DMA Corporation has bonds on the market with 12.5 years to maturity, a YTM of 7.3 percent, and a current price of $1,057. The bonds make semiannual payments and have a par value of $1,000.

Problem 7-8 Coupon Rates [LO2]

DMA Corporation has bonds on the market with 12.5 years to maturity, a YTM of 7.3 percent, and a current price of $1,057. The bonds make semiannual payments and have a par value of $1,000.

                                       

What must the coupon rate be on these bonds? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Coupon rate

%

 

Explanation:

Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:

P = $1,057 = C(PVIFA3.65%,25) + $1,000(PVIF3.65%,25)

Solving for the coupon payment, we get:

C = $40.01

Since this is the semiannual payment, the annual coupon payment is:

2 × $40.01 = $80.03

And the coupon rate is the annual coupon payment divided by par value, so:

Coupon rate	=	$80.03 / $1,000
Coupon rate	=	.0800, or 8.00%

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

 

Enter

25

7.3% / 2

±$1,057

$1,000

N

I/Y

PV

PMT

FV

Solve for

$40.01

 

$40.01(2) / $1,000 = 8.00%