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?

Question

Quizplus · Accepted Answer

The correct coupon amount can be found by setting the present value of the bond's payments equal to its par value, considering the possibility of being called if interest rates drop. If the bond is callable at €1,075 when the interest rate drops to 6.5%, the firm would choose to call the bond in that scenario. The expected value of the bond next year, considering both interest rate scenarios, is the average of its value if called (€1,075) and its value if not called, which would be the coupon plus the par value since it's a perpetual bond. Given the current interest rate of 7%, the equation to find the correct coupon (C) is:$$ \frac{C}{0.07} = \frac{1}{2} \left( \frac{C + 1075}{1.065} + \frac{C + 1000}{1.0825} \right) $$Solving this equation gives a coupon close to €75.42, making choice B correct.

A ﬁRm Wishes to Issue a Perpetual Callable Bond