Morgan would like to purchase a bond that has a par value of $1,000, pays $80 at the end of each year in coupon payments, and has 10 years remaining until maturity. If the prevailing annualizedyield on other bonds with similar characteristics is 6 percent, how much will Morgan pay for the bond?

Question

Quizplus · Accepted Answer

To calculate the present value of the bond, we need to use the present value formula:
PV = C × [1 – (1 + r)-n] / r + FV / (1 + r)n
Where PV is the present value, C is the coupon payment, r is the annualized yield, n is the number of periods (years), and FV is the face value or par value of the bond.
Substituting the values in the formula:
PV = $80 × [1 – (1 + 0.06)-10] / 0.06 + $1,000 / (1 + 0.06)10
PV = $80 × [1 – (1.06)-10] / 0.06 + $1,000 / (1.06)10
PV = $80 × [1 – 0.55839] / 0.06 + $1,000 / 1.790849
PV = $80 × 8.50966 + $558.394655
PV = $685.57324
Therefore, Morgan will pay $685.57 for the bond, which is closest to option B ($1,147.20).

Morgan Would Like to Purchase a Bond That Has a Par