In 2013, Michael Dell and his private equity partner, Silver Lake, brought the previously publicly-held Dell Corporation private at a price of $13.75 per share, a price that was approved by Dell’s board and by a 57 percent majority vote of shareholders (70 percent of shares voted) on September 12. 2013. That price was arrived at after the board examined numerous estimates of the value of Dell by various outside experts and after an extensive, but ultimately unsuccessful, “go shop” canvassing of at least 60 other companies to explore their interest in making a higher offer.

Shareholders dissenting from the agreed upon price sued for appraisal rights, and the Delaware Chancery Court awarded those shareholders a “fair value” price of $17.62 per share on May 31, 2016 (In re: Appraisal of Dell Inc., C.A. No. 9322-VCL).

In a recent paper, I focus on the wide range of estimates of value submitted to Dell’s board and to the court. There were at least 65 such estimates ranging from $7.25 to $27.05 per share. The object of the paper is to analyze the finance methodology behind those estimates to understand why they were so different. That understanding may help courts and others decide on criteria for settling on a specific “fair value” price.

The first step in this analysis is to understand finance theory’s most widely used, most accepted, and most rigorous way to estimate a company’s value, and that is discounted cash flow (DCF) methodology. This is also the methodology most relied on by the court in this case. However, this methodology has significant shortcomings, and understanding those shortcomings shows why estimates of value vary so widely. Market prices are also used to estimate a company’s value, but they theoretically represent the market’s estimate of the discounted value of a company’s cash flows and are subject to the same shortcomings. Similarly, estimates of “break-up” or “sum of the parts” values ultimately rely on DCF estimates of the value of the parts.

To be sure, there are other valuation methods used by practioners such as “comparables” or “multiples.” In those methods a company’s value is estimated by comparing some metric to that of other similar transactions. For example, if a sales multiple were used for consumer products companies and recent transactions valued these companies at an average of 10 times sales, then a prospective sale of a similar company would also be valued at 10 times its sales. Depending on the industry, some have used multiples of earnings, multiples of book value, and in recent social media valuations multiples of the number of clicks a website registers.  But these rules of thumb are meaningless in themselves; they are only meaningful to the extent that they estimate the discounted value of future cash flows.

Discounted Cash Flow

The value of a corporation, or of any other financial asset, is defined in finance theory as the sum of the discounted value of all future cash flows, with cash flows forecast to infinity, an obviously impossible task. There are mathematical models that, under certain circumstance, make the calculations easier but no less imprecise. What’s more, different analysts make different estimates of future cash flows and of appropriate discount rates, and these different estimates lead to the wide range of “fair value” estimates seen in Dell.

This point is perhaps best illustrated in comments made by Eugene Fama, one of the founders of modern finance theory and key developer of efficient market theory, for which he was awarded the Nobel Prize in 2013. While his work generally shows that investors on average do not outperform the stock market, a rough estimate of his definition of an efficient market, it says little about whether stock prices reflect the inherent value, or “fair value,” of a company.

James Tobin, another Nobel Prize recipient, made a distinction between types of efficiency. He called one “information-arbitrage” efficiency, which is essentially the same as Fama’s definition, i.e. investors on average do not outperform the market, and he believed that markets were efficient in this respect. However, he distinguished that from what he called “fundamental-valuation” efficiency, by which he meant how well market prices reflected the discounted value of future cash flows, which is the definition of “fair value” as used by the court in Dell. He believed that markets can be “egregiously” inefficient in that respect.

Fama points out some shortcomings in DCF methodology. With regard to cash flow estimates, he states that “Our guess is that whatever the formal approach…” results from discounted cash flow analysis are a “wing and a prayer, and serendipity is an important force in outcomes.” (Fama, and Kenneth French, Industry Costs of Equity,” J. of Fin. Economics, 43, 1997)

He was similarly skeptical of the discount rate, the only other variable in the discounted cash flow formula. Although the discount rate is usually not as big a factor as cash flow estimates in determining value, it can be a very significant contributor to the inherent uncertainty in all valuation decisions. Fama states regarding the discount rate “i,” which in valuing a company is the company’s weighted average cost of capital (which is calculated using a company’s cost of equity): “Estimates of the cost of equity for industries are imprecise.  Estimates of the cost of equity for firms and projects are surely even less precise. … Most textbooks emphasize the uncertainty in projections of cash flows.  Our main point is that the cost of capital estimates used to discount cash flows are also unavoidably imprecise… Our message is that uncertainty of this magnitude … implies woefully imprecise estimates of the cost of equity.” Those imprecise estimates lead, of course, to imprecise estimates of the value of a company, since DCF calculations use the “woefully” imprecise cost of equity and the “wing and a prayer” estimates of future cash flows.

Courts have long recognized the uncertainty in business decisions, uncertainty that derives from predicting cash flows or other future events, and they have generally deferred to the judgment of directors in such matters under the well-established business judgment rule.

Attempted hostile takeovers provide an example of this deference, in contrast to the outcome in Dell. If a board decides that an attempted takeover offer is inadequate in light of advice from financial advisers, and that the target can achieve higher values in the future as an independent company, courts generally uphold the board’s decision and permit it to take strong defensive actions to defeat the takeover. In Dell, however, the board decided the opposite, that Dell could not, as an independent company, achieve the higher values estimated by financial advisers, but the court overrode the board’s judgment.

In explaining why it overrode the board’s judgment, the court made a distinction between “director liability” issues and “fair value,” saying the company and its advisers “…did many praiseworthy things, and it would burden an already long opinion to catalog them. In a liability proceeding, this court could not hold that the directors breached their fiduciary duties or that there could be any basis for liability.” However, it continued, “that is not the same as proving that the deal price provides the best evidence of the Company’s fair value.” The court enumerated several reasons for this distinction, but from a finance perspective, these reasons do not change the fact that the deal price approved by the board and a majority of the stockholders was, in their business judgment, the best price that could be achieved by going private, selling the company, or continuing as an independent company.

My paper examines various methodologies for valuing companies, especially discounted cash flow. Each was shown to be unreliable in establishing an “inherent,” “true,” or “fair value” of a company. Nevertheless, decisions must be made on valuations and the key question becomes who, in the face of inescapable uncertainty, should make such decisions. All parties in a valuation dispute have conflicting interests; sellers will look to choose estimates of variables in the DCF equation that produce higher values, while buyers will generally do the opposite. Even boards of directors may be perceived to have conflicts of interest, but their actions are the only ones subject to well established rules of judicial review. For these reasons, my paper concludes that the judgment of the board is the appropriate one in valuation decisions, provided, as stated previously, the board meets its fiduciary duty to the corporation and its shareholders and passes the usual judicial scrutiny of its actions under the business judgement rule.

This post comes to us from Donald Margotta, associate professor of finance at Northeastern University. It is based on his recent paper, “Dell Appraisal and the Business Judgement Rule,” available here.