Consider a three-year bond that has annual coupons of 5% per annum and a face value of 100. The bond may be called one year from now with a call price of $101.00. Also assume that the current interest rate is 5% pa and that the RBA is having a board meeting today. Analysts believe there is a 5% chance that interest rates will stay at 5% pa for the next 3 years and a 95% chance that interest rates will fall to 4% pa today and stay at that level for the next 3 years. Assuming annual compounding, what is the price today of this callable bond?

Hint: The price of a callable bond is equal to the probability that the bond is called multiplied by the present value of cashflows received if the bond is called plus the probability that the bond is not called multiplied by the present value of cashflows if the bond is not called.

101.92

100.00

102.64

100.10

101.83