Question

You find the following Treasury bond quotes. To calculate the number of years until maturity, assume that it is currently May 2016. The bonds have a par value of $1,000.

Rate	Maturity Mo/Yr	Bid	Asked	Chg	Ask Yld
??	May 27	103.5475	103.6353	+.3028	2.349
6.302	May 32	104.4965	104.6422	+.4305	??
6.168	May 42	??	??	+.5418	4.051

In the above table, find the Treasury bond that matures in May 2027. What is the coupon rate for this bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Coupon rate             %

Answer 1

Coupon Rate

Par Value = $1,000

Bond Price = $ 1,036.353 [$1,000 x 103.5353%]

Semi-annual YTM = 1.1745% [2.349% x ½]

Maturity Years = 22 Years [(May 2027 – May 2016) x 2]

Let’s take “C” as the annual coupon amount

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

$1,036.353 = C[PVIFA 1.1745%, 22 Years) + $1,000[PVIF 1.1745%, 22 Years]

$1,036.353 = [C x 19.28840] + $1,000 x 0.773457]

$1,036.353 = [C x 19.28840] + $773.46

[C x 19.28840] = $1,036.353 - $773.46

[C x 19.28840] = $262.90

C = $262.90 / 19.28840

C = $13.63

Semi-annual Coupon amount = $13.63

Annual Coupon Amount = $27.26 [$13.63 x 2]

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

So, Annual Coupon Rate = [$27.26 / $1,000] x 100

= 2.73%

“Therefore, The Bond’s Coupon Rate = 2.73%”