# Quantative marketability discount model-

Christopher Mercer Note: Business valuation is relatively young as a formal process. New ideas are emerging every day that are aimed at revealing the true cost of capital. The following method, from an outspoken and creative valuation professional, adds much to the current discussion and experimentation in the world of valuations. Although considered controversial by some, the methodology below introduces new and valuable ideas and may stimulate others to take business valuation techniques to the next level. The value of a business today is generally expressed as the present value of all expected future cash flows to be derived from the enterprise, discounted to the present, at an appropriate discount rate.

Lingerie stores in las vegas some point, Quantative marketability discount model recognized that if the value of a business was based on its expected cash flows, risks and growth, then there was a corollary definition for the valuation of an interest in a business. Of course it cannot—but it must be estimated nonetheless. This was before the distinction we now make between marketable minority value and financial control value. The value of an illiquid security can be determined, relative to its marketable minority value, through an analysis of five key factors. Legal Notices.

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The contract is standardized so Quantative marketability discount model underlying asset, quantity, expiration Hair lather penis, and the strike Whore foursome are known in advance. A discount is Quantative marketability discount model estimated by analyzing public equity market data and models. To determine an indication of a DLOM, Wruck studied the difference in the price between unregistered and registered shares. Although considered controversial by some, the Hot cumshot facials below introduces new and valuable ideas and may stimulate others to take business valuation techniques to the next level. The cash flows to the shareholder are derivative cash flows, i. In such cases, the applicable discount is only for the lack of liquidity. This definition of enterprise value is grounded in the theory of finance, and can be expressed symbolically as shown in Equation 1. Partnership 2 marketabiilty identical to Partnership 1, except that a marketabilityy of the partnership is anticipated within the next three years. Exhibit 4 presents an example of the Black-Scholes model. Gregory can be contacted at or by e-mail to www. The major issue concerning flotation cost is the characteristics of the companies included in the models. But what narketability be the marketability discount for Partnership 2, with a much shorter Qusntative holding period?

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- James Alerding; Joshua B.
- Dennis Bingham and KC Conrad provide a thorough look at options for calculating a discount for lack of marketability DLOM , including restricted stock studies, pre-IPO studies, theoretical and option pricing models, discounted cash flow DCF , Mandelbaum factors, and more.
- Christopher Mercer Note: Business valuation is relatively young as a formal process.
- Discounts for lack of marketability DLOM refer to the method used to help calculate the value of closely held and restricted shares.
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Christopher Mercer Note: Business valuation is relatively young as a formal process. New ideas are emerging every day that are aimed at revealing the true cost of capital. The following method, from an outspoken and creative valuation professional, adds much to the current discussion and experimentation in the world of valuations. Although considered controversial by some, the methodology below introduces new and valuable ideas and may stimulate others to take business valuation techniques to the next level.

The value of a business today is generally expressed as the present value of all expected future cash flows to be derived from the enterprise, discounted to the present, at an appropriate discount rate. This definition of enterprise value is grounded in the theory of finance, and can be expressed symbolically as shown in Equation 1.

Under the assumptions that all cash flows are reinvested in the enterprise at the discount rate, R or are distributed and available for reinvestment at R , and that cash flow CF will grow at a constant rate, G, the basic valuation equation has been shown to be equivalent to the Gordon Model the right-hand side of Equation 1. The Gordon Model is used almost universally to develop valuations under the income approach.

It is generally thought that the Gordon Model develops valuation indications at the marketable minority, or as-if-freely-traded, level of value. The Quantitative Marketability Discount Model QMDM was designed to employ the basic discounted cash flow model to value illiquid interests of closely held enterprises in the context of appraisals of the relevant business enterprises.

The value of an illiquid interest in an enterprise can be similarly defined, where the cash flow received by shareholders CFsh is generally less than the total cash flows of the enterprise CFe. This is expressed symbolically in Equation 2. Conceptually, if the cash flow expected to be received by shareholders is less than all of the cash flows of an enterprise, and if minority shareholders experience risks in addition to the risks of the enterprise, then value to the shareholder Vsh will be less than the freely traded value indicated by the Gordon Model.

The questions are: How much less? How can appraisers reliably determine the difference? Assume that the value of a closely held company has already been determined at the marketable minority level of value. The next objective is to determine the nonmarketable minority level of value.

A significant problem with traditional benchmark analysis is that qualitative comparisons do not allow the appraiser to consider the wide variation of investment characteristics among closely held securities. The degree of the necessary marketability discount for a particular closely held security should be based on the economic characteristics of that security.

The QMDM enables the appraiser to quantify marketability discounts based on the investment characteristics of each subject illiquid interest of a closely held enterprise. The value of an illiquid security can be determined, relative to its marketable minority value, through an analysis of five key factors. These five factors are the basic assumptions of the QMDM:. Three simplified examples of commercial partnerships can illustrate this point. In order of relative investment risk to partners, Partnership 3, with no interim cash flows, a long and uncertain expected holding period, and a return based entirely on an ultimate liquidation, is the riskiest.

Partnership 1 provides an attractive distribution and is less risky. Partnership 2, with an attractive yield and a near-term expectation of liquidation, is the least risky of the three. The concluded marketability discounts are also shown. An appraiser using benchmark analysis might be comfortable with this conclusion. But what should be the marketability discount for Partnership 2, with a much shorter expected holding period?

Benchmark analysis fails in such cases, but the QMDM enables the appraiser to quantify the impact of the shorter expected holding period. The QMDM provides a reliable mechanism to enable business appraisers to reach the next level in most valuations: from the derivation of a credible value at the enterprise level to the development of an equally credible conclusion at the nonmarketable minority level for illiquid interests of closely held businesses. Visit the new cpajournal. The QMDM Assume that the value of a closely held company has already been determined at the marketable minority level of value.

Expected growth in value. The expected growth in value at the marketable minority level provides the umbrella under which to consider the value of an illiquid security.

The QMDM assumes that value will be realized at the marketable minority level at some point in the future although this assumption can be modified to fit facts and circumstances. Expected dividends or distributions. Basic financial theory suggests that an illiquid investment that is expected to pay regular dividends or distributions is worth more than an otherwise identical investment that has no expected distributions. The QMDM quantifies the value of the expected distributions over the expected holding period of each particular investment, considering each dividend or distribution on a C corporation equivalent basis i.

This is an important distinction between the QMDM and a benchmark analysis. Appraisers cannot reasonably estimate the financial impact on marketability i.

Any appraiser can quantify that impact using the QMDM based on the facts and circumstances of an investment. Expected growth in dividends or distributions. Unless holding periods are somewhat lengthy and distributions are significant, the growth rate of dividends may not have much impact on the value of an illiquid security.

It is appropriate, however, to make an assumption in each case. The expected holding period for the investment. Investors making investments in illiquid securities estimate their expected holding periods before the realization of liquidity.

Investors in pre restricted stock transactions had expected holding periods of two years the period of restriction under Rule of the Securities Exchange Act of , plus the expected duration of liquidity based on dribble-out rules after that period of restriction lapsed. Since April , the Rule initial period of restriction has been reduced to one year.

Investors in closely held securities must estimate the expected holding period for their investments based on the facts and circumstances of each investment. The QMDM has been criticized by some who are concerned that the expected holding period cannot be estimated with certainty. Of course it cannot—but it must be estimated nonetheless. Uncertainty is one of the basic facts of the investment world. Appraisers cannot know the unknowable; however, they must make decisions in the face of uncertainty, just like hypothetical investors in the world of fair market value or real investors in the real world.

The required return discount rate. In the two equations above, R is the appropriate discount rate for the enterprise, and reflects the risks inherent in its cash flows. The cash flows to the shareholder are derivative cash flows, i. Appraisers using the QMDM begin with a base equity discount rate and add an investor-specific premium for the relevant risks to the shareholder. This is estimated much like increments to the enterprise discount rate are estimated for specific company risks in a buildup process.

The reasonableness of the required return, or interest rate for the interest holder, can be compared to the implied required returns estimated from restricted stock studies. Partnership 1. The sole asset of Partnership 1 is a shopping center that has no liabilities. A holding period of three to six years is anticipated. Partnership 2. Partnership 2 is identical to Partnership 1, except that a liquidation of the partnership is anticipated within the next three years.

Partnership 3. This partnership holds raw land. No economic distributions are expected. The expected holding period is five to 10 years. Editor: Martin J. The CPA Journal is broadly recognized as an outstanding, technical-refereed publication aimed at public practitioners, management, educators, and other accounting professionals. Our goal is to provide CPAs and other accounting professionals with the information and news to enable them to be successful accountants, managers, and executives in today's practice environments.

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This is because the terminal value incorporates the present value of all future cash flows. Your Practice. Appendix A provides a very well done case study with sample report language on a non-dividend paying company. Visit the new cpajournal. Finding a buyer can be difficult, and some nonmarketable securities cannot be resold at all because government regulations prohibit any resale. In our opinion, when valuing an operating company that is privately held or its securities , the appropriate benchmark for discounts is provided by the total private placement discount or the discount observed in the acquisition approach.

### Quantative marketability discount model. Samples in periodicals archive:

Three simplified examples of commercial partnerships can illustrate this point. In order of relative investment risk to partners, Partnership 3, with no interim cash flows, a long and uncertain expected holding period, and a return based entirely on an ultimate liquidation, is the riskiest.

Partnership 1 provides an attractive distribution and is less risky. Partnership 2, with an attractive yield and a near-term expectation of liquidation, is the least risky of the three. The concluded marketability discounts are also shown. An appraiser using benchmark analysis might be comfortable with this conclusion. But what should be the marketability discount for Partnership 2, with a much shorter expected holding period?

Benchmark analysis fails in such cases, but the QMDM enables the appraiser to quantify the impact of the shorter expected holding period.

The QMDM provides a reliable mechanism to enable business appraisers to reach the next level in most valuations: from the derivation of a credible value at the enterprise level to the development of an equally credible conclusion at the nonmarketable minority level for illiquid interests of closely held businesses.

Visit the new cpajournal. The QMDM Assume that the value of a closely held company has already been determined at the marketable minority level of value.

Expected growth in value. The expected growth in value at the marketable minority level provides the umbrella under which to consider the value of an illiquid security. The QMDM assumes that value will be realized at the marketable minority level at some point in the future although this assumption can be modified to fit facts and circumstances. Expected dividends or distributions. Basic financial theory suggests that an illiquid investment that is expected to pay regular dividends or distributions is worth more than an otherwise identical investment that has no expected distributions.

The QMDM quantifies the value of the expected distributions over the expected holding period of each particular investment, considering each dividend or distribution on a C corporation equivalent basis i. This is an important distinction between the QMDM and a benchmark analysis. Appraisers cannot reasonably estimate the financial impact on marketability i. Any appraiser can quantify that impact using the QMDM based on the facts and circumstances of an investment.

Expected growth in dividends or distributions. Unless holding periods are somewhat lengthy and distributions are significant, the growth rate of dividends may not have much impact on the value of an illiquid security.

It is appropriate, however, to make an assumption in each case. The expected holding period for the investment. Investors making investments in illiquid securities estimate their expected holding periods before the realization of liquidity. Investors in pre restricted stock transactions had expected holding periods of two years the period of restriction under Rule of the Securities Exchange Act of , plus the expected duration of liquidity based on dribble-out rules after that period of restriction lapsed.

Since April , the Rule initial period of restriction has been reduced to one year. Investors in closely held securities must estimate the expected holding period for their investments based on the facts and circumstances of each investment. The QMDM has been criticized by some who are concerned that the expected holding period cannot be estimated with certainty. Of course it cannot—but it must be estimated nonetheless.

Uncertainty is one of the basic facts of the investment world. Appraisers cannot know the unknowable; however, they must make decisions in the face of uncertainty, just like hypothetical investors in the world of fair market value or real investors in the real world.

The required return discount rate. In the two equations above, R is the appropriate discount rate for the enterprise, and reflects the risks inherent in its cash flows.

The cash flows to the shareholder are derivative cash flows, i. Appraisers using the QMDM begin with a base equity discount rate and add an investor-specific premium for the relevant risks to the shareholder. An investment in which the owner can achieve liquidity in a timely fashion is worth more than an investment in which the owner cannot sell the investment quickly. As such, privately held companies should sell at a discount to actual intrinsic value because of additional costs, increased uncertainty and longer time horizons tied to selling unconventional securities.

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Learn about Private Company A private company is a company held under private ownership with shares that are not traded publicly on exchanges. Understanding Business Valuations Business valuation is the process of determining the economic value of a business or company.

Discounts for lack of marketability DLOMs have frequently been the subject of controversy in valuations. The reason: applying a DLOM — an amount or percentage deducted from the value of an ownership interest to reflect the relative absence of marketability — can result in significant value reduction compared with the pro rata value of a business interest.

In analyzing data sets, several key weaknesses become evident: the demonstration of a selection bias i. Finally, results derived from data set analysis can lead to wide ranges of DLOMs that require a qualitative assessment in order to conclude specific value. Based on this understanding, and on empirical evidence after implementing various techniques, the implementation of option pricing models has been identified as the most appropriate method for estimating DLOMs.

The article then presents a simple case study and outlines a useful framework for valuing interests in private companies using an efficient, effective quantitative model. David Chaffe, in his option pricing study, highlighted a link between a DLOM and the cost to purchase a European put option. If one holds restricted or nonmarketable stock and purchases an option to sell those shares at the free market price, the holder has, in effect, purchased marketability for those shares. The price of this put is the discount for lack of marketability.

Because Chaffe relied on the Black-Scholes-Merton put option pricing model, the inputs to his model are the stock price, the strike price, the time to expiration, the interest rate, and volatility. In the Chaffe model, the stock price and the strike price equal the marketable value of the private company stock as of the valuation date. Due to its reliance on European options, the Chaffe model is downward-biased.

Consequently, the results derived by his model should be considered a lower bound for estimating DLOMs. Francis Longstaff, meanwhile, used a lookback put option — an exotic option with path dependency — to estimate DLOMs.

Yet the Longstaff model assumes that an investor has perfect market timing and, as a result, reflects an upper bound for DLOMs. Finally, there is disagreement over whether the Longstaff model concludes to a DLOM or to a liquidity premium that needs to be converted to a discount.

The revised model produces no discount in excess of These inputs are relatively rare in valuations, however. Like Finnerty, Stillian Ghaidarov also uses average-strike put options.

Past this point though, the Ghaidarov model can generate DLOMs that are significantly higher than the results indicated by restricted share studies. These should be used with caution. Overall, based on our experience in the respective inputs to these models, their levels of difficulty, and the generated estimates for different asset classes, we believe that the Finnerty model is the most appropriate method to estimate DLOMs for financial reporting purposes.

The discount associated with the illiquidity of each type of instrument included in a capital structure of a private company is directly related to its inherent rights and privileges.

From a valuation perspective, securities with higher seniority or more protective provisions are associated with a lower illiquidity discount due to the lower risk of receiving distributions below certain thresholds or beyond certain time frames expected by potential investors. When measuring the appropriate illiquidity discount in complex capital structures, one crucial complexity involves the search for a quantitative and qualitative way to differentiate the applicable discount among the various securities analyzed.

The BSOPM, which relies on such variables as asset price, strike price, expected term, risk-free rate, volatility, and dividend yield, is basically a contingent claim analysis that treats equity as a combination of call options associated with the claims of each security included in the capital structure. The strike prices of these options correspond to the participation thresholds of these securities, and the respective call options represent the value attributable to these securities above the specified strike prices or breakpoints based on the set of required assumptions.

After calculating the values of the call options, the next step is to calculate the delta that corresponds to each security. The delta measures the changes in the value of the call options relative to the change in the value of the asset price — in this case, the equity value of the company. In other words, the delta measures the relationship between the volatility of the equity value and the value of the specific security, which is considered to be a derivative instrument on the equity value of the company.

The volatility for each security class can then be expressed as the product of the aggregate delta, the leverage ratio based on the underlying asset price relative to the total claims of each security class , and the assumed equity volatility.

Based on the concluded asset volatility for each security, the appropriate DLOM is finally calculated based on the revised Finnerty model. Below, we present a simple case with a hypothetical capital structure that includes only one type each of preferred security, common units, and options on common stock.

Figure 1 shows a summary of the assumed capital structure. Figure 3 presents both the individual security volatility analysis and the calculation of the appropriate DLOM applicable to each security. As presented in line 8 in Figure 3 , the concluded asset volatility is lower for the most senior securities and higher for the more junior securities — a reasonable conclusion based on the expectations described earlier.

The same relationship is observed between the seniority of the securities and the concluded DLOM based on the Finnerty model, which relies on the concluded asset volatility for each security along with the assumptions for the expected holding term and the dividend yield. Figure 4 presents a sensitivity analysis based on different volatility, exit timing, and asset price assumptions, and on the impact on the concluded DLOM among the different securities.

Figure 4 reveals a positive relationship between the volatility or holding period assumption and the concluded DLOM. Higher volatility or holding period assumptions lead to higher applicable illiquidity discounts due to the greater uncertainty and risk concerning future realized distribution levels. The opposite relationship can be observed concerning the applicable asset price allocated: higher asset price inputs produce lower illiquidity discounts because of the lower risk associated with the probability of the analyzed securities being out of the money at the end of the holding period.

The framework outlined here is an expedient tool for valuing interests in private companies with a quantitative model that differentiates securities and assigns different illiquidity discounts based on their relative rights and privileges and on the remaining assumptions linked to the BSOPM framework and management inputs. However, qualitative factors associated with ownership control premiums, voting rights, or other protective provisions should always be considered in order to avoid determining an illiquidity discount that over- or understates the value of the subject interest.

Improve accuracy when valuing shares in complex multi-class capital structures by applying the appropriate method to determine a discount for lack of marketability. Download PDF. Authors Harris Antoniades. Court Case Review.

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