In Mercer’s Musings #2, we discussed the old and cold data on restricted stock transactions that have been misused by appraisers for decades.  My conclusion is that the various restricted stock studies are inadequate to meet current business valuation standards and that they should not be used as a basis for “guessing” the magnitude of marketability discounts for illiquid interests of closely held businesses.  This conclusion applies to all appraisals, including those prepared for the Internal Revenue Service.

Some readers of this blog will want to disagree and say that the use of restricted stock studies to develop DLOMs is an “accepted” methodology for IRS-related appraisals.  Whether “accepted” or not, the qualitative use of averages of studies is inadequate to develop reasonable conclusions regarding marketability discounts given the wide variety of valuation situations facing business appraisers.  It seems that many business appraisers simply want to keep their heads in the sand and avoid changing at almost any cost.

Basic Valuation Review

The Value of a Business

The value of a business is the present value of all expected cash flows from the business (into perpetuity) discounted to the present at a discount rate reflective of the risks associated with achieving those cash flows.  In other words, value is a function of expected cash flow, growth, and risk.

Every appraisal of every business entails an examination of expected cash flows (using income capitalization methods, discounted cash flow methods, guideline public company methods, or guideline transaction methods).  Appraisals also consider growth (long-term growth rates or finite period growth rates in a DCF method and then a long-term terminal growth rate).  In guideline public company or guideline transaction methods, expected growth may be implied in the selected multiples or considered specifically by business appraisers. And appraisers develop discount rates that reflect the risks associated with achieving expected cash flows (or multiples from markets that have risk embedded in them).

Business appraisers cannot value businesses without explicit (or implicit depending on valuation methodology) consideration of their expected cash flows, the growth of those cash flows, and the risks associated with achieving the cash flows of the businesses being valued.

The Value of an Interest in a Business

The value of an interest in a business is similarly defined by the expected cash flow to the interest, the expected growth in value of the interest over the expected holding period, and the expected terminal value of the interest at the end of the expected holding period.  That terminal value is normally assumed to be the expected value of the business at the marketable minority/financial control level at the end of the expected holding period of the interest.  These expected cash flows to the interest are then discounted to the present (or to the valuation date) at a discount rate reflective of the risks associated with achieving the expected cash flows to the interest.  This definition of the value of an interest in a business parallels the definition of the value of a business noted above.

The discount rate of the business of which a subject minority interest is a portion is the base level of risk for the subject interest of the business.  Hypothetical buyers of interests of businesses recognize that there are additional risks, above the risk of the business, to the prospective buyer of such an interest.  That incremental risk can be described as a holding period premium, which is necessary to appropriately reflect the risks associated with achieving the expected cash flows to the interest.  The sum of the discount rate of the business and the holding period premium can be called the required holding period return appropriate for the interest.

Why would any business appraiser who knows that valuation is a function of expected cash flows, growth, and the risks associated with achieving them not think about the hypothetical in quantitative terms?  However, when business appraisers use averages of restricted stock studies to attempt to “guess” at marketability discounts, they are basing their conclusions on a very weak form of qualitative analysis.

Valuation Premiums and Discounts

Recall from Mercer’s Musings #2, we quoted the ASA Business Valuation Standards regarding premiums and discounts.  The quote is from “BVS VII, Valuation Premiums and Discounts.”:

II. The concepts of discounts and premiums

C. A discount or premium is warranted when characteristics affecting the value of the subject
interest differ sufficiently from those inherent in the base value to which the discount or premium
is applied.

D. A discount or premium quantifies an adjustment to account for differences in characteristics
affecting the value of the subject interest relative to the base value to which it is compared.  (bold in original, italics added)

Paragraph II.C states, paraphrasing, that discounts and premiums quantify adjustments to account for differences in characteristics affecting the value of the subject interest.

Recall the figure in Mercer’s Musings #2 that showed averages, medians, a few standard deviations, and ranges of discounts in various studies of restricted stock discounts.

Nothing in this figure addresses the expected cash flows of minority interests in any businesses, their expected growth, or the risks associated with achieving those cash flows.  Therefore, nothing in this figure can enlighten business appraisers about the appropriate marketability discounts for minority interests in any business.  It really is that simple, in spite of the desire of many appraisers to keep doing things the old way.

Restating the Hypothetical

The hypothetical posed in Mercer’s Musings #2 calls for the valuation of 10% interests in two identical corporations at the marketable minority/financial control level of value.  The hypothetical is repeated below.

As seen in Lines 1 to 6, Company A and Company B are alike in all respects leading to identical valuations of $10 million each at the marketable minority/financial control level of value.  The hypothetical then describes two 10% minority interests that have the same pro rata value of $1 million at that same level (Lines 7 and 8).  The interests differ significantly from that point on.  The interest in Company A has a high dividend yield and slow expected growth (Lines 9 to 13).

The interest in Company B has a much lower dividend yield and much higher expected growth.  Note that the combined dividend yield (3%) and expected growth (9%) total 12%, or less than the discount rate for Company B of 13%.  This suggests that there are sufficient agency costs (like excess owner compensation) that reduce the overall base expected return by 1% for the interest in Company B relative to the interest in Company A (13%).

The hypothetical calls for estimates of marketability discounts for each of the interests for five-year expected holding periods and ten-year expected holding periods.  The beginning point for the required holding period returns is the 13% discount rate for each of Company A and Company B.  The hypothetical provides a required holding period return of 18% for the interest in Company A, representing a 5% holding period premium to the base discount rate.  The given required holding period return for the interest in Company B is 19.5%.  It should be intuitively obvious why the required return for Company B exceeds that of Company A.

The expected cash flow stream for the interest in Company A is more favorable to investors than the cash flow stream for the interest in Company B, so an additional holding period premium to the base discount rate of 13% is needed.  This is clear in the following figure, which provides the expected cash flows for the interests in Company A and Company B based on the assumptions in the hypothetical.  For simplicity, we show only the first five years of the total forecast period of ten years.

We can observe the following about the expected cash flow streams of the interests in Company A and Company B.

• Looking at the far right of the figure, the interest in Company A delivers cash flow more rapidly (32% is expected over the holding period and 68% in the terminal value) than the interest in Company B (only 11% over the expected holding period and 89% in the terminal value.  The hypothetical recognized this fact and called for a higher required holding period return for Company B (19.5%) than Company A (18%).  Interestingly, Company B delivers slightly more total cash flow ($1.734 million) than Company A ($1.706 million), but the timing of expected receipt is delayed, therefore increasing the riskiness of the interest in Company B.  These differences will define a portion of the differences in the values of the interests.
• The interest in Company A is expected to have quarterly distributions, so the mid-year discounting convention is used in estimating its value.
• The interest in Company B is expected to receive dividends at the end of each year, so the end-of-year convention is used.  The differences in discounting conventions will also impact the relative values of the interests in Company A and Company B.

We can pull it all together now with a few more calculations.  The figure will show only five years of projected cash flows, but the conclusions for the ten-year expected holding periods will also be shown for further perspective.

The figure shows all key assumptions of the valuations of the 10% interests in Company A and Company B.  We observe the following regarding Company A’s interest at the top portion of the figure.

• The expected distributions and terminal value are calculated on Lines 1 thru 3, repeating the projections of the figure above.
• Present value factors are calculated based on the assumed required holding period return of 18% and the mid-year discounting convention.
• The present value of all expected cash flows for the 10% interest in Company A for a five-year expected holding period is $925,055, which represents an implied marketability discount of about 7.5% (i.e., 1 – $925,055/$1,000,000).
• The implied marketability discount for the ten-year expected holding period is $839,978, which represents an implied marketability discount of 16.0%.

These discounts, some will say, are very low.  The reason for the relatively modest discounts is that the investment in the interest in Company A represents an attractive investment.  In the context of a fair market value determination, the hypothetical negotiations of hypothetical willing buyers and sellers would recognize the “characteristics of the investment” and reflect them in its pricing.

Now we look at calculations for the 10% interest in Company B at the bottom of the figure.

• The expected cash flows are repeated from above on Lines 11 to 13.
• Present value factors are calculated based on a 19.5% required holding period return and the end-of-year discounting convention, with the present values of expected cash flows calculated on Lines 16 and 17.
• The present value of all expected cash flows for the 10% interest in Company B for the five-year expected holding period is $748,817, which represents an implied marketability discount of 25.4%.
• The present value of all expected cash flows for the ten-year expected holding period is $588,560, which represents an implied marketability discount of 41.4%.

These discounts happen to fall within the broad range of 25% to 45% from the restricted stock studies summarized above.

The discounts for the 10% interest in Company A do not fall within this range.  What should we think about that?  Well, the range of restricted stock discounts in the summary figure above is from a minus 30% (that’s a premium or a negative discount) to a high discount of 91%.  The estimates of marketability discounts for Company A’s interest certainly fall within that broad range.  However, that fact provides no support for any concluded marketability discount.

Concluding Observations

We have just conducted two shareholder-level discounted cash flow analyses to estimate marketability discounts for two dissimilar minority interest investments.  It should be clear at this point that the hypothetical cannot be solved by using the “old and cold” averages of restricted stock studies.

Mercer’s Musings #4 will address the concept of valuation premiums and discounts in the context of the levels of value, which, according to some, is not a settled issue.  We will see.

In the meantime, be well, and, of course, please do comment either on the blog or on the post when it is placed on LinkedIn.

Chris