Faculty of law blogs / UNIVERSITY OF OXFORD

Appraisal Rights and Economic Growth

In appraisal proceedings and other disputes relating to valuation, the Delaware courts prefer the discounted cash flow (DCF) method if deal price cannot be trusted to indicate fair value. Under the DCF method, the usual approach is to calculate value year-by-year for the coming five years (the projection period) and to use projected average cash flow to calculate value for the period thereafter (the terminal period). Since cash flow differs from GAAP earnings primarily by netting out funds reinvested in the firm (plowback), future returns can be expected to grow. Thus, one must adjust for expected growth during the terminal period. The standard practice is to reduce the discount rate by the projected inflation rate plus the projected GDP growth rate (or often half thereof) -- since a firm must keep up with inflation (lest it disappear over time) and since economic growth comes from returns generated by business in the aggregate.

Needless to say, projections of economic growth are speculative at best. So to use any such prognostication in the context of an appraisal proceeding should be inherently suspect. Moreover, at a discount rate of 10% – about the average market rate currently used by the courts – terminal value amounts to more than sixty percent of total value.  And to reduce the applicable discount rate from 10% to 7% (for example) increases the value of each dollar of terminal period return from about $6.21 to about $10.19. In other words, the effect of adjusting the discount rate for growth can be quite dramatic.

The temptation for manipulation is obvious. But there is no need to adjust the discount rate at all if plowback generates return at the same rate ordinarily required of the firm. If so, growth in value is equal to plowback. Thus, it would be far simpler and much less speculative to use projected GAAP earnings as the measure of return. To use cash flow together with an adjusted discount rate is akin to making Maraschino cherries – which are first soaked in lye to remove color and flavor and then soaked in food coloring and sugar to put it back.

The problem (if it is a problem) is that to use projected GAAP earnings rather than cash flow with a growth-adjusted discount rate is to presume that long-term growth in firm value is in fact limited to growth from plowback. But there is good reason to think that this is true since opportunities to generate above normal returns (economic rents) are likely to dissipate quickly because of competition. Still, it is possible that firms do grow by more than can be explained by plowback.

The data presented in this piece suggests that indeed growth comes wholly from plowback together with reinvestment of dividends. For the period since 1930, growth in the value of the S&P 500 can be fully explained by plowback (GAAP earnings less dividends) together with reinvestment by investors. While plowback has been just enough to match inflation, remaining growth in stock prices is slightly less than would be expected by dividend reinvestment (which is consistent with diversion by investors of some portion to consumption). The data since 2000 is somewhat different in that plowback has been less than inflation, but stock prices have nonetheless increased consistent with reinvestment. The bottom line is that stock prices seem to grow slightly more than the real GDP growth rate but a bit less than plowback plus the likely reinvestment rate. It follows that there is no reason for stockholders to expect any more growth than can be generated through plowback, and thus no need for courts to struggle with estimating growth rates. By using projected GAAP earnings as the measure of average long-term return, the courts can use an unadjusted discount rate to calculate terminal value.

This post is based on the paper ‘Appraisal Rights and Economic Growth’.

Richard A. Booth is the Martin G. McGuinn Professor of Business Law at Villanova University — Widger School of Law.


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