Question

A bond, yielding 8.2 percent on the market with 14 years to maturity, has a par value of $1000 and sells for $870. What must the coupon rate be on the bond if it pays semi-annually?

Answer 1

Semi annual required rate = 8.2%/2 = 4.1%

Number of semi annual periods = 14*2 = 28 periods

Let semi-annual coupon payment be x

Value of bond is equal to present value of all future coupon payments and the principal amount

870 = x*PVAF(4.1%, 28 periods) + 1000*PVF(4.1%, 28 periods)

870 = x*16.4726 +1000*0.3246

870 = 16.4726x + 324.6

x = $33.11

Hence, Annual coupon rate = 33.11*2/1000

= 6.622%

i.e. 6.62% approx.