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{{italic title}}
{{Multiple issues
[[File:Wissenshaft der logik.jpg|thumb|Title page of original 1816 publication]]
| refimprove = November 2009
{{Hegelianism}}
| essay-like = October 2008}}


'''''The Science of Logic''''' ({{lang-de|Wissenschaft der Logik}}, first published between 1812 and 1816) is the work in which [[Georg Wilhelm Friedrich Hegel]] outlined his vision of [[logic]], which is an ontology that incorporates the traditional Aristotelian [[syllogism]] as a sub-component rather than a basis. For Hegel, the most important achievement of [[German Idealism]], starting with [[Immanuel Kant|Kant]] and culminating in his own philosophy, was the demonstration that reality is shaped through and through by mind and, when properly understood, '''is''' mind. Thus ultimately the structures of thought and reality, subject and object, are identical. And since for Hegel the underlying structure of all of reality is ultimately rational, logic is not merely about reasoning or argument but rather is also the rational, structural core of all of reality and every dimension of it. Thus Hegel's ''Science of Logic'' includes among other things analyses of being, nothingness, becoming, existence, reality, essence, reflection, concept, and method. As developed, it included the fullest description of his [[dialectic]]. Hegel considered it one of his major works and therefore kept it up to date through revision. '''''The Science of Logic''''' is sometimes referred to as the ''Greater Logic'' to distinguish it from the condensed version of it he presented in what is called the ''Lesser Logic'', namely the Logic section of his ''Encyclopedia of the Philosophical Sciences''.
In [[financial markets]], '''stock valuation''' is the method of calculating theoretical values of companies and their [[stock]]s. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged ''[[Undervalued stock|undervalued]]'' (with respect to their theoretical value) are bought, while stocks that are judged ''overvalued'' are sold, in the expectation that undervalued stocks will, on the whole, rise in value, while overvalued stocks will, on the whole, fall.


==Brief history of the book==
In the view of [[fundamental analysis]], stock valuation based on fundamentals aims to give an estimate of their [[Intrinsic value (finance)|intrinsic value]] of the stock, based on predictions of the future cash flows and profitability of the business. Fundamental analysis may be replaced or augmented by market criteria – what the market will pay for the stock, without any necessary notion of intrinsic value. These can be combined as "predictions of future cash flows/profits (fundamental)", together with "what will the market pay for these profits?" These can be seen as "supply and demand" sides – what underlies the supply (of stock), and what drives the (market) demand for stock?
Hegel wrote 'The Science of Logic' after he had completed his ''[[Phenomenology of Spirit]]'' and while he was in [[Nuremberg]] working at a secondary school and courting his fiancée. It was published in a number of volumes. The first, ‘The Objective Logic’, has two parts (the Doctrines of Being and Essence) and each part was published in 1812 and 1813 respectively. The second volume, ‘The Subjective Logic’ was published in 1816 the same year he became a professor of philosophy at [[Heidelberg]]. ''The Science of Logic'' is too advanced for undergraduate students so Hegel wrote an Encyclopaedic version of the logic which was published in 1817.


In 1826 the book went out of stock. Instead of reprinting, as requested, Hegel undertook some revisions. By 1831 Hegel completed a greatly revised and expanded version of the ‘Doctrine of Being’, but had no time to revise the rest of the book. The Preface to the second edition is dated 7 November 1831, just before his death on 14 November 1831. This edition appeared in 1832, and again in 1834–5 in the posthumous Works. Only the second edition of ''Science of Logic'' is translated into English.
In the view of others, such as [[John Maynard Keynes]], stock valuation is not a ''prediction'' but a ''[[#Keynes's view|convention]],'' which serves to facilitate investment and ensure that stocks are [[liquidity|liquid]], despite being underpinned by an illiquid business and its illiquid investments, such as factories.


==Introduction==
== Fundamental criteria (fair value) ==
The most theoretically sound '''stock valuation method''', called income valuation or the [[discounted cash flow]] ('''DCF''') method, involves '''discounting of the profits''' (dividends, earnings, or cash flows) the stock will bring to the stockholder in the foreseeable future, and a final value on disposal.<ref>William F. Sharpe, "Investments", Prentice-Hall, 1978, pp. 300 et.seq.</ref> The discounted rate normally includes a [[risk premium]] which is commonly based on the [[capital asset pricing model]].


===Hegel's General Concept of Logic===
In July 2010, a Delaware court ruled on appropriate inputs to use in discounted cash flow analysis in a dispute between shareholders and a company over the proper fair value of the stock. In this case the shareholders' model provided value of $139 per share and the company's model provided $89 per share. Contested inputs included the terminal growth rate, the [[equity premium puzzle|equity risk premium]], and beta.<ref>[http://blogs.law.harvard.edu/corpgov/2010/07/16/delaware-provides-guidance-regarding-discounted-cash-flow-analysis/ Delaware Provides Guidance Regarding Discounted Cash Flow Analysis]. Harvard Law School Forum on Corporate Governance and Financial Regulation.</ref>
According to Hegel, logic is the form taken by the science of thinking in general. He thought that, as it had hitherto been practiced, this science demanded a total and radical reformulation “from a higher standpoint.” His stated goal with '''''The Science of Logic''''' was to overcome what he perceived to be a common flaw running through all other former systems of logic, namely that they all presupposed a complete separation between the ''content'' of cognition (the world of objects, held to be entirely independent of thought for their existence), and the ''form'' of cognition (the thoughts about these objects, which by themselves are pliable, indeterminate and entirely dependent upon their conformity to the world of objects to be thought of as in any way true). This unbridgeable gap found within the science of reason was, in his view, a carryover from everyday, phenomenal, ''un''philosophical consciousness.<ref>{{cite web|last=Hegel|first=G.W.F.|title=§ 35 - § 41|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlintro.htm#HL1_43|work=Hegel's Science of Logic|publisher=Allen & Unwin, 1969|accessdate=2 January 2012}}</ref>


The task of extinguishing this opposition within consciousness Hegel believed he had already accomplished in his book '''''[[Phenomenology of Spirit|Phänomenologie des Geistes]]''''' (1807) with the final attainment of Absolute Knowing: “Absolute knowing is the ''truth'' of every mode of consciousness because ... it is only in absolute knowing that the separation of the ''object'' from the ''certainty of itself'' is completely eliminated: truth is now equated with certainty and certainty with truth.”<ref>{{cite web|last=ibid|title=§ 51|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlintro.htm#HL1_43|accessdate=2 January 2012}}</ref>  Once thus liberated from duality, the science of thinking no longer requires an object or a matter outside of itself to act as a touchstone for its truth, but rather takes the form of its own self-mediated exposition and development which eventually comprises within itself every possible mode of rational thinking. “It can therefore be said,” says Hegel, “that this content is the exposition of God as he is in his eternal essence before the creation of nature and a finite mind.”<ref>{{cite web|last=ibid|title=§ 50 - § 53|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlintro.htm#HL1_43|accessdate=2 January 2012}}</ref>  The German word Hegel employed to denote this post-dualist form of consciousness was ''Begriff'' (traditionally translated either as Concept or Notion).
=== Stock Valuation Methods ===


===General Division of the Logic===
Stocks have two types of valuations. One is a value created using some type of cash flow, sales or fundamental earnings analysis. The other value is dictated by how much an investor is willing to pay for a particular share of stock and by how much other investors are willing to sell a stock for (in other words, by supply and demand). Both of these values change over time as investors change the way they analyze stocks and as they become more or less confident in the future of stocks.
The self-exposition of this unified consciousness, or Notion, follows a series of necessary, self-determined stages in an inherently logical, [[dialectic]]al progression. Its course is from the objective to the subjective "sides" (or ''judgements'' as Hegel calls them) of the Notion. The objective side, its ''Being'', is the Notion as it is ''in itself'' [''an sich''], its reflection in nature being found in anything inorganic such as water or a rock. This is the subject of Book One: The Doctrine of Being. Book Three: The Doctrine of the Notion outlines the subjective side of the Notion ''as'' Notion, or, the Notion as it is ''for itself'' [''für sich'']; human beings, animals and plants being some of the shapes it takes in nature. The process of Being’s transition to the Notion as fully aware of itself is outlined in Book Two: The Doctrine of Essence, which is included in the Objective division of the Logic.<ref>{{cite web|last=ibid|title=§ 78 - § 80|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlintro.htm#HL1_59|accessdate=2 January 2012}}</ref>  The ''Science of Logic'' is thus divided like this:
: '''Volume One: The Objective Logic'''
:: '''Book One: The Doctrine of Being'''
:: '''Book Two: The Doctrine of Essence'''
: '''Volume Two: The Subjective Logic'''
:: '''Book Three: The Doctrine of the Notion'''


This division, however, does not represent a strictly linear progression. At the end of the book Hegel wraps all of the preceding logical development into a single Absolute Idea. Hegel then links this final absolute idea with the simple concept of Being which he introduced at the start of the book. Hence the ''Science of Logic'' is actually a circle and there is no starting point or end, but rather a totality. This totality is itself, however, but a link in the chain of the three sciences of Logic, Nature and Spirit, as developed by Hegel in his '''''[[Encyclopedia of the Philosophical Sciences]]''''' (1817), that, when taken as a whole, comprise a “circle of circles.”<ref>{{cite web|last=ibid|title=§ 1814|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlabsolu.htm#HL3_824|accessdate=2 January 2012}}</ref>
The fundamental valuation is the valuation that people use to justify stock prices. The most common example of this type of valuation methodology is P/E ratio, which stands for Price to Earnings Ratio. This form of valuation is based on historic ratios and statistics and aims to assign value to a stock based on measurable attributes. This form of valuation is typically what drives long-term stock prices.


==Objective Logic: Doctrine of Being==
The other way stocks are valued is based on supply and demand. The more people that want to buy the stock, the higher its price will be. And conversely, the more people that want to sell the stock, the lower the price will be. This form of valuation is very hard to understand or predict, and it often drives the short-term stock market trends.


===Determinate Being (Quality)===
There are many different ways to value stocks.  The key is to take each approach into account while formulating an overall opinion of the stock.  If the valuation of a company is lower or higher than other similar stocks, then the next step would be to determine the reasons.


====Being====
==== Earnings Per Share (EPS) ====
'''A. Being'''


''Being'', specifically ''Pure'' Being, is the first step taken in the scientific development of ''Pure Knowing'', which itself is the final state achieved in the historical self-manifestation of ''[[Geist]]'' (Spirit/Mind) as described in detail by Hegel in '''''[[Phenomenology of Spirit|Phänomenologie des Geistes]]''''' (1807).<ref>{{cite web|last=ibid|title=§ 93|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbegin.htm#HL1_79|accessdate=26 December 2011}}</ref> This Pure Knowing is simply ''Knowing as Such'', and as such, has for its first thought product ''Being as Such'', i.e., the purest abstraction from all that is (although, importantly, not ''distinct'' from, or ''alongside'', all that is), having "no diversity within itself nor with any reference outwards. ... It is pure indeterminateness and emptiness."<ref name="Science of Logic&nbsp;— web">{{cite web|last=ibid|title=§ 132|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbegin.htm#HL1_79|accessdate=26 December 2011}}</ref>
EPS is the net income available to common shareholders of the company divided by the number of shares outstanding. Usually there will be two types of EPS listed: a GAAP (Generally Accepted Accounting Principles) EPS and a Pro Forma EPS, which means that the income has been adjusted to exclude any one time items as well as some non-cash items like amortization of goodwill or stock option expenses. The most important thing to look for in the EPS figure is the overall quality of earnings. Make sure the company is not trying to manipulate their EPS numbers to make it look like they are more profitable.  Also, look at the growth in EPS over the past several quarters / years to understand how volatile their EPS is, and to see if they are an underachiever or an overachiever. In other words, have they consistently beaten expectations or are they constantly restating and lowering their forecasts?


: EXAMPLE: Hegel claims that the [[Eleatics|Eleatic philosopher]] [[Parmenides]] was the person who "first enunciated the simple thought of pure being as the absolute and sole truth."<ref name="science of logic web">{{cite web|last=ibid|title=§ 136|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl083.htm#HL1_83|accessdate=26 December 2011}}</ref>
The EPS number that most analysts use is the pro forma EPS.  To compute this number, use the net income that excludes any one-time gains or losses and excludes any non-cash expenses like stock options or amortization of goodwill.  Then divide this number by the number of fully diluted shares outstanding.  Historical EPS figures and forecasts for the next 1–2 years can be found by visiting free financial sites such as Yahoo Finance (enter the ticker and then click on "estimates").


'''B. Nothing'''
Through fundamental investment research, one can determine their own EPS forecasts and apply other valuation techniques below.


''Nothing'', specifically ''Pure'' Nothing, "is simply equality with itself, complete emptiness, absence of all determination and content." It is therefore identical with Being, except that it is ''thought of'' as its very opposite. This distinction is therefore meaningful as posited by thought.<ref>{{cite web|last=ibid|title=§ 133|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_82|accessdate=26 December 2011}}</ref>
==== Price to Earnings (P/E) ====


: EXAMPLE: in Hegel's estimation, Pure Nothing is the absolute principle "in the oriental systems, principally in Buddhism."<ref name="science of logic web"/>
Now that you have several EPS figures (historical and forecasts), you'll be able to look at the most common valuation technique used by analysts, the price to earnings ratio, or P/E.  To compute this figure, take the stock price and divide it by the annual EPS figure.  For example, if the stock is trading at $10 and the EPS is $0.50, the P/E is 20 times. To get a good feeling of what P/E multiple a stock trades at, be sure to look at the historical and forward ratios.


'''C. Becoming'''
Historical P/Es are computed by taking the current price divided by the sum of the EPS for the last four quarters, or for the previous year.  You should also look at the historical trends of the P/E by viewing a chart of its historical P/E over the last several years (you can find on most finance sites like Yahoo Finance).  Specifically you want to find out what range the P/E has traded in so that you can determine if the current P/E is high or low versus its historical average.


Pure Being and Pure Nothing are the same, and yet absolutely distinct from each other. This contradiction is resolved by their immediate vanishing, one into the other. The resultant movement, called ''Becoming'', takes the form of reciprocal ''Coming-to-Be'' and ''Ceasing-to-Be''.<ref>{{cite web|last=ibid|title=§ 179|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl083.htm#HL1_105b|accessdate=26 December 2011}}</ref>
Forward P/Es reflect the future growth of the company into the figure.  Forward P/Es are computed by taking the current stock price divided by the sum of the EPS estimates for the next four quarters, or for the EPS estimate for next calendar or fiscal year or two.


: EXAMPLE: Hegel borrows Kant's example of the "hundred dollars" ['''''[[Critique of Pure Reason]]''''' (1787)] to emphasize that the unity of Being and Nothing in Becoming only applies when they are taken in their absolute purity as abstractions.  It is of course not a matter of indifference to one's fortune if $100 ''is'' or ''is not'', but this is only meaningful if it is presupposed that the one whose fortune it might or might not be, already ''is'', i.e., the $100's being or not must be referenced to an other's. This, then, cannot be Pure Being which by definition has no reference outwards.<ref>{{cite web|last=ibid|title=§ 140-§ 146|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl083.htm#HL1_83|accessdate=26 December 2011}}</ref>  [[Heraclitus]] is cited as the first philosopher to think in terms of Becoming.<ref name="science of logic web"/>
P/Es change constantly.  If there is a large price change in a stock you are watching, or if the earnings (EPS) estimates change, the ratio is recomputed.


====Determinate Being====
==== Growth Rate ====


=====A. Determinate Being as Such=====
Valuations rely very heavily on the expected growth rate of a company. One must look at the historical growth rate of both sales and income to get a feeling for the type of future growth expected.  However, companies are constantly changing, as well as the economy, so solely using historical growth rates to predict the future is not an acceptable form of valuation. Instead, they are used as guidelines for what future growth could look like if similar circumstances are encountered by the company.  Calculating the future growth rate requires personal investment research.  This may take form in listening to the company's quarterly conference call or reading a press release or other company article that discusses the company's growth guidance.  However, although companies are in the best position to forecast their own growth, they are far from accurate, and unforeseen events could cause rapid changes in the economy and in the company's industry.


The transition between Becoming and '''(a) ''Determinate Being as Such''''' is accomplished by means of ''[[Aufheben|sublation]]''. This term, the traditional English translation of the German word ''aufheben'', means  to preserve, to maintain, but also to cease, to put an end to. Hegel claims that it is “one of the most important notions in philosophy.” Being and Nothing were complete opposites whose inner unity needed to be expressed, or ''mediated'', by a third term: Becoming. Once having been accomplished through mediation, their unity then becomes ''immediate''. Their opposition, still extant in Becoming, has been “put an end to.” From the newly acquired standpoint of immediacy, Becoming becomes Determinate Being as Such, within which Being and Nothing are no longer discrete terms, but necessarily linked ''moments'' that it has “preserved” within itself. Sublation, then, is the ending of a logical process, yet at the same time it is its beginning again from a new point of view.<ref>{{cite web|last=ibid|title=§ 184 - § 187|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref>
And for any valuation technique, it's important to look at a range of forecast values. For example, if the company being valued has been growing earnings between 5 and 10% each year for the last 5 years, but believes that it will grow 15 - 20% this year, a more conservative growth rate of 10 - 15% would be appropriate in valuations. Another example would be for a company that has been going through restructuring. They may have been growing earnings at 10 - 15% over the past several quarters / years because of cost cutting, but their sales growth could be only 0 - 5%.  This would signal that their earnings growth will probably slow when the cost cutting has fully taken effect. Therefore, forecasting an earnings growth closer to the 0 - 5% rate would be more appropriate rather than the 15 - 20%. Nonetheless, the growth rate method of valuations relies heavily on gut feel to make a forecast.  This is why analysts often make inaccurate forecasts, and also why familiarity with a company is essential before making a forecast.


So, ''as'' moments of Determinate Being, Being and Nothing take on new characteristics as aspects of '''(b) ''Quality'''''. Being becomes emphasized, and, as Quality, is ''Reality''; Nothing, or ''Non-Being'', is concealed in Being’s background serving only delimit it as a specific Quality distinct from others, and, in so doing, is ''Negation in General'', i.e., Quality in the form of a deficiency. Quality, then, comprises both what a Determinate Being ''is'' and ''is not'', viz., that which makes it determinate in the first place.<ref>{{cite web|last=ibid|title=§ 195 - § 198|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref> Within Quality, however, Reality and Negation are still distinct from one another, are still ''mediated'', just like Being and Nothing were in Becoming. Taken in their ''unity'', that is, in their immediacy as, again, sublated, they are now only moments of '''(c) ''Something'''''.<ref>{{cite web|last=ibid|title=§ 208 - § 209|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref>
==== Price Earnings to Growth (PEG) Ratio ====


: EXAMPLE: Hegel contrasts his logically derived notion of Reality from the earlier metaphysical one present in the [[ontological argument|ontological “proof” of God’s existence]], specifically [[Leibniz]]’s formulation of it. In this theory, God was held to be the sum-total of all realities. These realities are taken to be “perfections,” their totality therefore comprising the most perfect being imaginable: God. Speculative logic, however, shows that Reality is inextricably bound up with its own negation, and so any grand total of these realities would not result in something strictly positive, e.g., God, but would inevitably retain, to an equal degree, the negation of all these realities. The mere addition of realities to each other, then, would not in any way alter their principle, and so the sum of all realities would be no more or less than what each of them already was: a Reality and its Negation.<ref>{{cite web|last=ibid|title=§ 201 - § 202|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref>
This valuation technique has really become popular over the past decade or so.  It is better than just looking at a P/E because it takes three factors into account; the price, earnings, and earnings growth rates. To compute the PEG ratio, divide the Forward P/E by the expected earnings growth rate (you can also use historical P/E and historical growth rate to see where it's traded in the past). This will yield a ratio that is usually expressed as a percentage.  The theory goes that as the percentage rises over 100% the stock becomes more and more overvalued, and as the PEG ratio falls below 100% the stock becomes more and more undervalued. The theory is based on a belief that P/E ratios should approximate the long-term growth rate of a company's earnings. Whether or not this is true will never be proven and the theory is therefore just a rule of thumb to use in the overall valuation process.


Something is the first instance in '''''The Science of Logic''''' of the “negation of the negation”. The first negation, Negation in General, is simply what a Determinate Being is ''not''. Hegel calls this “abstract negation”. When this negation itself is negated, which is called “absolute negation,” what a Determinate Being ''is'', is no longer dependent on what it is ''not'' for its own determination, but becomes an actual particular Something in its own right: a ''Being-Within-Self''. Its negation, what it is not, is now “cut off” from it and becomes another Something, which, from the first Something’s point of view, is an ''Other'' in general. Finally, just as Becoming mediated between Being and Nothing, ''Alteration'' is now the mediator between Something and Other.<ref>{{cite web|last=ibid|title=§ 210 - § 212|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref>
Here's an example of how to use the PEG ratio.  Say you are comparing two stocks that you are thinking about buying. Stock A is trading at a forward P/E of 15 and expected to grow at 20%.  Stock B is trading at a forward P/E of 30 and expected to grow at 25%. The PEG ratio for Stock A is 75% (15/20) and for Stock B is 120% (30/25). According to the PEG ratio, Stock A is a better purchase because it has a lower PEG ratio, or in other words, you can purchase its future earnings growth for a lower relative price than that of Stock B.


=====B. Finitude=====
==== Sum of Perpetuities Method ====


'''(a) Something and Other''' are separate from each other, but each still contains within itself, as moments, their former unity in Determinate Being. These moments now re-emerge as ''Being-in-Itself'', i.e., Something as Something only insofar as it is in ''opposition'' to the Other; and ''Being-for-Other'', i.e., Something as Something only insofar as it is in ''relation'' to the Other.<ref>{{cite web|last=ibid|title=§ 219 - § 224|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref> (Hegel’s view is in this way contrasted with Kant’s [[noumenon]], the unknowable “thing in itself”: Being-in-itself taken in isolation from Being-for-Other is nothing but an empty abstraction and to ask “what it is” is to ask a question made impossible to answer.)<ref>{{cite web|last=ibid|title=§ 227|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>
The PEG ratio is a special case in the [[Sum of Perpetuities Method]] (SPM) <ref name=SPM>{{cite journal|last=Brown|first=Christian|coauthors=Abraham, Fred|title=Sum of Perpetuities Method for Valuing Stock Prices|journal=Journal of Economics|date=October 2012|volume=38|issue=1|pages=59–72|url=http://business.uni.edu/economics/joe.htm|accessdate=20 October 2012}}</ref> equation.  A generalized version of the Walter model (1956),<ref name=Walter>{{cite journal|last=Walter|first=James|title=Dividend Policies and Common Stock Prices|journal=Journal of Finance|date=March 1956|volume=11|issue=1|pages=29–41|url=http://www.jstor.org/stable/2976527|accessdate=20 October 2012}}</ref> SPM considers the effects of dividends, earnings growth, as well as the risk profile of a firm on a stock's value.  Derived from the compound interest formula using the present value of a [[perpetuity]] equation, SPM is an alternative to the [[Gordon Growth Model]].  The variables are:


Something is now no longer only an isolated something, but is in both positive and negative relationship to the Other. This relationship, however, is then reflected back into the Something ''as'' isolated, i.e., ''in-itself'', and bestows upon it further determinations. ''What'' a Something ''is'' in ''opposition'' to an Other is its '''(b) ''Determination''''';<ref>{{cite web|last=ibid|title=§ 231|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref> what it is in ''relation'' to an Other is its '''''Constitution'''''.<ref>{{cite web|last=ibid|title=§ 233 - § 235|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>
*<math>P</math> is the value of the stock or business
*<math>E</math> is a company's [[earnings]]
*<math>G</math> is the company's constant growth rate
*<math>K</math> is the company's risk adjusted [[interest rate|discount rate]]
*<math>D</math> is the company's dividend payment


: EXAMPLE: A human being’s Determination is thinking reason, since that is what she unalterably is in ''opposition'' to her Other: nature. However, humans are entangled in nature in myriad other ways than just thinking rationally about it, and ''how'' humans react to this external influence ''also'' tells us about what they are. This is their Constitution, the part of their being that undergoes alteration in ''relation'' to its Others.<ref>{{cite web|last=ibid|title=§ 232|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>
::<math>P = (\frac{E*G}{K^2}) + (\frac{D}{K})</math>


The point at which Something ceases to be itself and becomes an Other is that Something’s '''''Limit'''''. This Limit is also shared by its Other which is itself an other Something only insofar as it is on the far side of this Limit. It is therefore by their common Limits that Somethings and Others are mediated with one another and mutually define each other's inner Qualities.<ref>{{cite web|last=ibid|title=§ 239|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>
In a special case where <math>K</math> is equal to 10%, and the company does not pay dividends, SPM reduces to the PEG ratio.


: EXAMPLE: The point at which a point ceases to be a point and becomes a line constitutes the Limit between them. However, a line is not ''only'' something ''other'' than a point, i.e., ''only'' a Determinate Being, but its very principle is at the same time defined by it, just as a plane is defined by the line and the solid by the plane, etc.<ref>{{cite web|last=ibid|title=§ 246|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>


From the perspective of the Limit, a Something ''is'' only a particular Something insofar as it is ''not'' something else. This means that the Something’s self-determination is only relative and entirely dependent on what it isn’t to be what it is. It is thus only temporary, contains its own Ceasing-to-Be within itself and so is '''(c) ''Finite''''', i.e., doomed to eventually cease to be. For Finite things, “the hour of their birth is the hour of their death.”<ref>{{cite web|last=ibid|title=§ 247 - § 249|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref> At this point the Limit ceases to play its mediating role between Something and Other, i.e., is ''negated'', and is taken back into the self-identity―the Being-Within-Self―of the Something to become that Something’s ''Limitation'', the point beyond which that Something will cease to be.<ref>{{cite web|last=ibid|title=§ 254|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref> The flip side of this, though, is that the Limit also takes its negative along with it back into the Something, this being the Other yet now as posited ''in'' the Something as that Something’s very own Determination. What this means is that, in the face of its own Limitation, the very Quality that defined the Something in the first place becomes the Other to its own self, which is to say that it no longer strictly ''is'' this Quality but now ''Ought'' to be this Quality. Limitation and the Ought are the twin, self-contradictory moments of the Finite.<ref>{{cite web|last=ibid|title=§ 255 - § 261|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>
Additional models represent the sum of perpetuities in terms of earnings, growth rate, the risk-adjusted discount rate, and accounting book value. <ref>Yee, Kenton K., Earnings Quality and the Equity Risk Premium: A Benchmark Model, Contemporary Accounting Research, Vol. 23, No. 3, pp. 833-877, Fall 2006 | URL= http://papers.ssrn.com/sol3/papers.cfm?abstract_id=921914 </ref>


: EXAMPLE: "The sentient creature, in the limitation of hunger, thirst, etc., is the urge to overcome this limitation and it does overcome it. It feels pain, and it is the privilege of the sentient nature to feel pain; it is a negation in its self, and the negation is determined as a limitation in its feeling, just because the sentient creature has the feeling of its self, which is the totality that transcends this determinateness [i.e., it feels it Ought not to feel pain]. If it were not above and beyond the determinateness, it would not feel it as its negation and would feel no pain."<ref>{{cite web|last=ibid|title=§ 266|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>
==== Nerbrand Z ====


Once again, sublation occurs. Both Limitation and the Ought point beyond the Finite something, the one negatively and the other positively. This beyond, in which they are unified, is the ''Infinite''.<ref>{{cite web|last=ibid|title=§ 269|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>
Given that investments are subject to revisions of future expectations the Nerbrand Z utilises uncertainty of consensus estimates to assess how much earnings forecasts can be revised in standard deviation terms before P/E ratios return to normalised levels. This calculation is best done with I/B/E/S consensus estimates. The market tends to focus on the 12 month forward P/E level, but this ratio is dependent on earnings estimates which are never homogenous. Hence there is a standard deviation of 12 month forward earnings estimates.


=====C. Infinity=====
[[The Nerbrand z]] is therefore expressed as


The negation that Being-in-Itself experienced in the Limitation, the negation that made it Finite, is again negated resulting in the affirmative determination of '''(a) the ''Infinite in General''''' which now reveals itself, not as something distinct from, but as the true nature of the Finite. “At the name of the infinite, the heart and the mind light up, for in the infinite the spirit is not merely abstractly present to itself, but rises to its own self, to the light of thinking, of its universality, of its freedom.”<ref>{{cite web|last=ibid|title=§ 273 - § 274|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>
:<math>Z = \frac{\frac{P}{H[P/E]} - E12}{stdev(E12)} </math>


This affirmation of the Infinite, however, carries with it a negative relation to an other, the Finite. Because of this, it falls back into the determination of the Something with a Limit peculiar to itself. This ''In''-finite, then, is not the pure Infinite, but merely the non-Finite. Hegel calls this the ''Spurious Infinite'' and it is this that is spoken of whenever the Infinite is held to be over and above―separated from―the Finite. This separateness is in itself false since the Finite naturally engenders the Infinite through Limitation and the Ought, while the Infinite, thus produced, is bounded by its Other, the Finite, and is therefore itself Finite. Yet they are ''held'' to be separate by this stage of thought and so the two terms are eternally stuck in an empty oscillation back and forth from one another. This Hegel calls '''(b) the ''Infinite Progress'''''.<ref>{{cite web|last=ibid|title=§ 275 - § 286|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>
where
H[P/E] = normalised P/E, e.g. a 5 year historical average of 12 month forward P/E ratios.


This impasse can only be overcome, as usual, via sublation. From the standpoint of the Finite, the Infinite cannot break free into independence, but must always be bounded, and therefore finitized, by its Other, the Finite. For further logical development to be possible, this standpoint must shift to a new one where the Infinite is no longer simply a derivation of the Finite, but where the Finite, as well as the Infinite in General, are but moments of '''(c) the ''True Infinite'''''. The True infinite bears the same relation of mediation to these moments as Becoming did to Being and Nothing and as Alteration did to Something and Other.<ref>{{cite web|last=ibid|title=§ 300 - § 304|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>
E12 = mean 12 month forward earnings estimates


: EXAMPLE: Hegel gives as a symbol of the Infinite Progress the straight line which stretches out to infinity in both directions. This Infinity is, at all times, the ''beyond'' of the Determinate Being of the line itself. True Infinity is properly represented by the “''circle'', the line which has reached itself, which is closed and wholly present, without ''beginning'' and ''end''.”<ref>{{cite web|last=ibid|title=§ 302|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>
stdev(E12) = standard deviation of 12 month forward earnings estimates.


This move is highly significative of Hegels’s philosophy because it means that, for him, “[it] is not the finite which is the real but the infinite.” The reality of the True Infinite is in fact “more real” than the Reality of Determinate Being. This higher, and yet more concrete, reality is the ''Ideal'' [''das Ideell'']: “The idealism of philosophy consists in nothing else than in recognizing that the finite has no veritable being.”<ref>{{cite web|last=ibid|title=§ 316|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>
A negative number indicates that earnings can be downgraded before valuations normalise.  As such, a negative number indicates a valuation adjusted earnings buffer. For example, if the 12 month forward mean EPS forecast is $10, the price of the equity is $100, the historical average P/E ratio is 15, and the standard deviation of EPS forecast is 2, then the Nerbrand Z is -1.67. That is, 12 month forward consensus earnings estimates could be downgraded by 1.67 standard deviation before P/E ratio would go back to 15.


As having been sublated, the mediation which was performed by the True Infinite between the Finite and the Infinite now has resulted in their ''immediate'' unity. This unity is called ''Being-for-Self''.<ref>{{cite web|last=ibid|title=§ 318|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>
==== Return on Invested Capital (ROIC) ====


====Being-For-Self====
This valuation technique measures how much money the company makes each year per dollar of invested capital.  Invested Capital is the amount of money invested in the company by both stockholders and debtors.  The ratio is expressed as a percent and you should look for a percent that approximates the level of growth that you expect.  In its simplest definition, this ratio measures the investment return that management is able to get for its capital. The higher the number, the better the return.


=====A. Being-for-Self as Such=====
To compute the ratio, take the pro forma net income (same one used in the EPS figure mentioned above) and divide it by the invested capital.  Invested capital can be estimated by adding together the stockholders equity, the total long and short term debt and accounts payable, and then subtracting accounts receivable and cash (all of these numbers can be found on the company's latest quarterly balance sheet).  This ratio is much more useful when you compare it to other companies that you are valuing.


At this point we have arrived back at simple Being from which all the previous developments had initially proceeded. This Being, though, is now in the standpoint of Infinity from which these developments can be seen as moments of itself and so it is '''(a) ''Being-for-Self as Such'''''. Until this point Determinate Being was burdened with Finitude, depended on the Other for its own determination, and so was only ''relatively'' determined Being. From the Ideal standpoint of Infinity, Being-for-Self has become free from this burden and so is ''absolutely'' determined Being.<ref>{{cite web|last=ibid|title=§ 320 - § 321|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl157.htm#HL1_158|accessdate=13 February 2012}}</ref>
==== Return on Assets (ROA) ====


As a consequence of having overcome this relativity, however, both sides of the relationship between Something and Other are now also in equal relation to the Infinite Being that they have become Ideal moments of. So, although through their relationship Something and Other mutually determine ''each other’s'' inner Qualities, they do not have the same effect on the Infinite Being―be it God, spirit or ego (in the [[Fichte]]an sense)―to which they are now objects. This Being is not just another Finite Other, but is the One for which they are and of which they are a part. The Being-for-Other of Finitude has become the '''(b) ''Being-for-One''''' of Infinity.<ref>{{cite web|last=ibid|title=§ 322|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl157.htm#HL1_158|accessdate=13 February 2012}}</ref>
Similar to ROIC, ROA, expressed as a percent, measures the company's ability to make money from its assets.  To measure the ROA, take the pro forma net income divided by the total assets.  However, because of very common irregularities in balance sheets (due to things like Goodwill, write-offs, discontinuations, etc.) this ratio is not always a good indicator of the company's potential. If the ratio is higher or lower than you expected, be sure to look closely at the assets to see what could be over or understating the figure.


: EXAMPLE: This Being-for-One recalls [[Leibniz]]’s [[monadology|monad]] because it involves a simple oneness that maintains itself throughout the various determinations that might take place within it. Hegel, however, is critical of Leibniz’s construction because, since these monads are indifferent to each other and, strictly speaking, are not Others to one another, they cannot determine each other and so no origin can be found for the harmony that is claimed to exist between them. Being-for-One, containing as it does the moments of determination within it, avoids this contradiction.<ref>{{cite web|last=ibid|title=§ 326|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl157.htm#HL1_158|accessdate=13 February 2012}}</ref>
==== Price to Sales (P/S) ====


If we now take in isolation that to which all the preceding moments refer, i.e., that which we now have immediately before us, we end up with '''(c) the ''One'''''.<ref>{{cite web|last=ibid|title=§ 328|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl157.htm#HL1_158|accessdate=13 February 2012}}</ref>
This figure is useful because it compares the current stock price to the annual sales.  In other words, it tells you how much the stock costs per dollar of sales earned. To compute it, take the current stock price divided by the annual sales per share. The annual sales per share should be calculated by taking the net sales for the last four quarters divided by the fully diluted shares outstanding (both of these figures can be found by looking at the press releases or quarterly reports).  The price to sales ratio is useful, but it does not take into account any debt the company has.  For example, if a company is heavily financed by debt instead of equity, then the sales per share will seem high (the P/S will be lower). All things equal, a lower P/S ratio is better. However, this ratio is best looked at when comparing more than one company.


=====B. The One and the Many=====
==== Market Cap ====


This '''(a) ''One in its Own Self''''', standing in negative relation to ''all'' its preceding moments, is entirely differentiated from each of them. It is neither a Determinate Being, nor a Something, nor a Constitution, etc. It is therefore indeterminate and unalterable. There is Nothing in it.<ref>{{cite web|last=ibid|title=§ 332 - § 334|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl164.htm#HL1_164|accessdate=13 February 2012}}</ref> Just as there is no criterion to distinguish Being and Nothing despite the fact that they are opposites, the One is also identical with ''its'' opposite, '''(b) the ''Void'''''. The Void can be said to be the Quality of the One.<ref>{{cite web|last=ibid|title=§ 335 - § 336|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl164.htm#HL1_164|accessdate=13 February 2012}}</ref>
Market Cap, which is short for Market Capitalization, is the value of all of the company's stock. To measure it, multiply the current stock price by the fully diluted shares outstanding.  Remember, the market cap is only the value of the stock.  To get a more complete picture, you'll want to look at the [[Enterprise Value]].


: EXAMPLE: At this stage, the Logic has incorporated the ancient [[atomism]] of [[Leucippus]] and [[Democritus]]. Hegel actually held the ancient philosophical notion of atomism in higher esteem than the [[atomic theory|scientific one]] of modern physics because the former understood the void not just as the empty space between atoms, but as the atom’s own inherent principle of unrest and self-movement. “Physics with its molecules and particles suffers from the atom ... just as much as does that theory of the State which starts from the particular will of individuals.”<ref>{{cite web|last=ibid|title=§ 338 - § 339|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl164.htm#HL1_164|accessdate=13 February 2012}}</ref>
==== Enterprise Value (EV) ====


The original transition of Being and Nothing to Determinate Being is again echoed here in the sphere of Being-for-Self. The One, though, as negatively related to all aspects of Quality excepting its own Quality of being the Void, cannot take on a Qualitative determinateness like Determinate Being did. In its own self-differentiation, it can only relate to itself as another self identical to it, that is, as another One. Since no new Quality has been taken on, we cannot call this transition a Becoming, but rather a ''Repulsion'', i.e., the positing of '''(c) ''Many''''' Ones.<ref>{{cite web|last=ibid|title=§ 340 - § 342|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl164.htm#HL1_164|accessdate=13 February 2012}}</ref>
[[Enterprise Value]] is equal to the total value of the company, as it is trading for on the stock market. To compute it, add the market cap (see above) and the total net debt of the company. The total net debt is equal to total long and short term debt plus accounts payable, minus accounts receivable, minus cash. The Enterprise Value is the best approximation of what a company is worth at any point in time because it takes into account the actual stock price instead of balance sheet prices{{Citation needed|date=September 2010}}. When analysts say that a company is a "billion dollar" company, they are often referring to its total enterprise value. Enterprise Value fluctuates rapidly based on stock price changes.


=====C. Repulsion and Attraction=====
==== EV to Sales ====


Once these many Ones have been posited, the nature of their relationship begins to unfold. Because it is the nature of the One to be purely ''self''-related, their relation to one another is in fact a ''non''-relation, i.e., takes place externally in the Void. From the standpoint of the one One, then, ''there are no other Ones'', that is, its relation to them is one of '''(a) ''Exclusion'''''. Seen from ''within'' the One there is only ''one'' One, but at the same time the One only exists in the first place through its negative external relation to ''other'' Ones, i.e., for there to ''be'' the one One there ''must'' be Many Ones that mutually Exclude one another.<ref>{{cite web|last=ibid|title=§ 349 - § 352|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>
This ratio measures the total company value as compared to its annual sales. A high ratio means that the company's value is much more than its sales. To compute it, divide the EV by the net sales for the last four quarters.  This ratio is especially useful when valuing companies that do not have earnings, or that are going through unusually rough times.  For example, if a company is facing restructuring and it is currently losing money, then the P/E ratio would be irrelevant. However, by applying an EV to Sales ratio, you could compute what that company could trade for when its restructuring is over and its earnings are back to normal.


: EXAMPLE: The idea that the One is entirely self-subsistent and can exist without the Many is, according to Hegel, “the supreme, most stubborn error, which takes itself for the highest truth, manifesting in more concrete forms as abstract freedom, pure ego and, further, as Evil.”<ref>{{cite web|last=ibid|title=§ 356|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>
==== EBITDA ====


Now that Many Ones have been posited out of their Repulsion from the One, their original Oneness reasserts itself and their Repulsion passes over to '''(b) ''Attraction'''''. Attraction presupposes Repulsion: for the Many to be Attracted by the One, they must have at first been Repulsed by it.<ref>{{cite web|last=ibid|title=§ 358|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>
EBITDA stands for earnings before interest, taxes, depreciation and amortization. It is one of the best measures of a company's cash flow and is used for valuing both public and private companies.  To compute EBITDA, use a company's income statement, take the net income and then add back interest, taxes, depreciation, amortization and any other non-cash or one-time charges. This leaves you with a number that approximates how much cash the company is producing.  EBITDA is a very popular figure because it can easily be compared across companies, even if all of the companies are not profitable.


The One having been restored to unity by Attraction now contains Repulsion and Attraction within it as moments. It is the ''Ideal'' One of Infinite Being, which, for Hegel, actually makes it ''more'' “real” than the merely ''Real'' Many. From the standpoint of this Ideal One, both Repulsion and Attraction now presuppose each other, and, taken one step further, each presupposes ''itself'' as mediated by the other.  The One is only a One with reference to another One―Repulsion; but this “other” One is in itself identical to, ''is'' in fact, the original One―Attraction: each is the moment of the other. This is the '''(c) ''Relation of Repulsion and Attraction''''', which at this point is only ''relative''.<ref>{{cite web|last=ibid|title=§ 361 - § 365|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>
==== EV to EBITDA ====


: EXAMPLE: Although in Hegel’s estimation a triumph of the explanatory power of metaphysics over the physics based on sense perception as it was then practised, he believed that [[Immanuel Kant|Kant]]’s '''''Metaphysische Anfangsgründe der Naturwissenschaft''''' ['''''[[Metaphysical Foundations of Natural Science]]'''''] (1786) retained many of the errors committed by the latter, foremost among these being that, since matter is given to the senses as already formed and constituted, it is taken to be such by the mind as well. The forces of Attraction and Repulsion that are supposed to act ''upon'' matter to set it in motion, then, are not seen also to be the very forces though which matter itself comes into being in the first place.<ref>{{cite web|last=ibid|title=§ 374, § 385|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_178|accessdate=13 February 2012}}</ref>
This is perhaps one of the best measurements of whether or not a company is cheap or expensive.{{Citation needed|date=September 2010}}  To compute, divide the EV by EBITDA (see above for calculations).  The higher the number, the more expensive the company is. However, remember that more expensive companies are often valued higher because they are growing faster or because they are a higher quality company.  With that said, the best way to use EV/EBITDA is to compare it to that of other similar companies.


Repulsion and Attraction are relative to one another insofar as the One is taken either as the beginning or result of their mediation with one another. Imparted with continuous, Infinite motion, the One, Repulsion and Attraction become the sublated moments of ''Quantity''.<ref>{{cite web|last=ibid|title=§ 370|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>
=== Approximate valuation approaches ===


===Magnitude (Quantity)===
==== Average growth approximation ====


====Quantity====
Assuming that two stocks have the same [[earnings growth]], the one with a lower [[P/E]] is a better value.  The [[P/E]] method is perhaps the most commonly used valuation method in the stock brokerage industry.<ref>Imam, Shahed, Richard Barker and Colin Clubb. 2008. The Use of Valuation Models by UK Investment Analysts. European Accounting Review. 17(3):503-535</ref><ref>Demirakos, E. G., Strong, N. and Walker, M. (2004) What valuation models do analysts use?. Accounting Horizons 18 , pp. 221-240</ref>  By using comparison firms, a target price/earnings (or P/E) ratio is selected for the company, and then the future earnings of the company are estimated.  The valuation's fair price is simply estimated earnings times target P/E.  This model is essentially the same model as Gordon's model, if k-g is estimated as the dividend payout ratio (D/E) divided by the target P/E ratio.
'''A. Pure Quantity'''


The previous determinations of Being-for-Self have now become the sublated moments of ''Pure Quantity''. Pure Quantity is a One, but a One made up of the Many having been Attracted back into each other out of their initial Repulsion. It therefore contains Many identical Ones, but in their coalescence, they have lost their mutual Exclusion, giving us a simple, undifferentiated sameness. This sameness is ''Continuity'', the moment of Attraction within Quantity. The other moment, that of Repulsion, is also retained in Quantity as ''Discreteness''. Discreteness is the expansion of the self-sameness of the Ones into Continuity. What the unity of Continuity and Discreteness, i.e., Quantity, results in is a continual outpouring of something out of itself, a perennial self-production.<ref>{{cite web|last=ibid|title=§ 395 - § 398|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_187|accessdate=21 February 2012}}</ref>
==== Constant growth approximation ====


: EXAMPLE: “[S]pecific examples of pure quantity, if they are wanted, are space and time, also matter as such, light, and so forth, and the ego itself.”<ref>{{cite web|last=ibid|title=§ 402|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl186.htm#HL1_188|accessdate=21 February 2012}}</ref> Hegel here sharply criticizes Kant’s antinomy, put forth in his '''''[[Critique of Pure Reason]]''''', between indivisibility and infinite divisibility in time, space and matter. By taking continuity and discreteness to be entirely antithetical to one another, instead of in their truth which is their dialectical unity, Kant becomes embroiled in self-contradiction.<ref>{{cite web|last=ibid|title=§ 404 - § 406, § 425|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl186.htm#HL1_188|accessdate=21 February 2012}}</ref>
The [[Gordon model]] or ''Gordon's growth model''<ref name="Ross">Corporate Finance, Stephen Ross, Randolph Westerfield, and Jeffery Jaffe, Irwin, 1990, pp. 115-130.</ref>
is the best known of a class of [[discounted dividend model]]s.  It assumes that dividends will increase at a constant growth rate (less than the discount rate) forever. The valuation is given by the formula:


'''B. Continuous and Discrete Magnitude'''
:<math>P = D\cdot\sum_{i=1}^{\infty}\left(\frac{1+g}{1+k}\right)^{i} = D\cdot\frac{1+g}{k-g} </math> .


Although unified in Quantity, Continuity and Discreteness still retain their distinction from one another. They cannot be cut off from each other, but either one can be foregrounded leaving the other present only implicitly. Quantity is a ''Continuous Magnitude'' when seen as a coherent whole; as a collection of identical Ones, it is a ''Discrete Magnitude''.<ref>{{cite web|last=ibid|title=§ 429 - § 431|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl186.htm#HL1_188|accessdate=21 February 2012}}</ref>
and the following table defines each symbol:
{| border="1" cellspacing="0" cellpadding="5"
|- style="background-color: #aaddcc; "
! Symbol
! Meaning
! Units
|-
|<math>\ P \ </math>
|''estimated stock price''
|$ or € or £
|-
|<math>\ D \ </math>
|''last [[dividend]] paid''
|$ or € or £
|-
|<math>\ k \ </math>
|''discount rate''
| %
|-
|<math>\ g </math>
| ''the [[earnings growth|growth rate of the dividends]]''
| %
|}


'''C. Limitation of Quantity'''
[http://www.fool.co.uk/qualiport/2000/qualiport000628.htm]


Quantity is the One, but containing within it the moments of the Many, Repulsion, Attraction, etc. At this point the negative, Excluding nature of the One is reasserted within Quantity. The Discrete Ones within Quantity now become Limited, isolated Somethings: ''Quanta''.<ref>{{cite web|last=ibid|title=§ 434 - § 436|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_200|accessdate=21 February 2012}}</ref>
==== Limited high-growth period approximation ====


====Quantum====
When a stock has a significantly higher growth rate than its peers, it is sometimes assumed that the [[earnings growth]] rate will be sustained for a short time (say, 5 years), and then the growth rate will [[Regression toward the mean|revert to the mean]]. This is probably the most rigorous approximation that is practical.<ref>[http://www.moneychimp.com/articles/valuation/dcf.htm Discounted Cash Flow Calculator for Stock Valuation<!-- Bot generated title -->]</ref>


=====A. [[Number]]=====
While these DCF models are commonly used, the uncertainty in these values is hardly ever discussed. Note that the models diverge for <math>\ k=g \ </math>
The first determination of quantum is ''Number''. Number is made up of a One or Many Ones—which, as quanta, are called ''Units''—each of which is identical to the other. This identity in the Unit constitutes the Continuity of Number. However, a Number is also a specific Determinate Being that encloses an aggregate of Units while excluding from itself other such aggregates. This, the ''Amount'', is the moment of Discreteness within Number. Both Qualitative and Quantitative Determinate Being have Limits that demarcate the boundary between their affirmative presence and their negation, but in the former the Limit determines its Being to be of a specific Quality unique to itself, whereas in the latter, made up as it is of homogeneous Units that remain identical to each other no matter which side of the Limit they fall upon, the Limit serves only to enclose a specific Amount of Units, e.g., a hundred, and to distinguish it from other such aggregates.<ref>{{cite web|last=ibid|title=§ 438 - § 444|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_202a|accessdate=30 March 2012}}</ref>
and hence are extremely sensitive to the difference of dividend growth to discount factor. One might argue that an analyst can justify any value (and that
would usually be one close to the current price supporting his call) by fine-tuning the growth/discount assumptions.


: EXAMPLE: The species of [[calculation]]—[[counting]], [[addition]]/[[subtraction]], [[multiplication]]/[[Division (mathematics)|division]], [[Exponentiation|powers]]/[[nth root|roots]]—are the different modes of bringing Numbers into relation with each other. Although the progress through these modes displays the same sort of dialectical evolution as does the Logic proper, they are nonetheless entirely external to it because there is no inner necessity in the various arrangements imposed on them by [[arithmetic]]al procedure. With the expression 7 + 5 = 12, although 5 added to 7 necessarily equals 12, there is nothing internal to the 7 or the 5 themselves that indicates that they should be brought in any sort of relation with one another in the first place.<ref>{{cite web|last=ibid|title=§ 445 - § 451|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl205.htm#HL1_205|accessdate=30 March 2012}}</ref> For this reason, number cannot be relied upon to shed any light on strictly philosophical notions, despite the ancient attempt by [[Pythagoras]] to do so. It can however be used to ''symbolize'' certain philosophical ideas. As for [[math]] as a pedagogical tool, Hegel presciently had this to say: “Calculation being so much an external and therefore mechanical process, it has been possible to construct [[Mechanical calculator|machines]] which perform arithmetical operations with complete accuracy. A knowledge of just this one fact about the nature of calculation is sufficient for an appraisal of the idea of making calculation the principal means for educating the mind and stretching it on the rack in order to perfect it as a machine.”<ref>{{cite web|last=ibid|title=§ 462 - § 471|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl205.htm#HL1_205|accessdate=30 March 2012}}</ref>
==== Implied Growth Models ====


=====B. Extensive and Intensive Quantum=====
One can use the Gordon model or the limited high-growth period approximation model
Taken in its immediacy, a Number is an ''Extensive Magnitude'', that is, a collection of a certain Amount of self-same Units. These Units, say ten or twenty of them, are the sublated moments of the Extensive Magnitudes ten or twenty. However, the Number ten or twenty, though made up of Many, is also a self-determining One, independent of other Numbers for its determination. Taken in this way, ten or twenty '''(a) differentiates''' itself from Extensive Magnitude and becomes an ''Intensive Magnitude'', which is expressed as the tenth or twentieth ''Degree''. Just as the One was completely indifferent to the other Ones of the Many yet depended on them for its existence, each Degree is indifferent to every other Degree, yet they are externally related to one another in ascending or descending flow through a scale of Degrees.<ref>{{cite web|last=ibid|title=§ 472 - § 478|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl217.htm#HL1_217|accessdate=30 March 2012}}</ref>
to impute an implied growth estimate. To do this, one takes the average P/E
and average growth for a comparison index, uses the current (or forward) P/E of
the stock in question, and calculates what growth rate would be needed for
the two valuation equations to be equal. This gives you an estimate of the
"break-even" growth rate for the stock's current P/E ratio. (Note : we are using
earnings not dividends here because dividend policies vary and may be influenced
by many factors including tax treatment).


Although thus differentiated from each other, Extensive and Intensive magnitude are essentially '''(b) the same'''. “[T]hey are only distinguished by the one having amount within itself and the other having amount outside itself.” It is at this point that the moment of the Something reasserts itself having remained implicit over the course of the development of Quantity. This Something, which reappears when the negation between Extensive and Intensive Magnitude is itself negated, is the re-emergence of Quality within the dialectic of Quantity.<ref>{{cite web|last=ibid|title=§ 479 - § 482|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl217.htm#HL1_217|accessdate=30 March 2012}}</ref>
===== Imputed growth acceleration ratio =====


: EXAMPLE: [[Weight]] exerts a certain [[pressure]] which is its Intensive Magnitude. This pressure, however, can be measured Extensively, in [[Pound (mass)|pounds]], [[kilogram]]s, etc. [[Heat]] or [[cold]] can be Qualitatively experienced as different [[Degree (temperature)|Degrees of temperature]], but can also be Extensively measured in a [[thermometer]]. High and low Intensities of [[note]]s are the results of a greater or smaller Amount of vibrations per unit of time. Finally, “in the spiritual sphere, high intensity of character, of talent or genius, is bound up with a correspondingly far-reaching reality in the outer world, is of widespread influence, touching the real world at many points.”<ref>{{cite web|last=ibid|title=§ 488 - § 491|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl217.htm#HL1_217|accessdate=30 March 2012}}</ref>
Subsequently, one can divide this imputed growth estimate by recent historical
growth rates.  If the resulting ratio is greater than one, it implies that the stock would
need to experience accelerated growth relative to its prior recent historical
growth to justify its current P/E (higher values suggest potential overvaluation).
If the resulting ratio is less than one, it implies that either the market expects
growth to slow for this stock or that the stock could sustain its current P/E
with lower than historical growth (lower values suggest potential undervaluation).
Comparison of the IGAR across stocks in the same industry may give estimates
of relative value.  IGAR averages across an industry may give estimates of relative expected changes in industry growth (e.g. the market's imputed expectation that an industry
is about to "take-off" or stagnate).  Naturally, any differences in IGAR between stocks
in the same industry may be due to differences in fundamentals,
and would require further specific analysis.


In the realm of Quantity, the relationship between Something and Other lacked any mutual Qualitative Determinateness. A One could only relate to another One identical to itself. Now, however, that Qualitative Determinateness has returned, the Quantum loses its simple self-relation and can relate to itself only through a Qualitative Other that is beyond itself. This Other is another Quantum, of a greater or lesser Amount, which, in turn, immediately points beyond itself to yet an Other Quantum ''ad infinitum''. This is what constitutes the self-propelled '''(c) Alteration of Quantum'''.<ref>{{cite web|last=ibid|title=§ 493 - § 496|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl217.htm#HL1_217|accessdate=30 March 2012}}</ref>
== Market criteria (potential price) ==
Some feel that if the stock is listed in a well organized stock market, with a large volume of transactions, the listed price will be close to the estimated fair value.{{Citation needed|date=July 2008}} This is called the [[efficient market hypothesis]].


=====C. Quantitative Infinity=====
On the other hand, studies made in the field of [[behavioral finance]] tend to show that deviations from the fair price are rather common, and sometimes quite large.{{Citation needed|Usable citation=http://badger.som.yale.edu/faculty/ncb25/ch18_6.pdf    date=July 2008|date=January 2011}}
Although a particular Quantum, of its own inner necessity, points beyond itself, this beyond is necessarily an Other Quantum. This fact, that Quantum eternally repulses itself, yet equally eternally remains Quantum, demonstrates the '''(a) Notion of Quantitative Infinity''', which is the self-related, affirmative opposition between Finitude and Infinity that lies within it.<ref>{{cite web|last=ibid|title=§ 497 - § 499|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl225.htm#HL1_225|accessdate=30 March 2012}}</ref> This irresolvable self-contradiction within Quantum yields '''(b) the Quantitative Infinite Progress'''. This progress can take place in one of two directions, the greater or the smaller, giving us the so-called “infinitely great” or “infinitely small.” That these “[[Infinitesimal|infinites]]” are each the ''Spurious Quantitative Infinite'' is evident in the fact that “great” and “small” designate Quanta, whereas the Infinite by definition is ''not'' a Quantum.<ref>{{cite web|last=ibid|title=§ 500 - § 503|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl225.htm#HL1_225|accessdate=30 March 2012}}</ref>


: EXAMPLE: Hegel here gives several examples of the appearance of the Spurious Quantitative Infinite in philosophy, namely in Kant’s notion of the [[Critique of Judgment|sublime]] and his [[categorical imperative]], as well as Fichte’s infinite ego as outlined in his '''''[http://www.marxists.org/reference/subject/philosophy/works/ge/fichte.htm Theory of Science]''''' (1810). At bottom of all these ideas, says Hegel, is an absolute opposition that is held to exist between the ego and its other, this latter taking the form, respectively, of art, nature and the non-ego in general. The opposition is supposed to be overcome by the positing of an infinite relation between the two sides, the ego’s level of morality, for example, ever increasing in proportion to a decrease in the power of the senses over it. According with the nature of the Spurious Quantitative Infinite, however, it does not matter how great a level the ego raises itself to, the absolute opposition between it and its other is there and everywhere reasserted and the whole process can have no other outcome than a desperate and futile longing.<ref>{{cite web|last=ibid|title=§ 504 - § 517|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl225.htm#HL1_225|accessdate=30 March 2012}}</ref>
Thus, in addition to fundamental economic criteria, market criteria also have to be taken into account [[market-based valuation]]. Valuing a stock is not only to estimate its fair value, but also to determine its '''potential price range''', taking into account market behavior aspects. One of the behavioral valuation tools is the [[stock image]], a coefficient that bridges the theoretical fair value and the market price.


The Quantitative Infinite negates Quantum, and Quantum in turn negates Infinity. As occurs so often in '''''The Science of Logic''''', a negation that is itself negated produces a new affirmative standpoint, the formerly negated terms having become the unified moments thereof. This standpoint is '''(c) the Infinity of Quantum''' from where it is seen that Infinity, initially the absolute Other of Quantum, essentially ''belongs'' to it and in fact ''determines'' it as a particular Quality alongside all the other Determinate Beings that had long since been sublated. This particular Quality which distinguishes Quantum from any other Qualitatively Determined Being is in fact the total lack of explicit self-determinateness that differentiated Quantity from Quality in the first place. The repulsion of Quantum from itself out into the beyond of Infinity, is actually a gesture ''back'' towards the world of Qualitative Determination, thus bridging once again the two worlds. This gesture is made explicit in the ''[[Ratio|Quantitative Ratio]]'', where two Quanta are brought into relationship with one another in such a way that neither one in itself is self-determined, but in relating to each other, they Qualitatively determine something beyond themselves, e.g., a [[Line (geometry)|line]] or a [[curve]].<ref>{{cite web|last=ibid|title=§ 530 - § 537|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl225.htm#HL1_225|accessdate=30 March 2012}}</ref>
== Keynes's view ==
In the view of noted economist [[John Maynard Keynes]], stock valuation is not an ''estimate'' of the fair value of stocks, but rather a ''convention,'' which serves to provide the necessary stability and [[liquidity]] for investment, so long as the convention does not break down:<ref>[http://www.pimco.com/LeftNav/Featured+Market+Commentary/FF/2009/McCulley+10-09+The+Uncomfortable+Dance+Between+V%E2%80%99ers+and+U%E2%80%99ers.htm The Uncomfortable Dance Between V'ers and U'ers], [[Paul McCulley]], [[PIMCO]]</ref><!-- Reference included to underline notability of this view. -->
{{quotation|
:Certain classes of investment are governed by the average expectation of those who deal on the Stock Exchange as revealed in the price of shares, rather than by the genuine expectations of the professional entrepreneur. How then are these highly significant daily, even hourly, revaluations of existing investments carried out in practice?
:In practice, we have tacitly agreed, as a rule, to fall back on what is, in truth, a convention. The essence of this convention – though it does not, of course, work out so simply – lies in assuming that the existing state of affairs will continue indefinitely, except in so far as we have specific reasons to expect a change.
:...
:Nevertheless the above conventional method of calculation will be compatible with a considerable measure of continuity and stability in our affairs, so long as we can rely on the maintenance of the convention. …
:Thus investment becomes reasonably 'safe' for the individual investor over short periods, and hence over a succession of short periods however many, if he can fairly rely on there being no breakdown in the convention and on his therefore having an opportunity to revise his judgment and change his investment, before there has been time for much to happen. Investments which are 'fixed' for the community are thus made 'liquid' for the individual.
|''[[The General Theory]],'' Chapter 12}}


: EXAMPLE: Hegel here engages in a lengthy survey of the history and development of the [[Differential calculus|Differential]] and [[Integral Calculus]], citing the works of [[Cavalieri]], [[Descartes]], [[Fermat]], [[Isaac Barrow|Barrow]], [[Isaac Newton|Newton]], [[Gottfried Wilhelm Leibniz|Leibniz]], [[Euler]], [[Lagrange]], [[John Landen|Landen]], and [[Lazare Carnot|Carnot]]. His main point of concern is the compulsion of [[mathematicians]] to neglect the infinitesimal differences that result from [[calculus]] equations in order to arrive at a coherent result. The inexactitude of this method of procedure results, says Hegel, primarily from their failure to distinguish between Quantum as the ''Quantity'' that each individual term of a [[Differential of a function|differential co-efficient]] represents, and the ''Qualitative'' nature of their relationship when in the form of a ratio. “''Dx'', ''dy'', are no longer quanta, nor are they supposed to signify quanta; it is solely in their relation to each other that they have any meaning, ''a meaning merely as moments''.”<ref>{{cite web|last=ibid|title=§ 538 - § 570|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl240.htm#HL1_240|accessdate=30 March 2012}}</ref>
== See also ==
 
* [[Stock selection criterion]]
====The Quantitative Relation====
* [[Bond valuation]]
 
* [[Real estate appraisal]]
'''A. The Direct Ratio'''
* [[Active management|Active portfolio management]]
 
* [[List of finance topics#Valuation|List of valuation topics]]
A [[ratio]], such as ''x'':''y'', is a ''Direct Ratio'' if  both terms of the ratio are delimited by a single Quantum, a constant, ''k'' (what Hegel calls in the language of his day the "exponent" of the ratio),
* [[Capital asset pricing model]]
:<math> k =  {y \over x}.</math>
* [[Value at risk]]
In the Direct Ratio, the previously sublated Quantitative moments of Amount and Unit are retrieved and brought into immediate relation with each other. One side of the ratio, ''y'', is a certain Amount relative to the other side, ''x'', which serves as the Unit whereby this Amount is measured. If the constant is given, then the Quantum on any one side of the ratio could be any Number, and the Number on the other side will automatically be determined. Therefore, the first Number of the ratio completely loses its independent significance and only functions as a determinate Quantum in relation to an other. Formerly, any single Number could simultaneously denote either an Amount or a Unit; now, it must serve exclusively as the one ''or'' the other in relation to another Number serving as the opposite. The constant would seem to bring these moments back into unity with each other, but in actuality, it too can serve ''only'' as either Amount ''or'' Unit. If ''x'' is Unit and ''y'' Amount, then ''k'' is the Amount of such Units,
* [[Mosaic theory (investments)|Mosaic theory]]
:<math> y = kx ;\,</math>
* [[Fundamental analysis]]
if ''x'' is Amount, then ''k'' is the Unit, the amount of which, ''y'', determines it,
* [[Technical analysis]]
:<math> x = y/k .\,</math>
* [[Fed model]] theory of equity valuation
As in themselves ''incomplete'' in this way, these Quanta serve only as the Qualitative moments of one another.<ref>{{cite web|last=ibid.|title=§ 674 - § 678|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl314.htm|accessdate=18 May 2012}}</ref>
* [[Undervalued stock]]
 
* [[John_Burr_Williams#Theory|John Burr Williams: Theory]]
'''B. Inverse Ratio'''
* [[Chepakovich valuation model]]
 
The ''Inverse Ratio'' is a ratio, ''x'':''y'', in which the relation between both sides is expressed in a constant which is their ''product'', i.e.,
:<math> k = xy\,</math>
or
:<math>y = {k \over x}.</math>
Whereas formerly with the Direct Ratio, the quotient between the two terms was ''fixed'', in the Inverse Ratio it becomes ''alterable''. Because the Inverse Ratio confines within itself many Direct Ratios, the constant of the former displays itself not merely as a Quantitative, but also as a Qualitative Limit. It is therefore a Qualitative Quantum. The Spurious Infinity/True Infinity dialectic again makes an appearance here as either term of the ratio is only capable of infinitely approximating the ratio's constant, the one increasing in proportion to a decrease in the other, but never actually reaching it (neither ''x'' nor ''y'' may equal zero). The constant is nonetheless ''present'' as a simple Quantum, and is not an eternal beyond, making its self-mediation through the two terms of the ratio an example of True Infinity.<ref>{{cite web|last=ibid.|title=§ 679 - § 687|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl314.htm|accessdate=18 May 2012}}</ref>
 
'''C. The Ratio of Powers'''
 
The ''Ratio of Powers'' takes the following form:
:<math>y = k^x.\,</math>
It is in this form of the Ratio, says Hegel, that “quantum has reached its Notion and has completely realized it.” In the Direct and Inverse Ratios, the relation between the constant and its variables was not continuous, the former only being a fixed proportionality between them, and the latter relating itself to them only negatively. With the Ratio of Powers, however, this relationship is not simply one of external limitation, but, as a Quantum brought into relationship with itself through the power, it is ''self-determining'' Limit. This self-determination constitutes the Quality of the Quantum, and finally demonstrates the full significance of the essential identity of Quality and Quantity. Originally, Quantity differentiated itself from Quality in that it was indifferent to what was external to it, that which it quantified. Now however, in the Ratio of Powers, what it relates itself to externally is determined by its ''own'' self, and that which relates externally to its own self has long since been defined as Quality. “But quantity is not only ''a'' quality; it is the truth of quality itself.” Quantum, having sublated the moment of Quantity that originally defined it and returned to Quality, is now what it is in its truth: ''Measure''.<ref>{{cite web|last=ibid.|title=§ 688 - § 694|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl314.htm|accessdate=18 May 2012}}</ref>
 
===Measure===
 
====Specific Quantity====
 
=====A. The Specific Quantum=====
 
“Measure is the simple relation of the quantum to itself ... ; the quantum is thus qualitative.” Previously, Quantum was held to be indifferent to the Quality of that which it quantified. Now, as Measure, Quality and Quantity though still distinct from one another are inseparable and in their unity comprise a specific Determinate Being: “Everything that exists has a magnitude and this magnitude belongs to the nature of the something itself.” The indifference of Quantum is retained in Measure insofar as the magnitude of things can increase or decrease without fundamentally altering their Quality, and yet their essential unity nevertheless manifests at the Limit where an alteration in Quantity ''will'' bring about a change in Quality.<ref>{{cite web|last=ibid|title=§§712-717|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=26 August 2012}}</ref>
 
: EXAMPLE: [[Aristotle]] gives the example of a head from which hairs are plucked one by one. It’s Quality of being a head of hair remains if only a few hairs are gone, but at a certain point, it undergoes Qualitative Alteration and become a bald head. Although the Quantitative change is gradual, the Qualitative one, oftentimes, is “unexpected”. “It is the cunning of the Notion to seize on this aspect of a reality where its quality does not seem to come into play; and such is its cunning that the aggrandizement of a State or of a fortune, etc., which leads finally to disaster for the state or for the owner, even appears at first to be their good fortune.”<ref>{{cite web|last=ibid|title=§§718-722|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=26 August 2012}}</ref>
 
=====B. Specifying Measure=====
 
Insofar as Quantity describes the upper and lower Limits between which a specific Quality can maintain itself, it serves as a '''(a) ''Rule'''''. The Rule is an arbitrary external standard or Amount that measures something other than itself. Although it is often tempting to assume so, there is in actuality no object that can serve as a completely universal standard of measurement, i.e., be pure Quantity. Rather, what is involved in measurement is a ratio between two Qualities and their inherent Quantities, the one made to act as the '''(b) ''Specifying Measure''''' of the other, this other, however, being itself just as capable of measuring that which it is being measured by.<ref>{{cite web|last=ibid|title=§§725-729|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=26 August 2012}}</ref>
 
: EXAMPLE: In the measure of [[temperature]], we take the expansion and contraction of [[Mercury (element)|mercury]] relative to the [[heat]] it contains as a Quantitative Rule for the increase or decrease of temperature in general by dividing the range of its change in magnitude into a scale of [[arithmetical progression]]. Tempting though it is to believe, this is not the measure of temperature ''as such'', but only the measure of how Quantitative change specifically affects the Quality of mercury. The water or air the mercury [[thermometer]] measures has a very different Qualitative relationship to changes in the Quantity of heat which do not necessarily bear any direct relation to mercury’s. Thus, what is actually going on when we take a temperature is a relationship of comparison between two Qualities and their respective natures when exposed to a Quantitative increase or decrease in heat, and ''not'' a universal determination by some disembodied, abstract “thing” that is temperature ''itself''.<ref>{{cite web|last=ibid|title=§730|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=26 August 2012}}</ref>
 
So long as we arbitrarily use the Quantitative properties of some Quality or other as a Rule to Measure the magnitude of other Qualities, we abstract from it its Qualitative nature. However, once we have established a Quantitative ratio between two or more Qualities, we can give this ratio an independent existence that Quantitatively unites things that are Qualitatively distinct. We can thus take the Qualities of both sides into account, the independent, or ''Realized'', Measure serving as their '''(c) ''Relation'''''. This Measure necessarily involves variable magnitudes since the Qualitatively distinct ways in which different things relate to Quantity can only be registered in their respective rates of increase or decrease relative to each other. Further, in order for each side of the ratio to fully reflect the distinctiveness of the Quality it represents, both sides must be Quantitatively self-related, i.e., take the form of powers as in the case of the Ratio of Powers explicated above.<ref>{{cite web|last=ibid|title=§§731-734|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=27 August 2012}}</ref>
 
: EXAMPLE: [[Velocity]] is the ratio of [[space]]’s relation to [[time]]:
:: <math>v = {d \over t}.</math>
: It is only an intellectual abstraction, though, since it merely serves to measure space by the Rule of time or time by the Rule of space. It supplies no objective standard for the inherent Quantitative relation to each other that pertains to their specific Qualities. The [[Equations for a falling body|formula for a falling body]] comes closer,
:: <math> d = at^2\,</math>
: but here time is still serving as an arbitrary Rule, that is, it is assumed to vary in a simple arithmetical progression. It is the form of motion described by [[Kepler's laws of planetary motion|Kepler’s third law of planetary motion]] that comes closest for Hegel to being a Realized Measure of the relation between the inherent Qualities of space and time:
:: <math> d^3 = at^2\,.</math><ref>{{cite web|last=ibid|title=§735|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=27 August 2012}}</ref>
 
=====C. Being-For-Self in Measure=====
 
Although now united by the Quantitative Ratio, the two or more Qualities thus brought into relation retain their mutual separation as distinct Qualities. For example, even though we can determine the Quantitative relationship between space and time in the example of a falling body, each of them can still be considered on its own, independent of the other. However, if we then take the constant produced by the ratio of the two sides as a self-subsistent Something in its own right, that is, a ''Being-For-Self'', then the two formerly entirely distinct Qualities become its own sublated moments, their very natures now seen to have been in fact derived from this relation of Measure in the first place.<ref>{{cite web|last=ibid|title=§§738-741|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=27 August 2012}}</ref>
 
====Real Measure====
 
=====A. The Relation of Self-Subsistent Measures=====
 
''Real Measure'' gives us a new standpoint external to the different Measures being brought into relation with each other, this relation now designating the independent existence of an actual physical Something. This Something gains its Qualitative determination from the Quantitative '''(a)''' '''''combination between two Measures''''' immanent in it, i.e., [[volume]] and [[weight]]. One designates an inner Quality, in this case weight; the other designates an external Quality, in this case volume, the amount of space it takes up. Their combination gives us the ratio of weight to volume which is its [[specific gravity]]. The constant that results from this ratio is the inner characteristic Real Measure of the thing in question, but, taking the form as it does of a mere number, a Quantum, this constant is likewise subject to alteration, i.e., addition, subtraction, etc. Unlike mere Quantum, however, the Real Measure of a thing is inwardly determined, and so preserves itself somewhat in alteration. If two material things are combined, the dual Measures of the one are added to those of the other. The degree to which they exhibit self-preservation is registered in the ''internal'' Measure—weight in this case—which ends up being equal, after combination, to the sum of the original two Measures; the degree to which they exhibit Qualitative alteration is registered in the ''external'' Measure—space in this case—which does ''not'' necessarily result in a sum equal to its parts, but often in the case of material substances exhibits a diminution in overall volume.<ref>{{cite web|last=ibid|title=§§745-748|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>
 
If we adopt the constant of one specific Real Measure as our Unit, the constants of other Real Measures can be brought into relation to it as Amounts in a '''(b) ''series of Measure relations'''''. Since it is arbitrary which one Real Measure in such a series will serve as the Unit, there are as many incommensurable series of Measure relations as there are individual Real Measures. However, when two Real Measures, which are themselves ratios, are combined, the result is a new ratio of those ratios, itself designated by a constant in the form of a Quantum. If ''this'' constant is adopted as the Unit, instead of an individual Real Measure, then what were two incommensurable series are now made commensurable with each other in a common denominator. Since each Real Measure within a series forms such a constant with every other member in that series, ''any'' individual series in which a particular Real Measure serves as the Unit can be made commensurable with any ''other'' series with a ''different'' Real Measure as Unit. Since it is a thing’s Real Measure that determines its specific Quality, and since that Real Measure is in turn derived from the Quantitative relation it has with other Real Measures in the form of a series of constants, it would appear that, as in Determinate Being above, Quality is only relative and externally determined. However, as we have seen, a Real Measure also has an ''internal'' relation that gives it a self-subsistence that is indifferent to any external relation. Therefore, the series of Quantitative relationships between these Real Measures only determines the '''(c) ''[[Elective Affinities|Elective Affinity]]''''' between their different Qualities, but not these Qualities themselves.<ref>{{cite web|last=ibid|title=§§749-753|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>
 
The Quantity/Quality dialectic manifests itself in the realm of Elective Affinity in that a Real Measure within in a series will not necessarily resonate Qualitatively with those in another series even if they bear a proportional Quantitative relationship. In fact, the specific Quality of a particular Real Measure is in part registered by the other Real Measures it has a special Affinity for, that is, ''how'' it responds to Quantitative Alteration. It is the Intensive side of Quantity (see above) such as it relates to specific Real Measures that determines its Qualitative behaviour when subject to changes in Extensive Quantity.<ref>{{cite web|last=ibid|title=§§755-756|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>
 
: EXAMPLE: Hegel makes it clear that the above analysis applies to the system of chemical affinities and that of [[Harmony|musical harmony]]. In the case of the latter, for example, each individual [[Musical note|note]] is a Real, self-subsistent Measure, consisting as it does of a specific internal ratio between, say, the length and thickness of a guitar string. An individual note, however, only achieves meaning in its relation to a system of other notes that are brought into Quantitative relation to each other through a specific note that serves as the Unit, or [[Key (music)|key]]. A note serving as the key in one system, is equally an individual member in other systems in which other notes play this role. Notes that harmonize when played together are demonstrating their Elective Affinity for one another, that is, the higher Qualitative unity that results from a combination in which each individual note nevertheless retains its self-subsistence.<ref>{{cite web|last=ibid|title=§754|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>
 
=====B. Nodal Line of Measure-Relations=====
 
The relation of Elective Affinity is an external relation between two Real Measures that is determined by their Quantitative aspects. In and of themselves, each Real Measure retains its Qualitative indifference to all others, even those it has Affinity for. Real Measures, however, are also subject to ''internal'' alteration akin to what has already been discussed in “Measure” above, i.e., that its Quality can be maintained only within a certain Quantitative range beyond which it undergoes a sudden “leap” into another Quality. These different Qualities form ''Nodes'' on a line of gradual Quantitative increase or decrease.<ref>{{cite web|last=ibid|title=§§769-773|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>
 
: EXAMPLE: [[Natural numbers]] consist of a series of numbers that gradually increase by one in perpetual succession. However, some of these numbers relate in specific ways to others, being their [[Multiple (mathematics)|multiple]], [[Exponentiation|power]] or [[Nth root|root]], etc., and thus constitute “Nodes.” Transition from the liquid to the [[Freezing point|frozen state]] in water does not occur gradually with a diminution of temperature, but all of a sudden at 0°C. Finally, the “state has its own measure of magnitude and when this is exceeded this mere change in size renders it liable to instability and disruption under that same constitution which was its good fortune and its strength before its expansion.” Thus, contrary to Aristotle’s doctrine that ''[[natura non facit saltum]]'', according to Hegel nature ''does'' make leaps.<ref>{{cite web|last=ibid|title=§§774-778|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_368|accessdate=27 November 2012}}</ref>
 
=====C. The Measureless=====
Measure, being the unity of Quality and Quantity, now transitions into its version of the Infinite, the ''Measureless'', which accordingly is the unity of the Qualitative and Quantitative Infinites. In the Measureless, the Quantitative Infinite is manifested in the potential of the Nodal line to increase endlessly; the Qualitative Infinite is manifested as the eternal beyond of any particular Qualitative determination. Seeing as the successive determinations are self-generated by an internal Quantitative Alteration of Measure, they can now be seen, from the standpoint of the Measureless, to be different ''States'' of one and the same ''Substrate''. The nature of the Substrate is not tied, like the Something was, to a merely external Qualitative appearance, but represents the underlying unity of a variety of internally determined appearances, which are its States.<ref>{{cite web|last=ibid|title=§§779-84|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_371|accessdate=27 November 2012}}</ref>
 
====The Becoming of Essence====
 
'''A. Absolute Indifference'''
 
This Substrate, as what persists through the succession of States, is in a relation of ''Absolute Indifference'' to every particular determination—be it of quality, quantity or measure—that it contains. It is merely the abstract expression of the unity that underlies their totality.<ref>{{cite web|last=ibid|title=§§785-786|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl375.htm#HL1_375|accessdate=29 April 2013}}</ref>
 
'''B. Indifference as Inverse Ratio of its Factors'''
 
Taken in its immediacy, this Indifference is simply the result of all the different determinatenesses that emerge within it. It itself does not determine its own inner fluctuations, i.e., is not ''self''-determining. However, in accordance with the measure relations developed so far, each of its moments are in reciprocal, quantitatively determined ratios with one another. Formerly, from the standpoint of Quality, a sufficient Quantitative increase or decrease would result in a sudden transition from one Quality to another. Now, with Absolute Indifference as our standpoint, every possible Qualitative determination is already implicitly related to every other by means of a Quantitative ratio.  Every Quality is connected to, and in equilibrium with, its corresponding other. It is therefore no longer meaningful to say that something can have “more” or “less” of one Quality than another as if each Quality were absolutely distinct from each other. Whatever Quality there is “more” of in one thing than another can be equally said to be a “less” of whatever Quality exists in its stead in the other, i.e., there is an ''Inverse Ratio of their Factors''. So, with a so-called “Quantitative” change, “one factor becomes preponderant as the other diminishes with accelerated velocity and is overpowered by the first, which therefore constitutes itself the sole self-subsistent Quality.” The two Qualities are no longer distinct, mutually exclusive determinations, but together comprise a single whole.<ref>{{cite web|last=ibid|title=§§787-796|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl375.htm#HL1_375|accessdate=29 April 2013}}</ref>
 
: EXAMPLE: Here, Hegel makes a powerful argument in favour of the explanatory powers of his speculative philosophy over those of empirical science, specifically with regards to the concepts of [[centripetal]] and [[centrifugal]] forces as they are supposed to relate the [[elliptical motion]] of celestial bodies. If, as is supposed by science, such an orbit is made up of an inverse relation of centripetal and centrifugal forces—the former predominating over the other as the body approaches [[perihelion]], the reverse if approaching [[aphelion]]—then the sudden overtaking of the stronger force by the weaker that takes place on either end of the orbit can only be explained by some mysterious ''third'' force. Indeed, what is to stop the dominant force from completely overtaking the weaker, causing the body either to crash into whatever it is orbiting or to fly off at ever accelerating speeds into space? Only the inherent unity of the two Qualities, centripetal and centrifugal, arrived at by the ascension of thought to Absolute Indifference, can adequately explain the Notion of the elliptical orbit, says Hegel.<ref>{{cite web|last=ibid|title=§§797-802|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl375.htm#HL1_375|accessdate=29 April 2013}}</ref>
 
'''C. Transition into Essence'''
 
Strictly within the realm of Being, the underlying unity behind all its determinations necessarily stands externally, and in contradiction, to those determinations themselves. The transition to Essence occurs when these determinations reabsorb this unity back into themselves, i.e., they sublate it. The inherent contradiction between difference and unity is resolved when the latter is posited as the ''negative'' of the former. So, from henceforth it cannot be said that they simply emerge ''within'' the Substrate of Indifference, but that this “substrate” itself ''is'' their very own living self-relation. In other words, the differences between all the determinations of Being, namely the Quantitative difference and the inverse ratio of factors, are no longer self-subsistent, but in fact are mere moments in the expression of the implicit unity that rules them and, themselves, “''are'' only through their repulsion from themselves.” Being has finally determined itself to no longer be simply affirmative Being, i.e., that which characterized Being as Being in the first place, but as a ''relation'' with itself, as ''Being-With-Self'', or ''Essence''.<ref>{{cite web|last=ibid|title=§§803-806|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_383|accessdate=29 April 2013}}</ref>
 
==Objective Logic: Doctrine of Essence==
 
===Reflection-Within-Self===
 
====Illusory Being====
 
=====A. The Essential and the Unessential=====
 
The immediate characteristic displayed by Essence, once it finally emerges from Being, is simply that it is ''not'' Being.  This apparently puts us back into the sphere of Determinate Being (see above), where each side of a relation mutually determined the Other side as being ''not'' what ''it'' is. In this immediate, merely relative relation, Essence and Being thus become the ''Essential'' and the ''Unessential'', respectively. There is nothing arising within this relation, however, to tell us ''what'' it is about something that is Essential and what Unessential. Those that apply this mode of thinking to something are making an arbitrary distinction, the opposite of which could always be claimed with equal justification. What saves Essence from falling back in to the relativism of Determinate Being is the very radical and absolute distinction from Being that defines it as Essence in the first place. Being cannot therefore simply preserve itself as an Other relative to Essence, but, having been sublated by Essence, it has for that very reason itself become ''nothingness'', a ''non-essence'', ''Illusory Being''.<ref>{{cite web|last=ibid|title=§§819-822|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlessenc.htm#HL2_394a|accessdate=5 August 2013}}</ref>
 
=====B. Illusory Being=====
 
So in its relation to Essence, Being has lost its being, has become Illusory. All the determinations of Being covered in the first third of the '''''Science of Logic''''' are no longer self-subsistent, but only “are” at all as negations of Essence. This total dependence on Essence means that there is nothing any longer in Being itself upon which any of its own determinations can be based, i.e., there is no longer any ''mediation'' within Being. This role is entirely taken up by Essence which is ''pure'' mediation relative to Illusory Being's ''pure'' immediacy. Hegel claims this is the mode of thought that corresponds to [[Philosophical skepticism|ancient skepticism]] as well as the “modern” [[German idealism|idealism]] of [[Leibniz]], [[Immanuel Kant|Kant]], and [[Fichte]]. Illusory Being, though not Essence itself, nevertheless ''belongs'' entirely to Essence. It is that through which Essence generates itself as what it is, namely, the ''purely negative'' as regards Being. The constant appearance and disappearance of the empty manifestations of Illusory Being can now be seen as Essence's ''own'' self-generating movement, its own ''Reflection''.<ref>{{cite web|last=ibid|title=§§823-832|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlessenc.htm#HL2_394a|accessdate=5 August 2013}}</ref>
 
=====C. Reflection=====
 
Reflection in the sphere of Essence corresponds to Becoming in the sphere of Being. However, in Being, this movement was between a positive—pure Being—and a negative—pure Nothingness. Here however, the two terms are Illusory Being and Essence. Illusory Being, as has already been established, is a nullity, nothingness. Essence, by definition, is non-being, ''absolute negativity''. So Reflection, the movement between them, is the movement of ''nothing to nothing'' and so back to itself. Both these terms, in being ''absolutely negative'', are identical to one another: Essence ''is'' Illusory Being and Illusory Being ''is'' Essence. They are, however, also ''relatively negative'', in that the one is, by definition, ''not'' what the other is. This contradiction manifests in Essence in that it ''presupposes'' or ''posits'', ''on its own'', that which it immediately differentiates itself from: Illusory Being. This absolute recoil upon itself is Essence as '''a) ''Positing Reflection'''''.<ref>{{cite web|last=ibid|title=§§833-845|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl399.htm#HL2_399|accessdate=5 August 2013}}</ref>
 
The next determination of Reflection, '''b) ''External Reflection''''', shifts the emphasis from the absolute negativity, or nothingness, in which the posited Illusory Being and its positing Essence find their ''identity'', to the relative negativity upon which their ''opposition'' is based. Although it “knows” that the Illusory Being it finds immediately before it has been posited by none other than ''itself'', External Refection nevertheless regards this Being as something ''external'' to it from which it returns to itself. What concerns it, therefore, is no longer the act of positing itself, but the specific ''determinateness'' of that which is posited, since it is this and nothing else that establishes its externality in the first place.<ref>{{cite web|last=ibid|title=§§846-849|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl399.htm#HL2_399|accessdate=5 August 2013}}</ref>
 
: EXAMPLE: Hegel offers for comparison with his notion of External Reflection the “reflective judgement” of Kant, which, in the '''''[[Critique of Judgement]]''''', is described as the faculty of the mind that determines the ''universals'' that lie behind immediately given ''particulars''. This action is similar to that of External Reflection with the crucial difference that, for Hegel, the universal does not simply lie “behind” the particular, but ''generates'' the particular from itself and so is the particular's own true ''Essence''. The immediate particular upon which Kant's judgement works is, in actuality, simply a ''nothingness'' posited by Reflection itself solely in order to generate its equally null universal, Essence.<ref>{{cite web|last=ibid|title=§§850-852|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl399.htm#HL2_399|accessdate=5 August 2013}}</ref>
 
With Positing Reflection, the Illusory Being that was posited was only a means for Essence's mediation with itself. Now, with '''c) ''Determining Reflection''''', not only is the moment of Illusory Being foregrounded again, but the specific determinations of this Being come into play as well. The absolute nothingness of Essence forms the background to any and all of the determinations it chooses to Reflect itself off of. These Determinations of Reflection—formerly known as Determinate Beings when they were in the realm of Quality (see above)—therefore share in the nullity that undergirds them. This nullity actually serves to fix them eternally in their specific determination and preserve them from Alteration, because they no longer relate to each other externally as Others to one another, but ''internally'' as equals in Essence's nothingness. All the possible determinations of Being are thus preserved negatively in Essence as free ''Essentialities'' “floating in the void without attracting or repelling one another.”<ref>{{cite web|last=ibid|title=§§853-859|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl399.htm#HL2_399|accessdate=5 August 2013}}</ref>
 
====The Essentialities====
 
=====A. Identity=====
 
In the sphere of Being, above, Qualities were determined only ''relatively''. What something ''was'', was determined entirely by that which differentiated it from what it ''wasn't'', i.e., it was ''negatively'' determined by its Other.  Here in Essence however, the negativity necessary to establish determination is no longer directed outward, towards an Other, but ''inward''. This is because Essence is in itself ''absolute negativity'', nothingness, and it follows that any determination made therein will share in this negativity and itself be essentially nothing. Therefore, an ''Essentiality'', as opposed to a Quality, is essentially ''the same'' as its other—they are both essentially nothing. As self-determining, whatever determination Essence takes on is freely self-generated, it “is what it is,” and so is simple ''Identity-with-self''. This absolute Identity rests on the ''absolute'' negativity that unites Essence with its Essentialities. However, if we recall from “Reflection” above, Essence is also negative ''relative'' to its Essentialities. The Essentialities are ''determined'' Essence and, as we know, determination by definition involves negation. Therefore, while the Essentialities are absolutely Identical in their shared nothingness, their ''absolute'' negativity, they are equally absolutely ''Different'' in their determinations, their ''relative'' negativity.<ref>{{cite web|last=ibid|title=§§819-822|url=https://www.marxists.org/reference/archive/hegel/works/hl/hl409.htm#HL2_411b|accessdate=13 August 2014}}</ref>
 
: EXAMPLE: Here Hegel embarks on a critique on one of the most basic assumptions of classical logic, the [[Law of Identity]], usually expressed as A=A. Although superficially the immediate truth of this proposition cannot be denied, further reflection reveals that nothing absolute can be derived from it. For it can only hold true provisionally insofar as A is ''different'' from not-A. The Law of Identity, the purpose of which is to draw an absolute distinction between identity and difference, therefore contains difference as a necessary moment implicitly within it. The paucity of the absolute truth it is meant to represent becomes very clear when applied empirically. “If ... to the question 'what is a plant?' the answer is given 'A plant is—a plant', the truth of such a statement is at once admitted by the entire company on whom it is tested, and at the same time it is equally unanimously declared that the statement says ''nothing''.”<ref>{{cite web|last=ibid|title=§§875-884|url=https://www.marxists.org/reference/archive/hegel/works/hl/hl409.htm#HL2_411b|accessdate=13 August 2014}}</ref>
 
=====B. Difference=====
 
The Difference of Reflection must be distinguished from the Otherness of Determinate Being. The latter is a relative relation between two Determinate Beings whereby they distinguish themselves one from the another and in turn determine themselves as specific Beings based on this distinction. In the sphere of Reflection, however, any determination ''posited'' by Essence is, ''as'' a determination, necessarily Different from the absolute negativity that is its Essence. The Difference of Reflection, therefore, is different in relation to its ''own self'', and so it is not relative but '''a) ''Absolute Difference'''''.<ref>{{cite web|last=ibid|title=§§885-889|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl409.htm#HL2_411b|accessdate=13 August 2014}}</ref>
 
Absolute Difference contains both Difference ''and'' Identity within it as ''moments'' just as, conversely, Identity contains itself and Difference as ''its'' moments. The relation between Identity and Difference takes the form of one term reflecting off the other back into itself: Difference off of Identity back into itself or Identity off of Difference back into itself. “This is to be considered as the essential nature of reflection and as the ''specific, original ground of all activity and self-movement''.” Because each of these two moments are self-related in this way, they do ''not'' mutually determine one another. Instead, they are indifferent to one another. Therefore, Difference is '''b) ''Diversity'''''.<ref>{{cite web|last=ibid|title=§§890-901|url=https://www.marxists.org/reference/archive/hegel/works/hl/hl409.htm#HL2_411b|accessdate=13 August 2014}}</ref>
 
Yet another duality emerges at this point. ''As moments'', Identity and Difference require each other and are bound up with one another: one term could not exist without the other. But at the same time, they absolutely ''negate'' one another and only ''are'' at all by virtue of their mutual negation of each other. So if we are an external party concerned with a specific determination of Identity, the moment of Difference, though intrinsic to the fact of this Identity, is very far from our minds. That it is Different from other things does not concern us or it at the moment: it is ''implicit''. The category of Identity itself, however, is ''not'' determined by whatever it is that it is applied to, but by its reflection off of Difference back into itself. So if, from our external standpoint, that which comprises the ''Identity'' of something cannot be established without a Comparison of ''Likeness'' with something else. What specifically is ''Different'' about something can similarly only be determined by a Comparison of ''Unlikeness'' between it and something else. Like and Unlike, being external to the things they refer to, can each be equally applied to one and the same Determination. Things are Like each other insofar as the are not Unlike each other and vice versa: the two terms are mutually exclusive insofar as they refer to the same thing, but ''in themselves'', apart from the things they refer to, there is no difference between them. Since any aspect may be externally selected to demonstrate the Likeness and Unlikeness of any two things, these terms really only refer, not intrinsically to their objects, but to ''themselves'' only and, as likewise self-referred, are indistinguishable from each other independent of their objects. Likeness and Unlikeness are both in fact only ''Likeness''. The ''internal'' union that existed between Identity and Difference which is merely implicit to the outside observer, therefore emerges again in external reflection between Likeness and Unlikeness, and thus overcomes the ''external'' Diversity that held Identity and Difference indifferently apart from each other. This reconstituted unity that thus comes out of Diversity is '''c) ''Opposition'''''.
 
The hidden, internal unity that bound the two moments of Identity and Difference together despite their apparent mutual indifference becomes explicit once they are mediated from the outside by Likeness and Unlikeness. They are no longer indifferent to one another but relate to each other intrinsically as Opposites. A given determination, as seen from its ''Positive'' aspect, is Likeness reflected back onto itself off of Unlikeness. Seen from its ''Negative'' aspect, it is Unlikeness reflected back onto itself off of Likeness. These two aspects, however, are the constitutive moments of one and the same overall determination. Although ''as a whole'', the Positive and Negative comprise a unity, the Positive ''on its own'' is also a self-subsistent being, as is the Negative ''on its own''. Because of this, the Negative can equally well be regarded as positive and vice versa. They are not Positive and Negative merely in comparison with one another, but each contains within itself the other as an essential element of its own determination.<ref>{{cite web|last=ibid|title=§§908-918|url=https://www.marxists.org/reference/archive/hegel/works/hl/hl409.htm#HL2_411b|accessdate=13 August 2014}}</ref>
 
: EXAMPLE: “An hour's journey to the east and the same distance traveled back to the west, cancels the first journey. ... At the same time, the hour's journey to the east is not in itself the positive direction, nor is the journey west the negative direction; ... it is a third point of view outside them that makes one positive and the other negative. ... [T]he distance covered is only one distance, not two, one going east and the other going west.” But at the same time, “the distance traveled east and west is the sum of a twofold effort or the sum of two periods of time.”<ref>{{cite web|last=ibid|title=§§922|url=https://www.marxists.org/reference/archive/hegel/works/hl/hl409.htm#HL2_411b|accessdate=13 August 2014}}</ref>
 
=====C. Contradiction=====
 
Both the Positive and the Negative are self-subsistent determinations: each side can stand on its own  without explicit reference to the other. At the same time, however, they completely exclude one another and in fact rely on this exclusion for their self-subsistence. In that sense, the Positive itself is constituted by the very Negative that it excludes; it is ''based'' on this exclusion and thus contains what it excludes it within itself. Ditto the Negative. This inclusion of what is excluded is what constitutes the Positive and the Negative as what they are. This is ''Contradiction''. (In the Negative, this self- contradiction is explicit, but it is no less the nature of the Positive.)
 
So, similar to Becoming above, the Positive and the Negative immediately transition the one into the other: the Positive ''includes'' the Negative which immediately ''excludes'' the Positive; the resulting Negative however also ''includes'' the Positive which in turn ''excludes'' the Negative and so on ''ad infinitum''. This mutual inclusion and exclusion cancels out the both of them. This results in nullity. Out of this nullity, the unity of the two sides is restored in the following way. As stated above, both the Positive and the Negative are each self-subsistent on their own, but it is a self-subsistence that is immediately obliterated by the other's. Now, however, arising out of their mutual destruction comes a self-subsistence that is common to the both of them. Instead of merely excluding each other, each side ''sublates'' the other, meaning that whatever is posited as Positive is ''at the same time'' equally the Negative of its Negative, and whatever is Negative is ''at the same time'' equally a Positive. The two sides posit and negate each other simultaneously, and in doing so they no longer destroy each other, but ''preserve'' one another. Therefore the Positive and Negative are in fact the ''same'' and this, their sameness—which nevertheless includes their Contradiction—is their Essence as ''Ground''.<ref>{{cite web|last=ibid|title=§§931-945|url=https://www.marxists.org/reference/archive/hegel/works/hl/hl431.htm#HL2_431|accessdate=13 August 2014}}</ref>
 
:EXAMPLE: [[Light]] is usually reckoned as purely Positive and [[dark]], purely Negative: the absence of light. However, it is not inherent to these terms that they should be so. Darkness can be taken to be a Positive in its own right “as the non-self-differentiating womb of generation” and vice versa. Furthermore, although they are usually defined as being mutually exclusive, the one being the absence of the other, there is a quantitative spectrum of [[grey]] and a qualitative spectrum of [[colour]] which exist between the one extreme and the other. The Ground would be a concept of “light” which includes all of the above.<ref>{{cite web|last=ibid|title=§§946-951|url=https://www.marxists.org/reference/archive/hegel/works/hl/hl431.htm#HL2_431|accessdate=13 August 2014}}</ref>
 
===Ground===
 
Simply put ground is the "essence of essence," which for Hegel arguably means the lowest, broadest rung in his ontology because ground appears to fundamentally support his system. Hegel says, for example, that ground is "that from which phenomena is understood." Within ground Hegel brings together such basic constituents of reality as form, matter, essence, content, relation, and condition. The chapter on ground concludes by describing how these elements, properly conditioned, ultimately will bring a fact into existence (a segue to the subsequent chapter on existence).
 
Hegel considers form to be the focal point of "absolute ground," saying that form is the "completed whole of reflection." Broken into components, form taken together with essence gives us "a substrate for the ground relation" (Hegel seems to mean relation in a quasi-universal sense). When we combine form with matter the result is "determinate matter." Hegel thinks that matter itself "cannot be seen": only a determination of matter resulting from a specific form can be seen. Thus the only way to see matter is by combining matter with form (given a literal reading of his text). Finally, content is the unity of form and determinate matter. Content is what we perceive.
 
"Determinate ground" consists of "formal ground," "real ground," and "complete ground." Remember with Hegel that when we classify something as determinate we are not referring to absolute abstractions (as in absolute ground, above) but now (with determinate ground) have some values attached to some variables—or to put it in Hegel's terminology, ground is now "posited and derived" with "determinate content."
 
In formal ground Hegel seems to be referring to those causal explanations of some phenomena that make it what it is. In a (uncharacteristically) readable three paragraph remark, Hegel criticizes the misuse of formal grounds, claiming that the sciences are basically built upon empty tautologies. Centrifugal force, Hegel states as one of several examples drawn from the physical sciences,
may be given as prime grounds (i.e. "explanation of") some phenomena, but we may later find upon critical examination that this phenomenon supposedly explained by centrifugal force is actually used to infer centrifugal force in the first place. Hegel characterizes this sort of reasoning as a "witch's circle" in which "phenomena and phantoms run riot."
 
Real ground is external and made up of two substrates, both directly applicable to content (which evidently is what we seem to perceive). The first is the relation between the ground and the grounded and the second substrate handles the diversity of content. As an example Hegel says that an official may hold an office for a variety of reasons—suitable connections, made an appearance on such and such occasion, and so forth. These various factors are the grounds for his holding office. It is real ground that serves to firstly make the connection between holding office and these reasons, and secondly to bind the various reasons, i.e. diverse content, together. Hegel points out that "the door is wide open" to infinite determinations that are external to the thing itself (recall that real ground is external). Potentially any set of reasons could be given for an official to be holding office.
 
In complete ground Hegel brings together formal and real ground, now saying that formal ground presupposes real ground and vice versa. Complete ground Hegel says is the "total ground-relation."
 
==Subjective Logic or the Doctrine of the Notion==
This "volume" is the third major piece within the Science of Logic.  Here Hegel introduces his Notion within which he extends Kant's basic schemes of judgement and syllogism classification.  Hegel shows that the true idea can only be based upon valid reasoning and objectivity.


==References==
==References==
{{Ibid|date=June 2014}}
{{Reflist}}
{{Reflist}}


==Editions of ''Science of Logic''==
==External links==
* translated by [[W. H. Johnston]] and [[L. G. Struthers]]. London: George Allen & Unwin, 1929
* translated by [[Henry S. Macran]] (''Hegel's Logic of World and Idea'') (Bk III Pts II, III only). Oxford, Clarendon Press, 1929
* translated by [[Arnold V. Miller|A. V. Miller]]; Foreword by [[John Niemeyer Findlay|J. N. Findlay]]. London: G. Allen & Unwin, 1969
* translated by George di Giovanni, Cambridge: Cambridge University Press, 2010
 
==Secondary literature==
* Bencivenga, Ermanno 2000. '' Hegel's Dialectical Logic'' Oxford.
* Burbidge, John W., 1995. ''On Hegel's Logic. Fragments of a Commentary Atlantic Highlands, N.J.
* Burbidge, John W. 2006. ''The Logic of Hegel's Logic. An Introduction''Peterborough, ON.
* Butler, Clark. 1996. ''Hegel's Logic. Between Dialectic and History'' Evanston.
* Carlson, David 2007. ''A Commentary on Hegel's Science of Logic'' New York: Palgrave MacMillan. 978-1403986283
* Di Giovanni, George (ed) 1990. ''Essays on Hegel's Logic'' Albany: New York State University Press.
* Harris, Errol E. 1983. ''An Interpretation of the Logic of Hegel'' Lanham.
* Harris, William T. 1985. ''Hegel's Logic: A Book on the Genesis of the Categories of the Mind. A Critical Exposition'' Chicago.
* Hartnack, Justus, 1998. ''An Introduction to Hegel's Logic''. Indianapolis: Hackett. ISBN 0-87220-424-3
* Houlgate, Stephen, 2006. ''The Opening of Hegel's Logic: From Being to Infinity'' Purdue: University Press.
* Rinaldi, Giacomo, 1992. ''A History and Interpretation of the Logic of Hegel'' Lewiston: Edwin Mellen Press.
* Roser, Andreas, 2009. ''Ordnung und Chaos in Hegels Logik''. 2 Volumes, New York, Frankfurt, Wien. ISBN 978-3-631-58109-4
* Trisokkas, Ioannis, 2012. ''Pyrrhonian Scepticism and Hegel's Theory of Judgement. A Treatise on the Possibility of Scientific Inquiry'' Boston: Brill.
* Winfield, Richard Dien, 2006. ''From Concept to Objectivity. Thinking Through Hegel's Subjective Logic'' Aldershot: Ashgate. ISBN 0-7546-5536-9.


==External links==
{{stock market}}
* Source text (German) ''Wissenschaft der Logik'' [http://www.gutenberg.org/etext/6729 Vol. 1] [http://www.gutenberg.org/etext/6834 Vol. 2]
* [http://www.marxists.org/reference/archive/hegel/ollindex.htm Outline of Hegel's Logic at marxists.org]
* [[s:The Meaning of Hegel's Logic/Introduction|The Meaning of Hegel's Logic]] (commentary at Wikisource)
* [http://www.marxists.org/archive/dunayevskaya/works/1961/01/26.htm Dunayevskaya : Rough Notes on Hegel's SCIENCE OF LOGIC]
* [http://www.marxistoutlook.com/article7.htm Terry Button : Hegel’s Logic&nbsp;– A Brief Synopsis]
* [http://www.marxists.org/archive/lenin/works/1914/cons-logic/ch01.htm Lenin : Consepectus of Hegel’s Science of Logic]
* [http://archive.org/details/LectureCourseInHegelsScienceOfLogic-RichardDienWinfield Lecture Course in Hegel's Science of Logic - Richard Dien Winfield (Audio)]


[[Category:Works by Georg Wilhelm Friedrich Hegel]]
{{DEFAULTSORT:Stock Valuation}}
[[Category:Logic literature]]
[[Category:Fundamental analysis]]
[[Category:Philosophy books]]
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In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged undervalued (with respect to their theoretical value) are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will, on the whole, rise in value, while overvalued stocks will, on the whole, fall.

In the view of fundamental analysis, stock valuation based on fundamentals aims to give an estimate of their intrinsic value of the stock, based on predictions of the future cash flows and profitability of the business. Fundamental analysis may be replaced or augmented by market criteria – what the market will pay for the stock, without any necessary notion of intrinsic value. These can be combined as "predictions of future cash flows/profits (fundamental)", together with "what will the market pay for these profits?" These can be seen as "supply and demand" sides – what underlies the supply (of stock), and what drives the (market) demand for stock?

In the view of others, such as John Maynard Keynes, stock valuation is not a prediction but a convention, which serves to facilitate investment and ensure that stocks are liquid, despite being underpinned by an illiquid business and its illiquid investments, such as factories.

Fundamental criteria (fair value)

The most theoretically sound stock valuation method, called income valuation or the discounted cash flow (DCF) method, involves discounting of the profits (dividends, earnings, or cash flows) the stock will bring to the stockholder in the foreseeable future, and a final value on disposal.[1] The discounted rate normally includes a risk premium which is commonly based on the capital asset pricing model.

In July 2010, a Delaware court ruled on appropriate inputs to use in discounted cash flow analysis in a dispute between shareholders and a company over the proper fair value of the stock. In this case the shareholders' model provided value of $139 per share and the company's model provided $89 per share. Contested inputs included the terminal growth rate, the equity risk premium, and beta.[2]

Stock Valuation Methods

Stocks have two types of valuations. One is a value created using some type of cash flow, sales or fundamental earnings analysis. The other value is dictated by how much an investor is willing to pay for a particular share of stock and by how much other investors are willing to sell a stock for (in other words, by supply and demand). Both of these values change over time as investors change the way they analyze stocks and as they become more or less confident in the future of stocks.

The fundamental valuation is the valuation that people use to justify stock prices. The most common example of this type of valuation methodology is P/E ratio, which stands for Price to Earnings Ratio. This form of valuation is based on historic ratios and statistics and aims to assign value to a stock based on measurable attributes. This form of valuation is typically what drives long-term stock prices.

The other way stocks are valued is based on supply and demand. The more people that want to buy the stock, the higher its price will be. And conversely, the more people that want to sell the stock, the lower the price will be. This form of valuation is very hard to understand or predict, and it often drives the short-term stock market trends.

There are many different ways to value stocks. The key is to take each approach into account while formulating an overall opinion of the stock. If the valuation of a company is lower or higher than other similar stocks, then the next step would be to determine the reasons.

Earnings Per Share (EPS)

EPS is the net income available to common shareholders of the company divided by the number of shares outstanding. Usually there will be two types of EPS listed: a GAAP (Generally Accepted Accounting Principles) EPS and a Pro Forma EPS, which means that the income has been adjusted to exclude any one time items as well as some non-cash items like amortization of goodwill or stock option expenses. The most important thing to look for in the EPS figure is the overall quality of earnings. Make sure the company is not trying to manipulate their EPS numbers to make it look like they are more profitable. Also, look at the growth in EPS over the past several quarters / years to understand how volatile their EPS is, and to see if they are an underachiever or an overachiever. In other words, have they consistently beaten expectations or are they constantly restating and lowering their forecasts?

The EPS number that most analysts use is the pro forma EPS. To compute this number, use the net income that excludes any one-time gains or losses and excludes any non-cash expenses like stock options or amortization of goodwill. Then divide this number by the number of fully diluted shares outstanding. Historical EPS figures and forecasts for the next 1–2 years can be found by visiting free financial sites such as Yahoo Finance (enter the ticker and then click on "estimates").

Through fundamental investment research, one can determine their own EPS forecasts and apply other valuation techniques below.

Price to Earnings (P/E)

Now that you have several EPS figures (historical and forecasts), you'll be able to look at the most common valuation technique used by analysts, the price to earnings ratio, or P/E. To compute this figure, take the stock price and divide it by the annual EPS figure. For example, if the stock is trading at $10 and the EPS is $0.50, the P/E is 20 times. To get a good feeling of what P/E multiple a stock trades at, be sure to look at the historical and forward ratios.

Historical P/Es are computed by taking the current price divided by the sum of the EPS for the last four quarters, or for the previous year. You should also look at the historical trends of the P/E by viewing a chart of its historical P/E over the last several years (you can find on most finance sites like Yahoo Finance). Specifically you want to find out what range the P/E has traded in so that you can determine if the current P/E is high or low versus its historical average.

Forward P/Es reflect the future growth of the company into the figure. Forward P/Es are computed by taking the current stock price divided by the sum of the EPS estimates for the next four quarters, or for the EPS estimate for next calendar or fiscal year or two.

P/Es change constantly. If there is a large price change in a stock you are watching, or if the earnings (EPS) estimates change, the ratio is recomputed.

Growth Rate

Valuations rely very heavily on the expected growth rate of a company. One must look at the historical growth rate of both sales and income to get a feeling for the type of future growth expected. However, companies are constantly changing, as well as the economy, so solely using historical growth rates to predict the future is not an acceptable form of valuation. Instead, they are used as guidelines for what future growth could look like if similar circumstances are encountered by the company. Calculating the future growth rate requires personal investment research. This may take form in listening to the company's quarterly conference call or reading a press release or other company article that discusses the company's growth guidance. However, although companies are in the best position to forecast their own growth, they are far from accurate, and unforeseen events could cause rapid changes in the economy and in the company's industry.

And for any valuation technique, it's important to look at a range of forecast values. For example, if the company being valued has been growing earnings between 5 and 10% each year for the last 5 years, but believes that it will grow 15 - 20% this year, a more conservative growth rate of 10 - 15% would be appropriate in valuations. Another example would be for a company that has been going through restructuring. They may have been growing earnings at 10 - 15% over the past several quarters / years because of cost cutting, but their sales growth could be only 0 - 5%. This would signal that their earnings growth will probably slow when the cost cutting has fully taken effect. Therefore, forecasting an earnings growth closer to the 0 - 5% rate would be more appropriate rather than the 15 - 20%. Nonetheless, the growth rate method of valuations relies heavily on gut feel to make a forecast. This is why analysts often make inaccurate forecasts, and also why familiarity with a company is essential before making a forecast.

Price Earnings to Growth (PEG) Ratio

This valuation technique has really become popular over the past decade or so. It is better than just looking at a P/E because it takes three factors into account; the price, earnings, and earnings growth rates. To compute the PEG ratio, divide the Forward P/E by the expected earnings growth rate (you can also use historical P/E and historical growth rate to see where it's traded in the past). This will yield a ratio that is usually expressed as a percentage. The theory goes that as the percentage rises over 100% the stock becomes more and more overvalued, and as the PEG ratio falls below 100% the stock becomes more and more undervalued. The theory is based on a belief that P/E ratios should approximate the long-term growth rate of a company's earnings. Whether or not this is true will never be proven and the theory is therefore just a rule of thumb to use in the overall valuation process.

Here's an example of how to use the PEG ratio. Say you are comparing two stocks that you are thinking about buying. Stock A is trading at a forward P/E of 15 and expected to grow at 20%. Stock B is trading at a forward P/E of 30 and expected to grow at 25%. The PEG ratio for Stock A is 75% (15/20) and for Stock B is 120% (30/25). According to the PEG ratio, Stock A is a better purchase because it has a lower PEG ratio, or in other words, you can purchase its future earnings growth for a lower relative price than that of Stock B.

Sum of Perpetuities Method

The PEG ratio is a special case in the Sum of Perpetuities Method (SPM) [3] equation. A generalized version of the Walter model (1956),[4] SPM considers the effects of dividends, earnings growth, as well as the risk profile of a firm on a stock's value. Derived from the compound interest formula using the present value of a perpetuity equation, SPM is an alternative to the Gordon Growth Model. The variables are:

  • P is the value of the stock or business
  • E is a company's earnings
  • G is the company's constant growth rate
  • K is the company's risk adjusted discount rate
  • D is the company's dividend payment
P=(E*GK2)+(DK)

In a special case where K is equal to 10%, and the company does not pay dividends, SPM reduces to the PEG ratio.


Additional models represent the sum of perpetuities in terms of earnings, growth rate, the risk-adjusted discount rate, and accounting book value. [5]

Nerbrand Z

Given that investments are subject to revisions of future expectations the Nerbrand Z utilises uncertainty of consensus estimates to assess how much earnings forecasts can be revised in standard deviation terms before P/E ratios return to normalised levels. This calculation is best done with I/B/E/S consensus estimates. The market tends to focus on the 12 month forward P/E level, but this ratio is dependent on earnings estimates which are never homogenous. Hence there is a standard deviation of 12 month forward earnings estimates.

The Nerbrand z is therefore expressed as

Z=PH[P/E]−E12stdev(E12)

where H[P/E] = normalised P/E, e.g. a 5 year historical average of 12 month forward P/E ratios.

E12 = mean 12 month forward earnings estimates

stdev(E12) = standard deviation of 12 month forward earnings estimates.

A negative number indicates that earnings can be downgraded before valuations normalise. As such, a negative number indicates a valuation adjusted earnings buffer. For example, if the 12 month forward mean EPS forecast is $10, the price of the equity is $100, the historical average P/E ratio is 15, and the standard deviation of EPS forecast is 2, then the Nerbrand Z is -1.67. That is, 12 month forward consensus earnings estimates could be downgraded by 1.67 standard deviation before P/E ratio would go back to 15.

Return on Invested Capital (ROIC)

This valuation technique measures how much money the company makes each year per dollar of invested capital. Invested Capital is the amount of money invested in the company by both stockholders and debtors. The ratio is expressed as a percent and you should look for a percent that approximates the level of growth that you expect. In its simplest definition, this ratio measures the investment return that management is able to get for its capital. The higher the number, the better the return.

To compute the ratio, take the pro forma net income (same one used in the EPS figure mentioned above) and divide it by the invested capital. Invested capital can be estimated by adding together the stockholders equity, the total long and short term debt and accounts payable, and then subtracting accounts receivable and cash (all of these numbers can be found on the company's latest quarterly balance sheet). This ratio is much more useful when you compare it to other companies that you are valuing.

Return on Assets (ROA)

Similar to ROIC, ROA, expressed as a percent, measures the company's ability to make money from its assets. To measure the ROA, take the pro forma net income divided by the total assets. However, because of very common irregularities in balance sheets (due to things like Goodwill, write-offs, discontinuations, etc.) this ratio is not always a good indicator of the company's potential. If the ratio is higher or lower than you expected, be sure to look closely at the assets to see what could be over or understating the figure.

Price to Sales (P/S)

This figure is useful because it compares the current stock price to the annual sales. In other words, it tells you how much the stock costs per dollar of sales earned. To compute it, take the current stock price divided by the annual sales per share. The annual sales per share should be calculated by taking the net sales for the last four quarters divided by the fully diluted shares outstanding (both of these figures can be found by looking at the press releases or quarterly reports). The price to sales ratio is useful, but it does not take into account any debt the company has. For example, if a company is heavily financed by debt instead of equity, then the sales per share will seem high (the P/S will be lower). All things equal, a lower P/S ratio is better. However, this ratio is best looked at when comparing more than one company.

Market Cap

Market Cap, which is short for Market Capitalization, is the value of all of the company's stock. To measure it, multiply the current stock price by the fully diluted shares outstanding. Remember, the market cap is only the value of the stock. To get a more complete picture, you'll want to look at the Enterprise Value.

Enterprise Value (EV)

Enterprise Value is equal to the total value of the company, as it is trading for on the stock market. To compute it, add the market cap (see above) and the total net debt of the company. The total net debt is equal to total long and short term debt plus accounts payable, minus accounts receivable, minus cash. The Enterprise Value is the best approximation of what a company is worth at any point in time because it takes into account the actual stock price instead of balance sheet pricesPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.. When analysts say that a company is a "billion dollar" company, they are often referring to its total enterprise value. Enterprise Value fluctuates rapidly based on stock price changes.

EV to Sales

This ratio measures the total company value as compared to its annual sales. A high ratio means that the company's value is much more than its sales. To compute it, divide the EV by the net sales for the last four quarters. This ratio is especially useful when valuing companies that do not have earnings, or that are going through unusually rough times. For example, if a company is facing restructuring and it is currently losing money, then the P/E ratio would be irrelevant. However, by applying an EV to Sales ratio, you could compute what that company could trade for when its restructuring is over and its earnings are back to normal.

EBITDA

EBITDA stands for earnings before interest, taxes, depreciation and amortization. It is one of the best measures of a company's cash flow and is used for valuing both public and private companies. To compute EBITDA, use a company's income statement, take the net income and then add back interest, taxes, depreciation, amortization and any other non-cash or one-time charges. This leaves you with a number that approximates how much cash the company is producing. EBITDA is a very popular figure because it can easily be compared across companies, even if all of the companies are not profitable.

EV to EBITDA

This is perhaps one of the best measurements of whether or not a company is cheap or expensive.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. To compute, divide the EV by EBITDA (see above for calculations). The higher the number, the more expensive the company is. However, remember that more expensive companies are often valued higher because they are growing faster or because they are a higher quality company. With that said, the best way to use EV/EBITDA is to compare it to that of other similar companies.

Approximate valuation approaches

Average growth approximation

Assuming that two stocks have the same earnings growth, the one with a lower P/E is a better value. The P/E method is perhaps the most commonly used valuation method in the stock brokerage industry.[6][7] By using comparison firms, a target price/earnings (or P/E) ratio is selected for the company, and then the future earnings of the company are estimated. The valuation's fair price is simply estimated earnings times target P/E. This model is essentially the same model as Gordon's model, if k-g is estimated as the dividend payout ratio (D/E) divided by the target P/E ratio.

Constant growth approximation

The Gordon model or Gordon's growth model[8] is the best known of a class of discounted dividend models. It assumes that dividends will increase at a constant growth rate (less than the discount rate) forever. The valuation is given by the formula:

P=D⋅∑i=1∞(1+g1+k)i=D⋅1+gk−g .

and the following table defines each symbol:

Symbol Meaning Units
P estimated stock price $ or € or £
D last dividend paid $ or € or £
k discount rate %
g the growth rate of the dividends %

[1]

Limited high-growth period approximation

When a stock has a significantly higher growth rate than its peers, it is sometimes assumed that the earnings growth rate will be sustained for a short time (say, 5 years), and then the growth rate will revert to the mean. This is probably the most rigorous approximation that is practical.[9]

While these DCF models are commonly used, the uncertainty in these values is hardly ever discussed. Note that the models diverge for k=g and hence are extremely sensitive to the difference of dividend growth to discount factor. One might argue that an analyst can justify any value (and that would usually be one close to the current price supporting his call) by fine-tuning the growth/discount assumptions.

Implied Growth Models

One can use the Gordon model or the limited high-growth period approximation model to impute an implied growth estimate. To do this, one takes the average P/E and average growth for a comparison index, uses the current (or forward) P/E of the stock in question, and calculates what growth rate would be needed for the two valuation equations to be equal. This gives you an estimate of the "break-even" growth rate for the stock's current P/E ratio. (Note : we are using earnings not dividends here because dividend policies vary and may be influenced by many factors including tax treatment).

Imputed growth acceleration ratio

Subsequently, one can divide this imputed growth estimate by recent historical growth rates. If the resulting ratio is greater than one, it implies that the stock would need to experience accelerated growth relative to its prior recent historical growth to justify its current P/E (higher values suggest potential overvaluation). If the resulting ratio is less than one, it implies that either the market expects growth to slow for this stock or that the stock could sustain its current P/E with lower than historical growth (lower values suggest potential undervaluation). Comparison of the IGAR across stocks in the same industry may give estimates of relative value. IGAR averages across an industry may give estimates of relative expected changes in industry growth (e.g. the market's imputed expectation that an industry is about to "take-off" or stagnate). Naturally, any differences in IGAR between stocks in the same industry may be due to differences in fundamentals, and would require further specific analysis.

Market criteria (potential price)

Some feel that if the stock is listed in a well organized stock market, with a large volume of transactions, the listed price will be close to the estimated fair value.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. This is called the efficient market hypothesis.

On the other hand, studies made in the field of behavioral finance tend to show that deviations from the fair price are rather common, and sometimes quite large.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

Thus, in addition to fundamental economic criteria, market criteria also have to be taken into account market-based valuation. Valuing a stock is not only to estimate its fair value, but also to determine its potential price range, taking into account market behavior aspects. One of the behavioral valuation tools is the stock image, a coefficient that bridges the theoretical fair value and the market price.

Keynes's view

In the view of noted economist John Maynard Keynes, stock valuation is not an estimate of the fair value of stocks, but rather a convention, which serves to provide the necessary stability and liquidity for investment, so long as the convention does not break down:[10] 36 year-old Diving Instructor (Open water ) Vancamp from Kuujjuaq, spends time with pursuits for instance gardening, public listed property developers in singapore developers in singapore and cigar smoking. Of late took some time to go China Danxia.

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

Template:Stock market

  1. ↑ William F. Sharpe, "Investments", Prentice-Hall, 1978, pp. 300 et.seq.
  2. ↑ Delaware Provides Guidance Regarding Discounted Cash Flow Analysis. Harvard Law School Forum on Corporate Governance and Financial Regulation.
  3. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  4. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  5. ↑ Yee, Kenton K., Earnings Quality and the Equity Risk Premium: A Benchmark Model, Contemporary Accounting Research, Vol. 23, No. 3, pp. 833-877, Fall 2006 | URL= http://papers.ssrn.com/sol3/papers.cfm?abstract_id=921914
  6. ↑ Imam, Shahed, Richard Barker and Colin Clubb. 2008. The Use of Valuation Models by UK Investment Analysts. European Accounting Review. 17(3):503-535
  7. ↑ Demirakos, E. G., Strong, N. and Walker, M. (2004) What valuation models do analysts use?. Accounting Horizons 18 , pp. 221-240
  8. ↑ Corporate Finance, Stephen Ross, Randolph Westerfield, and Jeffery Jaffe, Irwin, 1990, pp. 115-130.
  9. ↑ Discounted Cash Flow Calculator for Stock Valuation
  10. ↑ The Uncomfortable Dance Between V'ers and U'ers, Paul McCulley, PIMCO
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