You own a bond that pays semiannual interest payments of $40. The bond is callable in 3 years at a premium of $80. What is the callable bond price if the yield to call is 9.7 percent?

Question

Quizplus · Accepted Answer

To find the callable bond price, we need to find the present value of all future cash flows, which include:

1) Semiannual interest payments of $40 for 3 years (6 payments in total)
PV of interest payments = 40[(1 - 1/(1 + 0.097/2)^6)/(0.097/2)] = 212.29

2) Call premium of $80 (paid at the end of year 3)
PV of call premium = 80/(1 + 0.097/2)^6 = 48.15

3) Face value of the bond (paid at maturity)
PV of face value = 1000/(1 + 0.097/2)^6 = 648.71

Therefore, the callable bond price is the sum of these PVs:

Callable bond price = PV of interest payments + PV of call premium + PV of face value
= 212.29 + 48.15 + 648.71
= $1,016.86

So, the best choice is B, $1,016.86.

You Own a Bond That Pays Semiannual Interest Payments of $40