Some complex financial instruments require that the Black-Scholes formula be used to measure their fair value. Examples of these complex instruments include derivatives that are options, bonds issued by the entity that are convertible into shares of the entity, and compensatory stock option plans.
Instructions
(a) For each example provided, explain why it requires the use of the Black-Scholes model in measuring fair value. Discuss how these instruments are initially recorded and subsequently measured under IFRS and ASPE.
(b) Discuss the inputs required in using the Black-Scholes formula for compensatory stock option plans and where this information comes from. Discuss the implications in determining the inputs under IFRS and ASPE.
(c) State the impact on the year-over-year compensation expense for newly granted compensatory stock option plans of making the following changes to the inputs used for the Black-Scholes formula, assuming all other inputs remain unchanged:
1. The risk-free rate has increased from 3% to 5%.
2. The volatility has decreased from 45% to 30%.
3. The expected life has increased from four years to six years.
(d) The Black-Scholes formula was originally designed to determine the fair value of options that are exchange traded. As a result, there has been some disagreement as to whether or not the Black-Scholes formula is the appropriate method to be used for measuring compensatory stock options. What are some of the arguments put forth to support this view? (Consider differences between exchange-traded options on shares and compensatory stock options provided to employees.)