Your company currently has par, coupon bonds with 10 years to maturity and a price of . If you want to issue new 10-year coupon bonds at par, what coupon rate do you need to set

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Your company currently has $1,000 par, 6.5% coupon bonds with 10 years to maturity and a price of $1,078. If you want to issue new 10-year coupon bonds at par, what coupon rate do you need toset? Assume that for both bonds, the next coupon payment is due in exactly six months.

We need to calculate the yield to maturity (YTM) of the current bonds. Since the bonds pay interests every 6 months, then the coupon = $32.50

YTM = {coupon + [(face value - market value)/n]}/[(face value + market value)/2]

YTM = {32.5 + [(1,000 - 1,078)/20]}/[(1,000 + 1,078)/2]

YTM = 28.6 / 1,039 = 0.275 x 2 = 5.5053% ≈ 5.51%

In order to sell the new bonds at par, the coupon rate must be 5.51%

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