A coupon bond with a par value of $1,000 and a 10-year maturity pays semi-annual coupons of $22

Finance Nov 03, 2020

A coupon bond with a par value of $1,000 and a 10-year maturity pays semi-annual coupons of $22. a. Suppose the current interest rate for this bond is 4% per year compounded semi-annually. What is the fair price of the bond? b. Is the bond selling above or below par value?

Expert Solution

No of periods = 10 years * 2 = 20 semi-annual periods

Bond Price = $\sum$ Coupon / (1 + YTM / 2)^period + Par value / (1 + YTM / 2)^period

Bond Price = $22 / (1 + 4% / 2)¹ + $22 / (1 + 4% / 2)² + ...+ $22 / (1 + 4% / 2)²⁰ + $1000 / (1 + 4% / 2)²⁰

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $22 * (1 - (1 + 4% / 2)^-20) / (4% / 2) + $1000 / (1 + 4% / 2)⁴

Bond Price = $1032.70

The bond is selling above par value since the calculated fair Bond price is above the par value of $1000.

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