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13 December, 17:22

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?

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  1. 13 December, 17:35
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    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
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