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Defining, Measuring & Defending Discounts for Lack of Liquidity. © Ashok Abbott, presentation created in collaboration with BVR. A Teleconference from Business Valuation Resources 1-888-BUS-VALU (287-8258) April 25, 2007

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defining measuring defending discounts for lack of liquidity

Defining, Measuring & Defending Discounts for Lack of Liquidity

  • © Ashok Abbott, presentation created in collaboration with BVR
  • A Teleconference from Business Valuation Resources
  • 1-888-BUS-VALU (287-8258)
  • April 25, 2007
  • Moderator: Shannon Pratt, CFA, FASA, MCBA, CM&AA, of Shannon Pratt Valuations, LLC
  • Panelists: Ashok Abbott, M.B.A., Ph.D. of Business Valuation, LLC
  • Rob Schlegel, ASA, MCBA of Houlihan Valuation Advisors
ancillary reading materials
Ancillary Reading Materials
  • Defining, Measuring & Defending Discounts for Lack of LiquidityPDF and PowerPoint Presentation
  • Does the ‘Myth of Liquidity’ Lead to Incorrect Discounts? special report from the December 2006 Business Valuation Update
  • Full court decisions and Business Valuation Update abstracts for related tax cases listed on slides 62 & 63 (abstract and decision not available for Barnes v. Commissioner and abstract not available for Estate of Berg v. Commissioner)
  • All downloads and links available at the BVR Teleconference pre-conference reading page:
learning objectives
Learning Objectives
  • Learn the distinguishing features between liquidity and marketability
  • Learn how to measure discounts for lack of liquidity and the cost of going public
  • Learn how to apply our model using recent court cases
  • Understand how to utilize this area’s new research in your practice
submitting questions
Submitting Questions
  • Email tc-questions@bvresources.comat any time during the Teleconference
  • The final 20-30 minutes is dedicated to telephone questions; the conference operator will announce Q&A time and provide instructions on how to join the queue
  • Traditionally, appraisers have cited studies of pre-initial public offering and restricted stock to conclude discounts for lack of marketability in the 20-50% range
  • Over the last three years, the Tax Court has rejected discounts for lack of marketability based on the average discount found in restricted stock studies
  • The latest rejection of the Quantitative Marketability Discount Model (QMDM) was in the Estate of Temple (March 2006)
  • There is a trend towards courts rejecting averages, and requiring specific transactions that are as close as possible to the subject company, and specific evidence of similar characteristics
levels of value
Levels of Value

Source: Guide to Business Valuations, Exhibit 8.8; it also appears in Standards of Value: Theory and Applications by Jay Fishman, Shannon Pratt and William Morrison, page 132

discount landscape
Discount Landscape
  • Subjective discounts are not acceptable
  • Courts have clearly indicated that they are looking for firm specific measures, supported by clear, relevant, empirical analysis
  • Scientific method is required to identify and substantiate discounts
core concepts
Core Concepts
  • Marketability
  • Liquidity
  • Holding period
  • Liquidation period
  • Price pressure
  • Price risk/volatility

Formal Definitions

  • Marketability versus liquidity: ASA definitions adopted July 2004
  • Marketability: The capability and ease of transfer or salability of an asset, business, business ownership interest or security
  • Liquidity: The ability to readily convert an asset, business, business ownership interest or security into cash without significant loss of principal
marketability liquidity what s the difference
Marketability & Liquidity: What’s the Difference?
  • Marketability denotes the right to sell an asset in an established and efficient capital market (public or private), within a reasonable time, with relatively low transaction costs, and with minimal effect on that security’s public market price
  • Liquidity denotes the ability to convert an asset into cash without diminishing its value; liquidity is a spectrum
  • A block with high liquidity will have low transaction costs, a short liquidation period and minimal discounts (e.g., bid-ask spread)
  • A block with low liquidity will have opposite characteristics


  • Registered stock in an Exchange-listed publicly traded firm
  • Registered stock in an Exchange-listed publicly traded firm subject to Reg. 144 restrictions
  • Unregistered stock in an Exchange-listed publicly traded firm
  • Unregistered stock in a closely held unlisted large firm (potential to go public)
  • Unregistered stock in a closely held unlisted small firm
liquidity differences within marketability classes
Liquidity Differences within Marketability Classes
  • Liquidity can differ significantly within each marketability class, based on the attributes of the asset
  • A significant block of Dow Jones Industrial Average included firm can be liquidated relatively easily, while stock of a small over the counter (OTC) firm may find few buyers in the short run without offering significant discounts
publicly traded equivalent value1
Publicly Traded Equivalent Value
  • Capital Asset Pricing Model (CAPM), Ibbottson premiums, or build-up rates using capital market proxies (e.g., small stock premium) provide an estimate of the publicly traded equivalent value (“PTEV”) of a privately held company
liquidity assumptions of the publicly traded equivalent value
Liquidity Assumptions of the Publicly Traded Equivalent Value

Finance literature recognizes four dimensions of liquidity:

  • Width (availability of a large number of buyers)
  • Depth (ability to absorb large volume)
  • Immediacy (ability to complete the transaction quickly)
  • Resiliency (absorbing large volume of trades without moving the price)
core issue in liquidity immediacy
Core Issue in Liquidity: Immediacy
  • Assumption: Market orders have immediate execution
  • Reality: Small at-the-market transactions of high trading volume public securities approach immediate execution
  • Large block transactions of thinly traded public securities are likely to occur off the floor or may need to dribble out
  • Even for actively traded shares, orders for above 10,000 shares may not be subject to the current bid-ask quote
  • Either way, a substantial delay and blockage discount may be relevant
effect of liquidity on security pricing returns
Effect of Liquidity on Security Pricing & Returns
  • Research shows significant difference between returns on liquid and illiquid publicly traded securities:
    • Brennan and Subrahmanyam (1996) show the return difference of the most liquid and least liquid shares on the New York Stock Exchange is 6.62% per year
    • This difference roughly translates to a discount for lack of liquidity (DLOL) of 35.5%
bid ask spread liquidity
Bid-ask Spread & Liquidity
  • Amihud and Mendelson (1986) demonstrate that stocks with higher bid-ask spreads have longer holding periods, thus lower trading activity
  • Stoll (1978) and Stoll (2000) suggest that trading activity plays an important role in explaining the cross-sectional variation in bid-ask spreads
recent changes in market liquidity
Recent Changes in Market Liquidity
  • Difference between liquidity of large market cap stocks and small market cap stocks has increased
  • The holding period for SEC Rule 144 securities has been reduced from two years to one year
  • Bid and ask spreads have declined with the change from fraction-of-a-dollar prices to decimal prices
  • Overall market trading volume has gone up several-fold in recent years; this is partly attributable to program trading strategies
changes in market liquidity private companies1
Changes in Market Liquidity& Private Companies
  • Minority interests in private companies have not benefited from the increased liquidity in the public markets
  • Consequently, the value difference between closely held minority interests and their assumed publicly traded counterparts has widened in recent years
  • SEC empirical studies covered larger publicly traded firms during years in which the public markets were less liquid; these studies may understate the actual discount for lack of marketability and ignore the potential discount for lack of liquidity for smaller firms
security markets liquidity differences between small and large stocks
Security Markets LiquidityDifferences Between Small and Large Stocks
  • There are significant differences among publicly traded firms of different sizes
  • Among the smaller stocks, 24% do not trade at all on a given day
  • The observed bid-ask spread is around 14%
  • The measured cost of trading for small lots for smaller firms is around 10%
  • Largest firms are much more liquid, have lower spreads and are less costly to trade
holding period
Holding Period
  • Holding period is discretionary
  • Investors elect to hold an asset for a certain period based on their investment preferences and expected returns
liquidation period
Liquidation Period
  • Liquidation period is determined by the prevailing market conditions
  • Liquidation period the time needed to liquidate a position in a manner that minimizes the total cost of the price pressure and price risk faced by the seller in response to the market availability of buyers and sellers
discount for lack of liquidity function of liquidation period
Discount for Lack of LiquidityFunction of Liquidation Period
  • Discount for lack of liquidity is tied to the anticipated liquidation period, not the discretionary holding period
  • A willing buyer will demand a discount to acquire an asset that cannot be liquidated immediately
  • An existing owner will be willing to discount the asset only to the extent of the anticipated loss of value during the liquidation period
price pressure
Price Pressure
  • Bid-ask spread
  • Listing price (ask)
  • Selling price (bid)
  • Liquidity can be stimulated by applying price pressure
  • Selling pressure results in lower bid price
  • Buying demand results in higher ask price
market failure
Market Failure
  • Frequently the price impact particularly for small firms or large blocks of large firms, is severe enough to result in a market failure
  • Sellers are not willing to sell at the offered low bid price
  • Buyers are not willing to buy at the high ask price
  • In such cases an orderly liquidation or dribble out is appropriate
  • Market failure is not a concept in appraisals because we have to state a given value on a specific date (there are no reserve bids)
price risk
Price Risk
  • Orderly liquidation exposes the holder to price risk
  • Longer liquidation period for volatile assets creates loss of ability to sell at favorable prices
  • Regulatory restraints (e.g.,Reg. 144) can require long liquidation periods
marketability discount approaches1
Marketability Discount Approaches

Empirical Studies

  • IPO studies
  • Restricted stock studies

Theoretical/Quantitative Models:

  • Mercer’s QMDM Model
  • (Adaptation of Discounted Cash Flow model incorporating an assumed liquidity horizon)

Option Pricing Models:

  • Black Scholes Put option
  • Look back Put option
empirical studies
Empirical Studies

IPO Studies:

  • New issue hype
  • Data based on insider transactions
  • Unpublished studies with noisy data
  • Does not address liquidity, only marketability
  • Lack of adequate analysis in the valuation report

Restricted Stock Studies:

  • Limited and defined holding period
  • Established public market
  • Transparent financial disclosure
  • May or may not address liquidity
quantitative marketability discount model
Quantitative Marketability Discount Model
  • Discounted Cash Flow model
  • Depends on holding period
  • Required rate of return
  • Growth rate
  • Assumptions influence results
is bajaj right
Is Bajaj Right?
  • Marketability or liquidity?
  • Pricing marketability assuming liquidity
put option based models
Put Option Based Models
  • Black-Scholes Put
  • Factors
  • Time to maturity
  • Variance of returns
  • Risk-free rate
  • Exercise Price
  • Asset price
look back put
Look Back Put

Measures price risk during period of liquidation

  • Ultimate no regret contract
  • Estimation requires two parameters
  • Liquidation period
  • Volatility
issues for consideration1
Issues for Consideration
  • Two components of the discount
  • DLOM: the cost of going public
  • DLOL: the cost of illiquidity (blockage)
  • Liquidation period
  • Price risk
abbott index cost of ipo and dlol
Abbott Index: Cost of IPO and DLOL

Cost of IPO

(Discount for lack of marketability)

Discount for lack of marketability & liquidity

Discount for lack of liquidity

marketability cost of ipo
Marketability: Cost of IPO

Identify determinants of IPO cost (based on the characteristics of the subject firm):

  • Size of the firm
  • Size of the block
  • Capital market conditions/liquidity/capacity of market to absorb
qualitative costs of an ipo
Qualitative Costs of an IPO
  • The IPO is a costly and risky approaches to raising capital
  • Significant expenses are incurred with no assurance that the IPO will be successful
  • It is not uncommon for changing market conditions to cause underwriters to cancel the IPO at the eleventh hour
  • Insiders/affiliates are subject to significant holding period requirements under SEC Rule 144 and/or underwriter restrictions
  • Insiders/affiliates are subject to significant trading restrictions based on SEC/company restrictions on trading during blackout time periods
reported costs of an ipo
Reported Costs of an IPO

SDC Platinum IPO data (1993-2003) used to estimate the cost of going public:

  • Large sample size analyzed - 7,824 IPO’s
  • IPO costs documented as

Accounting fees and expenses:

  • Legal fees and expenses
  • Underwriting fees
  • Financial advisor fees
ipo sample results
IPO Sample Results

IPO costs observed (as a percentage of IPO proceeds):

  • 6.05% Trimmed mean
  • 6.00% Trimmed median
  • 0.42% Trimmed minimum
  • 11.20% Trimmed maximum
  • 1.79% Standard deviation
ipo costs explanatory factors
IPO Costs: Explanatory Factors
  • IPO costs, as a percentage of the offering proceeds, decline with increasing values for:
    • Issuing firm size
    • Total offering size
    • Percentage Firm ownership offered in IPO
    • Observed market liquidity
regression results ipo costs
Regression Results: IPO Costs

Percentage Cost of IPO:

  • 4.305% + variable based on total market capitalization rank
  • Analysis is broken into deciles based on total market capitalization

Total market capitalization variables:

  • 5.663% - total market capitalization rank = 0)
  • 4.898% - total market capitalization rank = 1)
  • 3.769% - total market capitalization rank = 2)
  • 3.051% - total market capitalization rank = 3)
  • 2.695% - total market capitalization rank = 4)
  • 2.453% - total market capitalization rank = 5)
regression results ipo costs1
Regression Results: IPO Costs

Total market capitalization variables (continued):

  • 2.083% - total market capitalization rank = 6)
  • 1.677% - total market capitalization rank = 7)
  • 1.100% - total market capitalization rank = 8)
  • 0.000% - total market capitalization rank = 9)

Other variables:

  • -3.311% x market liquidity for capitalization size category = 
  • -0.00593 x percentage of firm offered
  • -0.00014 x amount of offering in millions of dollars
average market capitalization for decile rankings
Average Market Capitalization for Decile Rankings
  • Rank 0 = $17.7 million
  • Rank 1 = $48.7 million
  • Rank 2 = $100.0 million
  • Rank 3 = $153.0 million
  • Rank 4 = $247.7 million
  • Rank 5 = $412.6 million
  • Rank 6 = $717.0 million
  • Rank 7 = $1,295.5 million
  • Rank 8 = $2,837.8 million
  • Rank 9 = $22,856.2 million
cost of ipo example
Cost of IPO: Example
  • Total PTEV of equity of company is $180 million
  • Subject block is 25% of total outstanding shares
  • $45 million in PTEV
  • Market capitalization decile is rank 3
  • Market liquidity for capital size category 3 = 0.0656
  • Cost of IPO equation:

4.305% + 3.051% + (-3.311% x 0.0656) +

(-0.00593 x 25.0%) + (-0.00014 x 45) = 6.795%

  • Total discount for lack of marketability = 6.795%
cost of liquidity discount for lack of liquidity1
Cost of Liquidity: Discount for Lack Of Liquidity
  • Identify determinants of liquidity (based on the characteristics of the appropriate publicly traded guideline companies):
    • Stock trading volume
    • Stock price volatility
    • Estimated liquidation holding period (a function of trading volume and price volatility)
  • Develop an objective and statistically supportable metric for estimating risk exposure and the liquidation holding period
applying the theories1
Applying the Theories
  • One size does not fit all
  • Blanket approaches using historical averages are not sustainable
  • Case-specific analysis needed
tax cases phase i
Tax Cases Phase I
  • Estate of Berg v. Commissioner
  • Mandelbaum v. Commissioner
  • Barnes v. Commissioner
  • Estate of Davis v. Commissioner
  • Furman v. Commissioner
  • Estate of Hendrickson v. Commissioner
  • Estate of Weinberg v. Commissioner
  • Knight v. Commissioner
tax cases phase ii
Tax Cases Phase II
  • Gross v. Commissioner
  • Lappo v. Commissioner
  • McCord v. Commissioner
  • Okerlund v. United States
  • Peracchio v. Commissioner
  • Thompson, Estate of Josephine, v. Commissioner
  • Temple v. United States 2006
where do we go from here
Where Do We Go From Here?
  • Develop testable models
  • Empirically validate models
  • Apply these models to case-specific situations
  • Email tc-questions@bvresources.comat any time during the Teleconference
  • The conference operator will provide instructions on how to ask live questions
thank you for attending
Thank You for Attending!
  • Visit for a schedule of exciting upcoming sessions, as always, Teleconferences are good for two CPE credits
  • May 2nd, 409a Compliance featuring Bob Duffy, Scott Beauchene and Joel Johnson
  • May 23rd, Playing and Prospering By the New Valuation Rules featuring Al King and Matt Crow
  • May 24th, Overview of Buy-Sell Agreements (part 1 of 3) featuring Chris Mercer
  • May 31st, Lost Profit Damages featuring Nancy Fannon, Robert Gray and Thomas Burrage
  • June 14th, Application of Buy-Sell Agreements (part 2 of 3) featuring Chris Mercer
  • June 26th, Recruiting in the BV Profession featuring Jim Alerding, Megan Nail and Ron Seigneur
  • June 28th, ESOP Valuation featuring moderator Robert Reilly
  • July 19th, Buy-Sell Agreements and Valuation Related Issues (part 3 of 3) featuring Chris Mercer
  • July 25th, Electronic Discovery featuring Ron Seigneur, Melinda Harper and Shari Lutz
cpe credits
CPE Credits
  • All BVR Teleconferences are worth two interactive CPE credits
  • Be sure to complete the post-conference survey within five business days:
  • You should receive your CPE certificate via email within one week

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