Answer:
a. The value of a bond can be calculated as the present value of its future cash flows. In this case, the bond has a par value of $1,000 and a coupon rate of 5% paid annually, so it will pay annual coupon payments of $50 (0.05 * $1,000) for 10 years. At maturity, the bond will also pay back its par value of $1,000. The required rate of return for investors is 4%, so we can use this as the discount rate to calculate the present value of the bond’s future cash flows.
The present value of the bond’s annual coupon payments can be calculated using the formula for the present value of an annuity: PV = (PMT / r) * (1 - (1 / (1 + r)^n)), where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods. Substituting the values for this bond into the formula, we get: PV = ($50 / 0.04) * (1 - (1 / (1 + 0.04)^10)) = $388.51.
The present value of the bond’s par value at maturity can be calculated using the formula for the present value of a lump sum: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. Substituting the values for this bond into the formula, we get: PV = $1,000 / (1 + 0.04)^10 = $675.56.
Adding these two values together gives us the total present value of the bond’s future cash flows: $388.51 + $675.56 = $1064.07.
So, the value of this bond is $1064.07.
b. Since the calculated bond value ($1064.07) is greater than its par value ($1000), this bond sells at a premium. This happens because its coupon rate (5%) is higher than the required rate of return for investors (4%). This means that investors are willing to pay more than its par value to receive its higher coupon payments.
Step-by-step explanation: