56 INSIGHTS • WINTER 2011
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Valuing Stock Appreciation Rights (SARs)
in ESOP Sponsor Companies
Steve Whittington
ESOP Valuation Insights
Stock appreciation rights (SARs) are used in conjunction with ESOP stock purchase
transactions as an incentive plan for key executives (including the selling shareholder). It
is important for the ESOP financial adviser to understand (1) what SARs are and (2) how
SARs affect the value of the employer corporation stock at the outset of a stock purchase
transaction. It is also important for the ESOP financial adviser to understand how SARs
may affect future employer corporation stock valuations.
introduction
An employer corporation board that decides to
undertake a transaction in which the corporation’s
stock is sold to an employee stock ownership plan
(ESOP) can structure that stock sale transaction
in several ways. In its simplest form, the stock sale
transaction could be consummated by the selling
shareholders receiving full cash consideration for
the employer corporation shares that they have
sold. More commonly, however, there is a seller-
financing aspect to the ESOP employer stock pur-
chase transaction.
In the case of a seller-financed transaction, a
selling shareholder may receive several assets in
place of the employer corporation stock that he or
she has sold. These assets can include any combina-
tion of the following:
1. cash
2. a promissory note from the sponsor com-
pany (a “seller note”)
3. options
4. warrants
A stock appreciation rights (SAR) plan is usu-
ally set up in conjunction with the ESOP employer
stock purchase transaction for the benefit of either
the selling shareholder or the key executives of the
company (or both).
This discussion summarizes (1) how a SAR plan
is used in an ESOP transaction, (2) how SARs are
considered in the initial ESOP valuation, (3) and
how SARs are considered in future valuations.
dEFinition oF a stock
apprEciation right (sar)
A SAR is generally defined as the right to be paid
an amount equal to the increase in value of com-
pany stock from the date the SAR is granted until
the exercise date. A SAR is normally paid in cash.
However, the SAR could be paid in equivalent value
of stock. Or, the SAR could be paid in a combination
of cash and equivalent stock value. SARs often can
be exercised any time after they vest.
SARs differ from stock options. This is because,
when the option is exercised, an employee has to
pay the grant price and acquire the underlying secu-
rity. With a SAR, the employee does not have to pay
to acquire the underlying security. It is a straight
cash outlay for the company.
The SAR is effectively viewed as a cash bonus
plan for executives or key employees of a sponsor
company. If the selling shareholder or shareholders
is one of those executives, a SAR can be used to
capture additional consideration that may be due to
the selling shareholder.
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INSIGHTS • WINTER 2011 57
sars with an Esop
installation
When the decision is made to imple-
ment a SAR plan at the time of the ESOP
employer stock purchase transaction, the
rules that govern how the SAR plan will
operate are contained in a SAR Plan or
SAR Agreement for each eligible partici-
pant. From an employer stock valuation
standpoint, this Agreement is important
in terms of understanding the initial pric-
ing of the SARs, as well as the defined
vesting (and sometimes redemption)
schedule.
Initial Pricing
A leveraged ESOP employer stock pur-
chase transaction looks to provide the
selling shareholders with financial liquidity. The
sponsor company, in turn, takes on debt in the
amount of the equity of the entire sponsor company.
As such, at the conclusion of an ESOP purchase of
100 percent of the stock of the sponsor company,
the remaining equity is some minimal amount near
$0, not considering any tax benefits that the ESOP
may provide. As an example:
$1,000,000 equity in company/1,000 shares =
$1,000/share before the ESOP stock purchase
transaction
Now, the sponsor company assumes the
$1,000,000 in debt for all the shares of the company:
$1,000,000 equity value - $1,000,000 ESOP stock
purchase debt/1,000 shares = de minimis value,
around $0/share
The preceding example is important for SARs in
determining what the “strike price” of the SAR will
be. The setting of the SAR strike price is indicated
in the SAR Agreement. And, it will be negotiated
as some percentage of the pre-transaction value.
Therefore in the above example, the SAR strike
price could be:
n 25 percent of transaction value = $250/share
n 10 percent of transaction value = $100/share
n 5 percent of transaction value = $50/share
Regardless of the negotiated price (and, there-
fore, the percentage dilution to the ESOP), the SAR
price will be set well above the post-transaction per
share value of the sponsor company. This will ren-
der the SAR “underwater” and will cause it to have
a minimal value at the inception of the transaction.
It therefore follows that, from an employer stock
valuation standpoint, the SAR should be examined.
However, there would be no change to value in the
initial valuation.
While it may seem strange to have an initial value
of a SAR so much higher than the post-transaction
price, as was mentioned earlier, this is exactly the
point of the SAR plan; it is an incentive for the exec-
utives to improve the per share value of the sponsor
company from its de minimis $0 value to the strike
price of the SAR, making it “in the money.”
Vesting and Redemption Scheduling
The SAR Agreement lays out the vesting schedule
for each participant. As each SAR Agreement is
written per individual or per class of individuals, the
vesting schedule may be different from participant
to participant within the same overall plan. Further,
some SAR Agreements will differentiate between a
vesting schedule and a redemption schedule.
The vesting schedule describes the size and tim-
ing of the SAR award to a participant. Alternatively,
the redemption schedule describes the eligible
amount of the SAR that can be cashed in.
The vesting (and redemption) schedules are
important from a valuation standpoint. This is
because they illustrate the timing and sizes of future
SAR awards, which effectively are the future cash
commitments of the sponsor company.
58 INSIGHTS • WINTER 2011
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Now that the SAR Agreement has provided the
initial pricing and various schedules for the SARs
(again, per individual), we can consider some valua-
tion methods for how to synthesize the value of the
SARs going forward past the transaction date.
sar valuation procEdurEs
While a SAR and a stock option have different attri-
butes and income tax implications, it is acceptable
to value a SAR in the same manner as an option.
This is because of their similarity regarding “time
value of money” features.
The following methods can be used for valuing
options (and therefore SARs):1
n An option-valuation model, such as Black-
Scholes or a more advanced binomial (lat-
tice) model. It is noteworthy that this value
is a good approximation only if the estimate
of the share price is close to the share price
underlying the SAR values. Otherwise, the
valuation analyst would need to create
a new valuation using an option pricing
model.
n A second method, the exercise value meth-
od, provides only a lower bound for the
value of the SAR. This method assumes
that all SARs are exercised immediately
and thereby ignores the time value of
the options. The resulting valuation error
increases as SARs have longer time to
maturity, the sponsor company’s stock has
higher volatility, and the sponsor company’s
share price is closer to the exercise price.
For purposes of this discussion, we will concen-
trate on the first method and in particular the Black-
Scholes model for valuing SARs. While the computa-
tional notation is beyond the scope of this discussion,
there are a few things to note about the Black-Scholes
model in relation to valuing options or SARs:
n The SAR Agreement is important to secur-
ing one of the inputs for the Black-Scholes
model: the exercise price. This exercise
price will be the negotiated SAR price in
the Agreement. Therefore, the valuation
analyst will need the Agreement to perform
the calculation.
n The SAR Agreement will also aid the ana-
lyst in determining the valuation date and
expiration date inputs for the Black-Scholes
model. Vesting (and redemption) generally
does not take place immediately. Rather,
vesting (and redemption) will take place
over several years as the executives attempt
to increase the profitability of the company.
n There is a volatility input that is used
as a proxy for the volatility of the stock
you are valuing. A good proxy for this
is, for example, the New York University
Volatility Laboratory (VLAB) website:
http://vlab.stern.nyu.edu, which per-
forms volatility studies on the overall
market, market sectors, market indices
and single stocks.
n The valuation analyst will need a reli-
able proxy for a risk-free rate.
It is important to understand that in
valuing SARs using this method, the cal-
culation being performed is iterative in
nature. Therefore any modeling will need
to be carefully constructed to avoid any
circular references. This is because one of
the inputs in the Black-Scholes model is the
equity value per share.
Effectively what is happening is that
the model needs the equity value per share
(pre-SAR) to arrive at a SAR value, which
in turn is subtracted from the equity value,
which in turn affects the SAR value, and
so on.
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INSIGHTS • WINTER 2011 59
Therefore, the SAR computation needs to be set
up isolated from the rest of the valuation, and any
subsequent SAR value that needs to be subtracted
from the equity value can be manually entered at
the end of the valuation.
sar valuation For an Esop—
an ExamplE
To illustrate the steps of a SAR valuation, the fol-
lowing is a simplified example of an ESOP employer
stock valuation. The illustrative sponsor company
is an information technology (IT) contractor in the
defense department segment. The sponsor company
performs consulting and implementation of IT solu-
tions for the military on site (i.e. on military bases).
The sponsor company underwent a transaction
in April of 2007 to sell 100 percent of the outstand-
ing stock of the sponsor company to an ESOP. As
part of the work leading up to the employer stock
purchase transaction, the parties negotiated (1) that
there would be SARs put into place for two execu-
tives and (2) that the SAR consideration would be
25 percent of the transaction price. Therefore:
$11,650,000 employer stock transaction price x
25% SAR dilution = $2,912,500 SAR consideration
and
$2,912,500 SAR consideration/1,000,000 shares
= $2.9125 SAR price
The sponsor company stock price had a de
minimis value on the closing date. And, the sponsor
company stock price was therefore well below the
stated SAR strike price stated in the Agreement.
Therefore, at the closing date, the SAR didn’t affect
the employer stock value and would not affect the
employer stock value until it reached the exercise
price.
The sponsor company received a second valua-
tion in September of 2007 (the fiscal year end) and a
third in December of 2007 (for ESOP administration
reasons). The sponsor company’s stock price was
improving but still well below the SAR price. The
same was true for the annual employer stock valua-
tion performed in 2008.
For the 2009 annual employer stock valuation,
the sponsor company’s stock price had improved
and was greater than the SAR price. Therefore, the
SARs would have to be considered. In performing
the Black-Scholes model, the value conclusion for
the SAR is illustrated in Exhibit 1.
As mentioned earlier, each SAR plan is written
for each individual or class of individuals. In this
case, there were
two executives
and two differ-
ent plans. For
each plan, there
was a vesting
and a redemp-
tion schedule.
The plans are
illustrated
in
Exhibit 2.
By
this
p o
i n t
,
Executive
1
was 60 percent
vested (21,000
SAR units) but
would
only
be eligible to
redeem 20 per-
cent
(7,000
SAR units) in
2012 at the ear-
liest. Similarly,
Executive
2
was 100 per-
cent
vested
at
this
time
(10,000
SAR
units) but was
only eligible to
redeem 10 percent (1,000 SAR units) in 2012 at
the earliest.
Therefore, the redeem-eligible shares were used
in the calculation of the total SAR value for each
executive, as they supersede the vesting schedule
(i.e., they can’t redeem all the shares that are
vested immediately).
Further, the SAR agreement stated that the
redemption of the SARs was going to be a forced
redemption. This meant that each executive would
have to redeem the noted percentage of shares in
any given year. This is why, in the Black-Scholes
calculation, the expiration date of December 31,
2012, was selected.
Therefore, the total SAR value of each executive
as of the valuation date was:
Executive 1: $4.99 SAR value x (20% redemp-
tion x 35,000 SARs) = $35,000 total SAR value
(rounded)
Executive 2: $4.99 SAR value x (10% redemption x
10,000 SARs) = $5,000 total SAR value (rounded)
Exhibit 1
Illustrative Sponsor Company
Value Conclusion for the SAR
Total Equity Value (per share) (1)
7.12
$
Less: PV of Dividends
-
Current Price
7.12
$
Exercise Price (Per Share)
2.91
Years to Expiration
3.0027

Days to Expiration
1,096

Valuation Date
12/31/2009
Expiration Date (2)
12/31/2012
Volatility (3)
65.00%
Risk Free Rate (4)
4.31%
d1 (5)
1.4711

N(d1)
0.9294

N(-d1) or [1-N(d1)]
0.0706

d2 (5)
0.3448

N(d2)
0.6349

N(-d2) or [1-N(d2)]
0.3651

Dividend Yield
N/A
Call Value (per share) (6)
4.99

60 INSIGHTS • WINTER 2011
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These
SAR
values
represent
future cash out-
lays for the spon-
sor company. And,
as such, these SAR
values would need
to be subtracted
from the equity
value of the spon-
sor company.
However
as
mentioned
ear-
lier,
to subtract
the SAR amount
would change the
bottom line equity
number, which is
already an input in
the Black-Scholes
model. Therefore
it is necessary to
manually enter the
SAR amounts into
the valuation sum-
mary. Linking the
valuation analyses
together would cre-
ate a circular refer-
ence.
Exhibit 3 illus-
trates the “before”
and “after” per
share
valuation
summaries for the
sponsor company.
The two deduc-
tions for the Stock
A p p r e c i a t i o n
Rights of Executive
1 and Executive
2 were manually
inserted to avoid
an iterative cal-
culation. One can
see that the cumu-
lative effect of the
SAR plans on the
sponsor company
stock is a dilution
of $0.04 per share
($7.12 – $7.08).
summary and conclusion
As the sponsor company continues to increase
in profitability over time, this SAR valuation
exercise will typically be performed every time
an ESOP employer stock valuation is performed.
Presumably, the value of the SAR will increase as
sponsor company profitability increases (and as
the underlying employer stock value increases).
Also, the poten-
tial amount of the
SARs that is eligible
to be redeemed will
increase in future
years. The SAR obli-
gation may increase
independently
of
the increase in the
sponsor company
profitability.
In any security
valuation, sponsor
company stock or
otherwise, where
a SAR plan is in
place, it is important to address the future obliga-
tion to the SAR in the security valuation engage-
ment.
Ignoring the liability that is created as a result
of the SAR plan could lead to an overstatement in
the sponsor company equity value. In addition,
ignoring the liability associated with the SAR plan
could also create an unexpected liquidity problem
for the sponsor company when the SARs come due.
The above-mentioned method of addressing and
valuing SARs is just one of several valuation meth-
ods. All such valuation methods should generally
be considered by the valuation analyst during the
employer stock valuation process. This is because
every sponsor company, and every SAR plan, is
different.
Notes:
1. Tim Koller, Marc Goedhart, and David Wessels,
Valuation: Measuring and Managing the Value of
Companies, 4th ed. (New York: John Wiley & Sons,
2005), pp. 339–346.
Steve Whittington is an associate in our Atlanta office. Steve
can be reached at (404) 475-2317 or at scwhittington@
willamette.com.
“. . . it is very
important to
address the
future obligation
to the SAR in the
valuation engage-
ment.”
Exhibit 2
Illustrative Sponsor Company
SAR Plan Details
Executive 1-Vesting Schedule
(35,000 total SAR Units available)
Year
Percentage
2007
20
2008
40
2009
60
2010
80
2011
100
Executive 1-Redemption Schedule
Year
Percentage
2012
20
2013
25
2014
33.3
2015
50
2016
100
Executive 2-Vesting Schedule
(10,000 SAR total SAR Units available)
Year
Percentage
2007
33.3
2008
66.7
2009
100
Executive 2-Redemption Schedule
Year
Percentage
2010
NA
2011
NA
2012
10
2013
11.1
2014
12.5
2015
14.3
2016
16.7
2017
20
2018
25
2019
33.3
2020
50
2021
100
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INSIGHTS • WINTER 2011 61
Exhibit 3
Illustrative Sponsor Company
Before and After Valuation Summaries
"BEFORE" Valuation
$ in 000s, except for per share data
Indicated
Contribution
Valuation Method
EV
Weight
to EV
Discounted Cash Flow Method
17,400
$
80%
13,920
$
+ Guideline Public Company Method
17,700

10%
1,770

+ Guideline Merged and Acquired Company Method
16,100

10%
1,610

= Weighted Average MVIC (with equity on a controlling interest basis)
100%
17,300
− Market Value of Interest-Bearing Debt
(9,650)

− Warrant Right Agreement (Unfunded)
(159)

=
Indicated Equity Value (on a marketable, controlling interest basis)
7,491

− Discount for Lack of Marketability
-5%
(375)

=
Indicated Equity Value (on a nonmarketable, controlling interest basis)
7,116

÷ Total Shares
1,000

= Per Share Value
7.12
$
$ in 000s, except for per share data
Indicated
Contribution
Valuation Method
EV
Weight
to EV
Discounted Cash Flow Method
17,400
$
80%
13,920
$
+ Guideline Public Company Method
17,700
10%
1,770

+ Merged and Acquired Method
16,100
10%
1,610

= Weighted Average MVIC (with equity on a controlling interest basis)
100%
17,300
− Market Value of Interest Bearing Debt
(9,650)
− Stock Appreciation Rights (Roger Harris)
(35)

− Stock Appreciation Rights (Ron Gilbert)
(5)

− Warrant Right Agreement (Unfunded)
(159)

=
Indicated Equity Value (on a marketable, controlling interest basis)
7,451

− Discount for Lack of Marketability
-5%
(373)

=
Indicated Equity Value (on a nonmarketable, controlling interest basis)
7,079

÷ Total Shares
1,000

= Per Share Value
7.08
$
MVIC = market value of invested capital
EV - equity value
"AFTER" Valuation