Business appraisers routinely use the discounted cash flow model to value entire businesses. While a growing number of appraisers use a discounted cash flow model to value illiquid minority interests of businesses (22% according to a recent Business Valuation Resources Survey), the majority of appraisers continue to rely on restricted stock studies and pre-IPO studies in their marketability discount determinations.

The previous nine posts in this Deja Vu series have shown the uselessness of methods based on dated restricted stock or pre-IPO studies.

• Deja Vu #1: SEC Rule 144 (Pre-1997) as Background for Restricted Stock Discounts
• Deja Vu #2: The SEC Institutional Investor Study (Published 1971)  (Average Discount = 26%)
• Deja Vu #3: The Gelman (1972) (Average Discount = 25%) and Trout (1997) (Average Discount = 34%) Restricted Stock Studies
• Deja Vu #4: The Moroney Restricted Stock Study (1993) (Average Discount – 35%)
• Deja Vu #5: The Maher Restricted Stock Study (1976) (Average Discount = 35%)
• Deja Vu #6: The Silber Restricted Stock Study (1981-1988) (Average Discount = 34%)
• Deja Vu #7: The Mandelbaum Factors and “Benchmark Analysis” (1995)
• Deja Vu #8: Review of the FMV/Stout Restricted Stock Database
• Deja Vu #9: Pre-IPO Discounts Do Not Provide Valid Evidence for Marketability Discounts

This 10th post in the series looks back at the discounted cash flow model for businesses, then summarizes the model as it can be applied to interests in businesses or illiquid minority interests. The same valuation theory applies to both.

The Discounted Cash Flow Model for Businesses

The value of a business is defined by its expected cash flows and their growth, forecasted into perpetuity, and discounted to the present at a discount rate reflective of the risks associated with achieving those cash flows. In practice, valuation analysts routinely use a two-stage discounted cash flow model to develop value indications for businesses. First, there is a forecast of cash flows for a finite period, say five years, or until the cash flow forecast stabilizes. The value of all remaining cash flows after the finite forecast period is captured in the terminal value, which is, effectively, a capitalization of earnings or cash flows at the end of the forecast period. These cash flows are discounted to the present at an appropriate discount rate and equity value is determined. For simplicity, we will focus on the DCF model as applied to equity cash flows.

The two-stage model can be summarized in the following figure from Chapter 9 of Business Valuation: An Integrated Theory Third Edition.

The left side expression is the sum of present value of expected cash flows for a finite forecast period, discounted to the present at the equity discount rate appropriate for the business. The right side expression develops the terminal value in the numerator while the denominator reduces that future value in year f to the present. We can describe the enterprise DCF model in the following table.

The discussion should not be controversial to this point. However, we now look at the discounted cash flow model as applied to minority interests of businesses. We do so in the same manner as with the business DCF model.

The Discounted Cash Flow Model for Interests of Businesses

The value of a minority interest in a business is the present value of the expected cash flows to the interest over a reasonable expected holding period, including the realization of the terminal value at market value at the end of the expected holding period. The discount rate to reduce interest cash flows to the present is the equity discount rate (R) plus an increment of risk associated with the interest that is not present with the business itself. The DCF model for interests of businesses is, like the model applied to businesses, a two-stage model, which can be described in the following figure.

Unlike the business DCF model, which considers 100% of the equity cash flows of a business, the shareholder model considers only those cash flows expected for the interest being valued. The left side expression forecasts expected cash flows to the interest (CFsh) for the expected holding period (or over a reasonable range of expected holding periods). These cash flows are discounted to the present at the discount rate (Rhp), which is the sum of the equity discount rate R for the business and a premium for incremental risks associated with the interest.

The right hand equation develops the expected terminal value in the numerator. This is estimated based the expected equity value of the business at the end of the expected holding period. The denominator reduces that value to the present. The sum of the two expressions provides the value of the interest in the business, which is denoted as Vsh.

The marketability discount (or DLOM) is determined by the relationship between the value of the interest and the value of the business (or a pro rata share of the Veq(mm), or marketable minority/financial control value).

We can describe the shareholder level model for the interest in parallel with the business DCF model in the following figure.

In qualitative terms, we have just described the Quantitative Marketability Discount Model (QMDM), which is a shareholder-level discounted cash flow model. Shareholder level DCF models like the QMDM have distinct advantages over most other methods because they focus on the interest being valued in relation to the business it is part of. Several qualitative comments are appropriate.

1. Expected Holding Period. Every minority investment is made with the expectation for a finite expected holding period. The investment is made today, the expected benefits accrue over the holding period, and the investment is sold at (business) market value at the end of the expected holding period (or at a premium or discount to this expected value as the appraiser believes appropriate). No one knows the future with certainty because, as Yogi Berra said, “It hasn’t happened yet.”  But we have to make reasonable assumptions about the expected holding period (or a range of expected holding periods), whether short, intermediate or long, based on known facts at a valuation date. Appraisers cannot punt on this assumption because of lack of certainty.
2. Expected Dividends/Distributions. It should be obvious, but an interest that makes a regular distribution is worth more than an otherwise identical interest that does not. Appraisers cannot judge the difference in shareholder value in qualitative terms. Expected future dividends have present values and their present values must be calculated by developing an appropriate discount rate.
3. Expected Growth in Distributions. Consider two similar interests in businesses with identical expected dividends for the first year. For one business, there is no expectation for the dividend to grow. For the other, there is expected growth of 5% per year. The latter is clearly worth more than the former. The difference in value, however, cannot be judged qualitatively.
4. Timing of Distributions. Consider to otherwise identical interests. The first has a dividend that is paid annually, at the end of each year. The second interest expects the same annual distribution as the first, but it will be paid quarterly. The difference in value based on timing of distributions is a quantitative question, and not a qualitative one.
5. Growth in Value of the Business. Virtually every valuation of a business interest begins with a valuation of the business. That value represents the financial control/marketable minority value, which is the base value from which any discounts are taken. In order to estimate the terminal value at the end of expected holding periods, appraisers must make assumptions about the expected growth in value of the business over that time horizon. Factors such as expected return on equity, expected distributions, agency costs in the form of non-pro rata dividends, or suboptimal investments can inform the assumptions.
6. Required Holding Period Return. Appraisers develop equity discount rates when valuing businesses. We must develop required returns for illiquid minority investments, as well. There are a number of resources available to assist in estimating incremental risks associated with interests. But appraisers cannot punt on this issue, because all the expected future cash flows to interests being valued must be brought to their present values.
7. Value to Shareholder. The value to the shareholder, or the value of the interest, is the present value of the expected future benefits, both interim distributions and terminal value, discounted to the present at the required holding period return.

The marketability discount is determined based on the relationship between the value to the shareholder and the business value, as shown above, or, to repeat:

Concluding Thoughts

I reviewed all of the studies in this Deja Vu series except Quantifying Marketability Discounts, which introduced the QMDM and was published in 1997. That was some twenty-five years ago. I reviewed the FMV Stout Restricted Stock Database in 2005 in a second book on valuing shareholder cash flows. And we introduced the QMDM as a shareholder level discounted cash flow model to provide a reasonable method/model to estimate shareholder level values and marketability discounts. The first edition of Business Valuation: An Integrated Theory was published in 2004. The second edition was published in 2008. The current Third Edition was published in 2021.

The theory for valuing businesses and business interests is the same valuation theory. Value is a function of expected cash flows, their expected growth, and the risks associated with achieving the cash flows.

Be well,

Chris