The Country Inn has bonds outstanding with a par value of $1,000 each and a 5.25% coupon. The bonds mature in 8.5 years and pay interest semiannually. What is the current value of each of these bonds if the yield to maturity is 6.0%?

Question

Quizplus · Accepted Answer

First, we need to calculate the semiannual coupon payment:

$1,000 x 5.25% / 2 = $26.25

Next, we need to determine the number of semiannual periods:

8.5 years x 2 = 17 semiannual periods

Using the formula for present value of a bond:

P = [C / (1 + r/n)^(n*t)] + [F / (1 + r/n)^(n*t)]

where P = price of the bond, C = semiannual coupon payment, r = yield to maturity, n = number of compounding periods per year, F = par value of the bond, and t = number of years to maturity

Plugging in the values:

P = [$26.25 / (1 + 0.06/2)^(2*17)] + [$1,000 / (1 + 0.06/2)^(2*17)]

P = $462.62 + $487.01

P = $949.63

Therefore, the current value of each bond is $949.63, which is closest to choice B ($950.63).

The Country Inn Has Bonds Outstanding with a Par Value