Question

A bond with a $1,000 face value and an 8 percent annual coupon pays interest semiannually. The bond will mature in 15 years. The nominal yield to maturity is 11 percent. What is the price of the bond today?

Answer 1

Answer:

The price of the bond today is $784.27

Explanation:

Face value (FV): $1000

Coupon rate: 8% -> counpon received annually (PMT) is $80 (= $1000 * 8%)

Tenor: 15 years

YTM: 11%

Present value = Future Value/ (1+ YTM)^tenor

We can use excel to calculate Present Value of annual payment = PV(Rate,tenor,-PMT) = PV(11%,15,-80) = $575.27

The price of bond today = present value of face value + present value of coupon received annually

= 1000/(1+11%)^15+ 80/(1+11%)^15 + 80/(1+11%)^14+.... +80/(1+11%)^1

= 1000/(1+11%)^15 + $575.27

= $784.27