Final answer:
The current price of the $1,000 par value bond with a coupon rate of 9 percent and an 11 percent discount rate, with 15 years to maturity, is computed using the present value formula for both the coupon payment annuity and the lump sum return at maturity. After the calculation, the current price of the bond is found to be $794.51.
Step-by-step explanation:
To calculate the current price of a $1,000 par value bond with a coupon rate of 9 percent, paying annual coupons, with 15 years to maturity, and a yield to maturity (discount rate) of 11 percent, we need to use the present value formula for both the annuity (coupon payments) and the lump sum (par value at maturity).
The steps are as follows:
- Calculate the annual coupon payment: 9% of $1,000 = $90.
- Calculate the present value of the annuity (the coupon payments): PV = PMT x [(1 - (1 + r)-n) / r], where PMT is the annual coupon payment, r is the discount rate, and n is the number of periods. In our case, PV = $90 x [(1 - (1 + 0.11)-15) / 0.11].
- Calculate the present value of the lump sum (the par value at maturity): PV = FV / (1 + r)n, where FV is the future value or par value of the bond, r is the discount rate, and n is the number of periods. So, PV = $1,000 / (1 + 0.11)15.
- Add the present values from steps 2 and 3 to get the bond's total current price.
Using a financial calculator or present value tables, we calculate:
- Present value of the annuity: approximately $586.43
- Present value of the lump sum: approximately $208.08
- Total current price of the bond: $586.43 + $208.08 = $794.51
Therefore, the current price of the bond rounded to two decimal places is 794.51.