Morell Corp has a callable bond outstanding. The call provision guarantees that the bond won't be called in the first ten years of its life, and if it is called thereafter the bondholder will be compensated with an extra year's interest at the 12% coupon rate. The bond is now five years into its 25 year life. The market interest rate has fallen to 6%, so it is likely that the bond will be called as soon as the contract allows. What should the bond sell for today?

Question

Quizplus · Accepted Answer

To calculate the price of the callable bond, we need to compare the cash flows from holding the bond to those from holding a non-callable bond which has the same coupon rate, maturity, and market interest rate. 
For the non-callable bond, we can use the PV formula: 
PV = PMT * ((1 - (1 / (1 + r) ^ n)) / r) + FV / (1 + r) ^ n 
where PMT is the annual coupon payment, r is the market interest rate, n is the remaining number of years to maturity, and FV is the face value. 
So for this bond, we have: 
PMT = 0.12 * 1000 = 120 
r = 0.06 
n = 25 - 5 = 20 
FV = 1000 
PV(non-callable) = 120 * ((1 - (1 / 1.06^20)) / 0.06) + 1000 / 1.06^20 = $1,345.20

For the callable bond, we need to consider two cases: 
1. The bond is not called, and the cash flows are the same as for the non-callable bond. The bondholder will receive a total of 20 coupon payments of $120 each and the principal of $1000 at maturity. 
2. The bond is called after 10 years and the bondholder receives an extra year's interest of $120. The cash flows are therefore: 10 coupon payments of $120 each, plus a final coupon payment of $120 + $120 = $240, plus the principal of $1000.

We can use the PV formula again to calculate the price of the callable bond, and choose the lower value between the two cases (since the issuer will choose to call the bond if it is favorable to them). 
For the second case, we need to discount the extra year's interest back to present value at the market interest rate: 
PV(extra interest) = $120 / 1.06^10 = $65.99 
So the cash flows for the callable bond are: 
Case 1:   20 coupon payments of $120 each + $1000 principal 
Case 2:   10 coupon payments of $120 each + $240 final coupon payment + $1000 principal + $65.99 extra interest

Using the same PV formula: 
PV(case 1) = 120 * ((1 - (1 / 1.06^20)) / 0.06) + 1000 / 1.06^20 = $1,345.20 
PV(case 2) = 10 * 120 * ((1 - (1 / 1.06^15)) / 0.06) + 240 / 1.06^15 + 1000 / 1.06^20 + 65.99 / 1.06^15 = $1,277.29

Therefore, the price of the callable bond should be $1,277.29, since it is lower than the price of a comparable non-callable bond ($1,345.20).

Morell Corp Has a Callable Bond Outstanding