Final answer:
To find the NPV of a 5% coupon bond with $1,000 par value and 13 years until maturity, discount the semi-annual coupon payments and the par value at maturity by using the required rate of return as the discount rate, then subtract the bond's current price.
Step-by-step explanation:
To calculate the net present value (NPV) of purchasing a 5% coupon bond with a par value of $1,000 and 13 years until maturity, we need to discount the bond's future cash flows back to their present value. Since coupons are paid semi-annually, there will be 26 coupon payments of $25 each (5% of $1,000 divided by 2), plus the repayment of the par value at maturity. Using the required rate of return of 8.4% as the discount rate, each payment must be discounted back to its present value. Once all the present values of the future cash flows are summed up, we subtract the bond's price of $710 to find the NPV.
The NPV formula for a coupon bond is given by the sum of all present values of future cash flows minus the purchase price. In calculating present values, we use the formula PV = C / (1 + r/n)^(nt), where C is the cash flow, r is the annual discount rate, n is the number of times interest is compounded per year (2 for semi-annual), and t is the time in years until the cash flow occurs.
For example, think about a simple two-year bond. It was issued for $3,000 at an interest rate of 8%. After the first year, the bond pays interest of $240 (which is $3,000 × 8%). At the end of the second year, the bond pays another $240 in interest, plus the original $3,000 principal. Assuming an 8% discount rate, we calculate the present value of each cash flow and sum them to find out how much the bond is worth in present terms.