Nestle

Closing price on 14.3.2012
$56.30

How does an investor hope to profit from investing into a high quality growth company?

He can obtain his returns from:
1.  The dividends distributed by the company.
2.  The share price appreciation that reflects the better earnings of the company over time.
3.  Buying the share at a bargain to its fair or intrinsic price.

The long term investor will derive most of his gains from dividends and the share price appreciation of the above stock.

Let's assume that the investor was poor in his pricing of this stock and bought in 1996 at $24 per share (the highest price for that period), he would still has a lot of gains from the dividends and share appreciation of this stock when he holds this share to today.

If the investor was very good in his pricing of this stock and bought at the lowest price in 1998 at $13 per share, he would have a better return from the dividends and share appreciation of this stock when he holds this share to today.

The "worse" case scenario is not buying into this stock and holding cash, hoping to buy at very steep bargains that never arise.  The opportunity costs for holding cash instead of being invested into this stock over the short and long term can be very costly.

Warrants trading: What you need to know

Structured Warrants – Gearing & Greeks

In this article we will look at gearing factor and sensitivity coefficients – the Greeks which measure change in warrant value via change in other variables. 

Gearing & Effective Gearing: Structured warrants cost only a fraction of their underlying shares. They provide holders with greater exposure to price movements as they generally rise and fall more steeply in percentage terms. If a warrant is priced at RM0.30, and the underlying share is trading at RM1.50, the gearing is 5 times. The price of one warrant offers exposure to 5 shares. In bull markets, warrants will always be among the top risers and the opposite holds true in bear markets.

The definition of gearing is: 
Gearing = Share Price / Warrant Price (adjusted by exercise ratio) 

The following chart plots the relative price movements of a call and put warrant against corresponding movements in the underlying share price. Note the percentage change in the value of the underlying share compared with the value change in the call warrant and the put warrant. During a 3-month period, the underlying share price falls by 10% (at Point A) and increases by 8% (at Point B) - share price varies over an 18% range. In contrast, the call warrant fluctuates within a 75% range, while the put warrant fluctuates within an 80% range but in an opposite direction to the call. 
Gearing decreases as the share price increases. 

Delta & Gamma: Delta refers to the rate of change of warrant price for a given change in the underlying share price. For call warrants, the delta will fall between 0 and 1; for puts it will be between 0 and -1. At 0, the warrant is impartial to any moves on the underlying share. At 1, the warrant is expected to move sen-for-sen with the underlying share. Typically, at-the-money warrants will have a delta of 0.5. As the warrant moves in-the-money, the delta will approach 1. 

The most savvy of traders will aim for medium-delta warrants, in the range of 0.4 to 0.5. Any delta too low will denote an out-of-money warrant with strike too far away. 

The delta is a constantly changing number. The rate of change of delta is known as the gamma. One could visualise delta as the speed of the warrant, and gamma as the acceleration. The gamma simulates the changes on the warrant price for different underlying share price. Any move on the underlying share will move the delta higher, as with the gamma. 

Vega: Vega measures the sensitivity of warrant price to change in volatility. Vega is the highest for at-the-money warrants, and tends to be higher for longer-dated warrants. 

With several issuers issuing warrants on the same shares, the belief is that investors and traders should focus on the warrant with the lowest implied volatility. This is only true if the issuers will buy back their warrants at a proportionate volatility level. An example would be buying a warrant at an implied volatility of 45%, which the issuer buys back at 42% versus buying a warrant at a volatility of 40% that is bought back at a volatility of 30%. 

Theta: Also known as time decay, Theta is expressed in terms of sen or percentage per week (or per day closer to expiry). Eventually, the warrant will need to lose the time value entirely. But theta is not linear to time – it will get proportionately larger as it approaches expiry. 

Rho: Rho measures the sensitivity of warrant prices to changes in interest rates. However, the level of interest rates, as a variable, is likely to influence neither warrant pricing nor trading decision making process. 

Final Thoughts: The Greeks do not help answer which warrant to buy. However, they are reliable forecasting tools on the changes in warrant prices versus the underlying share price movements. 


Related:

Warrants trading: What you need to know  Parameters & Variables of Structured Warrants

http://bursaedge.blogspot.com/2012/02/warrants-education-2.html 

Business Valuation

Day One

Session One: 
• The Discounted Cash Flow Model
• Setting up the Model

Session Two : 
• The Big Picture of DCF Valuation
• Valuation Examples
• The Discount Rate Question

Session Three : 
• Open Q&A

Session Four : 
• Risk premiums and Betas
• The Cost of Debt
• Estimating Cash Flows

Session Five : 
• Estimating Growth Rates
• Estimating Growth Patterns
• The Terminal Value
• Closing Thoughts on DCF valuation

Session Six : 
• Open Q&A

Day Two

Session Seven : 
• Loose Ends in Valuation
-Cash, Cross holdings and other assets
-The Value of Control, Synergy and Transparency
-The Liquidity Discount
-Employee Stock Options

Session Eight : 
• The Allure of Relative Valuation
• Categorizing Multiples
• The Four Steps in Analyzing Multiples

Session Nine : 
• Open Q&A

Session Ten :
• Applying Multiples in Valuation
• Finding Comparable firms
• Controlling for differences
• Picking the Right Multiple

Session Elven :
• The Real Options Story
• The Option to Delay (and valuing patents and natural resource companies)
• The Option to Abandon
• The Option to Expand
• Equity in Troubled firms as options

Session Twelve : 
• Open Q&A

http://events.vccircle.com/events_details.php?event_id=72&ntype=1

China suffers biggest trade deficit in 20 years

Rachel Cooper
March 12, 2012 - 8:04AM

China has recorded its largest trade deficit in more than two decades as Europe's sovereign debt crisis subdued exports and oil imports rocketed.

The country's customs bureau said the shortfall was $US31.5 billion, thought to be its biggest since at least 1989. Imports rose 39.6 per cent from a year earlier, after a 15.3 per cent slump in January, while exports increased 18.4 per cent.

Analysts had expected a deficit as imports rebounded from temporary disruption after the unusually early Lunar New Year in January but they had predicted a greater rise in exports and a smaller increase in imports.

Efforts by Chinese companies to sell to the West have been hampered by the effects of the eurozone debt crisis and an anaemic economic recovery in the United States, although shipments to the US climbed 22.6 per cent from a year earlier to $US19.4b. Overseas sales to the European Union rose 2.2 per cent to $US19.4b after a 3.2 per cent drop in January.

Illustrating the increasing importance of trading with emerging markets, during the first two months of the year trade volumes with Russia jumped 31.9 per cent to $US13.51b.

Imports of copper last month were the second-highest on record, while net crude oil imports increased to a record to meet rising demand as farmers prepare for the planting season and the government adds to emergency stockpiles.

The figures came after statistics on Friday showed China's inflation rate slowing sharply in February and factory output growth also slipping. Data showed that inflation had fallen to 3.2 per cent last month, down from 4.5 per cent in January.

"Overall, economic conditions are getting weaker at a fast pace," said Zhiwei Zhang, a Nomura economist. "The slowdown is happening faster than the government expected."

There is speculation that China's moderating inflation and growth will lead the Government to loosen policy. Citigroup believes a cut in banks' reserve requirements may come as soon as this month.

"We would suggest that the inflation bubble in China last year is well and truly burst, and the policy easing can accelerate," said Gerard Lane, equity strategist at Shore Capital. "This would be beneficial for the likes of miners and other emerging market related stocks."

Song Yu, an economist at Goldman Sachs, suggested that the nation will still see a sizeable trade surplus for the full year as the deficit in early 2012 is largely seasonal.

Data in January and February was distorted by the timing of the New Year holiday, which fell in January this year and February last year.

The Daily Telegraph, London



Read more: http://www.smh.com.au/business/world-business/china-suffers-biggest-trade-deficit-in-20-years-20120312-1ut5z.html#ixzz1oqvZZGTL

Efficient Market Hypothesis: Fact Or Fiction? "Efficient" refers to informational efficiency only.

The efficient markets hypothesis (EMH) in all of its forms, whether strong, semi-strong, or weak, is normative, not positive, i.e., it is an assertion about the way markets should behave in an ideal, utopian world, not a statement about the way markets actually do work in the real, practical world. Simple observation shows that the EMH in all its forms is fallacious. Both Kindleberger and Mackay give historical examples of stock market irrationality and inefficiency.

The efficient markets hypothesis may have advanced many academic careers, but it has not demonstrably increased the wealth of any investor over what would have been created otherwise. The EMH and the related capital asset pricing model, as opposed to the operating enterprise valuation model, may be useful as a standard of market perfection in studies of the market as a whole, but not in the valuation or selection of common stocks for investment.

The term "efficient" in the efficient markets hypothesis refers to informational efficiency only. It does not include mechanical operational efficiency or necessarily societal welfare efficiency.

The EMH explicitly assumes that all market participants have access to the same information in either a strong, semi-strong, or weak sense of the hypothesis.

• This simplifying assumption is chosen because it is necessary for mathematical tractability and thus highly convenient. 
• What makes this assumption unacceptably implausible is the meaning of the term "information" which is often overlooked. 
• Data is not information. Rather, information is data that has been processed and interpreted with judgment based on intelligence, knowledge and experience. 
• Does anyone believe that all market participants are endowed equally, not with access to data, but with the same intelligence, knowledge and experience? 

Competitive, properly-regulated markets may approach the semblance of "data efficiency" in the relative sense of eliminating arbitrage opportunities subject to trading costs and taxes, but no market is efficient in any absolute sense of equating price at all times to intrinsic economic value. This margin between value and price is the major key to successful value investing.

Intrinsic economic valuation versus price bidding in the market.

There are over 5,000 stocks listed on the major U.S. stock exchanges.  Each common stock is continuously changing and never stays the same. Thus the number of stock "deals" is unlimited. 

• You do not have enough time to estimate the intrinsic economic value of every common stock for every moment of every trading session. 
• The competitive, open-outcry, price-auction markets continuously provide bid and ask price quotations. 

Pricing conventions are used to provide a semblance of rationality in lieu of valuation. These conventions include 

• price multiples such as the price/earnings, price/book value, price/dividends, price/cash flow, price/sales and other accounting ratios. 
• Stock pricing conventions vary in applicability and popularity.

Intrinsic economic valuation versus price bidding in the market. 


The stock market participants at the price-setting margin and occasionally the market as a whole are exceedingly irrational. The most important that concerns us is that, in stock market investing, no bidding system can ever replace human judgment and interpretation of the facts based on intelligence, knowledge, and experience.

The Relationship of Intrinsic Value to Market Price - tracing the various steps culminating in market price.

In Security Analysis by Graham and Dodd, 1934 edition on page 23: "The Relationship of Intrinsic Value to Market Price.--The general question of the relation of intrinsic value to the market quotation may be made clearer by the appended chart [see table below], which traces the various steps culminating in market price. 

It will be evident from the chart that the influence of what we call analytical factors over the market price is both partial and indirect--

• partial, because it frequently competes with purely speculative factors which influence the price in the opposite direction; and 
• indirect, because it acts through the intermediary of people's sentiments and decisions. 

In other words, the market is not a weighing machine, on which the value of each issue is recorded by an exact and impersonal mechanism, in accordance with its specific qualities. Rather should we say that the market is a voting machine, whereon countless individuals register choices which are the product partly of reason and partly of emotion.

Relationship of Intrinsic Value Factors to Market Price
I.General market factors				} Attitude of public toward the issue (leads to) } Bids and offers (lead to) } Market price
II.Individual factors	A.Speculative	1.Market factors	a.Technical
			b.Manipulative
			c.Psychological
	A.Speculative B.Investment	2.Future value factors	a.Management and reputation
			b.Competitive conditions and prospects
			c.Possible and probably changes in volume, price, and costs
	B.Investment	3.Intrinsic value	a.Earnings
			b.Dividends
			c.Assets
			d.Capital structure
			e.Terms of the issue
			f.Others

The radical difference between value and price is explained by John Burr Williams in The Theory of Investment Value as indicated in the following quotations: (1938: 33): 

• "If opinion were not founded in part on current dividends and changes therein, there would be nothing to prevent price and value from drifting miles apart." (1938: 191): 
• "Since market price depends on popular opinion, and since the public is more emotional than logical, it is foolish to expect a relentless convergence of market price toward investment value. Corroboration of estimates [of intrinsic economic value] by subsequent market action, therefore, ought not to be expected. After all, investment value and market price are two quite different things."

Thus:

Price is not value. Pricing is not valuation. Pricing models are not valuation models. Pricing models include: capital asset pricing model (CAPM), arbitrage pricing theory (APT), and option pricing.

 http://www.numeraire.com/margin.htm

Value versus Price - Two Perspectives on Worth

Value versus Price

Two Perspectives on Worth

	VALUATION	PRICING
End	truth -- intrinsic value	illusion -- marginal opinion
Means	method of appraisal *	auction mechanism
Terms	case-by-case	standardized
Institution	private contracts	public exchanges
Approach	rational, logical	arational, emotional
Knowledge	economics	psychology, sociology
Principle	theory of investment	ad hoc, empirical
Result	value range	single price
Precision	highly imprecise	highly precise
Accuracy	within value range	outside value range
Investment	real assets	claims on assets
Units	operating enterprise	common stock issue
Data Source	company reports	market-generated
Measurement	absolute	relative, comparative
Analysis Type	investment	portfolio of stocks
Analysis-Units	one company	compare two stocks
Analysis-Time	one point in time	compare two times
Horizon	long-term (years)	short-term (minutes)
Frequency	sporadic, on demand	continuous supply
Stability	slow, small changes	quick, large changes
Application	individual stock selection	stock trading
* In contrast, the method of anticipation emphasizes earnings growth for the sake of growth rather than the sake of value. Thus, it is not recommended for purposes of estimating value.

Margin of Safety

Intrinsic value is independent of the market and current quoted price. 


It is the absolute standard against which all market prices are compared. 

• Thus with the method of valuation, companies are considered neither under-valued nor over-valued relative to the stock market. 

This would be bringing truth to error for correction, a backward approach. 

• Rather, common stock issues are considered either under-priced or over-priced in the market relative to the intrinsic value of their companies. 

This brings error to truth for correction. 

• To identify mispriced stocks, the value of a company is compared to its stock market price.

The concept of price is not without ambiguity. 

• We can choose among closing price, opening price, asking price, bidding price, actual price of latest trade for any number of shares, or actual price of latest trade for the same number of shares in the contemplated transaction.

Thus we focus on the important concept of safety margin rather than emphasize price with its potential quick and large changes from one transaction to the next. 

• The variability of the price of a stock in part represents mispricing by the market. 
• Such lack of convergence of market price to intrinsic value, however transient, represents market inefficiency. 
• The irrationality of the stock market has been observed by de la Vega, John Maynard Keynes, Kindleberger, Lefèvre, Mackay, and others.

John Maynard Keynes in his General Theory (Book IV "The Inducement to Invest", Chapter 12 "The State of Long-Term Expectation", Section V, pages 156-157) introduced the metaphor of newspaper photograph competitions to explain the working of the stock market. 

• His explanation emphasized anticipation of the opinions of other market participants and the resulting infinite regress, i.e., I think that he thinks that I think that he thinks, ad infinitum. 
• This stresses that market prices are determined by opinion.

Safety margin represents an excess of intrinsic value over market price, or alternately, a discount of price below intrinsic value. 

• A safety margin of at least twenty percent is desirable. 
• Intrinsic value is what a company would be worth to a private owner independent of the stock market and its daily quotations. 
• The concept of a margin of safety was introduced by Graham and Dodd in Security Analysis. 

It is more important to wait for a favorable buy price than to be dependent on fortuitous timing to realize a profitable sell price. 

• A buy and hold approach involves more than the platitudinous adage to "buy low and sell high." 
• The margin of safety requires knowing when the buying price is low in absolute terms rather than merely relative to the market as a whole.

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

Warrants trading: What you need to know

Parameters & Variables of Structured Warrants

To figure out the relationship between share price and the associated warrant price, the investor has to break down the premium factor that he/she pays for. 
Premium, Intrinsic & Time Values: The premium measures the extra cost incurred when buying a warrant and “exercising” the warrant into share over direct share purchase. 
Premium = [(Warrant Price + Exercise Price) - Share Price) / Share Price] x 100% 
Example (Diagram 1): if a warrant priced at RM0.50, has an exercise price of RM1.00, while the underlying share price is RM1.20, the premium on the warrant is 25%. 
Premium (%) = [(0.50+1.00)-1.20]/1.20 x 100% = 25% 
Besides premium, there is another dimension of valuing structured warrants, based on intrinsic and time value. 
Warrant Price = Intrinsic Value + Time Value 
The intrinsic value of a warrant is the difference between share and exercise price. In our example, the warrant’s intrinsic value of RM0.20 represents the possibility of buying shares for RM1.00, even though the market share price is RM1.20 (Diagram 2). 
The additional RM0.30 is known as the time value. It reflects the payment for profit opportunity if the underlying share moves in the warrant buyer’s favour. In our example, if the warrant was to expire tomorrow, it would be priced around RM0.20. But if the warrant has 9 months before expiry, there's a high chance of the share price increasing. At a time value of RM0.30, this tells us that investors are willing to pay RM0.30 for the potential future gains before warrant expiry. The downside is that time value will fall closer to zero as the expiry date approaches. This is known as time decay. 
If a warrant is out-of-the-money, by definition the warrant has no intrinsic value. In this case, the time value component accounts wholly for warrant price. 
The price will not be lower than its intrinsic value due to the possibility of a risk-less arbitrage – where one buys the warrants and exercises them into shares, for a lower market share price. If a warrant is deep in-the-money, or expires shortly, the price may trade at a small discount to its intrinsic value. 
Valuing Premium & Time Value: A warrant with a time value of RM0.20 is not necessarily “cheaper” than one at RM0.30. Both premium and time value parameters must be used in comparisons. 
Deep out-of-the-money warrants have high premiums, which get lower when becoming more in-the-money. Premiums are regarded as measures of warrant price. While intrinsic value is directly related to share and fixed exercise price, the unpredictable nature of time value makes analysis difficult. 
Implied Volatility: In determining “fair value” of warrants, the most adopted pricing model is the Black-Scholes one. It takes into account the inter-relationship between share and exercise price, expiry date, risk-free interest rate and volatility. 
Volatility represents absolute price movements, of the underlying share over a time period. Traders need to understand that huge volatility is actually beneficial due to “limited loss, unlimited upside” characteristics of structured warrants. 
There are two volatility types – historical, which calculates past variations of underlying share price, and implied, which represents market expectations of future volatility in underlying share price. 
Examining historical volatility requires care, since short-term can differ from longer term. Besides underlying share direction, investors need to question if current volatility is likely to continue. 
Implied volatility is derived from working backwards the current warrant price through the Black-Scholes equation. A warrant is expensive if implied volatility outweighs historical volatility assuming full market efficiency. In reality, implied volatility takes into account maturity length, nature of warrants, and spot/strike levels. Implied volatility is generally higher for longer-dated warrants and put warrants and at-the-money warrants. 


http://bursaedge.blogspot.com/2012/02/warrants-education-2.html

Types of Growth and DCF models

Models of Investment Valuation





Declining DDM  



Constant DDM   


                
Slow Growth DDM  


             
Fast Growth DDM




Forecasts of Dividends or Free Cash Flow



Logit Growth DDM 
                     

2-Stage Growth DDM           



FCF Constant D/E                 



FCF Rising D/E




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

Some of the most common types of intrinsic economic valuation model.

Instead of estimating each cash flow for each time period using a general-purpose DCF model that can be used for any investment asset, we can make reasonable simplifying assumptions for different kinds of specific investments in order to develop formulas by which these estimates can be made.

• These formulas provide shortcuts to operationalize the theory, and represent different types of the dividend discount model (DDM). 
• In each model type, dividends or free-cash-flow continue forever, but a terminal price may be assumed to simplify the analysis. 
• These model types can be given names so as to emphasize their specific simplifying assumptions.

Some of the most common types of intrinsic economic valuation model are

• constant dividend in perpetuity,
• constant dividend growth rate in perpetuity, e.g., decline (negative growth), slow growth, and fast growth,
• constant multistage dividend growth rates, e.g., two-stage and three-stage,
• variable logistic (LOGIT) dividend growth rates,
• free-cash-flow (FCF) used to estimate the cash distributions to equity owners, e.g., free-cash-flow with constant financial leverage (debt/equity ratio) and free-cash-flow with increasing financial leverage (rising debt/equity ratio), which in turn can be used either in a general DCF model or in a specific DDM model,
• special situations handled by a general-purpose DCF model that is customized to fit the circumstances of each investment case, e.g., rapid growth by external merger or acquisition (M&A) or by internal sudden expansion. Relatively complex M&A models are available elsewhere. In such cases the capital gains component of total return can greatly dominate the dividend component, especially when the number of years of dividends in the analysis is small.

Following the example of John Burr Williams (1938), four types of models of investment valuation and four types of dividend forecasts are illustrated below.

• The vertical axis is cash flow, and the scale is log-linear except for FCF forecasts which is linear. 
• The horizontal axis is time in years, and it continues to infinity. 
• A company lives forever, but its estimate of dividends or cash flow can have a finite life with a capital gain at the end of the forecast period.

Types of Growth
Models of Investment Valuation
Declining DDM	Constant DDM	Slow Growth DDM	Fast Growth DDM
Forecasts of Dividends or Free Cash Flow
Logit Growth DDM	2-Stage Growth DDM	FCF Constant D/E	FCF Rising D/E

• Slow and fast growth are relative to current average growth rates, historical precedents and the discount rate used in the model.
• Fast growth includes speculative growth. 
• LOGIT growth is a special case of S-curve growth for rapid followed by slower growth phases. 
• These growth patterns may be used in multi-stage models with different patterns for different stages of growth. See theory for the mathematics behind these models.

These models have been implemented in DCF Valuator, a free online web-based application that estimates intrinsic value per share, goal implied value, range of value with Monte Carlo simulation scenarios, and rate of return on investment for any common stock in any currency. For a walk-through tour of the DCF Valuator, click here and invoke any of the model types in the table.

 http://www.numeraire.com/value.htm

DCF Valuation: The classic work of John Burr Williams

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


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


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

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


Thus, in words:

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

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

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

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

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

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


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

PE/G ratio

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


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


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


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

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

A rapidly growing company presents special problems in valuation.

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

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

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

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


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

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

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

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

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

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

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

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

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

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

Factors of Intrinsic Economic Value
Number	Description
1	general price level inflation rate
2	real interest rate
3	dividends or free cash flows to equity
4	discount rate or rates
5	currency exchange rate, where applicable

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

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


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


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


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

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