NON-VESTED SHARES
Sorin R. Straja, Ph.D., FRM
Montgomery Investment Technology, Inc.
200 Federal Street
Camden, NJ 08103
Phone: (610) 688-8111
sorin.straja@fintools.com
www.fintools.com
INTRODUCTION
Many companies decided to compensate their key employees using “restricted shares.” These
contracts imply that the employees will receive stock shares at a later date, without any market
condition, for a zero price. It should be noted that the Accounting Standards Codification™
(ASC) Topic 718 denotes these contracts as “non-vested shares” and reserves the term of
“restricted shares” for other instruments:
“Nonvested shares granted to employees usually are referred to as restricted shares, but this
Topic reserves that term for fully vested and outstanding shares whose sale is contractually or
governmentally prohibited for a specified period of time.”
(Accounting Standards Codification™ (ASC) 718-10-30-18 formerly FAS 123R Paragraph 21)
The following section presents the Fair Value computation for non-vested shares under different
conditions.
FAIR VALUE COMPUTATIONS FOR NON-VESTED SHARES
The non-vested shares, as other contracts awarded to the employees, cannot be transferred to
another party. However, this lack of transferability is not accepted by the Accounting Standards
Codification™ (ASC) Topic 718:
“A nonvested equity share or nonvested equity share unit awarded to an employee shall be
measured at its fair value as if it were vested and issued on the grant date.”
(Accounting Standards Codification™ (ASC) 718-10-30-17 formerly FAS 123R Paragraph 21)
Therefore, if dividend distributions are not expected during the restriction period, then the Fair
Value of one non-vested share is equal to the price of one common stock share.
If dividends are expected during the restriction period, and if the employee receives the
dividends (like the owner of common stock shares), then the Fair Value of one non-vested share
is equal to the price of one common stock share:
“The fair value of a share of stock in concept equals the present value of the expected future
cash flows to the stockholder, which includes dividends. Therefore, additional compensation
does not arise from dividends on nonvested shares that eventually vest. Because the measure of
Non-Vested Shares
© Montgomery Investment Technology, Inc. / Sorin R. Straja, Ph.D., FRM
March 2011
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compensation cost for those shares is their fair value at the grant date, recognizing dividends as
additional compensation would effectively double count the dividends.”
(FAS 123 Paragraph 205)
If dividends are expected during the restriction period, and if the employee does not receive the
dividends, then the Fair Value of one non-vested share is less than the price of one common
stock share:
“The recipient of an award of nonvested stock may not receive dividends paid on the stock
during the vesting period. In that situation, the Board concluded that the value of the award at
the grant date should be the fair value of a dividend-paying share of the stock reduced for the
present value of the dividends that will not be received during the vesting period.”
(FAS 123 Paragraph 206)
If dividends are expected during the restriction period, and if the employee does not receive the
dividends, then for continuous time dividends the Fair Value of one non-vested share is:
FV NonVested Share  Stock  e - y  T
If dividends are expected during the restriction period, and if the employee does not receive the
dividends, then for discrete time dividends the Fair Value of one non-vested share is:
n
FV NonVested Share  Stock   Di  e - IntRate  t i
i 1
In the above formulas Stock is the price of one common stock share on the Valuation Date, y is
the continuous time dividend yield, T is the time until vesting, Di is the discrete time dividend
distribution at time ti, and IntRate is the risk-free interest rate.
It should be noted that one non-vested share that does not receive dividends is equivalent to one
European style call option with:
1. The Expiration Date equal to the Vesting Date of the non-vested share; and
2. The strike price equal to zero.
The above two formulas are the result of the Black-Scholes-Merton for such an option under
continuous time dividend conditions and under discrete time dividend conditions, respectively.
Non-Vested Shares
© Montgomery Investment Technology, Inc. / Sorin R. Straja, Ph.D., FRM
March 2011
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PRESENT VALUE OF THE DIVIDENDS
The Present Value of the dividends distributed prior to the Vesting Date is the difference
between:
1. The Fair Value of the non-vested share receiving the dividend distributions; and
2. The Fair Value of the same non-vested share without dividend distributions.
If dividends are expected during the restriction period, then for continuous time dividends the
Present Value of the dividends distributed prior to the Vesting Date is:
PV Dividends  Stock  1 - e - y  T 
If dividends are expected during the restriction period, then for discrete time dividends the
Present Value of the dividends distributed prior to the Vesting Date is:
n
PV Dividends   Di  e - IntRate  t i
i 1
REFERENCES
Accounting Standards Codification™ (ASC) 718 Compensation – Stock Compensation.
Norwalk, CT: Financial Accounting Standard Board (FASB).
Available at
http://asc.fasb.org/topic&trid=2228938&nav_type=left_nav&analyticsAssetName=_left_nav_to
pic
FASB (Financial Accounting Standard Board). Statement of Financial Accounting Standards
No. 123. Accounting for Stock-Based Compensation. Norwalk, CT: Financial Accounting
Standard Board; (October 1995).
FASB (Financial Accounting Standard Board). Statement of Financial Accounting Standards
No. 123 (revised 2004). Financial Accounting Series. No. 263-C. Norwalk, CT: Financial
Accounting Standard Board; (December 2004).
Non-Vested Shares
© Montgomery Investment Technology, Inc. / Sorin R. Straja, Ph.D., FRM
March 2011
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