Calculate the value of a $1,000 bond which has 10 years until maturity and pays quarterly interest at an annual coupon rate of 12 percent. The required return on similar-risk bonds is 20 percent.

Question

Quizplus · Accepted Answer

First, we need to find the quarterly coupon payment:
12% annual coupon rate / 4 = 3% quarterly coupon rate
$1,000 bond face value x 3% quarterly coupon rate = $30 quarterly coupon payment
Next, we need to find the number of quarterly periods until maturity:
10 years x 4 quarters per year = 40 quarters
Using this information, we can now calculate the value of the bond using the formula for the present value of a bond:
PV = [C / r] x [1 - (1 + r)^-n] + [F / (1 + r)^n]
Where:
C = coupon payment per period
r = required rate of return per period
n = total number of periods
F = face value of the bond
Using the given values, we have:
PV = [$30 / 0.20] x [1 - (1 + 0.20)^-40] + [$1,000 / (1 + 0.20)^40]
PV = $656.77 (rounded to the nearest cent)
Therefore, the best choice is A.

Calculate the Value of a $1,000 Bond Which Has 10