Question

Madison Manufacturing has just issued a 15-year, 12% coupon interest rate, $1,000-par bond that pays interest annually. The required return is currently 11%, and the   company is certain it will remain at 11% until the bond matures in 15 years.

Assuming that the required return does remain at 14% until maturity, find the value of the bond with (1) 15 years, (2) 12 years, (3) 9 years, (4) 6 years, (5) 3 years, and (6) 1 year to maturity.

Plot your findings on a set of “time to maturity (x axis) – market value of bond (y axis).

All else remaining the same, when the required return differs from the coupon interest rate and is assumed to be constant to maturity, what happens to the bond value as time moves toward maturity? Explain in light of the graph in part b.

Answer 1

Number of years =15
Rate =11%
Coupon =12%*1000 =120

1) Value of bond with maturity of 15 years =PV of Coupons + PV of Par Value
=120*((1-(1+11%)^-15)/11%)+1000/(1+11%)^15=1071.91

2) Value of bond with maturity of 12 years =PV of Coupons + PV of Par Value
=120*((1-(1+11%)^-12)/11%)+1000/(1+11%)^12=1064.92

3)Value of bond with maturity of 9 years =PV of Coupons + PV of Par Value
=120*((1-(1+11%)^-9)/11%)+1000/(1+11%)^9=1055.37

4)Value of bond with maturity of 6 years =PV of Coupons + PV of Par Value
=120*((1-(1+11%)^-6)/11%)+1000/(1+11%)^6=1042.31

5)Value of bond with maturity of 3 years =PV of Coupons + PV of Par Value
=120*((1-(1+11%)^-3)/11%)+1000/(1+11%)^3=1024.44

6)Value of bond with maturity of 1 years =PV of Coupons + PV of Par Value
=120*((1-(1+11%)^-1)/11%)+1000/(1+11%)^1=1009.01

As the maturity of bond decreases the price of bond becomes closer to par value. in this case price of bond increases with decrease in maturity.