Gabriele Enterprises has bonds on the market making annual payments, with eight years to maturity, a par value of $1,000, and selling for $964. At this price, the bonds yield 6.7 percent. What must the coupon rate be on the bonds?

Coupon rate = 5.8%

Explanation:

The price of a bond is the present value (PV) of the future cash flows discounted at its yield.

So we will need to work back to ascertain the coupon rate

Step 1

Calculate the PV of redemption value and PV of interest payments

PV of Redemption

= 1.067^ (-5) * 1000

=723.06

PV of the annual interest rate

= price of the bond - PV of redemption

= $964 - 723.06

= 240.934

Step 2

Calculate the interest payment

Interest payment = PV of redemption value / annuity factor

Annuity factor = (1 - (1+r) ^ (-n)) / r

Annuity factor at 6.7% for 5 years

Factor = (1-1.067^ (-5)) / 0.067

= 4.1333

Interest payment = PV of the annual interest rate / Annuity factor

Interest payment=

=240.93/4.1333

=58.290

Step 3

Calculate the coupon rate

Coupon rate = interest payment / par value

Coupon rate = (58.290/1000) * 100

= 5.8%

Coupon rate = 5.8%