Forum Magazine: Unpacking law firm value — drivers & density

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This article originally appeared in the Spring 2020 issue of Forum magazine.

Valuation of law firms is neither a capital market nor regulatory requirement, but the exercise does have singular advantages. There is the determination of numerical value of law firms, of course, but the exercise also allows for a deeper comprehension of equity partner compensation, systematic market risk, taxes and future cash flows. Lastly, determining firm valuation also illustrates the similarities between shareholders and equity partners.

Law firm value can serve as a financial barometer of a firm’s execution of its strategy; and analyzing the components of value can help firms increase their value. Also, if and when external investments in the legal industry or capital market listings become feasible, valuation will become essential.

About a year ago, I introduced a valuation model that adapted the well-known two-stage dividend discount model, frequently used to value public companies with steady cash flows, to the law firm industry. This technique determines annual cash flows for five future years in the first stage and then develops a terminal value based on sustainable growth in the second stage. The consequent cash flows are discounted to the present using a cost of capital to ascertain total value of a law firm. In this article, we unpack valuation constituents to help toward a better understanding and usage by law firms.

Looking at 3 key metrics

A law firm’s current-year cash flow is derived from its operating income, as reported by The American Lawyer, by subtracting the salary component of equity partner compensation, income taxes and annual increases in working capital. The percentage growth in future cash flows is the value by which the current cash flow is expected to grow annually over the next 10 years. In other words, successively applying this percentage rate to a firm’s current cash flow leads to a profile of future cash flows from the year 2020 to the year 2029. Finally, a firm’s value is represented by the present value of all future cash flows from the current year to infinity, discounted by the cost of capital.

The concept of drivers

We would intuit that value is independently and positively correlated to its two underlying drivers: current-year cash flow and percentage growth in future cash flows. An examination of three selected Am Law 100 firms at the micro level; and the aggregate Am Law 100 at the macro level illustrates well the relationship between these factors.

Micro-level analysis

The three selected firms in Table 1 have quite similar operating and valuation parameters.

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First, compare Firm A with Firm B: Firm A’s operating income and cash flow are about double that of Firm B, yet its value of $4.6 billion is similar to Firm B’s $4.4 billion. How does such a large difference in operating parameters lead to a comparable value? The answer is in the percentage growth in future cash flows. Firm B’s growth rate of 6.5% is much higher than Firm A’s of 2.7%. This large 3.8% positive differential manifests itself as substantially higher cash flows for Firm B in future years, which more than offsets unfavorable variance in current-year cash flow. The net result of discounting all cash flows from present to year infinity leads to a very similar value for both firms.

Second, compare Firm B with Firm C: Firm B and Firm C have very similar revenues, operating incomes and cash flows. However, Firm C’s growth rate in future cash flows of 9.9% is 3.4% higher than that of Firm B at 6.5%. Should this positive difference lead to higher value for Firm C? That is indeed the case. Though Firm C’s current-year cash flow is similar to Firm B, its future cash flows are much higher, leading to its value of $5.5 billion – $1.1 billion higher than Firm B’s value of $4.4 billion.

This comparison of individual firms shows how two key drivers, current level of cash flow and percentage growth in future cash flows, interact in the mechanism of value creation.

Macro-level analysis

For the macro-level analysis, we first distribute the 100 law firms in the Am Law 100 into 10 equal groups (deciles) based on decreasing amount of 2019 value; such that the 10 firms in each succeeding decile will have a lower value compared to the 10 firms in the prior decile.

Then, we calculate the total current-year cash flow and average percentage growth in future cash flows for all the 10 firms in each of the 10 deciles. Graph 1 shows value versus current-year cash flow for each value decile – and a very high degree of correlation is evident. Graph 2 shows value versus percentage growth in future cash flows for each value decile – and a moderate degree of correlation is seen. Both correlations are certainly positive, but value appears influenced by current-year cash flow much more than it does by percentage growth in future cash flows.

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The concept of density

The concept of independent correlations leads to another interesting aspect of valuation: the concept of density. Density deals with the structural distribution of value across the 100 law firms in the Am Law 100. To understand density better, we return to the previous 10 value-based deciles, but now examine the relationship between these deciles. We consider in Graph 3 the total dollar amount of value in each decile (the red line which was also depicted in Graphs 1 and 2), and the cumulative percentage of these deciles (the blue bar).

We saw earlier in Graphs 1 and 2 that the value line was quite steep. This becomes even more apparent when reviewing cumulative percentages. Indeed, the top 10 firms cumulate to about one-third of the $247 billion total value of the Am Law 100; the top 20 firms account for about half; the top 30 firms make up about two-thirds; and the top 40 firms represent about three-quarters of the total value. Conversely, the bottom 50 firms combined only amount to about 17% of the total value of the Am Law 100.

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Obviously, this is a highly disproportionate distribution of value. Indeed, the value curve is steeper than the current-year cash-flow curve across the 10 deciles (as evident in Graph 1) due to the additional effect of the downward-sloping percentage growth curve. In other words, the top-heavy distribution of value is due to the combined effect of current cash flow and percentage growth in future cash flows.

The dual correlation of these two factors leads to even more concentration in value. Higher value firms not only have higher cash flow, but they also have a higher percentage growth in future cash flows. Consequently, this combination leads to a relative value boost.

On the other hand, lower-value firms have relatively lower cash flow and also lower percentage growth in future cash flows. Consequently, this mix depresses the value of those firms in a relative fashion. The joint impact of boosting and depression explains the high density seen in the top deciles.

Summary

Analyzing value leads to some very interesting insights. Its deconstruction highlights the two fundamental drivers; and the empirical analysis of data provides numerical support. We see here that law firm value is basically driven by a firm’s cash flow magnitude and its growth profile. And the conjoint effect of these two independent correlations leads to a disproportionate distribution of value across the Am Law 100.

Value analyses are an interesting theoretical exercise today, but may be a required process in the near future. As US-based law firms become more potentially open to prospects of outside investors or to listing in capital markets, such analyses of law firm value will become increasingly necessary.