By Chris Mercer
Let me first say that there is nothing magic about the concept of an expected holding period. Assume that the marketable minority value of a business is, indisputably, $1.00 per share. Assume that a restricted stock transaction occurred at $0.80 per share, or at a 20% discount.
What was the expected holding period for this transaction? We know that there is an expected rate of return for the business that we valued at $1.00 per share. Assume that the expected return is 15% per year over the next five years. We know that the investors who paid $0.80 per share had a required rate of return to invest in the illiquid (restricted) security. Assume that their required return is about 24%. Since we know the price they paid and their required return, we can solve for their implied expected holding period. We know that the security is expected to grow in value at 15% per year based on no dividends and total reinvestment. In three years, its expected future value will be about $1.52 per share. The expected future value of $0.80 per share compounded at the investors' 24% required return is also $1.52 per share. So we know that the expected holding period for the investors was about three years.
The bottom line is that for every discounted transaction (from a presumably marketable minority level), there is an array of expected holding periods and expected rates in value (for the enterprise) that will explain the discount. Appraisers must think about developing marketability discounts the way that investors think about pricing investments. And that is all about expected cash flow, expected risk and expected growth.
No rational investor enters into an illiquid investment with an infinite investment horizon. Every investor makes investments with an expectation of achieving an expected rate of return over a reasonable (though not precisely predictable) time horizon. The expected holding period of the QMDM is the appraiser's way of simulating the thinking of real life (and hypothetical willing) investors about investment horizons. There is no "one holding period fits all" or "best" expected holding period. Real life investors make decisions in the face of uncertainty based on information available up to the moment they write their checks. After that, they get whatever results they ultimately achieve. But they made their decisions based on facts and circumstances known at the time of their investments.
A good place to start for those concerned about how to develop expected holding periods in appraisal engagements would be Chapter 3 of my book (with Travis Harms) Business Valuation: An Integrated Theory. Chapter 1 is titled "Discounted Cash Flow and the Gordon Model: The Very Basics of Value." This is the most under-read and under-appreciated chapter in the business valuation literature (in my opinion). Next go to Chapter 3, which presents "The Integrated Theory of Business Valuation." This is the second most under-read and under-appreciated chapter in the business valuation literature (again, in my opinion). This chapter explains the various levels of value in the context of the Gordon Model and outlines the rationale for valuing illiquid minority interest using the DCF model. After these two chapters, take a look at Chapter 7, titled "Introduction to the QMDM: The Shareholder Level of Value." This chapter proves the theory outlined in Chapter 3. Then turn to Chapter 8, titled "The QMDM Assumptions in Detail." This important assumption is discussed at pp. 190-196, followed by detailed discussions of the other assumptions necessary to use the QMDM.
The value of every business is the present value of all expected future benefits (cash flows) to be derived from the business INTO PERPETUITY, discounted to the present at an appropriate (risk adjusted) discount rate. No one disagrees with this.
The value of an interest in a business is the present value of all expected future benefits (cash flows) to be derived from the interest OVER THE EXPECTED HOLDING PERIOD OR INVESTMENT HORIZON, discounted to the present at an appropriate (risk adjusted) discount rate.
Appraisers use the discounted cash flow model to value businesses. The QMDM is that same model applied to the expected cash flows attributable to interests in businesses over reasonable expected holding periods, discounted to the present at a discount rate that considers both the risks of the enterprise and the incremental risks of holding an illiquid interest in it.