Model helps investors and analysts evaluate stock prices.

William Welch

When is the price of a stock too high to be justified?

That is a question that investors and analysts alike need to answer as they make investment decisions. In the 1990s, a number of company’s stocks were priced very high relative to their free cash flow—what a company generates through its operations minus what it needs to maintain its capital.

The justification for the high stock prices? That the company’s growth prospects were very high. However, common sense and experience would say that there had to be something truly extraordinary about a market prospect for it to grow at an exceptionally high rate over the long term. If there were a way that people could evaluate whether the high prices were justified by high growth prospects, it would be extremely helpful.

Help came in the form of research by William Welch, chair of the Department of Finance in the College of Business Administration, who has written or co-written approximately 25 articles, and two former college colleagues, Simon Pak and Maria Deboyrie. They developed a model to look at a company from the point of view of free cash flow as well as from the perspective of what it would take for the company to sustain a high level of growth over time.

“There were models that enabled people to look at the issue when the company has positive free cash flow, but prior to our work, there was no model for companies with negative free cash flow,” he said. “As a result, our research was a major breakthrough, giving analysts and investors an additional parameter for assessing whether high growth prospect stocks were under- or over-priced.”

Part of what was revolutionary about the work was the mathematics that permitted the calculation of the required duration of the fast growth of a negative cash flow necessary to justify a stock’s high market value.

The model of growing a negative cash flow to a positive value was new,” Welch said. “Pak figured out a way to grow a negative number into positive territory in a continuous fashion through some pretty high-level mathematics. Consequently, we could look at the previously-un-modeled issue of negative cash flow.”

According to the authors, because their model “can be applied to companies with current negative free cash flow, [it] is very useful for the valuation of many young companies’ stocks that are in their early growth (still with negative free cash flow) stages.”

An explanation of the model and of the equations used in it was published in an article titled “Are High Stock Market Prices Justified? The Stock Market Price and the Implied Duration of Supernormal Growth,” in the Journal of Investing, a highly-regarded finance publication.

The authors applied the model themselves, looking at several companies whose stock seemed overpriced. They were surprised by the results.

“We discovered that, in fact, the prices were not out of bounds, but they were more reasonably-priced than we had assumed,” said Welch, who had framed the problem in terms of duration and who wrote the background section which set the new model in the context of previous research.

He assumes that others may have done a similar exercise.

“The actual computer model is proprietary, but we included the equations in our article, so a programmer could have used them to create a model,” he said. “Financials would be put into the model and then they would run the model—throughout the trading day or at the end of day—to see the implied duration.”

Though Welch acknowledged that research is a lot of work, he also finds it fun, “something with a practical application. Plus, I enjoy the actual modeling and the opportunity to answer a specific question using modeling techniques,” he said.

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