PV of par: 1,000 / 1.094^14
= 1000 / 3.51757
= $284.28732
Price - PV of par: 953 - 284.28732 = 668.71268 <- this is the PV of the coupons
Use PV ordinary annuity "PVoa" to solve for PMT (the coupon)
PVoa = PMT[((1 - (1 / (1 + r)^n)) / r]
668.71268 = PMT[((1 - 1 / 1.094^14)) / 0.094]
668.71268 = PMT[(1 - 0.28429) / 0.094]
668.71268 = PMT[7.61396]
PMT = 668.71268 / 7.61396]
PMT = 87.82713
coupon rate = PMT / face
87.82713 / 1000 = 0.08783, or about 8.783%
notice that the bond sells at a discount b/c coupon rate < market rate
yes
Merton Enterprises has bonds on the market making annual payments, with 14 years to maturity, and selling for $953. At this price, the bonds yield 9.4 percent.
Required:
What must the coupon rate be on Merton’s bonds?
