Key
Terms 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
FAS123 R: Share-Based Payment
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)
Back to top
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)
Back to top
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,
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.
- C: Value of stock
option
- S: Stock price
- E: Exercise price
- Ó: 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
Back to top
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 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.
Back to top
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
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.
Back to top
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)
Back to top
FAS 123: Accounting for Stock-Based
Compensation
FAS 123 STATUS
Issued: October 1995
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)
Back to top
FAS123 R: Share-Based Payment
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)
Back to top
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)
Back to top
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)
Back to top
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)
Back to top
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 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 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.
Back to top
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.
Back to top
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."
Back to top
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.
Back to top
|
Simple solutions for complicated option valuations and
corporate reportings