The enterprise discounted cash flow (DCF) model discounts future free cash flow (FCF) at the weighted average cost of capital (WACC), in order to arrive at an estimate of corporate value. Adding corporate value to non-operating assets minus the market value of debt and other relevant liabilities gives one an estimate of shareholder value. Whether implicitly or explicitly, the question of shareholder value, as with all cash-generating assets, is ultimately subject to discounted cash flow (DCF) analysis, because the value of such assets is equivalent to the “present value of the cash that can be taken out [them] during the remainder of [their] life”. However, while DCF analysis is, in principle, a well-grounded approach, in practice, it presents numerous problems. John Burr Williams, whose revelatory book, The Theory of Investment Value, established the undeniable merits of DCF analysis, was aware of its pitfalls. He dedicated a “A Chapter for Skeptics”, in which he countered that,
. . . the old-fashioned methods of appraisal in reality took cognizance of all the factors which give such intricacy to the new formulas, but the old methods did so implicitly, whereas the new methods do so explicitly.
Nevertheless, these pitfalls remain, chief among them being that estimates of uncertain events well into the future, are likely to be very wrong. The import of such errors can be discerned from an analysis of value:
Value = Present Value of Cash Flow During the Explicit Forecast Period + Present Value of Cash Flow After the Explicit Forecast Period
A firm’s “continuing value”, or “terminal value” is the value created after the explicit forecast period an often makes up a significant chunk of a firm’s total value. According to Tim Koeller, Marc Goedhart, and David Wessels’ magisterial textbook, Valuation, across four industries, tobacco, sporting goods, skin care and high tech, continuing value is responsible for between 56 percent to 125 percent of total value.
They explain that,
These large percentages do not necessarily mean that most of a company’s value will be created in the continuing-value period. Often, continuing value is large because profits and other inflows in the early years are offset by outflows for capital spending and working-capital investment—investments that should generate higher cash flow in later years.
That post-explicit forecast period is pregnant with uncertainty and importance. It is not simply that humans make forecasting mistakes: even a perfectly calculating machine with all the information in the world right now, would still err, given the irreducible complexity of the world and the greater opportunities for pure randomness, the more time goes on. Not only are forecasting errors more likely the further-out the forecast, there is a question of falsifiability: the proof of a long run forecast is so far off that it is unhelpful in making an investment decision. An analyst can retort to the skeptical reader of their projections, "Just wait and see!", without meaningful counter. A final problem is that, as shown by Philip Tetlock in his books Expert Political Judgment and Superforecasting, even experts are very bad at forecasting, and although one can be trained to improve one’s forecasting (I was tenth in the Good Judgment Project 2.0 tournament during the pandemic, for example), a diversified and large crowd is far more likely to arrive at a reasonable forecast than an individual forecaster. Between a well diversified and highly liquid market on the one hand, and the individual investor or analyst on the other, it is the well diversified and highly liquid market that is likely to have the greater success in predicting the long-term value of cash-generating assets.
It should also be said that cash flows are inherently uncertain, stochastic, they are not an unknown with a linear path, but an unknown with multiple possible paths, paths that are being cut off and branched from and created with each managerial decision. What one has before one is a tree of possibilities, each with different and unknown likelihoods, and whatever likelihoods are assigned are subjective, and simply because something is likely does not meant that it will happen. When discussing the profit maximisation in their great paper, "The Cost of Capital, Corporation Finance and the Theory of Investment", Franco Modigliani and Merton H. Miller explained that,
Under uncertainty there corresponds to each decision of the firm not a unique profit outcome, but a plurality of mutually exclusive outcomes which can at best be described by a subjective probability distribution. The profit outcome, in short, has become a random variable and as such its maximization no longer has an operational meaning. Nor can this difficulty generally be disposed of by using the mathematical expecta-tion of profits as the variable to be maximized. For decisions which affect the expected value will also tend to affect the dispersion and other characteristics of the distribution of outcomes. In particular, the use of debt rather than equity funds to finance a given venture may well in-crease the expected return to the owners, but only at the cost of in-creased dispersion of the outcomes.
That concern should apply to forecasting future cash flows.
It is said that Carl Jacobi, that sublime German mathematician, would urge his students, when faced with difficult problems, to, "Man muss immer umkehren" or, l“invert, always invert.” A reverse DCF model, as described by Michael J. Mauboussin and Alfred Rappaport in Expectations Investing, inverts the problem by shifting the focus of a DCF model from forecasting to determining the expectations implied in the market price, for, as they explain,
...stock prices quickly reflect revised, but perhaps miscalculated, expectations. To succeed, investors must first skillfully read expectations and then use the best available tools to decide whether and how today’s expectations will change.
Then, using the improved fundamental data garnered thanks to the accounting adjustments that uncover the true economics of a business, one can weigh these expectations against the economic record.
Price-Implied Expectations (PIE) Analysis
So, rather than forecasting a company's cash flows, one exploits the relationships that underpin shareholder value, to determine at what future stage, estimated shareholder value per share equals the current share price. These relationships are simple:
- Revenue x net operating profit before tax (NOPBT) margin = net operating profits before tax (NOPBT)
- NOPBT - cash taxes = net operating profit after tax (NOPAT)
- NOPAT - net investment, i.e. the change in invested capital = FCF
- FCF discounted by WACC = corporate value
- Corporate value + non-operating assets - the market value of debt and other relevant liabilities = shareholder value
Revenue growth, NOPBT margin, and the investment rate, are the operating value drivers, while the cash tax rate, WACC, and the market-implied forecast period, or market-implied competitive advantage period (MICAP), are the other value determinants. With these elements, we can answer how much a company will growth, what its economic profit margin (ROIC-WACC) will be, and for how long it will be able to earn economic profits. By forecasting for growth and economic profitability, we can solve for the MICAP.
In all scenarios, I calculate continuing value as NOPAT/WACC, which is known as the convergence formula. NOPAT/WACC is used because it values the company when it is making no new net investments or invests in projects that earn zero net present value (NPV). In other words, this continues the logic of economic book value (EBV) in starting from the assumption that competition will erode away any advantages a firm has and returns on invested capital (ROIC) will converge toward WACC. As Koller et al warn,
The fact that the growth term has disappeared from the equation does not mean that the nominal growth in NOPAT will be zero. The growth term drops out because new growth adds nothing to value, as the RONIC [return on new invested capital] associated with growth equals the cost of capital. This formula is sometimes interpreted as implying zero growth (not even with inflation), but this is not an accurate interpretation.
I start with consensus revenue growth numbers for as many years as I can get, so as to capture what the crowd believes the company's growth prospects look like. Then, I converge upon historical averages, and in year 51 to 100 of my forecast? I use a 3% growth rate, i.e. the long-run geometric GDP growth rate of the US economy since 1929. For forecasts of non-US firms, I adjust accordingly. Forecasts are adjusted so that they never exceed past growth rates, except when testing price-implied expectations. The revenue growth rate is the only outside input I use. Given the quality of the data that arises from my accounting adjustments, I use historical averages from my calculations of NOPBT margin, cash operating tax rates, net investment -which I break out into changes for net working capital and adjusted fixed assets-, and WACC, to complete my toolkit. Throughout a forecast period, I tend not to change to NOPBT margin, cash operating tax rate, and WACC.
To unearth the price implied expectations, I forecast over as long a period as it takes to arrive at a shareholder value per share that is equal to the current share price. Mauboussin has a wonderful page discussing the mechanics of how one does PIE analysis, along with a very helpful spreadsheet that you can play around with.
Insights from Using my Reverse DCF Model
In my report, "Meta Platforms: Its Economics and Valuation", I remarked that,
Using my reverse DCF model, we can uncover the expectations implied by the current stock price of $515.45. In order to justify its current price, Meta must grow revenues by 13.6% a year for the next 14 years, while maintaining a 35.95% NOPAT margin, and compounding invested capital by 12.16% a year. In that scenario, Meta would earn $961 billion in revenue, nearly thrice Alphabet's LTM revenue. This scenario also implies that Meta would average a ROIC of 40.88%, compared to its lifetime ROIC average of 31.4%. Meta last had a ROIC greater than 40% in 2018. At the end if its competitive advantage period (CAP), Meta would earn a NOPAT of $345 billion. This is the -nothing-goes-wrong scenario. The reader can see how I solved for this in my attached spreadsheet, under the sheet titled, "Price-Implied Expectations".
In my report, "Diamond Hill is Undervalued Regardless of Challenges to its Growth and Profitability", I found that,
At current prices, the firm has a PEBV of 0.88, which implies that the market expects NOPAT to permanently decline by 12% from current levels, with revenue declining by -0.88% a year. This is strangely catastrophist considering that, despite its challenges, Diamond Hill more than doubled its 2022 NOPAT in 2023, and, if anything, Diamond Hill can be accused of having volatile NOPAT, rising one year, and declining the next. The reader can see how I arrived at this conclusion in the sheet titled, "Price-Implied Expectations" in my accompanying spreadsheet.
Reverse DCFs force one into acknowledging the market's expectations for a company, and create such a burden of proof for an investment thesis to be accepted that they have the benefit of resulting in low portfolio turnovers and reducing costs, while properly assessing the risk inherent in an investment.