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 cost of the call provision to the ﬁrm if the bond sells for €1,000 today?

Question

Quizplus · Accepted Answer

The cost of the call provision can be calculated by comparing the value of the bond without the call feature to the value with the call feature. Without the call feature, the bond is a perpetual bond that pays €70 annually (7% of €1000). If interest rates fall to 6.5%, the value of the bond would increase because it would be paying a higher interest rate than the market rate. The new value would be €70 / 0.065 = €1076.92. However, because the bond is callable, it will be called away at €1075 instead of being allowed to rise to its full value of €1076.92. The cost of the call provision is the difference between the bond's value without the call (€1076.92) and the call price (€1075), which is €1.92. However, since this event (interest rate dropping to 6.5%) has a 50% probability, the expected cost is 0.5 * €1.92 = €0.96. The discrepancy in the answer choices suggests a need for a different approach or interpretation, focusing on the immediate impact on the bond's pricing and the expected outcomes based on the given probabilities and outcomes. Given the options, none directly align with this calculation, indicating a more complex valuation method or an error in the initial calculation approach.

A ﬁRm Wishes to Issue a Perpetual Callable Bond