A Firm Wishes to Issue a Perpetual Callable Bond

Essay

A firm wishes to issue a perpetual callable bond. The current interest rate is 6%. Next year, there is a 30% chance that the interest rate will be 4.5% and a 70% chance that the rate will be 8.0%. The bond is callable at $1,000 plus an additional coupon payment and it will be called if the interest rate drops to 4.5%.
If the bond is priced at $1,000, what is the cost to the firm of the call provision?