EXECUTIVE SUMMARY
|
It is essential for
board members, executive officers, CFOs,
auditors and private equity investors
to comprehend option-pricing
models used to determine the per-share
values of common and preferred shares.
The AICPA Practice
Aid,
Valuation of Privately-Held-Company
Equity Securities Issued as Compensation
, describes three methods of
allocating value between preferred and
common equity, which include:
Current Value Method (“CVM”)
Probability Weighted Expected
Return Method (“PWERM”)
Option-Pricing Method (“OPM”)
OPM, which is based
on the Black-Scholes model, is
a common method for allocating equity
value between common and preferred shares.
Valuation models must
be tailored to the specific
facts and circumstances of the equity in
the company being valued.
Andrew C. Smith, CPA/ABV,
ASA, CVA, CMA, is a partner and the
managing director of valuation services at
The McLean Group. Jason C.
Laurent, AVA, is an analyst at
The McLean Group. Their e-mails are asmith@mcleanllc.com
and jlaurent@mcleanllc.com,
respectively. The McLean Group is a middle
market investment bank that performs
business valuations for public and private
companies. The McLean Group’s Web site is
www.mcleanllc.com. |
All companies with preferred stock need to
be fluent in the application of an option-pricing
method since it is often used to determine the
per-share value of their common or preferred
securities. An understanding of option-pricing
models is no longer the exclusive domain of a
small group of accountants. Now, board members,
executive officers, CFOs, auditors and private
equity investors should have an awareness and
understanding of the option-pricing models.
Today, companies are being financed with hybrid
forms of capital that go well beyond plain-vanilla
common equity and interest-bearing debt. It is not
unusual for a business to carry debt that can be
converted to equity or equity that is entitled to
a liquidation preference. To complicate matters
further, some rounds of financing incorporate
caps, accrued dividends, performance warrants and
other valuation complexities. An understanding of
these financial structures and their effect on
value is essential for several interested parties:
Valuation analysts need to
understand the ramifications of a company’s
capital structure on the value of its equity
securities.
Executive management needs
to know the effect that a round of financing may
have on the fair value of a company’s existing
securities and capital structure.
Private equity investors
need to understand the effect that
their investment has on the fair value of other
equity securities in order to better structure
their transactions. Accordingly, we have
presented an example to help valuation analysts,
senior executives and investors through the
structured-finance maze.
ALLOCATING EQUITY VALUE BETWEEN DIFFERENT
CLASSES OF EQUITY In 2004, the
AICPA released its Practice Aid titled
Valuation of Privately-Held-Company Equity
Securities Issued as Compensation (please
note that due to changes made to professional
standards since this practice aid was originally
issued, it is out of print and no longer available
for purchase through the AICPA Web site). The
guide summarizes many of the valuation standards
and procedures that have been adopted by the
profession. The guide also describes three methods
of allocating value between preferred and common
equity, which include:
Current Value Method (“CVM”)
Probability Weighted Expected Return
Method (“PWERM”)
Option-Pricing Method (“OPM”)
The CVM has practical limitations on its
use. Specifically, it should be used in two cases:
(1) when a liquidity event is imminent and (2)
when the business is at such an early stage of
development that there is no material progress on
the company’s business plan and there is no
reasonable basis to estimate value beyond the
preferred preference. The PWERM is
especially difficult to apply due to the
significant level of subjectivity it requires. The
probability of various exit scenarios and the
value of the business at such exit events is very
difficult to support. As a result, the OPM
is a commonly used method for allocating equity
value between common and preferred shares. The OPM
is more quantitative as it relies on the
Black-Scholes-Merton model. Although the
Black-Scholes formula was not designed for private
companies, the accounting profession applies it in
various situations, ranging from stock options to
common equity valuation, and it continues to be
the basis for the OPM.
OVERVIEW OF KEY STEPS FOR THE
OPTION-PRICING METHOD Below, we
have summarized the steps and general processes in
applying the option-pricing method.
Step 1—Determine Business Value and
Black-Scholes Assumptions
Business Value—As the OPM
values invested capital as a call option on a
company’s value, the analyst must first determine
which value to use. Conceptually, this value
should be the amount claimholders would receive in
a liquidity event. Accordingly, it is reasonable
to estimate this value by using the implied
enterprise value derived from the market-based and
income-based analyses as of the valuation date.
Since the fair value of interest-bearing debt (net
of excess cash) is typically known, it can be
subtracted from enterprise value.
Time to Liquidity
Event—This is one of many
assumptions that can be difficult to pin down, but
the question that it raises is a significant one:
How much time exists until there is a planned or
likely liquidity event, such as a sale, public
offering or other exit event? Of course, no
company has a crystal ball and many professionals
are often frustrated trying to defend the
assumption. Interaction at the board level is
often warranted.
Risk-Free Rate—The
risk-free rate is the most obvious assumption.
Typically, it is the rate available on a
government security whose term matches the assumed
time to liquidity. The analyst must then compute a
continuously compounded equivalent rate for the
Black-Scholes calculation.
Volatility—This measure
should be based on the standard deviation of
quoted market prices. In the case of a public
company, volatility can be derived easily from the
company’s historical stock prices. For private
companies, volatility can be estimated by
analyzing comparable public companies’ historical
stock performances. It should be noted that the
range of the stock returns sampled should cover
the same period as the estimated time to
liquidity. The OPM is highly sensitive to
volatility and great care should be taken in
estimating the volatility factor.
Step 2—Understanding the Capital Structure
Convertible debt and preferred
stock come in many flavors, shapes and sizes. It
is critical to invest the time to properly
understand any conversion features. For example,
some private equity firms structure preferred
rounds that are effectively debt but labeled as
preferred stock for tax purposes (the preferred
never converts, instead it simply accrues a
dividend). Whereas, other more common preferred
rounds may have a choice of both realizing their
preferences and then participating with common
shareholders. Other preferred stock may be
structured to either convert to common or be paid
its preference, but not both. It is important to
understand the subtle differences of preferred
stock.
Step 3—Setting the Strike Prices for the
Different Classes of Equity
In general, classes of invested capital convert
in a sequential manner. Conversion starts with the
invested capital with the lowest price per common
stock equivalent (“CSE”). Subsequent conversion of
other invested capital will follow this pattern.
Step 4—Allocating Value
Value is then allocated to each equity class
based on each class’s ownership at different
equity levels, as determined by call options.
COMPREHENSIVE EXAMPLE
Step 1—Determine Business Value &
Black-Scholes Assumptions
For this example, we will look at a
hypothetical company (“XYZ” or “the Company”) and
assume an enterprise value of $50 million. We have
arbitrarily chosen the time to liquidity (two
years), volatility (50%), and the risk-free rate
(5%). Defining and properly supporting these
assumptions are paramount to a proper allocation
of value. Standard interest-bearing debt
that calls for periodic interest and principal
payments is typically valued at its face amount
(which is reasonable if the interest rates reflect
market rates). In our example, we have assumed a
net debt obligation of $1 million. Consequently,
the debt’s amount, net of any excess cash, is
subtracted from the company’s enterprise value to
determine the underlying value used in the OPM.
XYZ’s enterprise value of $50 million less its net
debt of $1 million results in an underlying value
attributable to remaining invested capital of $49
million.
Step 2—Understanding the Capital Structure
The hypothetical preferred
rounds were structured so that Preferred A
benefits from its liquidation preference and its
conversion to common. In contrast, Preferred B is
entitled to either its liquidation
preference or its conversion to common.
The Company’s capital structure in terms of CSEs
is summarized in Exhibit
1.
Step 3—Setting the Strike Prices for the
Different Classes of Equity
Under the OPM, the point at which each class of
equity becomes “in-the-money” is viewed as a call
option. It is therefore necessary to determine the
underlying value where each class would receive
value, known as the strike price.
Value for Payoff to Common Shareholders
Conceptually, payoff begins to
accrue to common equity when all other contractual
obligations have been fulfilled. In our example,
XYZ’s common shareholders will start receiving
some proceeds when the Company’s debt and amounts
owed to preferred shareholders have been paid. We
used the preferred shares’ liquidation value as of
the time to liquidity, which includes any accrued
and accumulated dividends. Doing so allows for the
preferred shares’ respective dividend rate to
affect the value attributed to each equity class.
Consequently, common shareholders will be able to
receive value after the preferred stockholders and
convertible debt holders have received their
preferences. For XYZ, the underlying value
for payoff to the common shareholders is $13.5
million, which is the total after $1 million of
convertible debt, $6 million of Preferred A (face
value plus two years of accumulating dividends),
and $6.5 million of Preferred B (face value plus
two years of accumulating dividends). Accordingly,
common equity will be modeled with a call option
with a $13.5 million strike price.
Analyzing the Participation of Each Equity
Class After common stock
and fully participating securities, the additional
classes of invested capital will convert based on
their respective price per common stock
equivalent, with the lowest converting first. Exhibit
2 summarizes the strike price or equity value
when each class of equity will participate.
Preferred A Preferred
A is participating as it benefits from both its
liquidation preference and also its automatic
conversion to common after its liquidation
preference has been realized. Preferred A’s value
is derived from a combination of call options.
First, its liquidation preference is modeled with
a call option with a strike price of $1 million on
the underlying value since Preferred A is paid
after the convertible debt. Then, the value of its
automatic conversion feature is estimated using a
call option that has a strike price of $13.5
million, or the underlying value necessary for
payoff to begin to common shareholders. Lastly,
the dilution from the subsequent conversion of the
remaining invested capital will be taken into
account as detailed in our final allocation of
value.
Options Options differ
from other types of invested capital in that these
securities carry a strike price. Consequently, the
exercise of options will not only dilute a
company’s equity, but also provide cash proceeds.
As with other forms of invested capital that carry
an option to buy a company’s equity, the necessary
enterprise value for exercise must first be
assessed. It is assumed that vested and non-vested
options as of the valuation date will be exercised
upon a liquidity event. All granted options should
typically be included in the model. In the
example, there are 100,000 vested and non-vested
options at a strike price of $0.20. The payoff to
common shareholders starts at $13.5 million, with
both converted Preferred A and common shares
outstanding, for a total of 600,000 CSEs
outstanding. However, at $13.5 million, the common
stock equivalents have a $0 per-share price.
Options will be exercised only if the 700,000
outstanding shares (CSEs and options) have a
per-share price of at least $0.20, the options’
exercise price. Accordingly, the underlying value
must be $140,000 over the $13.5 million floor for
the 700,000 common stock equivalents to have a
per-share price of $0.20. Also, the cash
proceeds from the exercise of options must be
taken into account. At an underlying value of
$13,640,000, 100,000 options will be exercised
providing $20,000 in cash proceeds. Accordingly,
the floor level of $13,640,000 for the exercise of
options should be reduced by $20,000 to
$13,620,000.
Convertible Debt In
the example, XYZ has a $1 million debt liability
that can convert to 100,000 common shares, while
700,000 CSEs are currently outstanding (common,
Preferred A, and options). For the debt to
convert, the per-share price of the Company’s CSEs
must be at least $10 so that the value of the
converted shares equals $1 million. At $10 per
share and 800,000 outstanding shares (700,000 CSEs
and 100,000 from the debt’s conversion), the
underlying value must be $20,480,000 [the $13.5
million starting point for payoff to common, plus
an additional $8 million (or $10 per share with
800,000 CSEs outstanding), less the $20,000 of
cash proceeds from the options, less the forgiven
$1 million debt]. It should be highlighted that if
the debt converts, the Company is no longer
responsible for the original $1 million liability.
Preferred B Preferred
B is modeled in a similar way to the convertible
debt. As it can only benefit from its liquidation
preference or its conversion to common, we need to
calculate the value at which the Preferred B would
convert. For Preferred B to participate in the
equity of the Company for a value greater than its
preference, the underlying value must be
$64,480,000 [the $13.5 million starting point for
payoff to common, plus an additional $58.5 million
(or $65 per share with 900,000 CSEs outstanding),
less the $20,000 of cash proceeds from the
options, less the forgiven $1 million of
convertible debt, and less the forgiven Preferred
B preference]. Similar to the convertible debt, if
Preferred B converts, it will not benefit from its
preference.
Step 4—Allocating Value
The next step is to allocate XYZ’s enterprise
value between its different classes of equity.
First, Exhibit
3 summarizes the key assumptions to the model.
XYZ’s equity structure is illustrated in Exhibit
4. In this example, all proceeds up to $1
million would go to convertible debt. The next $6
million (the tranche from $1 million to $7
million) would be paid to Preferred A. Similarly,
the next $6.5 million would be received by
Preferred B. Then the next $120,000 (the tranche
from $13.5 million to $13.62 million) would be
split between Preferred A, receiving 17%, and
common shareholders, who would receive 83%.
Once we understand the capital structure and
the behavior of the equity classes at different
levels of value, we then derive the value of the
respective call options by using the Black-Scholes
model. The value of each equity tranche represents
the difference between each call option price (or
the incremental change in value for each option).
Exhibit
5 summarizes the value for each option based
on the strike price for each equity class.
Next, we allocate the value of each equity
tranche to the equity classes that participate in
it, based on their respective percentage of
ownership, as summarized in Exhibit
6 (note, totals may not recompute due to
rounding). Based on the information
presented above, we are able to model each class
of invested capital as a combination of call
options. The total value for the various classes
of equity must total the $49 million value of the
respective invested capital.
CONCLUSION
Like many issues in business valuation
today, best practices are evolving and there are
disparities among professionals. Many issues in
valuation are still unresolved and subject to
debate (such as reflecting voting and non-voting
rights, applicability of discounts for lack of
marketability, etc.), and the applications and
underlying details of the option-pricing method
are no exceptions. Valuation models must be
tailored to the specific facts and circumstances
of the company and the securities being valued.
| AICPA
RESOURCES
JofA articles
A
Bid for Fair Value, Sept. 07, page
42
Frontline
Reaction to FASB 123(R), April 07,
page 54
No
Longer an ‘Option,’ April 05, page
63
Conferences
AICPA/ASA National Business
Valuation Conference 2008, Nov. 10—12, Las
Vegas
AICPA National Business
Valuation School, Aug. 18—22, Lewisville
(Dallas), Texas For more
information or to register, go to www.cpa2biz.com,
or call the Institute at 888-777-7077. | |