Final answer:
The value of a bond is calculated by discounting the future cash flows at the yield-to-maturity rate. For a 3 year, 11% semi-annual bond with a face value of $2,000 and a YTM of 15%, one needs to discount the six coupon payments and the final face value payment to get the bond's present value.
Step-by-step explanation:
The value of a bond can be determined by discounting the future cash flows of the bond payments at the required yield-to-maturity (YTM). In this scenario, the bond pays 11% semi-annually on a face value of $2,000, leading to interest payments of $110 every six months. The financial analyst is estimating the bond's value using a YTM of 15%, so we must discount these payments at this rate.
To find the present value of each payment, the formula PV = C / (1+r)^n is used, where C is the coupon payment, r is the discount rate (YTM / 2), and n is the number of periods. For this 3-year semi-annual bond, there will be six total interest payments of $110, plus the final principal payment of the face value.
To calculate the present value of the bond, we sum the present values of all future payments:
•PV of interest payments = $110 / (1+0.075)^1 + $110 / (1+0.075)^2 + ... + $110 / (1+0.075)^6
•PV of face value = $2,000 / (1+0.075)^6
After computing these, we can add them to find the final value of the bond.