Saturday, 10 March 2012

DCF Valuation: The classic work of John Burr Williams

The valuation model for estimating the investment value of an operating enterprise in the private market, independent of the stock market price quotations, is based on the discounted cash flow (DCF) method using the time value of money. 


The classic work of John Burr Williams (see the models section at theory ) is the basis for the development of most equity valuation models, and his work is here referred to as the DCF Model rather than the narrower misleading name of Dividend Discount Model or DDM


For academic models of equity valuation, see Investments by Brodie, Kane and Marcus in General Books, or go to textbook models. For less academic approaches to firm valuation, see Damodaran on Valuation in Special Books, or go to his practical modelsof equity valuation. For a practical firm valuation model, see the McKinsey model tutorial with an example company valuation and downloads in a working paper at the Stockholm School of Economics. The McKinsey approach is the subject of the book titled Valuation by Tom Copeland et al in General Books.

The general model can be expressed verbally, mathematically, and graphically. 


Thus, in words:

1. If you commit your cash to a particular investment opportunity, then what cash can you expect to get out of it in return? What is your reward for abstinence and risk-taking?

2. What are the estimated net cash flows attributable to this proposed investment; i.e., what are the expected dividend distributions and the future terminal selling price?

3. What is the present value of these net cash flows, discounted at an appropriate rate of interest? This is the intrinsic economic value of the equity investment.

4. What is the margin of safety, both in dollars and in percentage? Is the intrinsic value per share of common stock greater than the stock market asking-price quotation by an amount sufficiently compelling to justify a long-term commitment to this particular investment?


Mathematically, the DCF model can be expressed both in an abstract standard form for the general case and in many concrete forms for simplifying special cases. Conceptually, the DCF Model is like an ideal of Plato which manifests itself in different empirical forms. We refer to these empirical forms types of the DCF Model. In all forms, the net present value of the investment, i.e., its intrinsic economic value, is equated with the sum of the products of each net cash flow and its discount rate. After intrinsic value has been estimated from fundamental data, it can be expressed in terms of earnings, book value, dividends, sales, cash flow, or other accounting measures, but this is not necessary. 

Graphically, the model can be expressed in two dimensions as a horizontal time line with vertical bars showing positive and negative net cash flows, above and below the line respectively, from the date of your investment at time zero to the date of your future sale at the end of your horizon for this investment.


http://www.numeraire.com/value.htm

PE/G ratio

Some investment strategies seek growth for its own sake or growth for the sake of growth rather than growth for the sake of value. 


Wall Street wisdom (pardon the oxymoron) adheres to the KISS principle as its highest virtue: Keep It Short and Simple. Most highly prized by brokers are slogans that fit easily on t-shirts and bumper stickers. 


As an example, one popular investment rule of thumb is that for a fully and fairly valued growth stock, the stock's price-to-earnings ratio should be equal to the percentage of the growth rate of the earnings per share of the associated company, i.e. PE = G. As with any such rule of thumb, this is not only superficial but also arbitrary and capricious. 


A common screen based on this heuristic is the ratio of the PE ratio to the EPS growth rate, or the PE/G. In an effort to better fit the historical performance of cyclical stocks and large-cap stocks, ad hoc variations on the PE/G ratio include 

  • (1) using an estimated future growth rate instead of an historical growth rate or PE/FG, 
  • (2) adding the dividend yield percentage to the EPS growth rate percentage or PE/DG, and 
  • (3) adding two time the dividend yield percentage to the EPS growth rate percentage or PE/2DG.

A rapidly growing company presents special problems in valuation.

A rapidly growing company presents special problems in valuation. John Burr Williams (1938:560) succinctly writes "They had high hopes for their business, but no logical evaluation of these hopes in terms of stock prices. The very fact that [the company] was one of the hardest of all stocks to appraise rationally was the reason why it sold at the most extravagant prices, for speculation ever feeds on mystery, as we have seen before."

The problem with estimating an approximate appraisal value for rapidly growing companies is presented most clearly in the St. Petersburg Paradox. As David Durand wrote: "With growth stocks, the uncritical use of conventional discount formulas is particularly likely to be hazardous; for, as we have seen, growth stocks represent the ultimate in investments of long duration. Likewise, they seem to represent the ultimate in difficulty of evaluation." 

For practical purposes, it is sometimes sufficient to estimate either the upper bound or the lower bound of the investment value range of a stock.

The investment value of a stock is conceptually a single point value, the mean of the distribution of investment value. Operationally, investment value is estimated as a range of values. 


For practical purposes, it is sometimes sufficient to estimate either the upper bound of the investment value range to deselect a stock or the lower bound of the investment value range to select a stock. 

  • As an example, if the upper bound of investment value of a given stock is confidently estimated to be no higher than $50 per share and the current quoted market price for this stock is $75 per share, then this particular stock can be deselected. 
  • Similarly, if the lower bound of investment value of another stock is confidently estimated to be at least $50 per share and the current quoted market price for this stock is $25 per share, then this particular stock can be selected.

Concerning the range of estimated appraisal values, Williams (1954:32-33) explained: 
"Scholar: Yes, economics supplies the answer to many questions of great practical importance. 
Skeptic: How can it possibly do so if it lacks the mathematical precision of astronomy? 
Scholar: Economics is more like chemistry than it is like astronomy. Or rather, it is like that branch of chemistry known as qualitative analysis, in contrast to quantitative analysis. In economics, just as in qualitative analysis, you don't always have to have an exact answer to have a useful one. For instance, if a chemist testifies in court that a dead man was found to have enough arsenic in his system to kill an ox, let alone a human being, then it really doesn't matter whether the amount of arsenic involved is two grams or ten, so long as the chemist is absolutely sure that what he found was really arsenic and not a related substance like tin or antimony. Precise measurement is unnecessary. The same is true in economics.

The four basic factors needed to appraise the intrinsic value of an operating enterprise and thus its common stock equity


An important distinction is the difference between reported accounting value (book value or net worth per share) and intrinsic economic value (discounted future dividends per share).

  • Book value does not reflect inflation and obsolescence, nor does it include intangible assets such as "franchises" and technological prowess resulting from R&D expenditures. 
  • In addition, book value per share is merely a mechanical screening ratio set at an arbitrary cutoff point which does not reflect judgment and does not reliably distinguish between underpriced bargain stocks and fairly-priced junk stocks.


Intrinsic economic value of an operating enterprise is appraised by use of discounted cash flow techniques in the so-called dividend discount model originated by John Burr Williams.

  • He made allowance for both dividends and future selling price. 
  • He also explains how the transposed dividend discount model can be used to determine what the market as a whole is expecting, and this can be compared with the investor's expectation.


As John Burr Williams (1938: page 466) wrote: "in other words, Investment Analysis usually measures the relative rather than the absolute value of any stock, and leaves to the economist the broad question of whether stocks in general are selling too high or too low. ... From the point of view of this book, which is concerned with absolute rather than relative value, ... "

According to Williams (1938), the four basic factors needed to appraise the intrinsic value of an operating enterprise and thus its common stock equity, two economy-wide factors and two company-specific factors. The economy-wide factors are general price level inflation and the real interest rate. The company-specific factors are the estimated future net cash distributions to the stockholders and the discount rate or rates applied to those cash receipts. For foreign companies, a fifth factor may be required: the currency exchange rate, which is discussed at length by Williams (1954). This is important enough to justify a table to repeat it for emphasis.
Factors of Intrinsic Economic Value
Number
Description
1
general price level inflation rate
2
real interest rate
3
dividends or free cash flows to equity
4
discount rate or rates
5
currency exchange rate, where applicable

Is faith in speculation about future earnings more, or less, reasonable than faith in appraisal of today's value?

Reliance on the earnings estimates of experts can range from blind faith at one end of the spectrum to reasoned faith at the other end.. 


Even if an investor knows the difference between either cash flow or "free" cash flow, however defined, and true long-term economic earnings, and even if an investor accepts the operating definition of earnings used by experts, the acceptance of their estimates of earnings and growth in earnings constitutes an act of faith. 


Is faith in speculation about future earnings more, or less, reasonable than faith in appraisal of today's value?


Forward-looking statements about capital spending plans, R&D projects, share (re)purchase programs, and other uncommitted contingent activities find their public forum in press releases that are carefully worded to avoid class action lawsuits by disgruntled shareholders.

The important point is that growth per se does not always create value for the common stock owners. As John Burr Williams wrote (1938: 419): "That a non-growing industry can be profitable is shown ... , and that a fast-growing industry can be unprofitable is shown ... "

Statements about future earnings growth rates are opinions, not facts.

There are three main types of estimates of the future. In order of increasing sophistication, they can be referred to as the naive, the gullible, and the expert. 
  • The naive forecast is based on linear trend extrapolations. 
  • The gullible forecast is based on analysts' estimates, such as provided by S&P Compustat's Analysts' Consensus Estimates, ACE, or by Institutional Brokers Estimate System, I/B/E/S. 
  • The expert prediction is based on rigorous systematic study of a company, its industry, and the economy.
John Neville Keynes in his Scope and Method originated the use of the term "positive" to refer to "what is" and the term "normative" to refer to "what should be."   These terms make the distinction between 
  • facts about the present, on one hand, and 
  • opinions about either the speculative future or an ideal state on the other hand, respectively. 
The important point here is that statements about future earnings growth rates are normative, not positive. They are opinions, not facts. 
  • No one's crystal ball is any more reliable than any one else's. 
  • Therefore, if not self-reliant, then one must rely on the expert opinion of others who have different agendas and conflicting interests. 
Similarly, statements about efficient and rational markets where all prices instantly converge to intrinsic value are normative, not positive. 
  • They are not reality, but rather utopian ideals approached by stock markets as complex aggregates but not by individual stocks. 
  • Perfectly efficient markets are necessary as a fixed standard for comparison, and thus serve a useful methodological function.

The valuation method considers no daily quotes, no charts, no breaking headlines, and no hot tips.

The method of valuation contrasts with both the method of forecasting growth for the sake of growth and the method of technical analysis. 


The valuation method considers no daily quotes, no charts, no breaking headlines, and no hot tips. 

  • Also, it does not take at face value any broker opinions or brokerage house research: neither fresh, bullish-sales biased, investment-banking compromised, buy/sell/hold recommendations with occasional self-contradictions and internal inconsistency for presentation to the larger institutional customers, nor stale versions of these same recommendations repackaged for smaller individual customers. 


  • Most importantly, no forecasts: neither those for official public consumption, nor the private "whispered" versions shared among colleagues. 
In short, no distractions, just the relevant facts. This, of course, does not greatly increase the demand for such information services.

There is no intrinsic value of gold or other commodities. They are inert, non-earning assets.

There is no intrinsic value of gold or other commodities. They are inert, non-earning assets. 

  • As an investment, gold is a pure speculation because there is no internal creation of value. 
  • Industrial metals, such as copper, are less speculative than precious metals because their prices more generally reflect demand and supply. 
Nevertheless, extrinsic factors operating through buyers and sellers determine the price of every commodity. 


In contrast, for equities and other claims on assets, their value is intrinsic because it is generated by the underlying operating enterprise in the form of earnings, dividends, and cash flows. 


There are no intrinsic prices, only intrinsic values.


http://www.numeraire.com/value.htm

Economic value refers to intrinsic, long-term, ultimate value of an operating enterprise as determined by net cash flow analysis.

The term value can refer to either accounting value, market value, or economic value. 


Measures of accounting value include book value per share, net worth per share, net asset value per share, and net tangible asset value per share. 


Market value refers to common stock equity capitalization or financial "size", and is equal to the share price times the number of shares outstanding. Publicly-traded market value includes only those shares that are not held in private accounts. 


Measures of accounting value and market value can be used for quick mechanical screening criteria for filtering out common stocks for further investigation. 


In contrast, economic value refers to intrinsic, long-term, ultimate value of an operating enterprise as determined by net cash flow analysis using spreadsheets and formulas. 

Intrinsic value is independent of quoted market prices. Accounting value is commonly confused with economic value.