Final answer:
The value of the bond is $1,088.75 when the required rate of return is 4.72%.
Step-by-step explanation:
To calculate the value of the bond, we need to find the present value of all the future cash flows generated by the bond. The bond pays a 5.06% coupon rate, which means it pays 5.06% of the face value in interest payments every year. Since the bond makes monthly interest payments, the annual coupon payment is $50.60 (5.06% of $1,000). The bond has a maturity of 19 years, so it will make a total of 19 * 12 = 228 interest payments. The required rate of return is 4.72%, which represents the investor's opportunity cost of capital. We can use the formula for the present value of an annuity to calculate the value of the bond:
PV = C * [(1 - (1 + r)^(-n)) / r] + F / (1 + r)^n
Where PV is the present value, C is the coupon payment, r is the required rate of return, n is the number of interest payments, and F is the face value of the bond. Plugging in the values, we get:
PV = $50.60 * [(1 - (1 + 0.0472/12)^(-228)) / (0.0472/12)] + $1,000 / (1 + 0.0472/12)^228 = $1,088.75.
So the value of this bond, given a 4.72% required rate of return, is $1,088.75.