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%

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