A 5-year Circular File bond with a face value of $1,000 pays interest once a year of $45 and sells for $964.

A 5-year Circular File bond with a face value of $1,000 pays interest once a year of $45 and sells for $964.

a. What are its coupon rate and yield to maturity? (Do not round intermediate calculations. Enter the coupon rate as a whole percent and the yield to maturity as a percent rounded to 2 decimal places.)


b. If Circular wants to issue a new 6-year bond at face value, what coupon rate must the bond offer?


Explanation

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.
Coupon rate = $45 / $1,000 = 0.045, or 4.5%

To compute the yield to maturity, use trial and error to solve for r in the following equation:

$964=$45× [1r−15r   ×   (1  +   r)] + $1,0005(1  +   r)⇒ r= 5.34%
Using a financial calculator, compute the yield to maturity by entering
n = 5, PV = (−)964, FV = 1,000, PMT = 45; compute i = 5.34%.

Verify the solution as follows:

PV=$45× [10.05339−150.05339(1.05339)]+$1,00051.05339=$964.00
b.
To sell a bond at its face value, the bond's coupon rate must be set equal to the yield to maturity of currently outstanding bonds. Thus, the new bond must offer a coupon rate of 5.34%.