Final answer:
The present value of a bond is calculated by discounting its future cash flows, consisting of the annual coupon payments and the principal amount, to their present values using the current market interest rate. Variations in market interest rates will inversely affect the bond's present value. The correct answer is option (a) 4.0%.
Step-by-step explanation:
To find the present value of a 6-year bond with an 8.0% coupon rate when the market rate is a) 4.0%, b) 7.5%, and c) 9.0%, one must discount the future cash flows of the bond to their present value using the market interest rate. The bond's cash flows consist of annual interest payments and the return of the principal at maturity. For each scenario, we use the following present value formula for an annuity and a lump sum:
- Present Value of the Annuity (PVA) = C * [(1 - (1+r)^-n) / r]
- Present Value of the Lump Sum (PVLS) = F / (1+r)^n
Where C is the annual coupon payment, r is the market interest rate (in decimal form), n is the number of periods, and F is the face value of the bond. The total present value would then be the sum of PVA and PVLS. This method is used to discount each of the bond's annual interest payments as well as the principal returned at maturity.
When conducting these calculations, we observe that as the market interest rate increases, the present value of future cash flows decreases, indicating an inverse relationship between bond prices and market interest rates.