A firm wishes to issue a perpetual callable bond.The current interest rate is 9%.Next year,there is a 40% chance that the interest rate will be 5% and a 60% chance that the rate will be 13.3333%.The bond is callable at €1,090,and it will be called if the interest rate drops to 5%. What is the bond's value today if the coupon is set at €100?

Question

Quizplus · Accepted Answer

To calculate the bond's value, we need to calculate the present value of the coupon payments and the present value of the bond's final payment.

The present value of the coupon payments can be calculated using the formula:
PV(Coupon) = (Coupon amount / Interest rate) x (1 - 1 / (1 + Interest rate)^n), where n is the number of years until the bond is callable.

PV(Coupon) = (100 / 0.09) x (1 - 1 / (1 + 0.09)^∞)
PV(Coupon) = €1,111.11

The present value of the bond's final payment can be calculated using the formula:
PV(Final payment) = Final payment / (1 + Interest rate)^n, where n is the number of years until the bond is callable and the final payment is the callable price of €1,090.

PV(Final payment) = 1,090 / (1 + 0.09)^∞
PV(Final payment) = €12,111.11

To calculate the total present value of the bond, we need to consider the probability of the bond being called next year if the interest rate drops to 5%. If the rate drops to 5%, the bond will be called at €1,090. If the rate remains at 9% or increases to 13.3333%, the bond will not be called and will continue to pay the coupon.

The total present value of the bond can be calculated as follows:

PV(Total) = [PV(Coupon) x 0.4 + PV(Coupon + Final payment) x 0.6]
PV(Total) = [(100 / 0.09) x (1 - 1 / (1 + 0.09)^∞) x 0.4] + [(100 / 0.09 + 1,090) x (1 - 1 / (1 + 0.09)^∞) x 0.6]
PV(Total) = €762.39 + €143.23
PV(Total) = €905.62

Therefore, the answer is C) €905.62

A Firm Wishes to Issue a Perpetual Callable Bond