Question

PLEASE SHOW ME HOW TO SOLVE THIS ALGEBRAICALLY. SPECIFICALLY SHOW HOW TO GET THE COUPON PAYMENT PLEASE.

Smiley Industrial Goods has bonds on the market making annual payments, with 13 years to maturity, and selling for $1,095. At this price, the bonds yield 6.4 percent. What must the coupon rate be on these bonds?

Answer 1

Calculation of the annual coupon rate on the Bond

Par Value of the Bond = $1,000

Price of the Bond = $1,095

Annual Yield to maturity of the Bond = 6.40%

Maturity Period = 13 Years

Let’s take “X” as the annual coupon amount of the Bond

Price of the bond = Present Value of the semiannual coupon amounts + Present Value of the Par Value

$1,095 = X[PVIFA 6.40%, 13 Years) + $1,000[PVIF 6.40%, 13 Years]

$1,095 = [X x 8.649443] + [$1,000 x 0.446436]

$1,095 = [X x 8.649443] + $446.44

[X x 8.649443] = $1,095 - $446.44

[X x 8.649443] = $648.56

X = $648.56 / 8.649443

X = $74.98

The annual coupon payment = $74.98 per year

The coupon rate is calculated by dividing the annual coupon amount with the par value of the Bond

So, Annual Coupon Rate = [$74.98 / $1,000] x 100

= 7.50%

“Therefore, the Coupon rate on the Bond = 7.50%”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.