A portfolio manager is considering the purchase of a bond with a 5.5% coupon rate that pays interest annually and matures in three years. If the required rate of return on the Bond is 5%, the price of the bond per 100 of par value is closest to:
A) 98.65.
B) 101.36.
C) 106.43.

Question

Quizplus · Accepted Answer

The price of a bond can be calculated using the present value of its future cash flows, which include the annual interest payments and the principal repayment at maturity. The formula for the price of a bond is:$$ \text{Price} = \frac{C}{(1+r)} + \frac{C}{(1+r)^2} + \frac{C}{(1+r)^3} + \frac{F}{(1+r)^3} $$Where:- $C$ is the annual coupon payment (\$100 * 5.5% = \$5.5),- $r$ is the required rate of return (5% or 0.05),- $F$ is the face value of the bond (\$100).Plugging the values into the formula gives:$$ \text{Price} = \frac{5.5}{(1+0.05)} + \frac{5.5}{(1+0.05)^2} + \frac{5.5}{(1+0.05)^3} + \frac{100}{(1+0.05)^3} $$$$ \text{Price} = \frac{5.5}{1.05} + \frac{5.5}{1.1025} + \frac{5.5}{1.157625} + \frac{100}{1.157625} $$$$ \text{Price} = 5.2381 + 4.9882 + 4.7474 + 86.3833 $$$$ \text{Price} \approx 101.36 $$Therefore, the price of the bond per 100 of par value is closest to 101.36.

A Portfolio Manager Is Considering the Purchase of a Bond