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APB25: Accounting for Stock Issued to Employees
APB25, Scope of Opinion
Binomial Option Pricing Model
Black-Scholes Option Pricing Model
Dividend Yield Rate
Expected Option Life
Suboptimal Factor
FAS123: Accounting for Stock-Based Compensation (superseded by FASB ASC Topic 718 - Stock Compensation)
FAS123 R: Share-Based Payment (superseded by FASB ASC Topic 718 - Stock Compensation)
FAS148 Summary
FAS128: Earnings per Share
FAS128 Summary
Fair Value of Stock Option
Risk-Free Interest Rate
Volatility
Warranty

APB 25: Accounting for Stock Issued to Employees

APB 25 STATUS

Issued: October 1972

Effective Date: For awards granted after December 31, 1972

(Financial Accounting Standards Board)

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APB25, Scope of Opinion

APB25, Par. 4

This Opinion deals with accounting for stock issued to employees through both non-compensatory and compensatory plans (a plan is any arrangement to issue stock to officers and employees, as a group or individually).
(Financial Accounting Standards Board)

Binomial Option Pricing Model

Binomial Model, also called Lattice Model or Tree Model, was first introduced by Cox, Ross, and Rubinstein to price American stock options in 1979. The model divides the time to an option’s expiry into a large number of intervals, or steps. At each step it computes that the stock price will move either up or down with a given probability. This model also takes into considerations of the underlying stock’s volatility, the time to expiration, the risk free interest rate and dividend amount/yield.

As shown in the above diagram, the structure of the model is a branch network in which the underlying stock price can move either up or down by a limited amount at each node. The weighted present values of the terminal node values are summed to determine the value of the underlying option. At expiry the option values for each possible stock price are known as they are equal to their intrinsic values. The model then works backwards through each time interval, calculating the value of the option at each step. At the point where a dividend is paid the model takes this into account. The final step is at the current time, time 0, and stock price, where the fair value of the option is calculated.

Black-Scholes Option Pricing Model

In the early 1970s, Fischer Black and Myron Scholes made a major breakthrough by deriving a differential equation that must be by the price of any derivative dependent on a non-dividend-paying stock. They used the equation to compute values for European cal and put option on the stock.

To compute the value by using Black-Scholes Option Pricing Model, five inputs are needed: stock price, exercise price, risk-free rate, time to expiration date, and volatility. Black-Scholes Generalized Model has one more assumption: a company paying a continuous dividend during the life of option. According to FASB123 (superseded by FASB ASC Topic 718 - Stock Compensation), six inputs are needed to compute the fair value of options. Black-Scholes Generalized Model is used in the Model to compute the fair value of option for public companies and the minimum value of options for non-public companies.

formula.jpg (8163 bytes)

C:        Value of stock option

S:        Stock price

E:        Exercise price

�:        Annual volatility of stock in %

q:        Dividend yield rate

r:         Risk-free rate

t:         Expected life of option

e:        Base of the natural logarithm

Ln:       Natural logarithm

N(x): Cumulative normal distribution function

N'(x):   Normal density function

Dividend Yield Rate

The dividend rate paid by a company has a significant impact on the stock option value. Options holders generally have no dividend rights until they actually exercise the options and become shareholders. Thus, the options are less valuable than the related stock. The higher the expected dividend yield, the lower the option value. FAS 123 (superseded by FASB ASC Topic 718 - Stock Compensation) requires company to estimate the expected dividend yield rate over the expected life of the option. If a company has a past history of increases in dividends which is reasonably expected to continue in the expected life of option, the current dividend yield likely should be modified to reflect that expectation.

Expected Option Life

The expected option life is the estimated time period when the option would be exercised by the option holder. The longer the life, the more time the option holder has available to allow the stock price to increase without personal investment and risk, and thus the more valuable the option. Companies most likely will estimate the expected option life based on actual experience with similar grants. FAS123 (superseded by FASB ASC Topic 718 - Stock Compensation) provides some factors to consider in estimating the expected life of an award of stock options: the vesting period of the grant, the average length of time similar grants have remained outstanding in the past, and the expected volatility of the underlying stock.

Suboptimal Factor

A suboptimal exercise factor of "2" means that exercise is generally expected to occur when the share price reaches two times the share option's exercise price. Option-pricing theory generally holds that the optimal (or profit-maximizing) time to exercise an option is at the end of the option's term; therefore, if an option is exercised prior to the end of its term, that exercise is referred to as suboptimal. Suboptimal exercise also is referred to as early exercise. Suboptimal or early exercise affects the expected term of an option. (Footnote 79, page 70, FAS123 R (superseded by FASB ASC Topic 718 - Stock Compensation))

FAS 123 STATUS

Issued: October 1995 (superseded by FASB ASC Topic 718 - Stock Compensation)

Effective Date: For fiscal years beginning after December 15, 1995

This Statement provides financial accounting and reporting standards for stock-based employee compensation plans. It also applies to transactions in which entities issue their equity instruments to acquire goods or services from non-employees. According to FAS 123, those transactions must be accounted for based on the fair value of the consideration received or the fair value of the equity instruments issued, whichever is more reliably measurable.

(Financial Accounting Standards Board)

FAS123 R: Share-Based Payment (superseded by FASB ASC Topic 718 - Stock Compensation)

Issued: December 2004

This Statement is a revision of FASB Statement No. 123, Accounting for Stock-Based Compensation. This Statement supersedes APB Opinion No. 25, Accounting for Stock Issued to Employees, and its related implementation guidance.

This Statement is effective:

For public entities that do not file as small business issuers—as of the beginning of the first interim or annual reporting period that begins after June 15, 2005

For public entities that file as small business issuers—as of the beginning of the first interim or annual reporting period that begins after December 15, 2005

For nonpublic entities—as of the beginning of the first annual reporting period that begins after December 15, 2005.

(Financial Accounting Standards Board)

FAS148 Summary: Accounting for Stock-Based Compensation—Transition and Disclosure—an amendment of FASB Statement No. 123 (Issued 12/02)

Summary

This Statement amends FASB Statement No. 123, Accounting for Stock-Based Compensation, to provide alternative methods of transition for a voluntary change to the fair value based method of accounting for stock-based employee compensation. In addition, this Statement amends the disclosure requirements of Statement 123 to require prominent disclosures in both annual and interim financial statements about the method of accounting for stock-based employee compensation and the effect of the method used on reported results.

(Financial Accounting Standards Board)

FAS 128: Earnings per Share

FAS 128 STATUS

Issued: February 1997

Effective Date: For financial statements for both interim and annual periods ending after December 15, 1997

(Financial Accounting Standards Board)

FAS 128 Summary

This Statement provides standards for computing and presenting earnings per share (EPS) and applies to entities with publicly held common stock or potential common stock. It simplifies the standards for computing earnings per share previously found in APB Opinion No. 15, Earnings per Share, and makes them comparable to international EPS standards.

(Financial Accounting Standards Board)

Fair Value of Stock Option

The objective in determining the fair value of a stock option is to estimate the amount a willing buyer would pay a willing seller for the option on the grant date. FAS 123 (superseded by FASB ASC Topic 718 - Stock Compensation) defines a fair value based method of accounting for an employee stock option or similar equity instrument and encourages all entities to adopt that method of accounting for all of their employee stock compensation plans. However, employee stock options generally are not traded or sold, and therefore no market quotes are available. As a result, companies are required to estimate the fair value of an option using valuation techniques.

FAS 123 (superseded by FASB ASC Topic 718 - Stock Compensation) requires that all six of the following inputs be used in the option pricing model:

Current price of the underlying stock on the date of grant

Exercise price of the option

Expected dividend yield of the stock over the option's life

Expected volatility of the stock over the option's life

Expected life of the option

Risk-free interest rate during the life of the option

The input assumptions made on the grant date normally are held constant regardless of subsequent actual experience, and the fair value per option would not be remeasured. For example, the fair value would not be adjusted subsequent to the grant date for increases or decreases in the stock price or changes in the stock's volatility or actual dividend yield, or if the actual life of the option (i.e., the period from date of grant to date of exercise) varied from the original expectation.

Risk-Free Interest Rate

The FASB defines the risk-free interest rate in Statement 123 as the rate currently available for zero coupon U.S. Government issues with a remaining term equal to the expected life of the options being valued. Such data is not publicly available for free.

Volatility

Volatility of a stock price is a measure of uncertainty about future stock price movements. It generally reflects the propensity of the underlying stock to fluctuate either up or down. Volatility is essentially a mathematical measure of the amount by which a stock price has fluctuated or is expected to fluctuate during a period. Usually it is quoted as the annual standard deviation of a instrument's price. The higher the volatility, the higher the potential for gain under the option and, the higher the fair value of option. FAS 123 requires companies to estimate the expected volatility of stock over the expected life of the option. If historical stock price volatility is not considered indicative of future trends, a company would have to adjust historical volatility for use in the valuation model. Please refer to "Appendix F: Calculating Historical Volatility, FAS123."

Warranty

A security that gives the holder the right - but not the obligation - to buy shares of common stock directly from a company at a fixed price for a given time period.

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