Question

What is the price of a 3-year bond with a coupon rate of 6% and face value of $1,000? Assume the bond is trading at 6% yield, and that coupons are paid semi-annually. Assume semi-annual compounding.

Answer 1

As both coupon rate and yield are equal, that is 6%, therefore, Price of the bond would be equal to its face value irrespective of its maturity time-period. However, calculations are provided below to explain why price and face value are same in this case.

Coupon rate = 6%; T = 3 years

YTM = 6%; Face Value = 1000

Since, coupon is paid semi-annually, then number of time periods = 3 * 2 = 6

Similarly, coupon rate for each period = 6% / 2 = 3%; Yield for discounting = 6% / 2 = 3%

Interest Payment per period = 3% * 1000 = 30

Interest will be paid for 6 periods and at the 6th period, principal of 1000 will also be repaid

In price of bond calculation, interest payment for 6 period can be treated as an annuity of 30 for 6 periods and principal can be discounted using FV / (1+r)ⁿ formula

Price of bond = (30 / 3%) * (1 - (1+3%)^-6) + 1000 / (1+3%)⁶

Price of bond = 162.52 + 837.48 = 1000

Hence, both Face value and Price of bond are $1000