This blog post is based on Chapter 8 of the newly released Business Valuation: An Integrated Theory, Third Edition  (Wiley Finance Series, Mercer and Harms) and references two exhibits from Chapter 2.  It addresses the question of why the values of illiquid minority interests are (almost always) lower than the marketable minority values of businesses.  The answer is not because restricted stock discounts exist.

The Value of a Business

To place restricted stock discounts into theoretical perspective, we note that the value of the equity of a business is a function of three factors:

• The expected cash flows to equity
• The expected growth in those cash flows
• The risks associated with their expected receipt

Exhibit 2.2 illustrates the truth of the above definitional statement.

This equation is, of course, the Gordon Model, which we refer to as the fundamental valuation equation. It values all future cash flows of a business into perpetuity.  And this equity value is at the marketable minority or financial control level of value.  The equation summarizes the discounted cash flow model under the assumptions that all cash flows are distributed to owners (or reinvested into the business at the discount rate Requity, and that cash flows grow into perpetuity at the constant rate of GequityCF.

The Value of an Interest in a Business

The value of an interest in a business at the nonmarketable minority level of value is also a function of three very similar factors:

• The expected cash flows to the interest over the expected holding period of the investment. Note that expected cash flows to the interest are derivative of the expected cash flows of the business (less than or equal to)
• Expectations for cash flow growth over the holding period, including the terminal value at the end of the expected holding period (which is assumed to occur at the marketable minority/financial control level of value)
• The risks associated with future cash flows to the interest over the expected holding period

Exhibit 2.21 illustrates the truth of the above definitional statement.

Unlike the fundamental valuation equation, the shareholder level discounted cash flow model values expected cash flows for a finite (but perhaps not precisely known) expected holding period.  It then assumes that liquidity occurs at the end of the expected holding period at the marketable minority level, or when the objective of the investment is achieved.

In Exhibit 2.21, R_hp is the discount rate that brings expected shareholder level cash flows over the expected holding period of investment to the present.  Accept for the moment that R_hp is generally greater than R_Equity, the discount rate of the business.   We will prove why this is true as we proceed.

A Bit of Valuation Logic

Let’s drill down just a bit and ask why the nonmarketable minority level of value (or the shareholder level of value) is most often less than the marketable minority level of value (market value of equity of a business)?

• Look at Exhibit 2.2.  To determine equity value at the marketable minority / financial control level of value, expected equity cash flows are capitalized into perpetuity.  100% of the expected equity cash flows are capitalized.  The assumption is that for a marketable security, shareholders have access to the capitalized value of 100% of expected future cash flows by executing a sale order with their brokers (“cash in three days”).  The capitalization rate is based on the equity discount rate less expected growth of the business.
• Not look at the left side of Exhibit 2.21.  To determine the shareholder level of value, the present values of expected cash flows to holders, which is less than the expected equity cash flows of the business, are discounted to the present for a finite expected holding period.  Investors seldom know the expected holding period with certainty, but they must make reasonable estimates.  The risks to the shareholders of illiquid interests are logically greater than those of the business itself.  Rhp is greater than R.  Again, we will prove this as we proceed. If cash flow to the shareholder is less than expected equity cash flows for a finite expected holding period, and risks are greater, the present value of expected cash flows to the interest will be less than the corresponding expected cash flows to the business.  Assume for the moment that expected growth in value is the same for both the interest and the business.
• Looking at the right side of Exhibit 2.21, we see that the numerator of the terminal value is the estimated marketable minority value at the end of the expected holding period.  That value is then discounted to the present from that point to the present at Rhp.  Investors in illiquid interests bear the incremental risks of the holding period until the end of their investments.  In Exhibit 2.2, the “terminal value” in the implied DCF through the expected finite holding period is discounted to the present at R.  The terminal value of the second stage of Exhibit 2.21 is the marketable minority value at that point.  It is discounted to the present at Rhp, and not R.  So the second portion of the illiquid minority value is lower than the implied second stage in Exhibit 2.2.

The difference between the marketable minority value and the nonmarketable minority value is the marketability discount, or DLOM as some prefer.  Illiquid values are lower than liquid values because of differences in their respective expected cash flows, risks and growth.  We will build on this conclusion as we proceed.

Business Valuation: An Integrated Theory, Third Edition is newly released and available on Amazon.  The book introduces the Integrated Theory on an enterprise basis together with the original equity basis in Part One.  There is new and enlightening discussion of the income approach and the market approach in the context of the Integrated Theory as we talk about enterprise valuation in Part Two of the book.  Part Three of the book develops valuation at the shareholder level and presents the QMDM, or the Quantitative Marketability Discount Model.

In the next post, we will discuss these concepts in light of business valuation standards.

Until next time, be safe and be well!

Chris