Estimating
Illiquidity Discounts
When
you take an equity position in an entity, you generally would like to have the
option to liquidate that position if you need to. The need for liquidity arises
not only because of cash flow considerations but also because you might want to
change your portfolio holdings. With publicly traded firms, liquidation is
simple and generally has a low cost Ð the transactions costs for liquid stocks
are a small percent of the value. With equity in a private business,
liquidation costs as a percent of firm value can be substantial. Consequently,
the value of equity in a private business may need to be discounted for this
potential illiquidity. In this section, we will consider the determinants of
this discount and how best to estimate it.
The
illiquidity discount is likely to vary across both firms and buyers, which
renders rules of thumb useless. Let us consider first some of the factors that
may cause the discount to vary across firms.
1. Liquidity of assets owned by the
firm: The fact that a
private firm is difficult to sell may be rendered moot if its assets are liquid
and can be sold with no significant loss in value. A private firm with
significant holdings of cash and marketable securities should have a lower
illiquidity discount than one with factories or other assets for which there
are relatively few buyers.
2. Financial Health and cashflows of
the firm: A private firm
that is financially healthy should be easier to sell than one that is not
healthy. In particular, a firm with strong income and positive cash flows
should be subject to a smaller illiquidity discount than one with negative
income and cash flows.
3. Possibility of going public in the
future: The greater the
likelihood that a private firm can go public in the future, the lower should be
the illiquidity discount attached to its value. In effect, the probability of
going public is built into the valuation of the private firm. To illustrate,
the owner of a private e-commerce firm in 1998 or 1999 would not have had to
apply much of a illiquidity discount to his firmÕs value, if at all, because of
the ease with which these firms could be taken public in those years.
4. Size of the Firm: If we state the illiquidity discount as a percent of the
value of the firm, it should become smaller as the size of the firm increases.
In other words, the illiquidity discount should be smaller as a percent of firm
value for firms like Cargill and Koch Industries, which are worth billions of
dollars, than it should be for a small firm worth $15 million.
The illiquidity discount is also likely to vary across
potential buyers because the desire for liquidity varies among individuals. It
is likely that those buyers who have deep pockets and see little or no need to
cash out their equity positions will attach much lower illiquidity discounts to
value, for similar firms, than buyers that have less of a safety margin.
How
large is the illiquidity discount attached to private firm valuations? This is
a very difficult question to answer empirically because the discount itself
cannot be observed. Even if we were able to obtain the terms of all private
firm transactions, note that what is reported is the price at which private
firms are bought and sold. The value of these firms is not reported and the
illiquidity discount is the difference between the value and the price.
In
fact, much of the evidence on illiquidity discounts comes from examining
Òrestricted stockÓ at publicly traded firms. Restricted securities are
securities issued by a publicly traded company, but not registered with the
SEC, that can be sold through private placements to investors, but cannot be
resold in the open market for a two-year holding period, and limited amounts
can be sold after that. When this stock is issued, the issue
price is set much lower than the prevailing market price, which is observable,
and the difference is viewed as a discount for illiquidity. The results of
three studies that have looked at the magnitude of this discount are
summarized.
In
summary, then, there seems to be a substantial discount attached, at least on
average, when an investment is not liquid. Much of the practice of estimating
illiquidity discounts seems to build on these averages. For instance, rules of
thumb often set the illiquidity discount at 20-30% of estimated value and there
seems to be little or no variation across firms.
Silber (1991) also examined factors that
explained differences in discounts across different restricted stock by
relating the size of the discount to observable firm characteristics including
revenues and the size of the restricted stock offering. He reported the
following regression.
LN(RPRS)
= 4.33 +0.036 LN(REV) - 0.142 LN(RBRT) + 0.174 DERN + 0.332 DCUST
where,
RPRS
= Restricted Stock Price/ Unrestricted stock price = 1 Ð illiquidity discount
REV
= Revenues of the private firm (in millions of dollars)
RBRT
= Restricted Block relative to Total Common Stock in %
DERN
= 1 if earnings are positive; 0 if earnings are negative;
DCUST
= 1 if there is a customer relationship with the investor; 0 otherwise;
The
illiquidity discount tends to be smaller for firms with higher revenues,
decreases as the block offering decreases and is lower when earnings are
positive and when the investor has a customer relationship with the firm.
These
findings are consistent with some of the determinants that we identified in the
previous section for the illiquidity premium. In particular, the discounts tend
to be smaller for large firms (at least as measured by revenues) and for
healthy firms (with positive earnings being the measure of financial health).
This would suggest that the conventional practice of using constant discounts
across private firms is wrong and that we should be adjusting for differences
across firms.
If
we do decide to adjust the illiquidity discount to reflect the differences
across private firms, we are faced with an estimation question. How are we
going to measure these differences and build them into an estimate? There are
two ways of doing this. The first is to extend the analysis done for restricted
securities into the illiquidity discount; in other words, we could adjust the
discount factor for the magnitude of a firmÕs revenues and whether it has
positive earnings. The second is to apply some of the empirical work that has
been done examining the magnitude of the bid-ask spread for publicly traded
firms to estimating illiquidity discounts.
Consider
again the regression that Silber presents on restricted stock. Not only does it
yield a result specific to restricted stock, but it provides a measure of how
much lower the discount should be as a function of revenues. A firm with
revenue of $20 million should have an illiquidity discount which is 1.19% lower
than a firm with revenues of $10 million. Thus, we could establish a benchmark
discount for a profitable firm with specified revenues (say $100 million) and
adjust this benchmark discount for individual firms that have revenues much
higher or lower than this number. The regression can also be used to
differentiate between profitable and unprofitable firms. Figure 24.1 presents
the difference in illiquidity discounts across both profitable and unprofitable
firms with different revenues, using a benchmark discount of 25% for a firm
with positive earnings and $10 million revenues.
There are clearly dangers
associated with extending a regression run on a small number of restricted
stocks to estimating discounts for private firms, but it does provide at least
a road map for adjusting discount factors.
The
biggest limitation of using studies based upon restricted stock is that the
samples are small. We would be able to make far more precise estimates if we
could obtain a large sample of firms with illiquidity discounts. We would argue
that such a sample exists, if we consider the fact that an asset that is
publicly traded is not completely liquid. In fact, liquidity varies widely
across publicly traded stock. A small company listed over-the-counter is much
less liquid that a company listed on the New York Stock Exchange which in turn
is much less liquid that a large capitalization company that is widely held. In
fact, the difference between the bid price and the ask price that we observe on
publicly traded assets can be viewed as a measure of the cost of instant
liquidity. An investor who buys an asset, changes her mind and decides to sell
the asset immediately will pay the bid-ask spread.
While
the bid-ask spread might only be a quarter or half a dollar, it looms as a much
larger cost when it is stated as a percent of the price per unit. For a stock
that is trading at $2, with a bid-ask spread of 1/4, this cost is 12.5%. For
higher price and very liquid stocks, the illiquidity discount may be less than
0.5% of the price, but it is not zero.
What
relevance does this have for illiquidity discounts on private companies? Think
of equity in a private company as a stock that never trades. On the continuum
described above, you would expect the bid-ask spread to be high for such a
stock and this would essentially measure the illiquidity discount.
To
make estimates of the illiquidity discounts using the bid-ask spread as the
measure, you would need to relate the bid-ask spread of publicly traded stocks
to variables that can be measured for a private business. For instance, you
could regress the bid-ask spread against the revenues of the firm and a dummy
variable, reflecting whether the firm is profitable or not, and extend the
regression done on restricted stocks to a much larger sample. You could even
consider the trading volume for publicly traded stocks as an independent variable
and set it to zero for a private firm. Using data from the end of 2000, for
instance, we regressed the bid-ask spread against annual revenues, a dummy
variable for positive earnings (DERN: 0 if negative and 1 if positive), cash as
a percent of firm value and trading volume.
Spread
= 0.145 Ð 0.0022 ln (Annual Revenues) -0.015 (DERN) Ð 0.016 (Cash/Firm Value) Ð
0.11 ($ Monthly trading volume/ Firm Value)
Plugging
in the corresponding values Ð with a trading volume of zero Ð for a private
firm should yield an estimate of the bid-ask spread for the firm.