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?
A) -$71.43.
B) $0.00.
C) $77.41.
D) $178.57.

Question

Quizplus · Accepted Answer

The cost of the call provision can be calculated by comparing the value of a callable bond to that of an otherwise identical non-callable bond. If the interest rate drops to 6.5%, the firm will call the bond at $1,075. If the interest rate rises to 8.25%, the bond will not be called, and its value will be determined by the new interest rate. The expected value of the bond next year, considering the call option and the interest rate changes, is the average of its value if called ($1,075) and its value if not called, which can be calculated using the new interest rate of 8.25%. The value if not called can be determined by the formula for a perpetual bond: Value = Coupon / Interest Rate. Assuming a $70 coupon (from the 7% interest rate on the $1,000 bond), if not called and the rate goes to 8.25%, the value would be $70 / 0.0825 = $848.48. The expected value next year is thus (1,075 + 848.48) / 2 = $961.74. The cost of the call provision is the difference between the bond's value without the call ($1,000 / 0.07 = $1,428.57) and its expected value with the call ($961.74), which is $1,428.57 - $961.74 = $466.83. However, since none of the provided options match this calculation, it appears there has been a mistake in the calculation process. The correct approach involves directly assessing the impact of the call feature on the bond's price, considering the probabilities and outcomes given, without incorrectly applying formulas or assumptions not supported by the given choices.

A Firm Wishes to Issue a Perpetual Callable Bond