Question

Bond prices and maturity dates. Moore Company is about to issue a bond with monthly coupon payments, an annual coupon rate of 10%, and a par value of $1,000. The yield to maturity for this bond is 13%. 

a. What is the price of the bond if it matures in 15, 20, 25, or 30 years? 

b. What do you notice about the price of the bond in relationship to the maturity of the bond? 

a. What is the price of the bond if it matures in 15 years? 

Answer 1

(a) Number of periods to maturity = n

Yield to Maturity = r = 13%/12 monthly = 0.13/12

Monthly Coupon Payment P = 10%*1000/12 = $8.33

Face Value FV = $1000

Hence, Present Value of bond = PV = P/(1+r) + P/(1+r)² + .... + P/(1+r)ⁿ + FV/(1+r)ⁿ = P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ

When n = 15 years = 180 months, PV = 8.33[1 - (1+0.13/12)^-180]/(0.13/12) + 1000/(1+0.13/12)¹⁸⁰ =  $802.15

When n = 20 years = 240 months, PV = 8.33[1 - (1+0.13/12)^-240]/(0.13/12) + 1000/(1+0.13/12)²⁴⁰ =  $786.33

When n = 25 years = 300 months, PV = 8.33[1 - (1+0.13/12)^-300]/(0.13/12) + 1000/(1+0.13/12)³⁰⁰ =  $778.04

When n = 30 years = 360 months, PV = 8.33[1 - (1+0.13/12)^-360]/(0.13/12) + 1000/(1+0.13/12)³⁶⁰ =  $773.70

(b) Hence, as the maturity period of the bond increases, the present value of the bond reduces