Question

Suppose a​ five-year, $1,000 bond with annual coupons has a price of $903.04 and a yield to maturity of 6.3%. What is the​ bond's coupon​ rate?

Answer 1

Calculation of the annual coupon rate on the Bond

Par Value of the Bond = $1,000

Price of the Bond = $903.04

Annual Yield to maturity of the Bond = 6.30%

Maturity Period = 5 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

$903.04 = X[PVIFA 6.30%, 5 Years) + $1,000[PVIF 6.30%, 5 Years]

$903.04 = [X x 4.17821] + [$1,000 x 0.73677]

$903.04 = [X x 4.17821] + $736.77

[X x 4.17821] = $903.04 - $736.77

[X x 4.17821] = $166.27

X = $166.27 / 4.17821

X = $39.80

The annual coupon payment = $39.80 per year

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

So, Annual Coupon Rate = [$39.80 / $1,000] x 100

= 3.98%

“Therefore, the Coupon rate on the Bond = 3.98%”

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.