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Both the Black-Scholes and lattice models require an assumption for expected dividend yields.

9.6.1 Expected dividend yields in the Black-Scholes model

Selecting the expected dividend yield assumption usually does not require extensive analysis. A common practice is to assume that current dividend yields or cash dividend payments in effect at the grant date will continue in the future. The dividend yield assumption is usually determined (1) by dividing the most recent dividend paid by the current stock price, or (2) as an average of one or more recent dividend payments divided by the stock price on their respective declaration dates. These methods work if dividend yields are expected to remain reasonably stable and, if so, may be used with the Black-Scholes model without further adjustment. Higher dividend yields reduce the fair value of options; lower dividend yields increase the fair value of options.
A company with highly volatile stock prices and relatively stable cash dividend payments may find that dividend yields are also volatile. Such companies may have to use a longer history to obtain a reasonable estimate of future dividend yield. For example, a company whose quarterly dividend remains at $0.10 per share, while its stock price trades regularly between $20 and $40, will find that its historical yield fluctuates between 1% and 2%. This company could estimate its dividend yield over a longer period (e.g., the option’s expected term) while considering the effect of recent stock-price changes up to the grant date on expected future yields.
When a company has had a pattern of increasing or decreasing dividend yields, and this pattern is expected to continue, it may be appropriate to reflect this pattern in the expected dividend yield assumption. For example, a company with a history of significant and steady increases in cash dividend payments might indirectly forecast a continuation of those increases regardless of future changes in the stock price by using a slightly higher dividend yield assumption. If the estimated increases are large enough, an option pricing model reflecting a forecast of increases in cash dividend payments may result in a lower fair value than an otherwise similar model reflecting the historical percentage dividend yield. A model reflecting a percentage dividend yield assumes the percentage yield remains constant (i.e., dividends in the future will change in proportion to changes in stock price), whereas a forecast of steeply increasing cash dividends may result in higher future dividend yields and therefore, a lower fair value.
In a case where a company recently experienced a significant change in stock price, without a comparable change expected in future dividend amounts that would maintain the company's average historical dividend yield levels, it may be appropriate to consider only current and/or near term future expected dividend amounts (annualized) compared to the stock price on the grant date, when determining the expected dividend yield assumption. Because under the standard Black-Scholes model stock prices are expected to increase in the future on average at the risk-free rate of return, this basis for determining the dividend yield for use in the Black-Scholes model would also be appropriate for companies that have a consistent pattern of gradual annual dividend increase in the amount of cash dividends without regard to increases or decreases in stock price.

9.6.2 Expected dividend yields in lattice models

The usual adaptation of the Black-Scholes model for dividend-paying stocks uses a single dividend yield estimate, which is input as a percentage of the stock price with that yield held constant as a percentage of stock price over the expected term of an option. Lattice models have been adapted to reflect dividends, which are assumed to be specific fixed-dollar amounts, as an alternative to using a constant dividend-yield forecast. The assumed cash dividend payments may be further assumed in a lattice model to change over an option's contractual term (e.g., continuing a pattern of steady increases or decreases). These models also allow for explicit input of changing dividend yields or amounts over different periods. Lattice models can simulate the fact that, in certain circumstances, employees may be expected to exercise slightly earlier than they otherwise would, specifically timing exercises in order to capture a large dividend payment. This may result in a further reduction in fair value (under a refined lattice model as compared to a Black-Scholes model) for options on stocks that pay large dividends.

9.6.3 Dividend-protected awards

Generally, option holders are not entitled to receive dividends that are paid on the underlying shares of an option or other equity award. Certain stock options or other equity awards may be structured to provide option holders a form of dividend protection. For example, an option may be structured so that the exercise price is adjusted downward during the term of the option to reflect dividends paid on the underlying shares. Dividend protection features should be reflected in the estimate of the fair value of the stock option. Where the exercise price is reduced by an amount equal to the per-share dividend payments made on the underlying shares, the effect of the dividend protection may often be reasonably approximated by using an expected dividend assumption of zero and the unadjusted grant date exercise price in the option pricing model. Other types of dividend protection, such as the payment of nonrefundable cash dividend equivalents to holders of unexercised options or unvested awards may result in somewhat larger effects. Companies should assess the impact of other features on the fair value of the stock option, considering the form of dividend protection provided. See SC 2.9 for guidance on the accounting treatment of cash dividend payments received by award holders.

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