A semiannual coupon bond has a 5% coupon rate, a $1,000 face value, a current value of $1,020, and 3 years until the first call date. What is the call price if the yield to call is 5.5%?

Question

Quizplus · Accepted Answer

To find the call price, we need to calculate the present value of the bond using the higher of the coupon rate and the yield to call. Since the yield to call is 5.5%, which is higher than the coupon rate of 5%, we will use the yield to call to calculate the present value.

Using the formula for the present value of a bond:
PV = C x [1 - 1/(1+r)^n]/r + F/(1+r)^n
where PV = present value, C = coupon payment, r = yield to call, F = face value, and n = number of periods until call

We can plug in the given values:
PV = 25 x [1 - 1/(1+0.055)^6]/0.055 + 1,000/(1+0.055)^6
PV ≈ $1,039.15

Therefore, the call price is $1,039.15, which is closest to answer choice C, $1,040.

A Semiannual Coupon Bond Has a 5% Coupon Rate, a $1,000