Question

To the nearest dollar what is the current price of a 9%, $1000 annual coupon bond that has eighteen years to.marurity and a yield to maturity of 7.01%? Also Indicate if its a premium or discount bond.

Answer 1

Bond pricing = V =?

Face value of bond = F = 1,000

Annual coupon payment (I) = 1,000 × 9% = 90

Yield to maturity (YTM) = 0.0701

Number of remaining years (n) from the date of bond pricing = 18

By the use of formula as below:

V = (I/YTM) [{(1 + YTM)^n – 1} / (1 + YTM)^n] + {F / (1 + YTM)^n}

    = (90 / 0.0701) [{(1 + 0.0701)^18 – 1} / (1 + 0.0701)^18] + {1,000 / (1 + 0.0701)^18}

    = 1283.88 [(1.0701^18 – 1) / 1.0701^18] + (1,000 / 1.0701^18)

    = 1283.88 (2.385622 / 3.385622) + (1,000 / 3.385622)

    = 1283.88 × 0.704633 + 295.366

    = 904.66 + 295.366

    = 1200.03

    = 1,200 by rounding

Answer: Bond price is $1,200.

Answer: Since the bond price is higher than face value ($1,200 > $1,000), the bond would be issued at a premium. It is a premium bond.