Final answer:
To determine the current price of a Hilton bond with a face value of $1000, a 4.000% coupon rate, and a yield to maturity of 6.533%, one must discount the semi-annual coupon payments and the face value back to their present value using the current yield to maturity as the discount rate.
Step-by-step explanation:
To calculate the current price of a Hilton bond when the current yield to maturity is 6.533%, the coupon payments and the face value of the bond must be discounted back to the present value using the yield to maturity as the discount rate. Since the bond pays semi-annual coupons of 4.000% on a $1000 face value, the semi-annual coupon payment is $20. With a maturity date of May 1, 2031, and considering that today is December 1, 2022, there are 17 coupon payments remaining. Using the present value formula for each cash flow and summing them up will give the current bond price.
The present value of the coupons is calculated as the annuity with a formula PV = C (1 - (1 + r)^-n) / r and the present value of the face value paid at maturity as PV = F / (1+r)^n, where C is the coupon payment, F is the face value, r is the discount rate per period (YTM/2), and n is the number of periods (total semi-annual periods until maturity). A financial calculator or spreadsheet software can facilitate these computations to find the current price of the bond.
Understanding yield to maturity, coupon rate, and present value calculations are crucial for this valuation process. In general, as the example provided suggests, when the market interest rates rise, the price of bonds issued at lower interest rates will fall. This is because newer issues in the market offer a higher return, making the older, lower-yielding bonds less attractive unless they are discounted. Likewise, when market interest rates fall, existing bonds with higher coupon rates appear more attractive, and their price increases.