Question

Dufner Co. issued 17-year bonds one year ago at a coupon rate of 7.3 percent. The bonds make semiannual payments. If the YTM on these bonds is 5.3 percent, what is the current dollar price assuming a par value of $1,000

Answer 1

The current dollar price assuming a par value of $1,000 is $ 1,213.95

Step-by-step explanation:

The current price is computed as shown below:

The coupon payments will be as follows:

= (7.3% ÷ 2) × $ 1,000 (Since the payments are semi annual, hence divided by 2)

= $ 36.5

YTM will be as follows:

= (5.3% ÷ 2) (Since the payments are semi annual, hence divided by 2)

= 2.65%

N is computed as follows:

= (17 - 1 ) × 2 (Since the payments are semi annual, hence multiplied by 2)

= 32

So, the price of the bond will be as follows:

= Coupon payment x [
`[ (1 - 1 / (1 + r)^n ] / r` ] +
`Par value / (1 + r)^n`

= $ 36.5 × [ ( 1 -
`(1)/((1 + 0.0265)32)` ] / 0.0265 ] +
`(1000)/(1.0265^(32))`

= $ 36.5 × 21.39526 + $ 433.0255

= $ 780.92699 + $ 433.0255

= $ 1,213.95