July 2003
A Primer on the Quantitative Marketability Discount Model
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:
The QMDM in Operation
Not all marketability discounts are 35%. 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 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.
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