Different type of callable bond question

[shawn Boon]

Company A intends to issue callable, perpetual bonds with annual coupon payments. The bonds are callable at $1,300. One-year interest rates are 12 percent. There is a 50 percent probability that long-term interest rates one year from today will be 17 percent, and a 50 percent probability that they will be 6 percent. Assume that if interest rates fall the bonds will be called.

What coupon rate should the bonds have in order to sell at par value?

[Gandalf]

Let c be the coupon rate.

If interest rates rise, you receive payments of 1000c forever. The PV of that stream is [PV of a perpetuity due of 1000c @17%]/1.12.

If interest rates fall, you get the coupon and the call value, the PV of that stream is [1300+1000c]/1.12.

They are equally likely, so solve:

.5*(PV if rise)+.5*(PV if fall) = 1000.