Question

A bond issued by TOYOTA has 30 years to maturity with a face value of $ 1000. The market's required yield to maturity for a similar rated debt was 8.5% per annum. The coupon rate is 10.5%. TOYOTA pays interest to bond holders on a semi annual basis on January 15 and July 15.

Calculate the current price of the bond.

          B^d :Price = -2 on 5 quantity + 940

          B^s : Price= quantity + 500

a) In the following month, due to an unexpected economic downturn, the required yield to maturity for a similar rated debt decreased to 5%. Calculate the current price of the bond.

b) Should the maturity increase to 35 years, calculate the price of the bond.

Answer 1

Ans. Calculation of current price of bond

Face value 1000

YTM 8.5% semi annual 4.25%

Maturity 30yrs or 60 half annual

Rate 10.5%, half yearly coupon payment $52.5

Current price of bond : 52.5X(1+1.0425/1.0425)⁶⁰ + 1000X(1/1.0425)⁶⁰

: 52.50X21.49 +1000X.0865 =1128.23+86.5 =$1214.73

a) if YTM decrease to 5%, half yearly 2.5%

Calculation of market price of bond = 52.5X(1+1.025/1.025)⁶⁰ + 1000X(1/1.025)⁶⁰

= 52.5X30.90+1000X.477 = 1622.25+477 = $2099.25

d) maturity increase to 35yrs, remaining all are same as orignal

coupon rate 10.5%

YTM8.5% or half yearly 4.25%

total no of coupon payment 70

calculation of bond price = 52.5X22.25 +1000X.23 =1168.12+230 = $1398.13