A Primer on the Quantitative Marketability Discount Model

BUSINESS VALUATION

By Z. 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?

The QMDM

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. On the basis of historical studies of restricted stock transactions involving public securities, many appraisers have agreed, based on benchmark analysis, that the appropriate marketability discount is approximately 35%. 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:

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). An investor wants to estimate the value to be achieved in the future: the terminal value of the QMDM’s shareholder investment analysis.

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.e., after corporate taxes, either required for a C corporation or expected to be distributed for tax pass-through entities). This is an important distinction between the QMDM and a benchmark analysis. Appraisers cannot reasonably estimate the financial impact on marketability (i.e., value) of a given level of expected dividends based on qualitative comparisons with anything. 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-1997 restricted stock transactions had expected holding periods of two years (the period of restriction under Rule 144 of the Securities Exchange Act of 1934), plus the expected duration of liquidity based on dribble-out rules after that period of restriction lapsed. Since April 1997, the Rule 144 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.e., except in the case of enterprises that distribute 100% of cash flows; they are a subset of the cash flows of the enterprise and subject to the same risks as the cash flows of the enterprise. From the shareholders’ viewpoint, however, there are additional risks, such as that the cash flows will not be distributed, that the interest cannot be transferred, etc. 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.

The QMDM in Operation

Not all marketability discounts are 35%. Three simplified examples of commercial partnerships can illustrate this point.

Partnership 1. The sole asset of Partnership 1 is a shopping center that has no liabilities. Partnership 1 makes a regular distribution for pass-through taxes and makes a regular economic distribution equivalent to 3% on a C corporation equivalent basis. The partnership is expected to grow in value at about 3% per year, and distributions are expected to grow somewhat more slowly. A holding period of three to six years is anticipated. A midpoint required return of 15% was developed using the Adjusted Capital Asset Pricing Model (the buildup method) after considering the factors above.

Partnership 2. Partnership 2 is identical to Partnership 1, except that a liquidation of the partnership is anticipated within the next three years. The midpoint required return would be 13%, with the risk of the investment being moderated by the shorter expected holding period.

Partnership 3. This partnership holds raw land. A hunting lease on the land provides just enough cash flow to pay taxes on the land and the minimal expenses of the partnership’s operation. No economic distributions are expected. The expected holding period is five to 10 years. The greater risk of this investment (relative to the other two) caused the appraiser to increase the midpoint required return to 21%.

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 assumptions of the QMDM are summarized for each of the partnerships in the Exhibit. The concluded marketability discounts are also shown.

The conclusions were reached based on the range of calculated discounts provided by the range of expected holding periods and a range of discount rates of the assumed required returns, plus or minus 1%.

The concluded marketability discount for Partnership 1 is 30%. 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 marketability discount for Partnership 2 is a mere 15%. Appraisers, using benchmark analysis, might not apply such a small marketability discount, yet the economics of the investment simply do not warrant a 35% discount. Finally, the concluded marketability discount for Partnership 3 is 60%; again, because the economics of the investment warrant this level of discount. Yet most appraisers using benchmark analysis would be “uncomfortable” straying this far from 35%.

Interestingly, the average of the three marketability discounts is indeed 35%. The examples were created to illustrate that realistic factual situations can yield an average marketability discount of 35%, yet individually provide a wide range of realistic conclusions based on realistic fact patterns.

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.

Z. Christopher Mercer, ASA, CFA, is the chief executive officer of Mercer Capital Management, Inc., Memphis, Tenn.

Editor:
Martin J. Lieberman, ASA, CPA/ABV

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