CORRESP 1 filename1.htm corresp
 

UDR, INC.
1745 Shea Center Drive
Suite 200
Highlands Ranch, Colorado 80129
June 22, 2007
VIA EDGAR
Mr. Daniel L. Gordon
Branch Chief
United States Securities and Exchange Commission
Division of Corporation Finance
100 F Street, N.E.
Washington, DC 20549
Mail Stop 4561
RE:   UDR, Inc.
Form 10-K for the fiscal year ended December 31, 2005
Filed March 7, 2006
File No. 001-10524
Dear Mr. Gordon:
This letter is a follow-up to our response letter to you dated April 10, 2007, and our subsequent telephone conversation with you on May 8, 2007, regarding the Annual Report on Form 10-K for the fiscal year ended December 31, 2005 filed by UDR, Inc., (formerly named United Dominion Realty Trust, Inc.) (the “Company”).
Houlihan Lokey Valuation Analysis
We wish to inform the Staff that subsequent to our telephone conversation with the Staff on May 8, 2007, and in response to the Staff’s comments regarding the Company’s Series C Out-Performance Program, Houlihan Lokey Howard & Zukin Financial Advisors, Inc. (“Houlihan Lokey”) was retained to review Citigroup’s valuation relating to our Series C Out-Performance Program. In the course of its review, Houlihan Lokey has identified some internal inconsistencies within the Citigroup model. Consequently, Houlihan Lokey was engaged to prepare a new valuation of the Company’s Series C Out-Performance Program as of June 1, 2005. A copy of the Houlihan Lokey valuation analysis is attached to this letter as Attachment A.
After reviewing the Houlihan Lokey valuation and considering our conversations with the Staff, we believe the Houlihan Lokey valuation provides a thorough and detailed analysis of the valuation of the Series C Out-Performance Program as of June 1, 2005.

 


 

Based on an initial stock price of $23.15 (the closing price of the Company’s common stock on June 1, 2005), a risk-free rate of 3.54% based on a three-year U.S. Treasury yield, and a volatility of 16.55%, Houlihan Lokey has estimated the value of each membership interest in the Series C limited liability company at approximately $3.32 as of June 1, 2005. Houlihan Lokey has estimated a range of lack of marketability discounts to be 30.74% to 36.34% using a volatility of 16.55%. (However, as set forth in the attached valuation, a greater marketability discount is supportable since the membership interests in the Series C limited liability company (the “LLC Interests”) are illiquid and Houlihan Lokey derives the marketability discount by comparing the more liquid Operating Partnership units to the Company’s publicly traded common stock. Unlike the Operating Partnership units, the LLC Interests are illiquid and non-transferable, subject to contractual restrictions and subordinate on liquidation to the Operating Partnership units.)
The following table sets forth the value of the Company’s Series C Out-Performance Program using the Houlihan Lokey model:
                                   
    Measurement   Assumed                   Houlihan Lokey
    Period   Stock Price   Volatility   Value as used   Discounted Value
 
  6/1/05-5/30/08   $ 23.15       16.55 %   $ 750,000     $1,585,134 to $1,724,574
Volatility Assumption Analysis
During our telephone conference on May 8, 2007, the Staff asked us to provide additional information regarding the volatility assumption. In response to this request, Houlihan Lokey has provided additional information and the basis and support for the volatility assumption in the attached valuation. As discussed on pages 15 through 17 and Appendix B of the attached valuation, Houlihan Lokey applied an expected volatility of 16.55% using the implied volatility approach. According to Houlihan Lokey, the implied volatilities derived from exchange-traded options are preferred over historical volatilities as they reflect the market’s forward-looking estimate of volatility and risk preferences, and according to Staff Accounting Bulletin No. 107, “implied volatility can be useful in estimating expected volatility because it is generally reflective of both historical volatility and expectations of how future volatility will differ from historical volatility.”
SAB 99 Analysis
The Company hereby represents to the Staff that the difference between the applications of the alternative valuation discounts used by the Company based on the Houlihan Lokey valuation is not material to the consolidated financial statements of the Company or any line item in its financial statements during the years ended December 31, 2005, December 31, 2006 and through the three months ended March 31, 2007. This difference would not have:

2


 

    masked a change in earnings or other trends;
 
    caused the Company to miss analysts’ expectations;
 
    changed the Company’s earnings from income to loss in any period;
 
    changed the Company’s compliance with loan covenants or other contractual requirements; or
 
    affected the Company’s compliance with regulatory requirements.
Furthermore, the difference did not involve concealment of an unlawful transaction. The Company believed and continues to believe that the valuation of the Series C Out-Performance Program and related accounting treatment are and were reasonable and in conformity with generally accepted accounting principles.
 
We hope this information is responsive to the Staff’s questions. In light of the complex nature of the valuation of these instruments, should the Staff have additional questions or concerns, we respectfully request that we speak via conference call in order to ensure that we can fully address the Staff’s questions and concerns in a timely and efficient manner.
Please direct any comments or inquiries regarding the foregoing to Warren L. Troupe, Esq., of Morrison & Foerster LLP; telephone: (303) 592-2255; facsimile: (303) 592-1510 or the undersigned; telephone: (720) 283-6139; facsimile (720) 283-2451.
Sincerely,
/s/ David Messenger
David Messenger
Senior Vice President and Chief Accounting Officer
cc:   William Demarest, U.S. Securities and Exchange Commission
Brian V. Caid, Esq., Morrison & Foerster LLP
Whitney Holmes, Esq., Morrison & Foerster LLP
Mark Kaspar, Ernst & Young LLP

3


 

Attachment A
 
JUNE 2007 Confidential Valuation of Series C Out-Performance Program as of June 1, 2005 Houlihan Lokey www.hlhz.com U.S. 800.788.5300 Europe +44 (0)20.7839.3355 Asia 852.3551.2300 Los Angeles•New York•Chicago•San Francisco•Minneapolis•Washingt on, D.C.•Dallas•Atlanta•London•Pari s•Frankfurt•Hong Kong


 

Houlihan Lokey Table of Contents Tab Executive Summary 1 Description of the Series C OPPSs 2 Valuation Analysis 3 Appendices Trinomial Lattice/Monte Carlo Simulation Valuation Framework A Implied Volatilities: Short-Term vs. Long-Term B Empirical Basis For A Discount for Lack of Marketability C Selected Biographies D Houlihan Lokey Table of Contents Tab Executive Summary 1 Description of the Series C OPPSs 2 Valuation Analysis 3 Appendices Trinomial Lattice/Monte Carlo Simulation Valuation Framework A Implied Volatilities: Short-Term vs. Long-Term B Empirical Basis For A Discount for Lack of Marketability C Selected Biographies D i


 

Executive Summary


 


 

Houlihan Lokey Executive Summary INFORMATION REVIEWED In connection with our engagement, we have made such reviews, analyses, and inquiries as we have deemed necessary and appropriate under the circumstances. Among other things, we have: reviewed previous valuation analyses of the Series C Out- Performance Program; reviewed the Amended and Restated Agreement of Limited Partnership of United Dominion Realty, L.P. (the "Operating Partnership") dated as of February 23, 2004 and the First Amendment to the Amended and Restated Agreement of Limited Partnership of the Operating Partnership dated as of June 24, 2005; reviewed the Operating Agreement of UDR Out- Performance III, LLC dated June 24, 2005 (the "Operating Agreement") and the First Amendment to the Operating Agreement dated November 7, 2006; discussed with the Company's legal counsel and management regarding the Series C Out- Performance Program and certain rights and restrictions of the Series C Out-Performance Program; reviewed certain publicly available financial information and other information furnished by the Company; examined the reported prices of the Company's common stock and the implied volatilities of the Company's exchange-traded options; reviewed various studies of transactions in restricted stock of publicly traded companies; and conducted such other studies, analyses, and inquiries as we have deemed appropriate. 2


 

Houlihan Lokey Executive Summary LIMITING FACTORS AND OTHER ASSUMPTIONS The professional fee for this engagement is not contingent upon the opinion of value set forth herein. This report is based on business, general economic, market, and other conditions that could be reasonably evaluated by Houlihan Lokey as of the Valuation Date. Subsequent events that could affect the conclusions set forth in this report include adverse changes in industry performance or market conditions and changes to the business, financial condition, and results of operations of the Company. Houlihan Lokey is under no obligation to update, revise, or reaffirm this Report. This Report is intended solely for the information of the person or persons to whom it is addressed, solely for the purpose stated, and may not be relied upon by any other person or for any other purpose without Houlihan Lokey's prior written consent. The conclusions set forth in this report are based on methods and techniques that Houlihan Lokey considers appropriate under the circumstances, and represent the opinion of Houlihan Lokey based upon information furnished by the Company, its advisors, and other publicly available sources. Houlihan Lokey has relied upon the Company's representations that the information provided by it, or on its behalf, is accurate and complete in all material respects. While all public information (including industry and statistical information) was obtained from sources we believe are reliable, Houlihan Lokey makes no representation as to the accuracy or completeness thereof, and we relied upon such public information without further verification. The opinions set forth in this Report are not intended by Houlihan Lokey, and should not be construed, to be investment advice in any manner whatsoever. Furthermore, no opinion, counsel, or interpretation is intended in matters that require legal, accounting, tax, or other appropriate professional advice. It is assumed that such opinions, counsel, or interpretations have been or will be obtained from the appropriate professional sources. Houlihan Lokey assumes that the Company has complied with all applicable federal, state, and local regulations and laws, unless the lack of compliance is specifically noted in this Report. Except to the extent specifically disclosed in writing to Houlihan Lokey, and noted herein, this report also assumes that the Company has no material contingent assets or liabilities no unusual obligations, or substantial commitments other than those incurred in the ordinary course of business, and no pending or threatened litigation that would have a material effect on the Company. 3


 


 

Description of the Series C OPPSs


 

Houlihan Lokey Description of the Series C OPPSs OVERVIEW OF UDR, INC.2 The Company is a self- administered real estate investment trust (REIT) that owns, acquires, renovates, develops, and manages apartment communities nationwide. The Company's common stock is traded on the New York Stock Exchange and is included in the S&P MidCap 400 Index. UDR is the fourth largest apartment REIT in the U.S. As of March 31, 2007, UDR's apartment portfolio included 244 communities with 70,325 apartment homes nationwide. The Company has elected to be taxed as a REIT under the Internal Revenue Code. To qualify as a REIT, a company must meet certain criteria that, among other things, generally require that (1) the company's assets consist primarily of real estate assets, (2) the company's income be derived primarily from real estate assets, and (3) at least 90% of the company's REIT taxable income (other than net capital gain) is distributed to stockholders. As a qualified REIT, the Company's net income is not subject to U.S. federal income taxes at the corporate level. The Company paid dividends of $1.25 per share in calendar year 2006, representing the 30th year of consecutive dividend increases to stockholders. UDR was formed in 1972 as a Virginia corporation. In June 2003, the Company's state of incorporation was changed from Virginia to Maryland. Corporate headquarters are located in Richmond, Virginia, and the principal executive offices are located in Highlands Ranch, Colorado. On March 14, 2007, the Company officially changed its name from United Dominion Realty Trust, Inc. to UDR, Inc. The Company's subsidiaries include two operating partnerships, Heritage Communities L.P. and United Dominion Realty, L.P. 2 Information presented in this section of our report is taken largely from the Company's annual report on Form 10-K, the Company's quarterly report on Form 10-Q, the Company's Web site, and discussions with management. 6


 

Houlihan Lokey Description of the Series C OPPSs OVERVIEW OF OPERATING SUBSIDIARIES The Company's operations principally take place in its two operating subsidiaries, Heritage Communities L.P. and United Dominion Realty, L.P. Heritage Communities L.P. (the "Heritage OP") is a Delaware limited partnership. As of March 31, 2007, there were 5,542,200 Heritage OP units outstanding, of which 5,215,210 units or 94% were owned by UDR and 326,990 units or 6% were owned by limited partners. United Dominion Realty, L.P. (the "Operating Partnership") is a Delaware limited partnership and, for purposes of this Report, the more significant of the two subsidiaries. As of March 31, 2007, there were 166,185,740 units ("OP Units") in the Operating Partnership outstanding, of which 157,001,747 units or 94% were owned by UDR and 9,183,993 units or 6% were owned by limited partners. The OP Units are generally non- transferable without the written consent of the general partner of the Operating Partnership, which is the Company. 7


 

Houlihan Lokey Description of the Series C OPPSs OVERVIEW OF THE SERIES C OUT-PERFORMANCE PROGRAM In May 2005, the Company's stockholders approved the Series C Out-Performance Program (the "Series C Program") pursuant to which executives and other key employees of UDR (the "Series C Participants") were given the opportunity to purchase interests in the Series C LLC (the LLC Interests), the only asset of which is the Series C Out-Performance Partnership Shares (i.e., the Series C OPPSs). The Series C Program is designed to provide the Series C Participants with the possibility of substantial returns on their investment if the total cumulative return on the Company's common stock, measured by the cumulative amount of dividends paid plus share price appreciation over a 36-month period from June 1, 2005 to May 30, 2008 (the "Measurement Period"), is at least the equivalent of a 36% total return, or 12% annualized ("Minimum Return"). At the end of the Measurement Period (i.e., May 30, 2008), if the total cumulative return on the Company's common stock satisfies these criteria, the Series C LLC, as holder of the Series C OPPSs, will receive distributions and allocations of income and loss from the Operating Partnership equal to the distributions and allocations that would be received on the number of OP Units obtained by: determining the amount by which the cumulative total return of the Company's common stock over the Measurement Period exceeds the Minimum Return (the "Excess Return"); multiplying 2% of the Excess Return by the Company's average market capitalization over the Measurement Period, up to a maximum of 1% of market capitalization and dividing by the 20-day volume-weighted average share price of Company's common stock on May 30, 2008. If, on May 30, 2008, the cumulative total return of the Company's common stock does not exceed the Minimum Return, the Series C Participants will forfeit their entire initial investment. 8


 

Houlihan Lokey Description of the Series C OPPSs RESTRICTIONS OF THE SERIES C OUT- PERFORMANCE PROGRAM The LLC Interests are subject to a number of restrictions not otherwise applicable to the OP Units, as summarized below: The Series C LLC has no right to receive distributions or allocations of income or loss from the Operating Partnership or to cause the Operating Partnership to redeem the Series C OPPSs prior to the earlier of (i) the expiration of the Measurement Period or (ii) the date of a change of control of the Company. The holders of the LLC Interests are not allowed to transfer, assign, convey, sell, encumber, or in any way alienate all or any part of his or her interest except (a) with the prior approval of the Board of Managers, which approval may be given or withheld at the sole discretion of the Board of Managers and (b) only after the Minimum Return has been achieved and a 36-month vesting period from the date of issuance of the interest has passed.3 The Series C OPPSs rank inferior to the other OP Units upon liquidation. 3 Operating Agreement, Section 9.1. 9


 

Houlihan Lokey Description of the Series C OPPSs CORPORATE STRUCTURE DIAGRAM Member Member Member Member UDR, Inc. Cash to purchase Membership Membership Interests Interests (and distributions Cash to if performance purchase OP threshold is met) Units Series C Out -Performance LLC United Dominion Realty , L.P. (Owns OP Units ) OP Units 10


 

Valuation Analysis


 


 

Houlihan Lokey Valuation Analysis LATTICE-BASED MODEL/MONTE CARLO SIMULATION APPROACH We used a trinomial lattice framework to simulate changes over time to the UDR common stock price. The UDR common stock price volatility input to the model is used to calculate the size and "risk-neutral" probability of each of the up-down movements through the nodes of the lattice model. up St +^ no change Current Stock Price (St) St down St ^ To traverse a full path through the lattice randomly, one of the three possible movements at each node on the path is randomly chosen by the Monte Carlo method consistent with the calculated probabilities, and this is repeated for a very large number of randomly selected paths. In valuing the Series C OPPSs, 1,000,000 paths are sampled through the trinomial lattice framework. Along each path, the payoff of the LLC Interests is calculated based on the contractual terms and the simulated UDR's common stock price performance. The payoff is discounted back to the beginning date of the lattice model. The security underlying the LLC Interests is the OP Unit which is assumed to be identical to UDR's common stock. The value of the LLC Interests is the expected value of the uncertain payoffs which is the average of the all the payoffs across the 1,000,000 simulated paths. Appendix A provides more detailed explanation of this valuation method and approach. 13


 

Houlihan Lokey Valuation Analysis PAYOFF CALCULATION The lattice model is set up for monthly time steps starting from the beginning through the end of the Measurement Period. For each time step between any two nodes along any path, the dividend for that monthly period paid at the ending node is calculated as the stock price at the beginning node multiplied by the pro-rated value of the dividend yield input. Over each monthly time step along any path, the accumulated dividends available at the beginning node are assumed to be reinvested in the stock itself and grow at the stock return rate over that time period along that path. At the end of any path, the Total Return is measured as the change in stock price between the beginning and end of that path, plus the dividends accumulated and grown by reinvesting over that path. The Excess Return at the end of any path is measured by the difference between the Total Return and the Minimum Return, where the Minimum Return is 36% of the stock price at the beginning of the path. The payoff cap for any path is calculated as 1% of the number of UDR common stock shares outstanding at the beginning of the path multiplied by the average stock price over the path. The total payoff to the Series C LLC at the end of any path is the smaller of the two: (i) the payoff cap and (ii) 2% of the Excess Return multiplied by the number of UDR common stock shares outstanding at the beginning of the path. The payoff for one LLC Interest is calculated as the total payoff divided by the number of authorized LLC Interests, 750,000. The value of one LLC Interest is calculated as the average payoff across all simulated paths and discounted back to the beginning of the Measurement Period (i.e., the valuation date). 14


 

Houlihan Lokey Valuation Analysis VALUATION INPUT: EXPECTED VOLATILITY Implied volatilities derived from exchange-traded options are preferred over historical volatilities as they reflect the market's forward-looking estimate of volatility and risk preferences. According to SEC's Staff Accounting Bulletin No. 107, "Implied volatility can be useful in estimating expected volatility because it is generally reflective of both historical volatility and expectations of how future volatility will differ from historical volatility." When valuing the Series C OPPSs as of June 1, 2005, a 3- year expected volatility for the period from June 1, 2005 through May 30, 2008 is required. Implied Volatility Approach On June 1, 2005, UDR's exchange-traded options were all short term with maturity ranging from 18 days to 7 months. The table below provides the implied volatilities of the at-the-money call and put options during the five trading days surrounding June 1, 2005: Call Option Put Option Date Date 5/27/2005 5/31/2005 6/1/2005 6/2/2005 6/3/2005 5/27/2005 5/31/2005 6/1/2005 6/2/2005 6/3/2005 Stock Price Stock Price Maturity $22.90 $23.05 $23.15 $23.04 $22.97 $22.90 $23.05 $23.15 $23.04 $22.97 6/18/2005 16.73% 18.44% 20.71% 18.64% 17.82% 18.74% 20.41% 19.39% 18.19% 17.57% 7/16/2005 18.46% 19.62% 20.98% 18.57% 18.78% 20.31% 20.72% 19.74% 17.69% 20.25% 10/22/2005 17.28% 17.79% 18.63% 18.11% 18.04% 19.14% 18.75% 19.11% 18.75% 18.24% 1/21/2006 19.20% 19.25% 19.22% 19.14% 19.79% 17.74% 17.38% 17.99% 17.31% 16.88% Source: OptionMetrics 15


 

Houlihan Lokey Valuation Analysis VALUATION INPUT: EXPECTED VOLATILITY (CONTINUED) Starting in January 2006, the maturity dates of UDR's exchange-traded options extended out to more than 24 months. For illustrative purposes, Appendix B depicts the daily term structure of the implied volatility of UDR's exchange- traded at-the-money call options from January 2007 through May 2007. Because of the mean- reverting nature commonly observed in the term structure of volatilities, UDR's longer-term options exhibited lower implied volatilities than its short-term options during this period. Appendix B also contains the calculations of UDR's long-term implied volatility as a percentage of its short-term implied volatility. During the period from January 2006 through May 2007, on an average basis, the implied volatility of the long-dated option (the longest maturity available at any given day) is approximately 80% of that of the short-term options.4 On June 1, 2005, the implied volatility of the short-term in-the- money call option is 20.71%. Using the relationship between short-term and long-term implied volatilities of 80%, the approximated 3-year expected volatility for UDR is 16.55%. This approach of deriving the long-term expected volatility benefits from the "hindsight reliance" as UDR's long-term exchange-traded options did not exist on June 1, 2005. But the time gap between June 2005 and January 2006 (the first available date for UDR's longer term exchange-traded options) is only approximately 7 months. In addition, this hindsight benefit is offset by the fact that the implied volatility of the at- the-money call option on June 1, 2005 is the highest of the 5 trading days, and it is also higher than the implied volatility of the at-the-money put option. Had an averaging method been used to compute the short-term implied volatility, the derived long-term expected volatility would have been lower: 4 In calculating the ratio, the short-term options are defined as observations with maturity 2 months or less and long-term options are those with maturity greater than 12 months. Certain observations are also excluded when the implied volatilities of certain long-term options are recorded as less than 10% or substantially higher than the volatilities of the short-term options. 16


 

Houlihan Lokey Valuation Analysis VALUATION INPUT: EXPECTED VOLATILITY (CONTINUED) Averaging the implied volatilities of the at-the-money call and put options on June 1, 2005: Short-term volatility: (20.71%+19.39%)/2 = 20.05% Long-term expected volatility: 20.05% * 0.8 = 16.04% Averaging the implied volatilities of the at-the-money call options from May 27 through June 3, 2005: Short-term volatility: (16.73%+18.44%+20.71%+18.64 %+17.82%)/5 = 18.74% Long-term expected volatility: 18.74% * 0.8 = 14.77% Blended Approach: Implied and Historical Volatility Since on June 1, 2005, UDR's exchange-traded options have terms less than one year, it may be prudent to consider other factors, such as the historical volatility. As of June 1, 2005, the historical volatility calculated using the 3-year look-back approach is 19.27%. The long-term expected volatility can also be estimated using a blended approach taking into consideration the general preference of putting more reliance on implied volatility. Taking two-thirds of the derived long-term implied volatility of 16.55% and one-thirds of the 3- year historical volatility of 19.27% gives rise to a weighted average expected volatility of 17.46%. The valuation of the LLC Interests is performed using the volatility input derived from both approaches. 17


 

Houlihan Lokey Valuation Analysis VALUATION INPUT: EXPECTED DIVIDEND YIELD The expected dividend yield is derived by annualizing the latest quarterly dollar dividend payout and dividing by the current stock price. Closest Dividend Payout Prior to June 1, 2005: April 13, 2005 Dollar Dividend: $0.30 per share Stock Price on June 1, 2005: $23.15 per share Expected Dividend Yield: ($0.30*4)/$23.15 = 5.18% 18


 


 

Houlihan Lokey Valuation Analysis DISCOUNT FOR LACK OF MARKETABILITY DISCOUNT OF THE UNDERLYING SHARES In the context of securities valuation, the term "marketability" refers to an investor's ability to convert an investment into cash, at the investor's discretion, with minimal cost, and a high degree of certainty. Registered securities which actively trade in a U.S.-based securities market are one of the best benchmarks of liquidity. All things being equal, investors prefer to invest in liquid assets. Accordingly, investors impose a discount to the price of assets that are not relatively liquid. Two reasons that investors discount the price of non- marketable (or illiquid) securities include: The number of potential buyers for non-controlling closely held securities is significantly smaller than the number of potential buyers for publicly traded securities. Financial institutions are rarely willing to hypothecate, or accept as loan collateral, closely held securities in the same manner as they would hypothecate publicly traded securities. APPLICABILITY TO THE LLC INTERESTS The gross value of the Series C OPPSs is determined based on UDR's publicly traded common stock. Thus, the determined gross value is on a publicly traded equivalent value (i.e., of equivalent marketability to the publicly traded securities from which the value was derived). However, the LLC Interests have substantially impaired marketability, contractual restrictions, and lower liquidation preference in comparison to the OP Units and UDR's publicly traded stock. Marketability is highly valued by investors, and therefore, the relative absence (lack) of marketability reduces an asset's fair value. A discount is needed to reflect the relative illiquidity and the restrictions of the LLC Interests. 20


 

Houlihan Lokey Valuation Analysis EMPIRICAL BASIS FOR A DISCOUNT FOR LACK OF MARKETABILITY For decades, valuation analysts have sought reliable, market- based evidence to aid in the quantification of discounts for lack of marketability. Three bodies of evidence have emerged from this research: (i) restricted stock studies; (ii) pre-IPO studies; and (iii) put option models. The table below summarizes the strengths and weaknesses of each approach and Appendix C provides detailed discussion: Line of Studies Observed Discounts Strengths Weaknesses Restricted Stock Studies of transactions Numerous studies over nearly The illiquidity of restricted Studies occurring prior to April 1997 30 years with consistent results. shares is only temporary as indicate discounts in a general Direct measurement of a liquid holders can sell shares after the range of approximately 25 to 35 and less-liquid security. restriction periods lapse. percent. Published studies heavily relied Thus, these studies Studies of transactions upon by practitioners and underestimate the discount for occurring after April 1997 courts. lack of marketability applicable indicated discounts in a general to a closely held security with range of approximately 10 to 20 long restriction period, such as percent. the LLC Interests. Pre-IPO Studies Three lines of studies covering Provides a more direct Fewer studies than those years 1980 to 2002 indicate comparison of the marketability pertaining to restricted stock. discounts in a general range of differences between closely held Passage of time between private 40 to 50 percent. shares and freely traded shares and public transaction may of a public company. introduce some "noise" in the Published studies heavily relied data. upon by practitioners and courts. Put Option Models The discount is positively Based on the actual methods Relatively recent introduction to correlated with the restriction that an investor can employ to practitioners. period and volatility. lock in a stock price during a period of non- marketability. 21


 

Houlihan Lokey Valuation Analysis ESTIMATING THE MARKETABILITY DISCOUNT: PUT OPTION APPROACH The use of put-option valuation models as a means of estimating marketability discounts has increased recently. By purchasing an option and guaranteeing a sale price at some point in the future, an investor has effectively "purchased" liquidity for the restricted shares. The price of the option therefore represents the cost of converting restricted securities into liquid assets. The calculated value of the put, expressed as a percentage of the market price of the shares, approximates the marketability discount. In other words, Non- marketable value = Marketable value - Put value. To quantify the amount of discount simply due to investors' inability to sell their holdings in adverse market conditions, the following parameters are used to estimate the value of the put option: Simulated average stock price at the end of the Measurement Period: According to the lattice-based Monte Carlo simulation model, the simulated average stock price is $22.04 per share (reflecting only the capital appreciation portion and not the cumulative dividends received during the 36-month vesting period). Long-term expected volatility: 16.55% and 17.46%.5 Restriction period or maturity: Unlike the regular restriction stock with a relatively short restriction period, upon meeting the vesting requirements, the holders of the LLC Interests own Series C LLC membership interests with an "infinite" restriction period. That equates to a put option with a perpetual (or indefinite) maturity date. For illustrative purposes, we have also estimated the value of the put option using a restriction period of one-, five- and 10-year assuming that the Company would be willing to provide a converting mechanism to buy the illiquid LLC Interests from the holders. Strike price: The analysis assumes that investors would not purchase the put option as a protection until the stock price increases by 10%, 20% and 30% with corresponding strike prices at $24.24, $26.44, and $28.65 respectively. 5 For consistent and illustrative purposes, the volatilities figures used in the estimating the gross value of the Series C OPPSs are used to estimate the put option value. 22


 

Houlihan Lokey Valuation Analysis ESTIMATING THE MARKETABILITY DISCOUNT: PUT OPTION APPROACH (CONTINUED) Volatility = 16.55% Time-to-Maturity I: Strike = $24.24 II: Strike = $26.44 III: Strike Price = $28.65 (Year) Put Value % as of Stock Price Put Value % as of Stock Price Put Value % as of Stock Price 1 $ 1.73 7.84% $1.89 8.56% $2.04 9.27% 5 $ 3.73 16.94% $4.07 18.48% $4.41 20.02% 10 $4.69 21.28% $5.12 23.21% $5.54 25.15% Perpetual $6.77 30.74% $7.39 33.54% $8.01 36.33% Volatility = 17.46% Time-to-Maturity I: Strike = $24.24 II: Strike = $26.44 III: Strike Price = $28.65 (Year) Put Value % as of Stock Price Put Value % as of Stock Price Put Value % as of Stock Price 1 $ 1.81 8.22% $1.98 8.97% $2.14 9.72% 5 $ 3.88 17.63% $4.24 19.23% $4.59 20.83% 10 $4.85 22.03% $5.30 24.03% $5.74 26.03% Perpetual $7.01 31.79% $7.64 34.68% $8.28 37.57% As shown, the longer the restriction period, the higher the put option value (or the greater the marketability discount).6 The marketability discount estimated assuming perpetual restriction ranges from 30.74% to 36.34% (based on a long-term expected volatility of 16.55%) and from 31.79% to 37.57% (based on a long-term expected volatility of 17.46%). This analysis attempts to quantify the discount due to illiquidity or lack of marketability. It does not capture other discounts arising from other contractual restrictions or the lack of liquidation preferences imposed on the LLC Interests. 6 The marketability discount is calculated by dividing the put option value by the simulated average stock price of $22.04 at the end of the Measurement Period. For put option with a finite maturity (i.e., 1, 5 and 10 years), the standard Black- Scholes option pricing model is used. For the put option with a perpetual maturity, the value is estimated based on the model and approach described in the following publications: H.U. Gerber and S. W. Shiu, "Martingale Approach to Pricing Perpetual American Options," ASTIN Bulletin International Actuarial Association, 1994, pp. 195-220; and Espen Gaarder Haug, The Complete Guide to Option Pricing Formulas, New York: The McGraw-Hill Companies, 2007, Chapter 3. 23


 

Appendices


 

Appendices Trinomial Lattice/Monte Carlo Simulation Valuation Framework Implied Volatilities: Short- Term vs. Long-Term Empirical Basis for a Discount for Lack of Marketability Selected Biographies


 

Houlihan Lokey Trinomial Lattice/Monte Carlo Simulation Valuation Framework SAMPLING THROUGH THE TRINOMIAL TREE V1 V2 V3 V4 V1,000,000 26


 

Houlihan Lokey Trinomial Lattice/Monte Carlo Simulation Valuation Framework TRINOMIAL LATTICE FRAMEWORK Based on the theoretical framework represented by the continuous-time stochastic differential equation: dS =(r d)Sdt +^SdW where S is the stock price r is the risk-free rate d is the continuous dividend yield ^ is the volatility W is the continuous-time Wiener process with a mean of zero and variance equal to dt The trinomial lattice is constructed from the discrete- time version: dx =^dt +^dW where x =ln(S), ^=(r-d)-^2 / 2 W is the continuous-time Wiener process with a mean of zero and variance equal to dt 27


 

Houlihan Lokey Trinomial Lattice/Monte Carlo Simulation Valuation Framework TRINOMIAL LATTICE FRAMEWORK (CONTINUED) Consider a trinomial model in which, over a small time interval ^t , the asset price can go up by ^x , stay the same or go down by ^x , with probabilities pu , pm and pd respectively. Match the first and second moments between the continuous time process and the trinomial tree over the time interval ^t to solve for respective probabilities E[^x] =pu (^x) +pm (0) +pd ( ^x) =^^t E[^x2 ] =p (^x2 ) +p (0) +p (^x2 ) =^2 ^t +^2 ^t 2 u m d pu +pm +pd =1 The probabilities for the up, down and middle movements possible at any node are thus given by pu =(a +b) / 2 pd =(a b) / 2 pm =1 ( pu +pd ) where a =(^2 ^t +^2 ^t 2 ) / ^x2 b =^^t / ^x ^x =^ 3^t Reference: Les Clewlow and Chris Strickland. Implementing Derivatives Model. New York: John Wiley & Sons, 1998. 28


 

Appendices Trinomial Lattice/Monte Carlo Simulation Valuation Framework Implied Volatilities: Short- Term vs. Long-Term Empirical Basis for a Discount for Lack of Marketability Selected Biographies


 

Houlihan Lokey Implied Volatilities: Short- Term vs. Long-Term TERM STRUCTURE OF IMPLIED VOLATILITIES January 2007 45% 40% 35% 30% Volatility 25% Implied 20% 15% 10% 5% 0% 0 0.5 1 1.5 2 2.5 Time Until Expiration (Years) 30


 

Houlihan Lokey Implied Volatilities: Short- Term vs. Long-Term TERM STRUCTURE OF IMPLIED VOLATILITIES (CONTINUED) February 2007 50% 45% 40% 35% Volatility 30% 25% Implied 20% 15% 10% 5% 0% 0 0.5 1 1.5 2 2.5 T ime Until Expiration (Years) 31


 

Houlihan Lokey Implied Volatilities: Short- Term vs. Long-Term TERM STRUCTURE OF IMPLIED VOLATILITIES (CONTINUED) March 2007 60% 50% Volatility 40% 30% Implied 20% 10% 0% 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time Until Expiration 32


 

Houlihan Lokey Implied Volatilities: Short- Term vs. Long-Term TERM STRUCTURE OF IMPLIED VOLATILITIES (CONTINUED) April 2007 35% 30% 25% Volatility 20% Implied 15% 10% 5% 0% 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time Until Expiration (Years) 33


 

Houlihan Lokey Implied Volatilities: Short- Term vs. Long-Term TERM STRUCTURE OF IMPLIED VOLATILITIES (CONTINUED) May 2007 50% 45% 40% 35% Volatility 30% 25% Implied 20% 15% 10% 5% 0% 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time Until Expiration (Years) 34


 

Houlihan Lokey Implied Volatilities: Short- Term vs. Long-Term LONG-TERM VOLATILITY AS A RATIO OF SHORT- TERM VOLATILITY Implied Volatility Implied Volatility Date Maturity (<=2m) Maturity (>=12m) Ratio Date Maturity (<=2m) Maturity (>=12m) Ratio 1/17/2006 30.98% 18.76% 0.61 3/22/2006 21.01% 19.36% 0.92 1/18/2006 33.79% 18.78% 0.56 3/23/2006 20.36% 19.09% 0.94 1/19/2006 18.51% 17.88% 0.97 3/24/2006 23.50% 19.54% 0.83 1/20/2006 20.22% 18.29% 0.90 3/27/2006 26.55% 18.88% 0.71 1/23/2006 18.40% 18.42% 1.00 3/28/2006 21.52% 18.74% 0.87 1/24/2006 18.85% 18.60% 0.99 3/30/2006 22.39% 21.27% 0.95 1/25/2006 19.32% 18.54% 0.96 3/31/2006 22.85% 18.98% 0.83 1/27/2006 20.33% 19.97% 0.98 4/3/2006 27.83% 21.37% 0.77 1/30/2006 19.05% 19.91% 1.05 4/4/2006 30.94% 20.01% 0.65 2/1/2006 18.44% 19.02% 1.03 4/5/2006 28.81% 19.84% 0.69 2/2/2006 19.15% 19.65% 1.03 4/6/2006 32.55% 20.11% 0.62 2/3/2006 22.62% 20.84% 0.92 4/7/2006 36.97% 20.27% 0.55 2/6/2006 20.17% 20.41% 1.01 4/10/2006 45.46% 20.71% 0.46 2/7/2006 19.27% 18.05% 0.94 4/11/2006 58.67% 23.15% 0.39 2/8/2006 19.12% 18.22% 0.95 4/13/2006 21.68% 21.56% 0.99 2/13/2006 19.94% 17.70% 0.89 4/17/2006 22.82% 21.15% 0.93 2/14/2006 18.79% 17.82% 0.95 4/18/2006 22.44% 20.36% 0.91 2/15/2006 17.71% 15.85% 0.89 4/19/2006 21.33% 20.06% 0.94 2/16/2006 17.97% 15.22% 0.85 4/20/2006 22.53% 20.58% 0.91 2/17/2006 18.39% 16.13% 0.88 4/21/2006 21.23% 20.22% 0.95 2/21/2006 19.95% 16.58% 0.83 4/24/2006 21.51% 19.54% 0.91 2/22/2006 16.90% 16.35% 0.97 4/25/2006 27.04% 18.87% 0.70 2/24/2006 18.67% 17.22% 0.92 4/26/2006 29.61% 20.90% 0.71 2/27/2006 22.42% 16.34% 0.73 4/27/2006 26.06% 19.53% 0.75 3/1/2006 16.49% 16.58% 1.01 5/1/2006 23.43% 18.74% 0.80 3/2/2006 16.84% 17.07% 1.01 5/2/2006 19.71% 18.95% 0.96 3/3/2006 16.94% 17.46% 1.03 5/3/2006 18.94% 19.62% 1.04 3/8/2006 16.66% 15.74% 0.94 5/5/2006 20.29% 19.29% 0.95 3/9/2006 19.82% 16.98% 0.86 5/8/2006 40.54% 16.73% 0.41 3/14/2006 78.39% 16.17% 0.21 5/9/2006 39.31% 17.44% 0.44 3/15/2006 19.81% 18.44% 0.93 5/10/2006 42.93% 17.60% 0.41 3/21/2006 24.58% 21.46% 0.87 5/11/2006 49.21% 18.24% 0.37 35


 

Houlihan Lokey Implied Volatilities: Short- Term vs. Long-Term LONG-TERM VOLATILITY AS A RATIO OF SHORT- TERM VOLATILITY (CONTINUED) Implied Volatility Implied Volatility Date Maturity (<=2m) Maturity (>=12m) Ratio Date Maturity (<=2m) Maturity (>=12m) Ratio 5/16/2006 21.55% 18.72% 0.87 7/13/2006 37.05% 19.23% 0.52 5/17/2006 19.05% 18.52% 0.97 7/14/2006 24.70% 19.74% 0.80 5/18/2006 28.18% 27.52% 0.98 7/17/2006 18.51% 18.85% 1.02 5/19/2006 20.96% 17.08% 0.81 7/19/2006 22.91% 19.07% 0.83 5/22/2006 20.52% 18.38% 0.90 7/20/2006 24.79% 19.21% 0.77 5/23/2006 18.70% 18.80% 1.01 7/21/2006 21.74% 18.90% 0.87 5/24/2006 19.32% 17.24% 0.89 7/25/2006 26.15% 19.13% 0.73 6/1/2006 18.09% 18.63% 1.03 7/26/2006 27.23% 24.40% 0.90 6/2/2006 33.97% 25.98% 0.76 7/27/2006 28.79% 24.75% 0.86 6/5/2006 39.51% 18.88% 0.48 7/28/2006 24.22% 23.65% 0.98 6/6/2006 44.18% 18.25% 0.41 7/31/2006 29.06% 24.35% 0.84 6/7/2006 43.21% 18.28% 0.42 8/1/2006 26.78% 23.70% 0.88 6/9/2006 49.44% 18.10% 0.37 8/2/2006 28.85% 18.38% 0.64 6/12/2006 21.15% 20.01% 0.95 8/3/2006 31.07% 17.78% 0.57 6/13/2006 19.58% 19.25% 0.98 8/4/2006 26.22% 17.09% 0.65 6/16/2006 20.65% 19.45% 0.94 8/7/2006 28.81% 24.92% 0.87 6/19/2006 19.04% 19.56% 1.03 8/8/2006 37.37% 24.13% 0.65 6/20/2006 18.68% 19.57% 1.05 8/9/2006 40.75% 25.06% 0.61 6/21/2006 19.64% 18.48% 0.94 8/10/2006 46.17% 25.70% 0.56 6/22/2006 20.82% 17.72% 0.85 8/14/2006 70.32% 25.91% 0.37 6/23/2006 21.40% 18.37% 0.86 8/15/2006 75.15% 25.53% 0.34 6/26/2006 19.19% 18.46% 0.96 8/23/2006 17.56% 17.61% 1.00 6/27/2006 20.82% 19.08% 0.92 8/30/2006 17.20% 16.94% 0.99 6/28/2006 18.05% 17.89% 0.99 9/5/2006 17.40% 17.20% 0.99 6/29/2006 30.55% 17.60% 0.58 9/7/2006 18.47% 18.20% 0.99 7/3/2006 25.64% 18.65% 0.73 9/11/2006 20.76% 18.33% 0.88 7/5/2006 26.09% 18.35% 0.70 9/13/2006 20.07% 18.21% 0.91 7/6/2006 27.48% 18.84% 0.69 9/14/2006 18.49% 18.58% 1.01 7/7/2006 31.09% 18.43% 0.59 9/15/2006 19.76% 18.33% 0.93 7/10/2006 33.78% 18.92% 0.56 9/18/2006 18.07% 18.33% 1.01 7/11/2006 35.99% 18.30% 0.51 9/19/2006 20.45% 18.57% 0.91 7/12/2006 43.94% 24.60% 0.56 9/20/2006 18.81% 18.61% 0.99 36


 

Houlihan Lokey Implied Volatilities: Short- Term vs. Long-Term LONG-TERM VOLATILITY AS A RATIO OF SHORT- TERM VOLATILITY (CONTINUED) Implied Volatility Implied Volatility Date Maturity (<=2m) Maturity (>=12m) Ratio Date Maturity (<=2m) Maturity (>=12m) Ratio 9/21/2006 19.03% 18.87% 0.99 11/27/2006 22.41% 19.52% 0.87 9/22/2006 18.12% 17.43% 0.96 11/28/2006 24.34% 22.60% 0.93 9/25/2006 20.08% 18.46% 0.92 11/29/2006 21.97% 16.91% 0.77 9/26/2006 20.09% 17.03% 0.85 11/30/2006 21.50% 17.41% 0.81 9/27/2006 19.21% 18.14% 0.94 12/1/2006 21.08% 17.01% 0.81 9/28/2006 19.54% 18.40% 0.94 12/4/2006 22.78% 17.42% 0.76 9/29/2006 19.65% 18.47% 0.94 12/5/2006 25.40% 17.42% 0.69 10/2/2006 19.11% 17.40% 0.91 12/6/2006 26.29% 17.77% 0.68 10/3/2006 18.84% 18.68% 0.99 12/7/2006 32.47% 28.61% 0.88 10/4/2006 19.83% 19.31% 0.97 12/8/2006 35.52% 28.98% 0.82 10/5/2006 22.53% 17.91% 0.79 12/11/2006 44.39% 28.30% 0.64 10/6/2006 22.67% 18.40% 0.81 12/12/2006 57.86% 29.02% 0.50 10/9/2006 26.40% 17.75% 0.67 12/14/2006 19.62% 19.03% 0.97 10/10/2006 30.80% 17.53% 0.57 12/18/2006 20.51% 18.37% 0.90 10/11/2006 36.86% 18.65% 0.51 12/19/2006 18.76% 17.75% 0.95 10/12/2006 20.37% 18.34% 0.90 12/22/2006 18.31% 18.13% 0.99 10/13/2006 17.97% 16.38% 0.91 12/27/2006 19.66% 18.57% 0.94 10/17/2006 42.52% 18.18% 0.43 12/28/2006 18.21% 17.70% 0.97 10/18/2006 17.61% 17.88% 1.02 12/29/2006 17.60% 18.34% 1.04 10/19/2006 18.77% 17.88% 0.95 1/3/2007 19.11% 17.87% 0.93 10/24/2006 18.48% 18.27% 0.99 1/4/2007 20.11% 18.22% 0.91 10/31/2006 17.46% 17.79% 1.02 1/5/2007 19.82% 18.56% 0.94 11/3/2006 18.34% 17.62% 0.96 1/8/2007 19.16% 17.95% 0.94 11/6/2006 20.27% 17.92% 0.88 1/9/2007 18.77% 16.99% 0.91 11/7/2006 19.10% 18.97% 0.99 1/10/2007 40.03% 16.20% 0.40 11/8/2006 22.00% 18.36% 0.83 1/11/2007 18.96% 16.11% 0.85 11/9/2006 20.32% 18.38% 0.90 1/16/2007 19.80% 16.78% 0.85 11/10/2006 18.48% 18.56% 1.00 1/18/2007 21.47% 19.45% 0.91 11/13/2006 19.09% 18.65% 0.98 1/19/2007 20.10% 15.81% 0.79 11/14/2006 18.41% 18.61% 1.01 1/24/2007 22.70% 16.01% 0.71 11/15/2006 18.96% 18.99% 1.00 1/25/2007 22.88% 15.83% 0.69 11/22/2006 22.86% 17.92% 0.78 1/29/2007 27.66% 16.75% 0.61 37


 

Houlihan Lokey Implied Volatilities: Short- Term vs. Long-Term LONG-TERM VOLATILITY AS A RATIO OF SHORT- TERM VOLATILITY (CONTINUED) Implied Volatility Implied Volatility Date Maturity (<=2m) Maturity (>=12m) Ratio Date Maturity (<=2m) Maturity (>=12m) Ratio 1/31/2007 23.14% 15.62% 0.68 4/4/2007 18.17% 18.55% 1.02 2/1/2007 23.68% 15.40% 0.65 4/5/2007 18.77% 15.99% 0.85 2/2/2007 24.11% 16.33% 0.68 4/9/2007 18.03% 17.48% 0.97 2/5/2007 27.04% 16.34% 0.60 4/10/2007 30.47% 18.73% 0.61 2/7/2007 19.33% 15.27% 0.79 4/11/2007 31.96% 19.86% 0.62 2/8/2007 23.58% 16.64% 0.71 4/12/2007 21.75% 19.45% 0.89 2/9/2007 23.53% 15.57% 0.66 4/16/2007 23.63% 19.44% 0.82 2/12/2007 39.34% 16.28% 0.41 4/18/2007 20.50% 19.80% 0.97 2/13/2007 33.68% 14.08% 0.42 4/19/2007 20.99% 19.60% 0.93 2/14/2007 46.62% 16.44% 0.35 4/20/2007 20.29% 19.34% 0.95 2/15/2007 15.53% 15.77% 1.02 4/23/2007 18.16% 18.20% 1.00 2/16/2007 16.06% 16.66% 1.04 4/24/2007 19.04% 14.37% 0.75 2/20/2007 15.39% 14.99% 0.97 4/27/2007 24.29% 10.05% 0.41 2/23/2007 17.97% 17.23% 0.96 4/30/2007 19.31% 12.96% 0.67 2/27/2007 23.50% 21.76% 0.93 5/2/2007 22.95% 18.27% 0.80 3/1/2007 32.11% 16.91% 0.53 5/3/2007 18.25% 11.15% 0.61 3/2/2007 26.85% 19.27% 0.72 5/4/2007 19.98% 11.58% 0.58 3/5/2007 38.34% 18.84% 0.49 5/7/2007 20.20% 10.34% 0.51 3/6/2007 26.62% 19.10% 0.72 5/8/2007 21.39% 10.42% 0.49 3/7/2007 26.02% 18.81% 0.72 5/9/2007 22.71% 10.71% 0.47 3/9/2007 22.41% 18.85% 0.84 5/10/2007 25.96% 10.81% 0.42 3/12/2007 31.57% 18.87% 0.60 5/15/2007 35.26% 11.16% 0.32 3/13/2007 54.53% 18.64% 0.34 5/16/2007 46.02% 10.28% 0.22 3/16/2007 21.27% 19.80% 0.93 5/17/2007 19.95% 11.61% 0.58 3/19/2007 24.96% 19.39% 0.78 5/18/2007 19.90% 11.16% 0.56 3/23/2007 27.21% 18.95% 0.70 5/21/2007 22.04% 14.91% 0.68 3/26/2007 24.88% 20.18% 0.81 5/24/2007 19.40% 19.24% 0.99 3/27/2007 27.48% 19.52% 0.71 5/25/2007 18.58% 11.76% 0.63 3/28/2007 22.53% 18.45% 0.82 3/29/2007 23.77% 20.54% 0.86 Average 0.80 4/2/2007 19.89% 17.58% 0.88 4/3/2007 18.72% 18.73% 1.00 38


 

Appendices Trinomial Lattice/Monte Carlo Simulation Valuation Framework Implied Volatilities: Short-Term vs. Long-Term Empirical Basis for a Discount for Lack of Marketability Selected Biographies


 

Houlihan Lokey Empirical Basis For A Discount for Lack of Marketability RESTRICTED STOCK STUDIES The general methodology of restricted stock studies is to compare the price at which restricted shares of publicly traded companies transacted with the price at which the same company's freely traded shares traded on the same day. Typically, the restricted shares transact at a discount to the freely traded shares, which provides direct evidence that investors demand a discounted price for a security with impaired marketability relative to the same security with unimpaired marketability. The observed transactions involve shares which are unregistered, but are sold under the "safe harbor" exemptions of Rule 144. Prior to the amendment of Rule 144 in 1997, the initial holding period for restricted securities was 24 months. The amendment reduced the holding period to 12 months. Once the holding period requirements have been met, the restricted shares may be sold into the public markets subject to certain volume restrictions which generally conclude after an additional 12 months. The following table summarizes the key restricted stock studies that examined transactions which occurred since the amendment of Rule 144 in 1997. Restricted Stock Studies: Transactions Which Occurred After April 29, 1997 Indicated Discount Years Number of Covered Study Transactions Mean Median 1997-2003 Houlihan Lokey 324 3.7% 8.4% 1997- 2005 FMV Opinions 231 21.8% 18.3% 1997-98 Columbia Financial Advisors 15 13.0% 9.0% 40


 

Houlihan Lokey Empirical Basis For A Discount for Lack of Marketability RESTRICTED STOCK STUDIES (CONTINUED) The following table summarizes the key restricted stock studies that examined transactions which occurred prior to the amendment of Rule 144 in 1997. Restricted Stock Studies: Transactions Which Occurred Before April 29, 1997 Indicated Discount Years Number of Covered Study Transactions Mean Median 1991-97 Houlihan Lokey 114 20.9% 17.1% 1980- 97 FMV Opinions 244 22.1% 20.0% 1996-97 Columbia Financial Advisors 23 21.0% 14.0% 1980-96 Management Planning 53 27.0% 25.0% 1991-95 Munroe, Park & Johnson 72 20.0% NA 1980-91 UCLA 44 25.0% 24.0% 1981-88 Silber 69 34.0% NA 1981-84 Willamette Management Associates 33 NA 31.0% 1978-82 Standard Research Consultants 28 NA 45.0% 1969-73 Maher 34 35.0% 33.0% 1968-72 Moroney 146 36.0% 33.0% 1968-72 Trout 60 33.0% NA 1968-70 Gelman 89 33.0% 33.0% 1966-69 Institutional Investor (SEC) 398 26.0% 26.0% As shown in the tables above, the studies of restricted stock transactions occurring prior to the amendment of Rule 144 in April 1997 indicate discounts in a general range of approximately 25 to 35 percent. However, the more recent studies of restricted stock transactions indicate somewhat smaller discounts in a general range of approximately 10 to 20 percent. This result is not surprising since the amendment of Rule 144 in 1997 served to shorten the length of the holding period restriction. Furthermore, this result confirms that investors demand greater discounts for securities with longer restrictions and more impaired marketability. 41


 

Houlihan Lokey Empirical Basis For A Discount for Lack of Marketability PRE-IPO STUDIES These studies analyze the private transaction prices (generally management stock purchases) associated with companies which subsequently (generally within one year) go public. The private transaction prices are then compared to the IPO prices to gauge the impact of lack of marketability. Like the restricted stock studies, the pre-IPO studies make comparisons against a baseline of freely traded stock in a public company. However, because the measure of comparison in the pre-IPO studies is nonmarketable stock in a closely held company, the resulting discounts may provide more direct evidence of the discount for lack of marketability applicable to a security that is truly nonmarketable (as opposed to temporarily restricted shares of publicly traded companies). Summary descriptions of the three leading pre-IPO studies follows: Emory & Co. conducted a series of nine pre-IPO studies covering the years 1980-2000. The Emory studies compare the prices of stock transactions occurring within five months prior to an IPO to the subsequent IPO price. Cumulatively, the Emory studies include 543 transactions and show revised mean and median discounts of 46 and 47 percent, respectively. Valuation Advisors conducted a series of three pre-IPO studies covering the years 1999-2001. The Valuation Advisors studies compare the prices of stock transactions occurring within certain periods up to 24 months prior to an IPO to the subsequent IPO price. For the transactions occurring between one and two years prior to the company's IPO, the mean observed discounts were 77.2, 71.6, and 49.3 percent, in 1999, 2000, and 2001, respectively. Willamette Management Associates conducted a series of pre-IPO studies coving the years 1975-2002. The studies compare the prices of stock transactions occurring within 36 months prior to an IPO to the subsequent IPO price. The studies make adjustment for changes in industry valuation and company earnings between the dates of the IPO and the prior transaction. Cumulatively, the studies include 1,080 transactions, with mean discounts for the individual studies ranging from 24.2 to 55.6 percent, and median discounts for the individual studies ranging from 31.8 to 62.7 percent. 42


 

Houlihan Lokey Empirical Basis For A Discount for Lack of Marketability PUT OPTION MODELS There are three different put option approaches: David Chaffe (1993) proposes that the discount for lack of marketability could be approximated by the value of a European put option, struck at the market price of the underlying security at the time of purchase of the restricted shares. The Chaffe model incorporates certain simplifying assumptions including no dividend payments by the underlying security. The Chaffe model protects the investor from a drop in the stock price over the term of the restricted period. However, it ignores the opportunity cost of not being able to trade in the event that prices rise in the future.7 Francis Longstaff (1995) proposes that the owner of non-marketable shares has in effect given up a "look-back" put option. A look-back put conveys the right to sell at the highest price attained by the subject shares during the life of the option. If investors feel that they can time the market, they will demand the value of a look-back put as the price for giving up marketability.8 John Finnerty (1997) assumes that an investor in restricted stock can purchase an average-strike or "Asian" put option on an equal number of shares with a time to expiration that matches the restriction period. Finnerty hypothesizes that investors have no special ability to time the market; his model is therefore based on Asian put options. An average- strike put conveys the right to sell at the average price attained by the subject shares during the life of the option. Thus, if investors cannot time the market, the restriction has the effect of depriving them of average trading profits. 9 7 David N.H. Chaffe, "Option Pricing as a Proxy for Discount for Lack of Marketability in Private Company Valuations," Business Valuation Review, December 1993. 8 Francis A. Longstaff, "How Much Can marketability Affect Security Values?" The Journal of Finance, December 1995. 9 John Finnerty, "The Impact of Transfer Restriction on Stock Prices," Working Paper, Fordham University, June 2003. 43


 

Appendices Trinomial Lattice/Monte Carlo Simulation Valuation Framework Implied Volatilities: Short-Term vs. Long-Term Empirical Basis for a Discount for Lack of Marketability Selected Biographies


 

Houlihan Lokey Selected Biographies CINDY W. MA, PH.D., CPA, CFA Dr. Ma is a Managing Director in the New York Office of Houlihan Lokey Howard & Zukin where her primary responsibilities as part of the firm's financial advisory practice include providing valuations, financial opinions, and expert witness testimony. She leads the firm's Derivatives and Risk Management Practice and is a member of the firm's Technical Standards Committee. She has over 18 years of extensive training, academic expertise and hands-on experience in commodities, derivatives, securities, structured transactions, hedging strategies, and risk management issues. She has a deep understanding of the economic, operational and institutional aspects of futures, forward, swap and option markets. Dr. Ma joined Houlihan Lokey from NERA Economic Consulting where she established and led the Employee Stock Options Valuation Practice. Prior to that, she was a Partner at Ernst & Young. She directed a number of significant litigation projects related to derivatives valuation, securities trading, hedging and risk management. She also advised the boards of directors of energy and financial companies on risk management, valuation and corporate governance issues. For over five years, she traded derivatives and designed new risk management products for a global commodity firm. Dr. Ma served as an adjunct professor at Columbia University where she taught a MBA course in futures and options. She also developed several corporate training programs on the complex aspects of capital markets. Dr. Ma graduated from Columbia University Graduate School of Business with a Ph.D. in Finance and from Indiana University with highest distinction with a B.S. in Accounting. She is a Chartered Financial Analyst and a Certified Public Accountant. She was also a member of the Financial Accounting Standards Board's Option Valuation Group. Dr. Ma has published several articles on energy, derivatives, risk management, valuation and corporate governance. She did her Ph.D. thesis in energy futures and options markets. She also co- authored a college textbook on futures and options. 45


 

Houlihan Lokey Selected Biographies JEFFREY S. TARBELL, ASA, CFA Mr. Tarbell is a senior vice president of Houlihan Lokey where his primary responsibilities as part of the firm's financial advisory practice include providing financial opinions including valuations, fairness opinions, and expert witness testimony. He is the co-head of the firm's Estate and Gift Tax valuation services group and is a member of the firm's Technical Standards Committee. Mr. Tarbell has more than 16 years of experience providing financial opinions and related advisory services to private and publicly traded companies in connection with corporate transactions. Prior to joining Houlihan Lokey, Mr. Tarbell was a principal and national director of financial advisory services for a national valuation firm. Prior to that he was a vice president in the M&A group of a boutique investment banking firm. Mr. Tarbell earned an M.B.A. from the University of Chicago Graduate School of Business and a B.S. from the University of Oregon. He is an accredited senior appraiser (ASA), certified in business valuation, of the American Society of Appraisers and a chartered financial analyst (CFA) of the CFA Institute. He is a member of the Portland Society of Financial Analysts, the National Center for Employee Ownership (NCEO). He is also a member of the Valuation Advisory Committee of The ESOP Association and the Steering Committee of the Oregon Technology Awards. He is an associate member of the National Association of Corporation Directors (NACD), the American Bar Association (ABA), the Oregon State Bar, and the Washington State Bar. He is licensed with the NASD as a General Securities Registered Representative (Series 7 and 63). Mr. Tarbell has qualified and testified as an expert witness in United States District Court, United States Tax Court, and in arbitration and deposition proceedings. On more than 50 occasions he has served as a consultant to attorneys during the litigation and dispute resolution processes. 46


 

Houlihan Lokey Selected Biographies SUNIL PANIKKATH, PH.D. Dr. Panikkath is a Vice President in the New York office of Houlihan Lokey Howard & Zukin where his primary responsibilities as part of the firm's Financial Advisory Services practice include providing client advice and expert testimony on derivatives valuation and risk management. Dr. Panikkath's work covers various aspects of the valuation of financial instruments and the statistical and econometric analysis of financial markets, including employee stock option valuation and the analysis of structured financial derivatives. Prior to joining Houlihan Lokey, Dr. Panikkath was with NERA Economic Consulting where his work covered valuation, risk analysis and risk measurement methodology and practice recommendations for various clients including commodity trading firms, hedge funds and large corporations. He also analyzed the structure and valuation of equity-based compensations schemes for several different corporate clients. Prior to NERA, Dr. Panikkath was at SAS Institute Inc., a leading provider of business analytical software solutions. At SAS, he held various positions across research and development, sales and marketing and client advisory. He was one of the principal designers of the firm's offering for enterprise-wide risk management. His contributions included the development of a Monte Carlo methodology based on the statistical idea of copulas for integrated risk measurement in large-scale problems. He advised a variety of clients in the financial services and energy industries across the globe on enterprise risk measurement and the effective and efficient implementation of enterprise risk technology. He also managed and participated in multiple engagements in risk technology implementation, including designing the overall architecture, writing the project plan, and designing and developing specific components. Dr. Panikkath received his Ph.D and M.S.B.A. in financial economics from Washington University in St. Louis. He received his undergraduate degree in Electrical Engineering from the Indian Institute of Technology in Madras. 47


 

Houlihan Lokey Selected Biographies DANIEL F. YU Mr. Yu is a Financial Analyst in the New York office of Houlihan Lokey Howard & Zukin. His primary responsibilities are to provide quantitative analysis for the Derivatives/Risk Management Practice. He has a strong background in programming including SAS, C/C++, and VBA and has extensive experience in derivatives valuation with different types of lattice-based models. Prior to joining Houlihan Lokey, he was an Analyst at NERA Economic Consulting where he performed quantitative analysis and derivatives valuation. He worked on many valuation projects on employee stock options and had extensive experience in the cleaning, standardization, analysis and modeling of employee exercise data. Mr. Yu obtained his M.S.E. in Financial Engineering from the University of Michigan, Ann Arbor and B.S. degree from Fudan University in China. He is a CFA Level 3 candidate and a member of Global Association of Risk Professionals (GARP). He has also finished the examination requirements for the Financial Risk Manager (FRM) certification. 48