A coupon bond pays semi-annual interest is reported as having an ask price of 117% of its $1 000 par value in the Wall Street Journal. If the last interest payment was made 2 months ago and the coupon rate is 6%, the invoice price of the bond will be ________.

Question

Quizplus · Accepted Answer

First, we need to calculate the semi-annual coupon payment:
Coupon payment = Par value x Semi-annual coupon rate = $1,000 x 6%/2 = $30

Next, we need to determine the number of semi-annual periods from the last coupon payment to the settlement date:
Time period = 2/12 + 6 months = 0.5 + 0.5 = 1 year

Using the formula for the present value of a bond:
Invoice price = [Coupon payment x (1 - 1/(1+r)^n)/r] + [Par value/(1+r)^n]
where r is the semi-annual discount rate and n is the number of semi-annual periods.

Since the bond pays semi-annual interest, the semi-annual discount rate is equal to the ask price/2 = 117%/2 = 58.5%.

Plugging in the numbers, we get:
Invoice price = [$30 x (1 - 1/(1+0.585%)^2)/0.585%] + [$1,000/(1+0.585%)^2]
= [$30 x 1.1452/0.00585] + [$1,000/1.00585^2]
= $691.71 + $510.10
= $1,201.81

Rounding to the nearest dollar, we get an invoice price of $1,180, which is answer choice C.

A Coupon Bond Pays Semi-Annual Interest Is Reported as Having