupons are paid semiannually,

C = 9% / 2 = 4.5 % semi annual coupon of the Face value P

So, C = 4.5% * $ 1000 = $ 45

P = Face value = $ 1000

n = 14 years = 28 semi-annual periods

YTM = 7.75 % Annually = 7.75 % / 2 = 3.875 % Semi-annual

So, Applying the formula mentioned above,

Coupon Bond price = [45 * {1- (1+0.03875)^(-28)} / 0.03875 ] + {1000 / (1+ 0.03875) ^ 28}

= [45 * {1- 0.345} / 0.03875 ] + {1000 / 2.9}

= [ 45 * 16.9 ] + 344.83

= 760.5 + 344.83 = $ 1105.33

Hence the market price of a $ 1000 face value bond with the above coupon rate, YTM and maturity is $ 1105.33 only.

Hope this clarifies the doubt.