The appraisal remedy under US corporation law is widely seen as intended to protect stockholders who are forced to sell their shares in a merger. But recently it has become common practice for appraisal arbitrageurs to buy target shares in order to assert appraisal rights. Aside from the question whether the law should permit johnny-come-lately hedge funds to buy into such claims, the puzzle is why it is at all profitable to do so.

One possible explanation is that Delaware appraisal courts use a so-called supply-side discount rate that is a bit lower than the raw historical rate. But it has also become almost standard practice to reduce the discount rate even more by the projected rate of inflation and GDP growth. Thus, appraisal arbitrage may be encouraged by awards that are skewed by questionable adjustments to the discount rate.

The supply-side rate reflects the belief of many finance scholars that future equity returns are unlikely to be as generous as in the past. Others note that about 1% of the 12% raw historical average return is attributable to increases in price/earnings ratios that cannot repeat. Indeed, some of the growth in stock prices – especially since 1975 – derives from investor diversification and resulting reduction in risk without a concomitant reduction in return. That cannot happen again. So the historical average must be a bit high.

The bigger problem may be that the courts often reduce the discount rate still further to adjust for growth in returns over the long haul. In practice, there is no need to adjust the discount rate for growth in the first few years – typically five – because cash flow is projected year-by-year. So growth and the diversion of returns to finance it – plowback – are baked into the numbers for this projection period. But half or more of the value of a business often comes from returns generated during the terminal period thereafter. This value is typically calculated based on a projected average of returns since projections more than five years out are unreliable. Since growth in GDP ultimately comes from growth in returns from business, courts often assume that returns will grow in lockstep.

Although it is convenient to use projected GDP growth (and inflation) as a surrogate, it is wrong to adjust the terminal period discount rate unless return is also reduced to reflect plowback. In most cases, growth comes from reinvestment of available cash at ordinary rates of return. But if so, the increase in value from a lower discount rate is exactly offset by the diversion of returns. If we know the company-specific plowback rate, there is no reason to use a projected average GDP growth rate.

To be sure, if a business finds opportunities that generate more return than its cost of capital, its value will grow. But such opportunities are rare and fleeting and will quickly be dissipated by competition. Moreover, many businesses are likely to run out of opportunities to expand even at an ordinary rate of return. Although it may be that established firms are better placed to identify unrelated growth opportunities, it is not clear that such skills give rise to value for which stockholders should be compensated.

It is folly to assume that growth in returns from business is spontaneously generated because the economy grows. Average GDP growth (about 3.4% in real terms since 1931) is significantly higher than average real growth in stock prices as measured by the S&P 500 (about 2.5% since 1925) much of which appears to be a one-time event. So even if GDP growth does ultimately derive from growth in returns, it appears to come disproportionately from small business.

Still, do we really need appraisal arbitrage? Perhaps. Bargaining happens in the shadow of the law. Where there is a robust appraisal remedy, bidders will be induced to pay a fair price up front. Thus, appraisal may ultimately benefit bidders by vouching for fairness of price, which may explain why bidders use the merger method rather than alternatives that trigger no appraisal remedy.

In the end, appraisal arbitrage may be an important force for efficiency – but only if we get the valuations right.

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