The Mirandolan - Joseph Noko

Competition, Equity Preference and the Decade Ahead for the S&P 500

Competition exists because firms, and in general, economic agents, have imperfect information. The irreducible complexity of the economy makes prediction a fraught exercise and veils the future with uncertainty. Contrary to the dominant neoclassical economic paradigm, if firms had perfect information, where one knows all the relevant facts to make a decision, as happens under perfect competition, they would not compete, it is the veil of uncertainty thrown over economic activity that makes competition necessary. The greater the uncertainty, the greater the competition. Competition is a learning process in response to ill-defined situations.
Joseph Noko, in “Uncertainty, Information and Digital Firms: a Framework for Understanding Meta Platforms and its Peers”

F.A. Hayek’s great insight was that competition is a discovery process that occurs precisely because economic agents have imperfect information. A neglected arena of competition is between active and passive management. If we employ the kind of transaction cost framework made famous by Ronald Coase, and which I have used to analyse Meta Platforms’ business model, it is clear that, assuming matching total returns between active and passive managers, passive managers exist because of the larger costs of active management. William F. Sharpe, in “The Arithmetic of Active Management”, makes a similar point, stating that,

If “active” and “passive” management styles are defined in sensible ways, it must be the case that
(1) before costs, the return on the average actively managed dollar will equal the return
on the average passively managed dollar and
(2) after costs, the return on the average actively managed dollar will be less than the
return on the average passively managed dollar
William F. Sharpe in “The Arithmetic of Active Management”

The reasons are obvious: active managers assume search costs for finding attractive investments, and they do this while facing overwhelming odds of failure. In his earthquake of a paper, “Do Stocks Outperform Treasury Bills?”, Hendrik Bessembinder found that, between 1926 and 2017, four in seven U.S. stocks had lower compound returns than one-month Treasuries. In terms of lifetime dollar wealth creation, he found that just four percent of public companies generated the net gain for the entire U.S. stock market, with the rest earning returns that merely matched Treasury bills. In “Long-Term Shareholder Returns: Evidence from 64,000 Global Stocks”, Bessembinder, Te-Feng Chen, Goeun Choi, and K.C. John Wei, found that this positive skewness of stock returns was a global phenomenon. Between 1990 and 2020, 55.2 percent of U.S. stocks and 57.4 percent of non-U.S. stocks, had lower compound returns than one-month U.S. Treasury bills. In terms of lifetime dollar wealth creation, they found that just 2.4 percent of the 64,000 firms they studied generated all the net gain of the global stock market. Ex-U.S., just 1.41 percent of firms generated $30.7 trillion in net wealth creation. The implications seem clear: an active manager is more likely to create a portfolio that underperforms one-month Treasuries, than outperforms it. This differs from Sharpe’s assertion that the difference between active and passive managers are fees. If only a sliver of the market is generating all its net gain, then a portfolio that does not capture the whole universe of stocks is unlikely to have returns that, pre-fees, match or exceed those of the market. Nonetheless, whether one views the arithmetic of active management from a Sharpean point of view or mine, active management is a loser’s game. Consider that, according to S&P Global’s SPIVA, which measures the performance of active managers against the S&P 500 and other indices across the world, in the last fifteen years, 87.98 percent of Large-Cap active managers have underperformed the S&P 500, and only 12.02% have outperformed.

Properly understood, risk should be viewed myopically, as being primarily the possibility of incurring a loss (the moment and existence of loss are more important than the knowledge of it), and secondarily, the possibility of underperforming some target rate of return.
Joseph Noko in “The Nature of Risk”,

It should be said that an index fund is not, strictly speaking, “passive”, nor does it represent the “market”. The S&P 500 is created around a simple set of rules: the 500 largest firms are chosen, each firm is allocated a share of the portfolio according to its relative size, and the portfolio is rebalanced every quarter. It should also be said that Claude Shannon’s demon, the Kelly criterion, Daniel Bernoulli’s work on risk, and Renaissance Technologies’ Medallion Fund, show that it is possible to beat the market while investing in firms that have zero-to-negative lifetime net gains. Moreover, the diligent investor can also work to make the necessary accounting adjustments to uncover a business’ true economics and properly value it. Investors such as Warren Buffet and Charlie Munger, Peter Lynch, and Davis Swensen, have displayed the requisite diligence and aptitude for this kind of work. In addition, active managers can reduce their search costs by hiring an investment research firm like New Constructs, who deploy their AI technology on thousands of financial reports to produce the best fundamental data in the world. Active investors have tools to bridge the gap between their results and those of passive investors, at the portfolio or accounting level, and this explains why the positive skewness is not as pronounced between active and passive managers as it is between stocks and one-month Treasuries. Nevertheless, it exists.

Time Preference and the Flow of Funds

It is an axiom of economics that an economic agent faces a number of choices when allocating capital: whether to save and invest, or to consume. Consumption occurs when an economic agent has a present preference for money, and uses their money to satisfy current wants, whereas saving and investment occur when an economic agent has a future preference for money and “lends” capital to an entrepreneur, either directly through the stock market, or indirectly by depositing money in the bank. The economic agent who prefers to defer consumption to some point in the future is paid an interest rate for doing so. At the aggregate level, society too has a time preference, with a changing appetite for consumption, saving and investment.

In Money in a Theory of Finance, John G. Gurley and Edward S. Shaw give a simple taxonomy of money, classifying it under “inside money” and “outside money”. These two kinds of money are produced by two sources: the government and the private sector. Inside money is composed of debt securities and loans created by private financial intermediaries, who exist to match the supply of capital, provided by savers, to the demand for it, emerging from investors. Outside money is so-called because it comes from outside the private sector, being a creation of the government. In the economic literature, it is often referred to as high-powered money, and colloquially, it is government money. Being from outside the private sector, the supply of outside money is not cancelled out by the demand for it, it is a net asset for the private sector.

These money forms are produced by a complex institutional structure made up of households, production firms, banks and governments. These sectors make decisions, and allocate capital, interacting with each other in the process, through the flow of inside and outside money, building up stocks of assets and liabilities. In keeping with double-entry bookkeeping, one investor’s financial asset is another’s liability, every transaction by one sector has an equivalent transaction in another, and every financial balance is met with an equivalent change in its net financial position. Wynne Godley, and Marc Lavoie, remark in their Monetary Economics,

Provided all the sectoral transactions are fully articulated so that ‘everything comes from somewhere and everything goes somewhere’ such an arrangement of concepts will describe the activities and evolution of the whole economic system, with all financial transactions (including changes in the money supply) fully integrated, at the level of accounting, into the processes which generate factor income, expenditure and production.
Monetary Economics, Wynne Godley, and Marc Lavoie

These economic activities can be demonstrated by way of a simple model of a closed economy, which is to say, an economy without any foreign trade or foreign capital flows. In this economy, there are just three sectors: households, firms and the government. This closed economy can be examined in terms of its sectoral balance sheets, balance sheets that may be combined as below:

In this simple model, households hold “cash instruments” issued by both firms and the government. By “cash instruments” means those financial instruments whose value is determined directly by the markets, such as securities, loans and deposits. Possessing no liabilities, their net worth is the sum of these cash instruments. Firms hold high-powered money as well as tangible assets, which they have acquired by issuing bonds and equities. The net worth of firms is zero. The government, possessing no assets, issued high-powered money to households and firms, and has a net worth that is the sum of these liabilities.

It can be said that the time preference of each part of the economy results in a demand for some type of money, a type of money that is supplied by another economic agent. In our simple model, a household’s preference for future consumption, or saving and investment, is a demand for the money of firms, in the form bonds and equities.

For our purposes, the question is, “What is the interest rate with which society is rewarded for investing in equities?” To simplify the problem, one can think of the S&P 500 as a single company whose outstanding shares have a market capitalization of $44.17 trillion. Companies supply these shares for investors at some market-determined price. This is our aggregate supply. Let “equity preference” or aggregate demand be the share of society’s portfolio devoted to equities. Where aggregate supply is a trivial thing to calculate, equity preference demands a more involved procedure. The pseudonymous author of the Philosophical Economics blog, Jesse Livermore, explains such a procedure in this article, “The Single Greatest Predictor of Future Stock Market Returns”. I encourage the reader to read it in conjunction with this article, as I have repurposed his calculation of aggregate demand for my own purposes.

Equity Preference and Future Returns

A more complex model of the sectoral balance sheets of the economy is presented by governments across the world and is known as a “flow of funds” report. The United States’ flow of funds accounts are prepared by the Flow of Funds section of the Federal Reserve, and published quarterly as the Z.1 Statistical Release. An early exponent of flow of funds analysis, Lawrence S. Ritter, wrote that,

The flow of funds is a system of social accounting in which (a) the economy is divided into a number of sectors and (b) a “sources- and-uses-of-funds statement” is constructed for each sector. When all these sector sources-and-uses-of-funds statements are placed side by side, we obtain (c) the flow-of-funds matrix for the economy as a whole. That is the sum and substance of the matter.
"An Exposition of the Structure of the Flow-of-Funds Accounts", Lawrence S. Ritter

Flow of funds accounts model the sectoral balances of an economy, that is, the financial stocks and flows of an economy, and the relationships between the two, in a consistent way. The sectors recognised within the flow of funds reporting are grouped into non-financial, and financial sectors. Of non-financial sectors, there are five: households and non-profit organisations, non-financial corporate business, federal government, state and local governments, and the rest of the world. Financial sectors consist of firms, including the Federal Reserve, and instruments.

The ebbs and flows of capital into and out of the equity market can be traced simply by cataloguing the market value of equities among investors. That alone, however, does not tell us a lot. What we want to know is how much of the aggregate or typical investor’s portfolio of cash instruments is allocated to equities.

When these entities borrow directly from investors, the investors get new bonds to hold. When the entities borrow from banks, the investors get new cash to hold. That’s because when a bank makes a loan, the money supply expands. The loan creates a new deposit that didn’t previously exist–some investor must now hold that deposit in his portfolio of assets.
It follows, then, that if we want to get an estimate of the total amount of bonds and cash that investors are holding at any given time, all we have to do is sum the total outstanding liabilities of each of the five categories of real economic borrowers. Those liabilities either translate into cash that an investor somewhere is holding (if the entity took a loan from a bank, which expands the money supply), or they translate into a bond that an investor somewhere is holding (if the entity borrowed directly from the investor). Note that the average bond trades close to par (with some above, and some below), so, in aggregate, the value of the liabilities approximates the total market value of the bonds.
Banks don’t generally hold stocks. So to estimate the total amount of stocks in investor portfolios, what we need to know is the total market value of all stocks in existence. We end up with the following equation:
Investor Allocation to Stocks (Average) = Market Value of All Stocks / (Market Value of All Stocks + Total Liabilities of All Real Economic Borrowers)
“The Single Greatest Predictor of Future Stock Market Returns”, Jesse Livermore

By real economic borrowers, Livermore means the following categories in Flow of Funds reporting: Households, Non-Financial Corporations, State and Local Governments, the Federal Government, and the Rest of the World, all of whom borrow from investors. His equation can be simplified to,

Equity Preference = Market Capitalisation to Stocks/Cash Instruments

In our simple model, household equity preference is $375/($200+$15+$375) = 6.6%. For the real economy, one is obliged to exclude financial intermediaries from this analysis, because they are obviously not investors, but matchmakers, holding financial assets on behalf of investors. The non-financial sector uses high-powered money kept by a financial intermediary and debt securities and loans borrowed from a financial intermediary, in order to finance purchases of equities. The share of equities held by the non-financial sector in relation to its financial assets and liabilities, represents the allocation to equities of the aggregate investor.

One can model this with data from FRED, the disaggregated data of which is also available.

One can then match this to the S&P 500's total returns compounded over subsequent decades, to produce the following riveting chart, for the January 1, 1952 to December 31, 2023 period:

How robust is this finding? Over that period, equity preference explained subsequent 10-year returns by an R-Squared of 0.7448618131, implying that 74.5 percent of the subsequent S&P 500 10-year total returns are explicable through U.E. equity preference.

One should say that people do not invest in equities for their own sake, one invests for future returns, and so one can say that as the demand for future returns increases, their supply decreases, and vice versa. Such is the relationship between the two that Livermore proposes to redefine total returns in the following way,

Total Return = Price Return from Change in Aggregate Investor Allocation to Stocks + Price Return from Increase in Cash-Bond Supply (Realized if Aggregate Investor Allocation to Stocks Were to Stay Constant) + Dividend Return

Forecasting Future Stock Market Returns

This is the longest period of practically uninterrupted rise in security prices in our history. The rise was more rapid than has ever been seen, and its speculative attraction influenced a larger part of the public than ever before," it read. "The psychological illusion upon which it was based, though not essentially new, has been stronger and more widespread than has ever been the case in this country in the past.
The Business Week, November 2, 1929

The current era is an era of astonishing returns, but, wealth destruction is fundamentally bound up with the nature of risk, and this era cannot go on. The truth of this model is that as the demand for future returns increases, the supply of those future returns declines. That lesson is borne out by the results of translating Livermore's framework into a forecasting model. Using a model I built to forecast 10-year S&P 500 total returns leads to an awful number: 1.16%, the average total returns that are likely, if the predictive value of the model holds, over the 2024-2033 decade, a return lower than that available by simply investing in Treasuries. As the market scales its halcyon heights, it has become almost unsustainably high.

What does this mean for the competition between active and passive investors? Instinctively, it is easy to reach for the conclusion that we are entering a golden age for active investors, but I think the true conclusion is that passive investment will continue to outperform active investors. Diversification is essential for investors because it lifts a portfolio's geometric returns toward its average returns, and this is the beauty of passive investment: one takes a group of stocks that are largely stocks that, across their life cycle, will deliver lower returns than Treasures, and convert them into a portfolio that delivers superior returns. Passive investors have the edge because they have no real information costs, costs which burden active investors. That reality will not change in the decade we have entered. So, if passive investors are earning 1.16% a year, the typical active investor will earn less. Few investors will enjoy the double-digit returns that have become a kind of lazy, achievable target.

Economic Book Value: An Estimate of a Stock’s Intrinsic Value

Superficially, a valuation methodology exists to help an investor estimate, within a reasonable range, how much something is worth. Investing, however, is not merely an intellectual exercise. The fundamental problem that an investor faces is that, while it is absolutely essential to invest in order to grow one’s wealth, the nature of risk is such that investing is more likely to destroy wealth than create it. This tendency toward wealth destruction is what Daniel Bernoulli called, “nature’s admonishment to avoid the dice”. The true purpose of a valuation methodology is to guide the investor toward those investment opportunities that offer returns greater than those earned by the market, while not exposing one to the risks of wealth destruction. The following valuation methodology, grounded upon a series of accounting adjustments I make, represents my process for estimating the intrinsic value of a business, or what I, following New Constructs, call its “economic book value”.

Principles and Definitions

An investor is, before anything, a reader in search of truth, a probabilistic truth scattered across the pages of periodic reports. Benjamin Graham and David Dodd summed up the investor’s mission thus:

In all of these instances he appears to be concerned with the intrinsic value of the security and more particularly with the discovery of discrepancies between the intrinsic value and the market price.
Security Analysis, by Benjamin Graham and David Dodd

The question remains, what is intrinsic value? Perhaps the best definition of intrinsic value is one proffered by Jesse Livermore of the perceptive Philosophical Economics blog, where he says, “The ‘intrinsic value’ of a security is the maximum price that an investor would be willing to pay to own the security if he could not ever sell it”. In other words, it is the maximum economic benefit if a shareholder was forced to hold a stock for the remainder of its life, and so, mathematically, it is equivalent to the present value of the cash that can be taken out of a business during the remainder of its life. It is noteworthy that John Burr Williams opened his ground-breaking, The Theory of Investment Value, with the words, “Separate and distinct things not to be confused, as every thoughtful investor knows, are real worth and market price…”, and went on to show that the “real worth” of a business could be determined by an “evaluation by the rule of present worth”. Consequently, a business’ intrinsic value is equal to the present value of its future net cash flows.

Since 1890, when Alfred Marshall published his Principles of Economics, we have known that the value, or economic benefit that arises from owning a business, is created when that business grows its revenue, and earns a return on invested capital (ROIC) in excess of the opportunity cost, or what standard financial theory now calls the “weighted average cost of capital” (WACC). This is equivalent to the following value driver formula:

Value = [NOPAT(1-g/ROIC)]/(WACC – g)

Here, NOPAT refers to net operating profit after taxes, or the profits that a business’ core operations earn after cash operating taxes have been paid; g refers to growth; ROIC to NOPAT/Invested Capital, where invested capital refers to the cumulative investments into a business; and WACC refers to the economic benefit that could be gained from investing in a similarly risky investment opportunity.

In practice, one does not use the aforementioned value driver formula given its assumption of constant growth ROIC for the remainder of a security’s life, but it is useful for showing how the value drivers relate. For a single period, value creation can be measured using economic profit, which is ROIC in excess of WACC, scaled by invested capital:

Economic Profit = Invested Capital x (ROIC – WACC)

Discounting a company’s future economic profits and adding that to its starting invested capital, provides one with an estimate of value:

Value = Starting Invested Capital + PV(Projected Economic Profit)

This approach is mathematically equivalent to the discounted cash flow (DCF) valuation.

Value can also be estimated using the cash-flow perpetuity formula, which assumes a constant growth rate, such that,

Value = FCF/(WACC – g)

Here, FCF refers to free cash flow, that is, the cash flows generated by a business’ core operations, after paying for incremental investments, or increase in invested capital.

FCF = NOPAT – Incremental Investment

The value principle comes with a corollary, what Richard Brealey, Stewart Myers, and Franklin Allen, in their textbook, Principles of Corporate Finance, refer to as the law of conservation of value: any activity that does not increase cash flows does not create value. One early application of this principle is the work of Merton Miller and Franco Modigliani, who showed that a business’ capital structure is irrelevant to its value, unless that capital structure changes the business’ cash flows.

Since 1890, we have also known that, over the long run, returns are driven down toward WACC, as a result of a gravitational pull of competition. The period in which a business can earn an economic profit is referred to as the “competitive advantage period”, or “growth appreciation period”. That period’s duration is highly dependent on the ferocity of competition within an industry. In highly competitive industries, value creation is fleeting, and in oligopolistic and monopolistic market structures, value creation is enduring. In Edward Chancellor’s examination of Marathon Asset Management’s capital cycle framework, Capital Returns, he explains the resulting ebbs and flows of capital thus,

Typically, capital is attracted into high-return businesses and leaves when returns fall below WACC. This process is not static, but cyclical – there is constant flux. The inflow of capital leads to new investment, which over time increases capacity in the sector and eventually pushes down returns. Conversely, when returns are low, capital exits and capacity is reduced; over time, then, profitability recovers. From the perspective of the wider economy, this cycle resembles Schumpeter’s process of “creative destruction” – as the function of the bust, which follows the boom, is to clear away the misallocation of capital that has occurred during the upswing.

This insight by Marathon has been given the imprimatur of academic backing, by way of the asset growth effect. In their paper, “Asset Growth and the Cross-Section of Stock Returns,” economists, Michael Cooper, Huseyin Gulen, and Michael Schill, found that a business’ asset growth is more predictive of its future abnormal returns than traditional value, size and momentum. Returning to the key value driver formula, it can be restated to reflect the corrosive impact of competition. The convergence formula reflects that return on net new investment will converge over time on the WACC, as a business’ competitive advantages are ground down by competition:

Continuing Value = NOPAT/WACC

Here, while a firm may grow, that growth does not result in any value creation whatsoever, as the return on new investment capital (RONIC) equals the opportunity cost. This leads to my measure of intrinsic value, which New Constructs refers to as “economic book value” and which has also been referred to as “pre-strategy value” because it is the perpetuity value of the business before management crafts a strategy to enhance that value:

Economic Book Value = (NOPAT/WACC) – Adjusted total debt (including off-balance sheet debt) + Excess cash + Unconsolidated Subsidiary Assets + Net Assets from Discontinued operations – Value of Outstanding Employee stock option liabilities – Under (Over) funded Pensions – Preferred stock – Minority interests + Net deferred compensation assets + Net deferred tax assets

In order to do all this, the investor must make a series of accounting adjustments that uncover the true economics of a business.

Step 1: Turn Accounting Statements Into Economic Statements

Annual reports are not merely long, and complex, with often abstruse language that seems calculated to befuddle the reader, they are also structured in ways that unintentionally disguise operating performance. To start with, financial statements are not designed to be particularly helpful for an investor seeking to understand the operating performance and value of a business. This is because they mix together core and ancillary business activities and transitory shocks. Income statements commingle operating income with interest expense and other non-core, non-recurring items; balance sheets mush together operating assets, non-operating assets and sources of financing; and cash flow statements blend operating cash flow with investing and financing cash flow. A trivial example from Meta Platform’s income statement from its 2023 10-K will serve as an example of this unhelpful structure:

“Interest and other income (expense), net”, are very obviously not part of Meta’s core business activities. This is, as I suggested, is a fairly trivial example, and “income from operations” is a deeply flawed attempt at estimating pre-tax core earnings. An added difficulty is that the elements we need to determine the operating performance of a business are not simply on the face of the financial statement, but they are sprinkled across the annual report, in the MD&A, the footnotes and notes. Moreover, managers are given enormous discretion in classifying items and how they can present disclosures. Further complications are that judgement must be exercised to determine a disclosure’s impact on operating performance and to place each disclosure in the proper economic category.

In addition, the auditor’s report is sometimes a source of information about the quality of a firm’s earnings. For instance, in its 2023 annual report, Meta’s auditors, Ernst & Young (EY), pointed to the difficulty in estimating loss contingencies, and “more-likely-than-not to be sustained” federal tax liabilities, interest and penalties sought by the Internal Revenue Service (IRS), and measuring qualifying tax benefits. Such matters usually demand of the reader an analysis of whether existing policies are conservative, and to note any changes in policy and their impact on earnings.

1.1 Create a NOPAT Statement

In their wonderful paper, “Core Earnings: New data and Evidence”, researchers Ethan Rouen, Eric C. So, and Charles C.Y. Wang, present an accurate, rigorous, replicable, and transparent way to estimate core earnings. Their paper is based on an analysis of the remarkable work by financial research firm, New Constructs, who use artificial intelligence and human analysts, to analyse thousands of 10-Ks, and classifies all earnings related quantitative disclosures into their appropriate economic category. At the time the paper was published, New Constructs analysed 60,000 10-Ks, between 1998 and 2017. One of the great achievements of this remarkable paper is that it presents an accurate, rigorous, replicable, and transparent approach to estimating core earnings, while also showing that there is enormous alpha to be gained from having an accurate measure of core earnings. It is that methodology that I use.

In order to get a sense of the recurring and repeatable profitability of the core business, I calculate its NOPAT. NOPAT excludes income from ancillary business activities and transitory shocks, is independent of a company’s capital structure, and is available not just to shareholders, as with GAAP net income, but to all capital providers. NOPAT must be defined in a way that is consistent with one’s definition of invested capital, so that NOPAT is entirely earned from invested capital.

This approach uses the same economic categories detailed in New Constructs’ work and Rouen, So and Wang’s paper, with input from that great textbook, Valuation, by Tim Koller et al. A great deal of judgement is involved in placing all the quantitative items into the correct economic adjustment category, as well as the patience to go through an entire annual report, to find both hidden and reported items. By “hidden” is meant those items that are off the face of the income statement, either because they are located in the MD&A or footnotes, or commingled within a reported item; whereas, by “reported” is meant those items that are on the face of the income statement. I calculate NOPAT from both an operating and financing perspective, which are mathematically equivalent, but for the sake of simplicity, below I will only present a detailed reconciliation of Meta’s 2022 GAAP net income with NOPAT, which shows the various adjustments that I make in order to calculate NOPAT, and which are added back to the firm’s GAAP net income.

Adjustments to convert reported GAAP income to NOPAT:

Remove asset write-downs hidden in operating expenses
Remove non-operating expenses hidden in operating earnings
Remove non-operating income hidden in operating earnings
Add back change in reserves
Remove income and loss from discontinued operations (except for REITs)
Add back implied interest for the present value of operating, variable and not-yet commenced leases
Add back foreign currency exchange losses and gains
Adjust for pension plan costs
Adjust for non-operating tax expenses
Historical Adjustments: Add back goodwill amortisation and include employee stock option expense prior to accounting changes
Remove reported non-operating items

An example of this is shown below, where I have estimated Meta’s NOPAT for the period 2011 to the last twelve months ending 1Q 2024:

1.2 Create an Invested Capital Statement

Invested capital is the accumulation of investments that have been made into a business’ core operations, in order to earn NOPAT. As with NOPAT, I calculate invested capital from both an operating and financing perspective, but for the sake of simplicity, the adjustments I make will be used to show a detailed reconciliation of Meta Platforms’ total assets to its invested capital. In the abstract, the adjustments to convert reported assets to invested capital are the following:

Add back off-balance sheet reserves
Add back off-balance sheet debt due to operating, variable and not-yet commenced leases
Remove discontinued operations
Remove accumulated Other Comprehensive Income
Add back asset write-downs
Remove deferred compensation assets and liabilities
Remove deferred tax assets and liabilities
Remove under or over funded pensions
Remove excess cash
Prior to 2002: Add back unrecorded and accumulated goodwill
Time-weight acquisitions
Remove non-operating unconsolidated subsidiaries

Applying this to Meta Platform’s balance sheet gives the following estimate of invested capital for the period 2011 to the LTM:

1.21 Calculate ROIC

With NOPAT and invested capital calculated, calculating ROIC is a trivial affair, simply a matter of dividing NOPAT by average invested capital, which averages invested capital from the beginning and end of the year while also adjusting for the impact of acquisitions during the year. ROIC uncovers the true economics of the company, matching cash returns from cash cumulative investments.

1.22 Calculate Free Cash Flow (FCF) and FCF Yield

FCF, the amount of cash available for distribution to all investors, is the dividend that a company could pay and reflects the profitability of the business. Having already given the formula for FCF in the "Principles and Definitions" section, below is a demonstration of what such a calculation looks like:

FCF Yields are assigned a risk/reward rating using the following classification:

Step 2: Calculate WACC

Next, I calculate the weighted average cost of capital (WACC). WACC is composed to two primary elements: the cost of equity and the cost of debt. I calculate the cost of equity using the capital asset pricing model (CAPM), with beta, its weakest and most controversial component, calculated to express the risk of the stock’s excess returns being lower than that of the market’s in a down market. This is known as D-CAPM. I normalize beta to reduce its impact on my calculations of WACC. For the United States, I use 30-year Treasuries as my risk-free rate. The cost of debt is calculated with the 30-year Treasury bond rate as the risk-free rate added to a spread based on that company’s credit rating, to get the marginal cost of debt. Market values are used, when available, to weight the costs of equity and debt, although, generally, debt values are book values and equity values are market values.

Step 3: Calculate Economic Profit

Economic profit, as already defined above, is "ROIC in excess of WACC, scaled by invested capital":

Economic Profit = Invested Capital x (ROIC - WACC)

There is a strong correlation between economic profits and market valuation, with a regression by New Constructs of the S&P 500 component companies economic profit and market valuations giving an R² of 0.66854, meaning that 66.854% of market values are explained by economic profits. New Constructs further explained that, "Note that the above regression analysis is based on the 489 companies in the S&P 500 that we cover except for Lorillard (LO). Because of its super high ROIC, including LO in the regression drives the r-squared up to 94%."

The goal of a rationally run business is to create value, which means earning as much economic profit as is possible. It is not surprising that markets reward businesses who achieve this goal. The difficulty is in having the expertise and diligence to make the accounting adjustments necessary to know what a business' true profitability is.

Step 4: Estimate Economic Book Value

Information from the first step will be brought to bear in this stage, to arrive at an estimate of intrinsic value, using economic book value as a measure of the maximum economic benefit that can be derived, based upon proven results, rather than on any attempts at forecasting how management can or will enhance value. The adjustments for economic book value, and indeed, for my discounted cash flow model, enterprise value calculations, are the following:

Below follows an estimate of Meta’s economic book value:

The subsequent PEBV ratios can be assessed with the risk/reward system below:

The Weighted Average Cost of Capital (WACC)

An investment is a choice to foregore present consumption in favour of future consumption, in exchange for which the investor is given a return which can simply be referred to as “interest”. The interest promised to the investor is either contractually defined, and capped, as with bonds, or, is uncertain and uncapped, as with equities, or some blend of both. By deferring present consumption and investing, investors stake a claim to a financial asset’s defined and capped or undefined and uncapped future cash flows, the net present value of which are estimated by discounting them at the prospective “interest rate”, or cost of capital. The weighted average cost of capital (WACC), first proposed by Franco Modigliani and Merton H. Miller in their paper, “The Cost of Capital, Corporation Finance and the Theory of Investment”, blends the interest rates promised to a firm’s differing sources of capital into a single number. Or, more properly, WACC blends a real cost, the cost of debt, and an expected return, that of equity, into a single number. Properly calculated, free cash flows (FCF) discounted by WACC will return the same value as equity cash flows discounted by the required return on equity. WACC allows one to properly value a firm’s future cash flows based on the differing interest rates its sources of capital require, whether they are certain claimants, its debt investors, or residual claimants, its equity investors, or some hybrid of the two. It is against this number that firms weigh, or should weigh their returns on invested capital (ROIC) to determine if they are creating value.

WACC is estimated by assessing the opportunity cost that investors bear when they invest. Given two equally risky propositions, an investor will “lend” their savings to that risky proposition that offers the highest rate of return. When one invests with a firm, that firm uses that capital to earn a greater rate of return, ROIC, than the rate of return the investor could get in a similarly risky investment. A firm with a ROIC of 15% at a time when investors could earn 8% in similarly risky propositions, creates value for its investors, because that means that their claim to future cash flows are either more certain, or larger.

WACC is composed of three elements: the cost of equity, the after-tax cost of debt, and the firm’s target capital structure. The formula I generally use to estimate WACC is given below, a formula that grows more complex the more complex the firm’s capital structure and simpler the simpler the firm’s capital structure:

WACC = (D/V)k_d(1-T_m) + (E/V)k_e + (P/V)k_p

where

D/V = target level of debt to value using market-based values
E/V = target level of equity to value using market-based values
kd = cost of debt
ke = cost of equity
Kp = cost of preferred capital
Tm = company’s marginal tax rate on income

I estimate the cost of equity using the capital asset pricing model (CAPM), with an important adjustment to reflect my views on risk. Eugene Fama and Kenneth French’s three-factor and five-factor models and other factor models are more accurate than standard CAPM, but one buys accuracy along with almost unmanageable complexity. Beta is the critical factor in CAPM, and measures a stock’s sensitivity to changes in a benchmark index, which serves as a proxy for the market. in the United States, I use the S&P 500 as the market proxy. Under CAPM, the expected return on a security is calculated as below:

Expected return = Risk-free rate + β(Market return – Risk-free rate)

where “β”, is, of course, beta, which measures firm-specific risk and can, because it is “unsystematic”, be reduced through portfolio diversification, and “Market return – Risk free rate” is the equity risk premium (ERP), the difference between the market’s expected return for the market and the risk-free rate and captures “systematic risk,” or that risk that cannot be diversified away. I use the yield on 30-year Treasuries as a proxy for the risk-free rate.

Of expected return, I cannot resists recalling an anecdote by Merton Miller,

I still remember the teasing we financial economists, Harry Markowitz, William Sharpe, and I, had to put up with from the physicists and chemists in Stockholm when we conceded that the basic unit of our research, the expected rate of return, was not actually observable. I tried to tease back by reminding them of their neutrino –a particle with no mass whose presence was inferred only as a missing residual from the interactions of other particles. But that was eight years ago. In the meantime, the neutrino has been detected.

Not only is the expected return not observable, the literature tends to conflate historical, expected, required and implied ERPs. The historical ERP (HEP) is the most objective, but it tells us little about the size of the premium in future, although even here there are differences in calculations and benchmarks that lead to different HEPs. I calculate the HEP by subtracting the average geometric return for the S&P 500 from the average geometric return for 30-year Treasuries (DGS30), for the 1977 to 2023 period, and then adjusting the figure downwards for survivorship bias, by the 0.8% excess returns by which Dimson, Marsh and Staunton found the U.S. markets had exceeded a 17-country composite return.

Is this the same as what I expect the premium to be? No, as I have discussed, I anticipate that this decade will see average S&P 500 returns of just over 1%, meaning my expected risk premium (EEP) is negative, but this is not the market's EEP. Moreover, I do not think there is a single and unique implied equity risk premium (IEP) or required risk premium (REP): these are subject values. In effect, I treat the HEP as my REP.

In his pathbreaking paper, "Portfolio Selection", Harry Markowitz equated risk with “volatility of returns” and this broad view of risk forms part of modern portfolio theory. Markowtiz proposed that investors maximise a utility function that matched expected returns, the arithmetic average of available returns, with their associated volatility. Under this model, investors seek to reduce their volatility for a given return or increase their returns for a given level of volatility. The trouble with his model was and has always been clear to Markowitz: this broad view of risk runs counter to one's intuition and ideas of risk, as I have explained before:

Since Harry Markowitz’s seminal 1952 paper, “Portfolio Selection”, it is generally accepted that risk is best measured in terms of a “volatility of returns”, in other words, the upward and downward swings in prices. Under this measure, if one expects a return of 10% from an investment, both the chance that the return will be lower, or higher than that expected return, are classed as risk! Few investors and managers, if any, would accept this view. Just eighteen years after Markowitz’ paper, one survey found that, across eight industries, most managers said they believed that semivariance, a measure of “downside risk”, was a more plausible measure of risk than variance. Decades later, that unease with theory remains. This notion of risk clearly goes against our intuition. One does not say, “There is a risk I will make a return greater than expected on this investment”. This notion of risk is also self-contradictory: it would seem perverse to imagine as rational behaviour a situation in which a person sought to limit all their risk, that is, both downside and “upside” risk. Defenders of the position would claim that when they refer to risk, they are of course referring to downside risk, which begs the question why the scope of this definition of “risk” allows for “upside risk” to be defined as such. It is not a merely academic argument: investors and managers make decisions based on risk measures that imply this very logic. It seems evident that whereas a person would want to limit their downside risk, they would be happy to have their profits run far in excess of what they expected.

Markowitz himself observed in his similarly titled tome, that his earlier use of variance as opposed to semi-variance, a measure of downside risk, was due to a lack of computing power and the greater familiarity that practitioners had with variance as opposed to semi-variance. Not only is "upside risk" not a risk, but, Markowitz observed that the use of variance assumes that returns are normally distributed. The great man was aware of the inherent absurdity of so catholic a notion of risk, saying that semi-variance was a “more plausible measure of risk” and that, “the semideviation produces efficient portfolios somewhat preferable to those of the standard deviation” . About the same time, A.D. Roy, in his paper, "Safety First and the Holding of Assets", noted that an investor is not interested in what happens on average, but will happen in a particular instance, and that the maximisation of expected value is incompatible with diversification. Roy criticised economic theory as being “set against a background of ease and safety”, rather than “poorly chartered waters” or hostile jungles, assumes “economic survival”, and thus being incapable of understanding why investors act as if they see disaster everywhere. Consequently, he modelled downside risk, or mean semivariance, because he felt that investors are driven by a “safety first” logic. Nevertheless, it was only in the 1980s, when post-modern portfolio theory was delivered by Frank Sortino and others, that a more myopic view of risk became the foundation of an alternative way of forming portfolios.

To conform with my myopic view of risk, I calculate downside beta as the sensitivity of a stock's excess logarithmic returns to the market's downside excess returns, where "excess return" is the difference between the stock or market return and the returns on the risk-free security. This is known as the D-CAPM approach. I use industry and sector averages based on five years of weekly prices, in order to minimise the impact of beta on my cost of equity measure. An example of this can be seen in this spreadsheet.

To estimate the cost of debt for firms, I use 30-year Treasuries as the risk-free rate, in conformity with prior remarks, and where that is unavailable, the 20-year rate. To that, I add the debt spread associated with its debt rating, per Moody's or S&P, on its long-term debt. This pre-tax cost of debt is then multiplied by (1-T_m) to get the after-tax cost of debt.

The cost of preferred stock is simply the preferred dividends divided by the value of preferred capital.

Regarding the target capital structure, I tend to use historical values rather than try and presume to know what managers will do. This is because firms tend to be very conservative about changing capital structures.

Diamond Hill's' WACC, for the period 2019 to the last twelve months (LTM) ending 2Q 2024, as I estimate it, is given below:

Free Cash Flow (FCF) and FCF Yield

Free cash flow (FCF) is the cash that is available to all investors, whether debt holders or shareholders, after taxes have been paid. This is the after-tax cash flow that would be earned if a business was entirely equity financed. Consequently, it is not only free from non-operating items, but from items related to capital structure as well. When John Burr Williams developed the theory of DCF analysis in his ground-breaking book, The Theory of Investment Value, he assumed that intrinsic value was a function of dividend flows and selling price, and that under certainty, the value of a business was the sum of its future dividends. (This idea would lead to Myron J. Gordon’s dividend discount model.) Therefore, one can view FCF as what a company could pay in the form of dividends. It can be defined as,

FCF = NOPAT – Change in Invested Capital

where change in invested capital is

Change in Invested Capital = Change in Net Working Capital + Change in Total Adjusted Fixed Assets

The level of available FCF must be assessed against the growth opportunities available for the business, in order to make a definitive determination about the quality of that FCF.

Below is my calculation of Diamond Hill’s FCF for the period 2019 to the last twelve months (LTM) ending 2Q 2024:

If the purpose of an investor is to buy assets whose price implies low expectations and sell those assets whose price implies high expectations, then the question one should ask here is, “What are the market’s FCF expectations?” This cab be ascertained by calculating the FCF yield:

FCF Yield = FCF/Enterprise Value

Where enterprise value is the value of a business for all its sources of financing. The FCF Yield is ranked according to the risk/reward rating below:

Invested Capital

Annual reports are not merely long, and complex, with often abstruse language that seems calculated to befuddle the reader, they are also structured in ways that unintentionally disguise operating performance. To start with, financial statements are not designed to be particularly helpful for an investor seeking to understand the operating performance and value of a business. This is because they mix together core and ancillary business activities and transitory shocks. Income statements commingle operating income with interest expense and other non-core, non-recurring items; balance sheets mush together operating assets, non-operating assets and sources of financing; and cash flow statements blend operating cash flow with investing and financing cash flow.
“Net Operating Profit After Tax (NOPAT)”, by Joseph Noko

Invested Capital = Total debt & leases + Equity Equivalents + Common Equity

where,

Total debt & leases = Short-term debt + long-term debt + operating, variable and not-yet commenced leases

From an operating perspective,

Invested Capital = Net Working Capital + Total Adjusted Fixed Assets

where,

Net Working Capital = Operating Current Assets – Non Interest-Bearing Current Liabilities

and,

Total Adjusted Fixed Assets = Tangible Assets + Intangible Assets + Other Assets

I make a number of adjustments to strip away the impact of non-recurring and non-core items in order to unearth the true economics of a business. An example of what that looks is given in the tables below, with Diamond Hill as my subject.

Firstly, I calculate Diamond Hill’s invested capital from an operating perspective, for the years 2019 to the last twelve months (LTM) ending 2Q 2024:

This can be reconciled with the firm's total assets, as shown below:

The virtue of this approach is that it gives me an insight into the true economics of a business while being replicable, scalable and transparent.

Net Operating Profit After Tax (NOPAT)

An added difficulty is that the elements we need to determine the operating performance of a business are not simply on the face of the financial statement, but they are sprinkled across the annual report, in the MD&A, the footnotes and notes. Moreover, managers are given enormous discretion in classifying items and how they can present disclosures. Further complications are that judgement must be exercised to determine a disclosure’s impact on operating performance and to place each disclosure in the proper economic category.

Therefore, in order to analyse the operating performance of a business, a rather mundane and yet very important task must be undertaken: the operating, non-operating and sources of financing items of each financial statement must be properly classified, not only on the face of these financial statements, but in the MD&A, the footnotes and notes. In doing so, I make a series of adjustments to convert the income, and balance sheets into net operating profit after tax (NOPAT), invested capital and free cash flow (FCF) statements that reveal the true economics of a business.

I calculate NOPAT from both an operating and financing perspective, which are mathematically equivalent. From a financing perspective,

GAAP Net Income

+ Adj. for Capitalized Expenses

+ Increase in Equity Equivalents

– Other Income

+ Other Expenses

– Hidden Items

+ Interest Expense After Taxes

= NOPAT

Whereas, from an operating perspective,

Operating Revenue

– Operating Expenses

– Hidden Items

= Earnings Before Interest and Taxes (EBIT)

+ Goodwill Amortization

= Earnings Before Interest, Taxes and Amortisation (EBITA)

+ Adj. for Capitalized Expenses

+ Income Equivalents

= Net Operating Profit Before Tax (NOPBT)

– Cash Operating Taxes

= NOPAT

An example of the fruits of this procedure is given below, where I first estimate Diamond Hill’s NOPAT from an operating perspective, for the years 2019 to the last twelve months (LTM), ending 2Q 2024:

This can be reconciled with the firm's GAAP net income, as shown below:

Unconsolidated Subsidiary Assets, a Valuation Adjustment

Unconsolidated subsidiaries, also referred to as investments in associates, investments in affiliated companies, and equity investments, are businesses wherein a firm has a significant stake that falls short of control, which equates to a 20% to 50% stake, and as such, they come under equity method accounting.
“Non-Operating Unconsolidated Subsidiaries, an Invested Capital Adjustment”, Joseph Noko

Where the unconsolidated subsidiary’s income is disclosed, I consider that income as operating and add it to my calculation of the parent company’s NOPAT, and invested capital and where it is not, I consider it as non-operating and it does not form part of my calculation of NOPAT, given the figures are undisclosed, and invested capital, and is added to my calculation of economic book value (EBV), just as if it were excess cash.

Excess Cash, a Valuation Adjustment

Firms use a portion of their cash and cash equivalents and investments as operating cash for the running of the business, and any cash beyond this amount is excess cash and a non-operating asset. As a rule of thumb, I assume that operating cash is equal to 5% of revenue, increasing or decreasing this requirement according to the firm’s operating profitability. Excess cash grants firms optionality, and protection against crisis, and, compounds as a consequence of a firm’s profitability.
“Excess Cash, an Invested Capital Adjustment”, Joseph Noko

As excess cash is not needed for operations, it can be distributed to shareholders, and so, I add it to my calculation of economic book value (EBV). In 2023, Meta Platforms had $61.48 billion in excess cash, which I added to my calculation of its EBV.

Discontinued Operations, a Valuation Adjustment

The logic of discontinued operations is that they are not a component of core operations and therefore, not only do their earnings not belong in a calculation of net operating profit after tax (NOPAT), they also do not belong in a calculation of the invested capital that generates NOPAT. So, I banish them from my calculation of invested capital.
“Discontinued Operations, an Invested Capital Adjustment”, Joseph Noko

When it comes to estimating economic book value (EBV), one can say that the logic of discontinued operations is that, if businesses are held for sale, the cash earned from that sale is cash that enriches shareholder value. Therefore, it makes sense to add the net assets of discontinued operations to EBV.

Deferred Compensation Assets and Liabilities, a Valuation Adjustment

Deferred compensation is that portion of employee compensation that has been set aside for future payment. Firms create plans to manage the assets that will be used to settle these liabilities. Consequently, deferred compensation assets are a non-operating liability, which is to say that they are not part of the invested capital that is used to earn net operating profit after tax (NOPAT) for shareholders.
“Deferred Compensation Assets, an Invested Capital Adjustment”, Joseph Noko

Although deferred compensation agreements create a liability for a business, that business may not match that liability with requisite assets. Deferred compensation assets are netted against deferred compensation liabilities to determine the funded status of the firm’s obligations. Where there is a net asset, that is added to my calculation of economic book value (EBV) and where there is a net liability, that is deducted from my calculation of EBV.