A firm wishes to issue a perpetual callable bond.The current interest rate is 7%.Next year,the interest rate will be 6.5% or 8.25% with equal probability.The bond is callable at €1,075,and it will be called if the interest rate drops to 6.5%. What is the correct coupon amount if the bond is priced to sell at par?

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The correct coupon amount is €75.42. This is because the bond is priced to sell at par, which means that the present value of the coupon payments must be equal to the present value of the face value. The present value of the coupon payments is calculated as follows:PV = C / rwhere:PV is the present valueC is the coupon paymentr is the interest rateThe present value of the face value is calculated as follows:PV = F / rwhere:PV is the present valueF is the face valuer is the interest rateIn this case, the face value is €1,075 and the interest rate is 7%. Therefore, the present value of the face value is €1,075 / 0.07 = €15,357.14.The coupon payment is calculated as follows:C = r * Fwhere:C is the coupon paymentr is the interest rateF is the face valueIn this case, the interest rate is 7% and the face value is €1,075. Therefore, the coupon payment is 0.07 * €1,075 = €75.25.The present value of the coupon payments is calculated as follows:PV = C / rwhere:PV is the present valueC is the coupon paymentr is the interest rateIn this case, the coupon payment is €75.25 and the interest rate is 7%. Therefore, the present value of the coupon payments is €75.25 / 0.07 = €1,075.00.Since the present value of the coupon payments is equal to the present value of the face value, the bond is priced to sell at par.

A Firm Wishes to Issue a Perpetual Callable Bond