Dufner Co. issued 15-year bonds one year ago at a coupon rate of 4.8 percent. The bonds make semiannual payments. If the YTM on these bonds is 5.3 percent, what is the current dollar price assuming a $1,000 par value? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

  $951.02

Explanation:

Each semi-annual payment will be ...

  (4.8%)/2 × $1000 = $24

There will be 2 payments per year for the remaining 14 years of the bond's life, for a total of 28 payments.

We want a YTM of 5.3%, so the discount rate we'll use for each 6-month interval is half that, or 2.65%. We'll use the same semi-annual discounting for the $1000 final payment as we do for the coupon payments.

Then the present value of that series of payments is ...

  present value of coupons = 24 × (1 -(1.0265^-28))/0.0265 = 470.234

The present value of the bond value at maturity is ...

  present value of mature bond = 1000 × 1.0265^-28 = 480.783

Then the total present value of the bond is ...

  bond price = pv of coupons + pv of mature bond = $470.234 +480.783

    = 951.02

The current dollar price of the bond is $951.02.

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We don't know what formula you are expected to use for this. The one used here is one found at an on-line investment site. (Second attachment.) In this formula, the YTM is the annual yield divided by the number of payments per year, and n is the total number of payments.

This math causes the YTM value to be compounded semi-annually, resulting in an annual yield of about 5.37%.

i think the answer is a. science center.

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