A company’s stock price reflects the consequences of managers’ operating and financing decisions. Operating decisions generally influence the amount and timing of future profits, while financing decisions impact the rate at which investors discount these inflows to a present value.
Strategic Finance has published many articles advising financial executives on how to evaluate significant decisions in each domain. Any such evaluation requires an estimate of a company’s cost of equity capital.
But traditional tools for estimating the cost of equity are of little use for most privately held corporations. Fortunately, an alternative exists. Let’s map out a simple framework to estimate the cost of equity for any incorporated business.
Two Commonly Used Models
The cost of equity is an opportunity cost—something foregone—that depends on the circumstances in effect when a particular decision is made. For example, an opportunity cost of investing in General Motors is what the investor gives up by not investing in Ford Motor Co. Academics and professionals agree that this invisible cost is both real yet impossible to measure with certainty. So, executives must resort to models when estimating the cost of equity.
The generally accepted tool for publicly traded companies is the Capital Asset Pricing Model (CAPM) put forth by Nobel Prize-winning professors in the 1960s. CAPM has been taught in business schools since the 1970s, appears in nearly every introductory finance textbook, and was a staple of my 1980s MBA experience. I’ve used CAPM many times to evaluate proposed investments and acquisitions.
The core idea is that the cost of equity of a company turns on share price responsiveness to stock market fluctuations. In the face of environmental shocks, a company’s share price moving more than a broad stock market index provides evidence of elevated risk that suggests a higher cost of equity.
The traditional version of CAPM estimates the cost of equity as the sum of a risk-free rate of return (approximated by the yield on a Treasury bond), plus an equity market risk premium (the compensation investors demand to hold risky stocks instead of Treasury bonds), modified by Beta (a measure of the responsiveness of a company’s stock price is to movements in the overall stock market):
Traditional Capital Asset Pricing Model (CAPM)
Estimated cost of equity = Risk-free rate + (Beta x Equity market risk premium)
The selection of specific values for these inputs spurs endless arguments among financial analysts, and some academics believe other factors should be added to this model to provide more refined estimates.
The biggest problem with CAPM is the need for a sizable number of share price quotes over time to calculate Beta. Of the hundreds of thousands of incorporated businesses in the United States, fewer than 5,000 are publicly traded with observable share prices.
An accepted alternative is the Gordon Growth Model (GGM), also discussed in nearly every introductory finance textbook. The idea is that a share of stock is worth what you can get out of it—in this case, the present value of future dividend payments expected to be collected by the share’s owner. The GGM values a share of stock as the present value of future dividends per share (DPS) that are expected to grow at a constant annual rate (g) in perpetuity, where future receipts are brought back to a present value using the cost of equity (k) as the discount rate. This infinite series converges nicely to a simple formula:
The biggest problem with the GGM is that many companies don’t pay dividends because their owners choose to retain all earnings for future reinvestment.
A Practical Alternative
My solution is to modify the GGM by substituting earnings per share (EPS) for DPS and then turning to outsiders to arrive at an estimated share price. This approach gives a defensible estimate for any corporation’s cost of equity.
This so-called EPS growth model requires three estimates: 1) next year’s earnings per share, 2) the long-term growth rate of earnings beyond next year, and 3) today’s share price assuming that the company is publicly traded:
The reasoning used in this model is that, eventually, all earnings get returned to owners through dividends. Remember, the GGM uses a perpetuity formula to address the indefinite lifespan of a corporation. Use of perpetuities contemplates a very long-term planning horizon.
To test the assumption that EPS is a good proxy for DPS over the long run, I took a sample of 17 publicly traded U.S. companies that were founded before 1900 (with an average age of 160 years when this article was written) to assess the fraction of earnings that are paid out as dividends by mature corporations. Dividend distributions generally take two forms: periodic payments to shareholders and repurchases where companies buy back stock from shareholders who surrender their shares.
For the three fiscal years ending in 2022, I summed total dividends and net income for each company. The three-year horizon smoothed fluctuations in earnings (companies often maintain stable dividends in the face of volatile earnings) and share repurchases (a company might buy back a lot of stock in one year and then little in the next).
I then divided total dividends by net income for each company in the sample. The average three-year dividend payout ratio for the 17 companies was 101%. The takeaway? Successful, mature companies become so efficient that they don’t necessarily need to reinvest much of their earnings to maintain productive capacity. Over the long run, DPS converge to EPS.
Selecting Three Model Inputs
The EPS growth model needs three inputs: a forecast for next year’s EPS, a long-term earnings growth rate, and an estimate for the company’s stock price, assuming that the shares were publicly traded. The goal of using a model is to arrive at a defensible estimate, not to calculate an unobservable value with a false sense of precision.
Next year’s EPS comes from the company’s financial forecasting efforts. A concern arises when abnormally low earnings or a loss is projected in the next year. If so, one should forecast the EPS expected to emerge when current problems have been overcome plus the number of years required to sort through the problem period. One would then discount that future value back to next year using a provisional cost of equity of perhaps 10% per year.
The model keeps things simple by using a single long-term earnings growth rate following next year’s results. One of my finance professors warned that, when forecasting a long-term accounting balance, selecting a growth rate greater than the 3% rate observed in developed economies is dangerous, because faster growth would cause that balance to eventually become bigger than the economy in which the company competes. Thus, as a first approximation, I recommend using a 3% long-term earnings growth rate.
The final input is an estimate of what a private company’s stock price would be if it were publicly traded. I offer two options. The easier approach is to hire a business appraiser to estimate the value of the company’s shares. Appraisers use specialized techniques and professional judgment to suggest a price at which property would be exchanged, assuming the buyer and seller have knowledge of all relevant facts and have no compulsion to trade.
The appraiser would likely look for comparable companies that are publicly traded, calculate the present value of expected future income, estimate the replacement cost of building the business from scratch, and then decide after considering qualitative factors. This exercise assumes that the shares are widely held and excludes any premium associated with selling a controlling interest in the company.
An issue with appraisers is that they don’t work for free. For instance, someone I know paid $11,000 for a onetime valuation of her business. A lower-cost approach is to share historical and forecasted earnings information with outsiders in exchange for their periodic estimates of what they think the company’s stock price would be if its shares were publicly traded.
Professional investors are in the business of reviewing companies to assess their prospects and value their securities. Investors tend to be interested in learning about new organizations. Management could find a circle of trusted independent investors who are willing to provide periodic valuations in exchange for confidential information at agreed upon intervals. The management team would make clear that the exercise is intended to estimate a market price, not to solicit bids to buy shares. To spark interest, management could offer to share estimate averages among surveyed investors.
An obvious worry is that participating investors would disclose confidential information to third parties. My experience in investor relations is that buy-side investors have strong incentives to avoid sharing data and investment ideas with competitors. Seasoned investors work hard to cultivate reputations for discretion and professionalism. Sell-side analysts who call on buy-side investors have different incentives and probably shouldn’t be part of a survey process.
Illustrative Examples
To add clarity, here are examples of estimating the cost of equity for four publicly traded corporations using CAPM and the EPS growth model. This exercise is merely meant to illustrate application of the two models—not validate either.
Table 1 compares cost of equity calculations for manufacturer Caterpillar, consumer packaged goods firm Colgate Palmolive, tech giant IBM, and retailer Walmart using publicly available data as of December 1, 2023. The CAPM estimates use the yield of the 10-year Treasury bond as the risk-free rate, a selection of 6% for the equity market risk premium, and a Beta calculation based on five years of monthly stock price observations. The EPS growth model uses the consensus analyst earnings estimate for next year’s EPS and a 3% long-term earnings growth rate.
There are plenty of caveats to this exercise, of course. Companies in Table 1 were selected to provide illustrative examples rather than statistical generalizations. Further, the EPS growth model uses the stock price on one day as the basis for estimating the cost of equity. Fickle capital markets can give rise to mispriced securities over extended periods of time. Finally, the calculations apply to large, successful, public companies and do not reflect equity costs of smaller, private companies. Investors demand higher returns—as reflected in larger equity costs—for small companies and nonliquid securities. Estimated equity costs will almost certainly be higher than those shown when this model is applied to most businesses.
The Bottom-Line Estimate
There’s an old saw that all models are wrong but some are useful. Under this standard, models shouldn’t be judged on whether predictions are always true but if they’re helpful. Think of it like this: Weather forecasting models are imperfect, but their predictions can help us decide what to pack for a trip.
In the end, the EPS growth model offers a defensible basis for estimating a private company’s cost of equity based on three simple inputs. Analysts using this model have the right—if not the obligation—to modify estimated equity costs up or down based on known factors not considered in the model.
