You own a bond that pays semiannual interest payments of $38. The bond is callable in 2 years at a premium of $76. What is the callable bond price if the yield to call is 7.9%?

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the two-year worth of interest payments:
PV of Interest = (38/1.0395) + (38/1.0395^2) = $72.12
Next, we calculate the present value of the bond if it were to be held to maturity:
PV of Bond = (1000/1.0395^1) + (1000/1.0395^2) + (1000/1.0395^3) + (1000/1.0395^4) + (1000/1.0395^5) + (1000/1.0395^6) + (1000/1.0395^7) + (1000/1.0395^8) + (1000/1.0395^9) + (1000/1.0395^10) + (1000/1.0395^11) + (1000/1.0395^12) = $1191.29
Now, we need to calculate the present value of the bond if it were to be called in two years:
PV of Callable Bond = (1000+76)/1.0395^2 + (38/1.0395) = $1,024.76
Since the callable bond will be called when PV of Callable Bond > PV of Bond, we need to adjust the PV of Callable Bond to account for the premium being paid at the call date:
Adjusted PV of Callable Bond = $1,024.76 - $76 = $948.76
Finally, we can calculate the yield to call using this adjusted PV and the remaining time to maturity:
$948.76 = $38/(1+(YTM/2))^4 + $38/(1+(YTM/2))^5 + $1000/(1+(YTM/2))^5
Using a financial calculator or trial and error, we can solve for YTM = 7.9%
Therefore, the callable bond price is the adjusted PV, which is $1,059.64 (Choice C).

You Own a Bond That Pays Semiannual Interest Payments of $38