Final answer:
To calculate the price of a $1,000 par value bond, you need to identify the annual coupon payment, calculate the present value of these payments over the bond's life, and add the present value of the par value due at maturity. the price is found by summing the present values of the coupon payments and the par value, with the bond likely selling for above face value because the yield to maturity is lower than the coupon rate.
Step-by-step explanation:
Calculating the Price of a Bond
The question at hand is asking about the determination of the current market value of a bond given its par value, coupon rate, yield to maturity (YTM), and the number of years until maturity. To calculate the price of a $1,000 par value, 16.0-year, annual bond with a 7.07% coupon rate and a yield to maturity of 6.37%, you would use the present value formula for bonds, which takes into account the present value of future coupon payments and the present value of the principal amount to be received at maturity.
Here is a step-by-step guide to calculate the price:
- Identify the annual coupon payment by multiplying the par value by the coupon rate ($1,000 * 7.07% = $70.70).
- Calculate the present value of all the annual coupon payments over the bond's 16-year lifespan. This is a series of payments and needs to be treated as an annuity.
- Calculate the present value of the par value, which will be received at the end of the 16-year period.
- Add the present values of the annuity of the coupon payments and the par value to get the current price of the bond.
The actual calculation would require the use of financial formulas or a financial calculator to compute the present value of an annuity for the coupon payments and the present value of a lump sum for the face value. Since the yield to maturity is lower than the coupon rate, we can anticipate that the bond would sell for more than its face value.