To determine the current price of the bond, coupon payments and face value are discounted at the yield to maturity rate, and then summed up to calculate the total present value.
To calculate the current price of a $1000 par value bond with 5 years to maturity, a 6% coupon, and a yield to maturity of 8% with semiannual interest payments, we need to discount the future cash flows of the bond to their present value.
First, we calculate the semiannual coupon payment as:
Coupon Payment = (Coupon Rate x Par Value) / Number of Payments per Year = (0.06 x $1000) / 2 = $30 per payment.
Since the bond pays interest semiannually, there will be 5 years x 2 payments per year = 10 payments.
Then, we discount each coupon payment and the face value at the yield to maturity:
Present Value of Coupons = $30 x (1 - (1 + 0.08 / 2)^-10) / (0.08 / 2)
Present Value of Face Value = $1000 / (1 + 0.08 / 2)^10
Finally, we add the present values of the coupons and the face value to find the current price of the bond:
Current Price = Present Value of Coupons + Present Value of Face Value
The current price of the bond is calculated by summing the discounted cash flows.