Final answer:
The current price of the Hilton bond an be calculated by discounting the future cash flows, which include the semi-annual coupons and the face value, at the current yield to maturity. Because the yield to maturity is higher than the coupon rate, the bond will sell for less than face value.
Step-by-step explanation:
The current price of a Hilton bond, with a face value of $1,000 and a coupon rate of 4.000%, can be determined by calculating the present value of its future cash flows discounted at the current yield to maturity of 6.533%. Since the last semi-annual coupon has been paid today, we will be discounting all future cash flows from this date. This includes the semi-annual coupon payments and the face value of the bond that will be paid at maturity.
To calculate the present value of these cash flows, we will use the present value of an annuity formula for the coupons, and the present value formula for a single sum for the face value. Given that the coupons are semi-annual, we should adjust the yield to maturity to a semi-annual rate and compute the present value of the annuity accordingly. The face value must also be discounted back by the number of semi-annual periods until maturity.
By summing the present values of the semi-annual coupons and the final payment of the face value, we can determine the current price of the bond. It is important to note that because the current yield to maturity (6.533%) is higher than the coupon rate (4.000%), the bond will sell for less than its face value.