Equity Valuation Methods

Insightful discussion on valuation methods from a blog.

http://www.theequitydesk.com/forum/forum_posts.asp?TID=2029&PN=7

Posted: 22/Feb/2009 at 9:31pm
Originally posted by kanaka_basi

Originally posted by kannanravi1


Hi Srini,
Discount rate is typically what you think you should earn for taking the risk of owning stocks. Typically many fund managers add a risk premium over the treasury bond rates (treasury rates are thought to be zero risk). Eg: If treasury rates are 5%, some may think that 10% should be the risk adjusted rate. Buffett always goes by the treasury rates because he believes that his picks have zero risk! So, I guess one has to find his own comfortable rate.

Kannan

PS: Any suggestions about how wrong/ right this method is??

Hi Kannan,

I saw this link http://www.moneychimp.com/articles/valuation/buffett_calc.htm which uses the discount rate as an opportunity cost of not investing in the least riskiest of asset classes (treasuries).

I thought that the expected confidence percentage (or probability that the earnings growth would be met) and the fact that my opportunity cost would be the treasury rate gave me the worst case scenario in trying to find the intrinsic value of the stock... and also the assumption that the compnay would grow only 5 years into the future...

Your opinions??


Hi,
I too use the very same link for my DCF calcs!! Good to see I am not alone! I typically use a confidence margin ranging from 50% to 75% (for companies with extremely strong moat I use 75%). I use the opportunity cost as the treasury rate (I don't track the rates religiously but use 6 to 8%). I also predict growth only for 5 years and love to get stocks with no growth priced in. Even if I assume growth I try to keep at or below the GDP growth rates. Don't know if this gives me worst case scenarios but hopefully I am being conservative enough so that I have cushions for any mistakes in my valuation. Also personally I think that the best way to be conservative and risk-free is through buying companies with significant moats. This is a qualitative factor though unfortunately. Buffett once stated that he uses risk-free treasury rates because he believes that the companies he buys in are as stable and risk free as a treasury bill!!

Intrinsic Value: There are two fatal weaknesses of any DCF model.

Why Stock "Value" Systems Have No Value

John Price, PhD

We regularly get asked how Conscious Investor is different from the countless "value" based software products and books available. The vast majority of "value" approaches are based upon a standard discount cash flow (DCF) model. They all purport to find what is called the intrinsic value or true value of a stock. This is the value the proponents claim that all rational investors should pay for the stock. Many of the authors and investment websites claim to base their intrinsic value approach upon the methods of Warren Buffett. In fact, it is actually very unlikely that he really uses any of these methods in anything vaguely resembling a formal approach. For example, Charlie Munger, the old friend of Buffett and the Vice-Chairman of Berkshire Hathaway, says that he has never seen Buffett do any discount value calculations. This is consistent with the answer he gave when asked about intrinsic value at the annual meeting of Berkshire Hathaway in 1996. "There is no formula to figure it out." He replied. "You have to know the business." Until recently, Buffett had never used a computer for anything, let alone for implementing any value models. Now he only uses it to play bridge on-line. When people write about Buffett I usually agree with most of the general observations made about his approach. The one area where Conscious Investor differs from the majority of Buffett followers (but quite likely not with Buffett himself) is in relation to the "valuation" model used. There are large numbers of DCF models. Stable growth models, two-stage models, three stage models and so on. Each of these models calculate the intrinsic value of the stock by discounting back to present time the stream of "cash" that is generated by the business. All I can say is that it is hard to believe that such simplistic and unreliable material is still taught in universities and promoted by stock analysts. The main problem is that people think that just because they can put some numbers into a formula they have found a useful and realistic model. Here we are talking about all the academics and writers who have limited understanding of the interface between mathematics and the real world. Two Fatal Weaknesses There are two fatal weaknesses of any DCF model. The first is that DCF models are unstable — small changes in the input values can lead to such large changes in the output that almost any number can be obtained. Here is a simple example showing just how unstable intrinsic value calculations are. The model uses the standard two-stage approach. We assume that the company spends ten years in the initial stage during which the cash per share (generally the free cash flow) that it generates grows by the rate given in the second column. After the initial stage comes the steady state period. During this period the cash is assumed to grow at the rate described in the third column. Finally, everything is discounted back to present time using the rate given in the fourth column. With small changes in the input variables, the output can shift from $23 to $58. I can't help getting the image in my mind of the host of an old television show saying, "Would the real intrinsic value please stand up?" Current Cash Initial Growth Rate Final Growth Rate Discount Rate Intrinsic Value $1.00 10% 4% 11% $23.09 $1.00 11% 5% 10% $33.50 $1.00 12% 6% 9% $58.00 And then you have to do the same estimate for the discount rate. If a model with this level of instability was proposed in a science class, it would be thrown out of the window. The second fatal weakness is that just because some model says it is generating something called intrinsic value does not mean that it is providing anything that really is "intrinsic value". And it certainly does not mean that it is giving something useful for investors. For example, just because a stock is undervalued (by some model or other) does not mean that it won't stay undervalued. This is quite different from saying that if a company has a strong economic performance, then eventually the market will acknowledge this by increased stock prices. Another weakness The instability described above is compounded by the fact that it is impossible to confirm the accuracy of two of the input variables. For example, the entry for the final growth rate requires that you estimate the growth rate of the cash not for another ten years, or even twenty years, but out to infinity! This is despite large studies showing that analyst forecasts for earnings over five years are no better than random. In contrast, in Conscious Investor we don't try to calculate the mythical concept of intrinsic value. We don't talk about whether a stock is undervalued or overvalued, whatever that may mean. Rather we define value in terms of the return you will get on an investment. Instead of intrinsic value, we talk about investment value or investment return. This is calculated using the proprietary tools STRETTM and STRETD®. STRET is a calculation of the annualized percentage profit or rate of return from owning the stock. STRETD is similar except that it assumes that dividends are reinvested. By calculating the actual return you can anticipate on your purchases, you get practical criteria whether it is worthwhile buying stock in a particular company or not. So in a nutshell, if you were to compare the stocks selected by Conscious Investor with other "value" models freely available on investor websites, you are unlikely to find much overlap between the selections. Despite the best intentions of would-be intrinsic value systems, the way that DCF models work either provide you with more or less random stocks or with stocks that you like and you (unconsciously) manipulate the data to make them appear undervalued. The Conscious Investor for more details ... The book The Conscious Investor: Profiting from the Timeless Value Approach by Dr John Price covers over 30 valuation methods including their assumptions, and their strengths and weaknesses.

http://www.conscious-investor.com/articles/articles/ar04value.asp

Using Discounted Cash Flow (DCF) Analysis to Value Stocks

Wall Street Prep Lessons: Cash Flow, DCF, WACC, LBO, M&A, Trading and Transactions

Discounted Cash Flow (DCF) Explained in Two Minutes

Simple DCF

Valuation

At the end of the day, every company is worth whatever the current value of all its future cash flows are discounted backward to today's terms.


It is a hint, not an answer.  Based on a lot of assumptions, using conservative figures.

1st 10 years Cash flow. using OWNERS EARNINGS (FCF).
Cash flow beyond the 10th year (Terminal value):  Assumes growth at 3% per year.
Add all the above discounted cashflows to get the present value..

Only the FCFs are hard data, all others are assumptions.

Time 14.13
http://www.youtube.com/watch?v=zA8udp8uRnw&feature=relmfu

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

The quantity of value is an estimate or approximation. Intrinsic value can be quantified as Net Present Value (NPV) based on Discounted Cash Flow (DCF) analysis.

The quantity of value is an estimate or approximation. The estimated quantity of value is based on an appraisal or a valuation. It can be expressed either as 

• an interval estimate or 
• a range of quantitative values, or 
• as a single-point estimate or 
• a single quantity of varying precision. 

Either way, intrinsic value can be quantified as Net Present Value (NPV) based on Discounted Cash Flow (DCF) analysis.

Price is not value, neither in concept nor in quantity. Price is a market-generated quantity. 

• The confusing term "market value" is really market price. 
• The confusing term "fair market value" is really fair market price. 
• The fair market price is the price that equals the single quantity that best approximates investment value. 

The best point estimate of investment value is the mean of the distribution of values rather than the median of the distribution of values or the midpoint of the range of values.

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

HOW WARREN BUFFET DETERMINES A FAIR PRICE

The real secret of Warren Buffett is the methods that he uses, some of which are known from his remarks, and some of which are not, that allow him to predict cash flows with some probability.

Various books about Warren Buffett give their explanations as to how he calculates the price that he is prepared to pay for a share with the desired margin of safety.

• Mary Buffett and David Clarke pose a series of tests, based on past growth rates, returns on equity, book value and government bond price averages.
• Robert G Hagstrom Jnr in The Warren Buffet Way gives explanatory tables of past Berkshire Hathaway purchases using a DCF model and owner earnings.

Ultimately, the investor must decide upon their own methods of arriving at the intrinsic value of a share and the margin of error that they want for themselves.

INTRINSIC VALUE: THE RIGHT PRICE TO PAY

INTRINSIC VALUE

Both Warren Buffett and Benjamin Graham talk about the intrinsic value of a business, or a share in it.  That is, to buy a business, or a share in it, at a fair price. 

But, having regard to the possibility of error in calculating intrinsic value, the careful of investor should provide a margin of error by only buying the business, or shares, at a substantial discount to the intrinsic value.

Buffett is said to look for a 25 per cent discount, but who really knows?

DEFINING INTRINSIC VALUE

Buffett’s concept, in looking at intrinsic value, is that it values what can be taken out of the business. 

He has quoted investment guru John Burr Williams who defined value like this:

‘The value of any stock, bond or business today is determined by the cash inflows and outflows – discounted at an appropriate interest rate – that can be expected to occur during the remaining life of the asset.’ – The Theory of Investment Value.

The difference for Buffett in calculating the value of bonds and shares is that the investor knows the eventual price of the bond when it matures but has to guess the price of the share at some future date.

WHAT WARREN BUFFETT SAYS ABOUT PREDICTING FUTURE CASH FLOWS

DISCOUNTED CASH FLOW (DCF)

This method of valuation is often referred to as the Discounted Cash Flow (DCF) valuation method, but, as Buffett has said in relation to shares, it is not easy to predict future cash flows and this is why he sticks to investment in companies that are consistent, well managed, and simple to understand. 

A company that is hard to understand or that changes frequently does not allow for easy prediction of future earnings and outgoings.

WHAT WARREN BUFFETT SAYS ABOUT PREDICTING FUTURE CASH FLOWS

In 1992, Warren Buffett said that:

‘Leaving question of price aside, the best business to own is one that over an extended period can employ large amounts of capital at very high rates of return. The worst company to own is one that must, or will, do the opposite – that is, consistently employ ever-greater amounts of capital at very low rates of return.’

It is well worth reading Buffet’s analogy relating DCF to a university education in his 1994 Letter to Shareholders.

So, it would seem that the intrinsic value of a share in a company relates to the DCF that can be expected from the investment. 

There are formulas for working out discounted cash flows and they can be complex but they give a result.

EXPLANATIONS OF DCF

The best explanation that we have read of DCF is by Lawrence A Cunningham in his outstanding book How to think like Benjamin Graham and invest like Warren Buffett.

A good online explanation is available here.

http://www.buffettsecrets.com/price-to-pay.htm