“Valuation and Financial Forensics – Educate, Communicate, Preserve”

“Valuation and Financial Forensics – Educate, Communicate, Preserve”

NACVA and IBA’s Annual Consultants’ ConferenceNACVA and IBA’s Annual Consultants’ Conference

Discount for Lack of Marketability (Liquidity) Models: A Comparative Analysis

Discount for Lack of Marketability (Liquidity) Models: A Comparative Analysis

Mainstream Track

and

Ashok Abbott, PhD present

Mainstream Track

and

Ashok Abbott, PhD present

May 27-30, 2009Boston, MA

May 27-30, 2009Boston, MA

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Please set pagers, cell phones, etc. on Please set pagers, cell phones, etc. on vibrate modevibrate mode or turn them off. or turn them off.

Please complete and hand in the Please complete and hand in the Presenter EvaluationPresenter Evaluation forms. forms.

Don’t forget to complete your CPE Don’t forget to complete your CPE Attestation Form.Attestation Form. Add your NACVA# Add your NACVA# (located on your name badge) and sign it. (located on your name badge) and sign it. Keep the white copy for your records. Turn Keep the white copy for your records. Turn in the yellow copy at the NACVA in the yellow copy at the NACVA Registration Desk.Registration Desk.

Discount for Lack of Marketability (Liquidity) Models: A Comparative Analysis

Discount for Lack of Marketability (Liquidity) Models: A Comparative Analysis

Ashok Abbott, PhDAshok Abbott, PhDAshok Abbott, PhDAshok Abbott, PhD

4

Comparative Analysis of Liquidity and Marketability Discount Models

5

Core Concepts in Discounting

Marketability Liquidity Holding period Liquidation period Price pressure Price risk/volatility

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Distinction between Marketability and Liquidity Marketability and Liquidity are aligned but

distinct concepts. 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.

7

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

8

Degrees of Marketability

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

9

Model Classes for DLOM QMDM- Quantitative Model of Discount for

Marketability, proposed by Z. Christopher Mercer(1997) Time Value Model proposed by John J.Stockdale

(2006) CAPM based approach to calculating illiquidity

discounts proposed by David I. Tabak which deals with lack of

diversification Meulbroek model for cost of lack of diversification Proposed by Lisa K. Meulbroek(2002) Time Volatility Models

10

Models considering Marketability and assuming Liquidity

Restricted Stock Discounts Registered vs. Unregistered Stock IPO cost studies

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Silber Model LN (RPRS) = 4.33 + 0.036 LN (REV) - 0.142 LN (RBRT) + 0.174 DERN - 0.332 DCUST

LN (RPRS) is natural logarithm of the relative price of restricted stock expressed in percentage terms [(p*/p) • 100].

LN (REV), the natural logarithm of the firm's revenues (in millions);

LN (RBRT), the natural logarithm of the restricted block relative to total common stock (in per cent);

DERN, a dummy variable equal to one if the firm's earnings are positive and equal to zero otherwise; and

DCUST, a dummy variable equal to one if there is a customer relationship between the investor and the firm issuing the restricted stock and zero otherwise.

12

Bajaj ( 2001)

Discount = a + 0.40 x Fraction of Shares Issued -0.08 x Z-Score + 3.13 x Standard Deviation of Returns + b 4 x Registration Indicator.

13

Abbott (2004)

DLOM (delisting change in value) = - 0.22220 +0.39571XCumexret +1.146XCap90X10^-5 +0.02491XTurnover

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Models Considering lack of diversification but assuming Marketability and Liquidity

Tabak Meulbroek

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Tabak

DLOM= 1-exponent ( σs2 / σm

2)XRPXT Discount for lack of diversification RP is the equity risk premium T is the time to liquidation

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Meulbroek DLOM= 1-(1/(1+R)n)

Where R is the product of the market risk premium multiplied by the difference between the asset’s beta and the ratio of standard deviation of returns for the asset and the market, a measure of incremental risk.

((σs / σm)- β)XRP

17

Models considering Delayed Liquidation as lack of Marketability

QMDM Stockdale

18

DCF Models QMDM /Stockdale

QMDM Framework The Expected Holding Period (HP) Expected Distribution Yield (D%) Expected Growth in Distributions (GD

%) Projected Terminal Value Stockdale Enhancements

19

Stockdale explicitly accommodates inherent

uncertainty in the estimated liquidation period.

Assumes a linear liquidation probability, the model is flexible enough to accommodate any selected probability distribution.

Allows for the starting point for the period of liquidation to be any time in future rather than the present time period

20

Time Volatility (Option) Models

Black Scholes Put (BSP) (Chaffee 1993) Average Price Asian Put (AAP) (Finnerty 2002) Look Back Put (LBP) (Longstaff 1995) (Abbott 2007)

21

BSP

Black Scholes Put (BSP) is a simple contract. It provides protection against any realized loss in value at maturity of the contract. (LOSS I) The minimum value any asset can reach is zero. Therefore, the maximum value payable under a BSP contract is the exercise price for the put.

22

BSP

P(T) = e-rT N(-d2)- N (-d1) Where d1= [(r+σ2/ 2) T]/ σT And d2 = d1- σT

The estimated BSP discount for lack of liquidity then becomes

P(T)/[1+P(T)]

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BSP Basics

σ is the standard deviation for the returns computed for the same

d1= [Lognormal(S/K) + (r+σ2/ 2) T]/ σT

d2 = d1- σT And N(-d1) and N(-d2) are the Normal

cumulative distribution probabilities Setting S=K=1

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Finnerty model :Asian Average Put

D(T) = V[ e rt N(r/ T +T / 2) –N (r/ T -T / 2)]

and 2 = σ2 T + Ln[2( e σ2 T - σ2 T -1)]

-2 Ln [e σ2 T -1]

25

Finnerty Model Discount

Once again setting V to 1, D(T) becomes

[ e rt N(r/ T +T / 2) –N (r/ T -T / 2)] and the corresponding discount for

lack of liquidity becomes D(T)/ 1+ D(T)

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Look Back Put

F ( V,T) = V(2+ σ2 T/ 2) N(σ2T /2)

+ V ( σ2 T/2) e (-σ2T

/8) -V

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Look back Put DISCOUNT

set V to 1, the LBP option premium becomes

F(T) = (2+ σ2 T/ 2) N( σ2 T /2) + (σ2 T/2) e (- σ2 T /8) -1

the corresponding LBP discount for lack of liquidity becomes

F(T)/ (2+ σ2 T/ 2) N( σ2 T /2) + (σ2 T/2) e (- σ2 T /8)

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Estimated DLOL

Low Volatility (Annual σ 0.10-0.30),

Low Risk free rate (3%),

short duration (1 year)

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Discounts ComparisonAnnual Standard Deviation BSP LBP AAP

0.1 2.56% 7.61% 4.00%

0.11 2.92% 8.33% 4.19%

0.12 3.27% 9.04% 4.38%

0.13 3.63% 9.75% 4.58%

0.14 3.98% 10.45% 4.77%

0.15 4.33% 11.14% 4.97%

0.16 4.68% 11.83% 5.17%

0.17 5.03% 12.51% 5.37%

0.18 5.38% 13.19% 5.56%

0.19 5.72% 13.86% 5.76%

0.2 6.07% 14.52% 5.96%

0.21 6.41% 15.17% 6.16%

0.22 6.74% 15.82% 6.35%

0.23 7.08% 16.47% 6.55%

0.24 7.41% 17.10% 6.75%

0.25 7.74% 17.74% 6.94%

0.26 8.07% 18.36% 7.14%

0.27 8.40% 18.98% 7.33%

0.28 8.72% 19.60% 7.52%

0.29 9.04% 20.20% 7.71%

0.3 9.36% 20.81% 7.90%

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Estimated DLOL

Mid range Volatility (Annual σ . 0.40-0.60),

Medium Risk free rate (6%), Medium duration (5 year)

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Annual Standard Deviation BSP LBP AAP

0.4 15.72% 48.38% 33.79%

0.41 16.18% 49.16% 34.22%

0.42 16.64% 49.92% 34.64%

0.43 17.09% 50.68% 35.06%

0.44 17.53% 51.41% 35.46%

0.45 17.97% 52.14% 35.86%

0.46 18.40% 52.85% 36.25%

0.47 18.83% 53.55% 36.63%

0.48 19.25% 54.23% 37.00%

0.49 19.66% 54.90% 37.36%

0.5 20.07% 55.56% 37.70%

0.51 20.47% 56.21% 38.04%

0.52 20.87% 56.84% 38.37%

0.53 21.26% 57.47% 38.69%

0.54 21.64% 58.08% 39.00%

0.55 22.02% 58.68% 39.30%

0.56 22.39% 59.27% 39.58%

0.57 22.76% 59.85% 39.86%

0.58 23.12% 60.42% 40.13%

0.59 23.47% 60.97% 40.39%

0.6 23.82% 61.52% 40.64%

32

Estimated DLOL

for High Volatility (Annual σ . 0.70-0.90),

High Risk free rate (9%), Long duration (10 year)

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Annual Standard Deviation BSP LBP AAP

0.7 19.56% 76.91% 59.57%

0.71 19.81% 77.30% 59.57%

0.72 20.07% 77.69% 59.58%

0.73 20.31% 78.06% 59.59%

0.74 20.55% 78.43% 59.59%

0.75 20.79% 78.79% 59.60%

0.76 21.02% 79.14% 59.60%

0.77 21.24% 79.48% 59.60%

0.78 21.46% 79.81% 59.61%

0.79 21.68% 80.14% 59.61%

0.8 21.89% 80.46% 59.61%

0.81 22.09% 80.78% 59.62%

0.82 22.29% 81.08% 59.62%

0.83 22.49% 81.38% 59.62%

0.84 22.68% 81.68% 59.62%

0.85 22.86% 81.97% 59.62%

0.86 23.04% 82.25% 59.63%

0.87 23.22% 82.52% 59.63%

0.88 23.39% 82.79% 59.63%

0.89 23.56% 83.06% 59.63%

0.9 23.72% 83.32% 59.63%

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