In May of 2007, as the markets were reaching new records (and moving closer to a bear market precipice and the financial crisis), Warren Buffett and Charlie Munger were discussing intrinsic value at the annual Berkshire Hathaway conference. The decade-long run for the current bull market and widespread concerns about elevated values in U.S. stocks leading to days like Tuesday, when the Dow Jones Industrial Average fell by close to 800 points, are reminders that getting at the true value of corporations is as important as it has ever been.

The concept of intrinsic value came up earlier this year when Buffett made the decision to change his trigger for buying back Berkshire shares from a quantifiable discount to the company's book value (1.2 times book value) to a discount to intrinsic value. In moving back to monitoring intrinsic value, Buffett invoked the method also used by J.P. Morgan CEO Jamie Dimon.

As buybacks across the corporate sector continue to reach new records, it becomes more questionable whether all of these companies are basing their share repurchases on a valuation metric that uncovers a discount in a stock's trading price to intrinsic value — or are just buying back stock to keep shareholders happy and prop up earnings. Jamie Dimon said on Tuesday at a Goldman Sachs conference that buying back stock when market prices are high is not a wise idea, and companies should be reinvesting in the business instead.

Now the issue of valuation isn't limited to buyback analysis. As many sectors within the S&P 500, including one of Buffett's favorites (banking) are in correction, every investor should be questioning the value of what they own in their stock portfolio.

Buffett recently bought $4 billion worth of J.P. Morgan, a bank stock that has since entered a correction, and if he performed his analysis right, he might be buying more of it now. So no one should be making rash decisions, and Buffett reminds the fearful that the stock market is there to serve investors, not instruct them (echoing Ben Graham's maxim).

But having conviction in the staying power of your market bets becomes much more difficult when everything stops going up in unison. As Buffett famously wrote in an early '90s annual letter and said at the 1994 shareholder meeting, "You don't find out who has been swimming naked until the tide goes out."

Over the years, in annual Berkshire Hathaway shareholder meeting Q&As and in annual letters, Buffett has made clear — if in a roundabout way — just how difficult a concept intrinsic value is to explain. At the 1998 meeting, Buffett described it as "the present value of the stream of cash that's going to be generated by any financial asset between now and doomsday. And that's easy to say and impossible to figure."

Maybe that is why he has written that "what counts for most people in investing is not how much they know, but rather how realistically they define what they don't know." That may also explain why he added, "An investor needs to do very few things right as long as he or she avoids big mistakes."

### The Classic Valuation Models

In the classic business text Business Analysis and Valuation, which he wrote with fellow Harvard University professor Paul Healy, Krishna Palepu laid out two primary models for calculation of intrinsic value: the discounted cash-flow model and the accounting earnings-based valuation model.

But Palepu noted in an email to CNBC that even in using these models, getting to an intrinsic value requires the input of some significant assumptions, such as how long a company's outperformance can last: "The key is to start with the company's strategy and current performance and ask how long that performance is likely to be sustainable, given the nature of the industry and competition. Much of the value estimate in DCF lies in terminal value."

Terminal value is the estimated value of a business beyond a reasonable earnings forecast period, which some finance experts put at three to five years. Terminal value can take two paths: assuming that a company will continue to have a normalized growth rate even after its best years are over, or it assigns a takeout price for the firm.

Palepu continued: "The accounting based valuation technique puts some discipline in estimating the terminal value by using the company's current book value, and also its 'advantage horizon' — the time period over which the company's competitive advantage, if any, is sustainable."

The reason why an intrinsic value model can work so well — in terms of making people like Buffett a lot of money — is because so few people can effectively master them. "Since value is about the future, it is obviously based on forecasts. Forecasts have to be based on assumptions," Palepu wrote via email. He added: "The question really is how to make your assumptions sensible and grounded in fundamentals. That is why it is called fundamental analysis. If there is a mechanical way to do this, it won't have much payoff in the investment process, since everyone would have the same information, and it is tough to make money with common information in a market. So assumptions are a double-edged sword. They are subjective, but they are also the source of superior investment returns."

The principles related to intrinsic value can be laid out, but there is no one formula into which an investor can plug the ideas and come out with the same result as Buffett. If nothing more, the attempt to understand the ideas and calculate a publicly traded company's intrinsic value, even done imperfectly, could help an investor avoid the big market blunders before hitting the buy button. Or an investor would be perfectly correct to come away from an attempt to understand intrinsic value and say, "I'd rather just buy an S&P 500 index fund" — Buffett also approves of that antistock-picking strategy.

### 1. the Bad News: There Is No Magic Method, and Most Companies Are Too Hard to Value.

Berkshire Hathaway Vice Chairman Charlie Munger provided one of the most frustrating definitions of intrinsic value ever.

"There is no one easy method that could be simply mechanically applied by, say, a computer and make anybody who could punch the buttons rich. By definition, this is going to be a game which you play with multiple techniques and multiple models, and a lot of experience is very helpful," Munger told Berkshire shareholders at the 2007 annual meeting.

Munger went on to deflate the hopes of any investor who is confident enough to think they have valuation mastered. When it comes to valuation of companies, even he and Buffett draw a blank most of the time. "We throw almost all decisions into the too hard pile, and we just sift for a few decisions that we can make that are easy. And that's a comparative process. And if you're looking for an ability to correctly value all investments at all times, we can't help you."

Buffett's statements about intrinsic value over the years can seem like a labyrinth as well.

When stating Berkshire's new buyback policy in July, Buffett said, "The tough part is coming up with the intrinsic value. There is a lot more to intrinsic value than P/E," and there is no way to work intrinsic value out to four decimal places, "or anything of the sort."

At the 1994 Berkshire annual meeting, Buffett said a corporation's publicly reported financial statements can only help so much. "The numbers in any accounting report mean nothing, per se, as to economic value. They are guidelines to tell you something about how to get at economic value. ... To figure out that answer, you have to understand something about business."

But he went on to say at that meeting, and on other occasions, that when it comes to intrinsic value, "the math is not complicated."

Maybe a bit of an overstatement. But where to begin?

### 2. Start by Breaking a Business down to Its Basics.

Consider an iconic business: the American family farm. That's what Buffett did at the 2007 Berkshire Hathaway annual meeting, when he tried a little harder than Munger to explain the concept in terms that anyone could understand.

Catalog the basic stats:

- The farm can produce 120 bushels of corn per acre.
- It can produce 45 bushels of soybean per acre.
- The price of fertilizer is X.
- The property taxes are Y.
- The farmer's labor is Z.

That simple accounting will lead the investor to a dollar value that can be generated per acre "using fairly conservative assumptions."

But those assumptions are a big part of the riddle.

"Let's just assume that when you get through making those calculations that it turns out to be that you can make $70 an acre. ... Then the question is how much do you pay for the $70? Do you assume that agriculture will get a little bit better over the years so that your yields will be a little higher? Do you assume that prices will work a little higher over time?"

An investor looking for a 7 percent return and predicting the acre's cash value at $70 annually could determine that the acre is worth $1,000. But you wouldn't want to pay that price.

"You know, if farmland is selling for $900, you know you're going to have a buy signal. And if it's selling for $1,200, you're going to look at something else," Buffett explained to Berkshire shareholders. "That's what we do in business. We are trying to figure out what those corporate farms that we're looking at are going to produce. And to do that, we have to understand their competitive position. We have to understand the dynamics of the business."

The most important dynamic of the business may be its cash-generating potential.

### 3. Place Value on Cash Generation.

Telling investors it is critical to "understand a business' competitive position" and the "dynamics of a business" are the kind of opaque clues that make this valuation concept so fuzzy. Even in the farm example, Buffett noted that the investors need to make assumptions about the future direction in agricultural commodity pricing, and even if reasonable assumptions can be made based on recent pricing trends in a market, they are still assumptions.

At that 2007 meeting, Buffett went even folksier than the farm, invoking Aesop's fables from 600 B.C. as the original source text for "the mathematics of investment":

"A bird in the hand is worth two in the bush."

For the investor, the questions that follow from this approach are:

- How sure can you be that there are two in the bush?
- Could there be even more?

"We are looking at a whole bunch of businesses, how many birds are they going to give us, when are they going to give them to us, and we try to decide which ones — basically, which bushes — we want to buy out in the future. It's all about evaluating future — the future ability — to distribute cash, or to reinvest cash at high rates if it isn't distributed."

Of course, investors who follow Berkshire know that is has never distributed cash, and even as it has conducted limited buybacks in recent years, Buffett remains against paying a dividend. Berkshire also is sitting on more than $100 billion in cash currently, and that is a balance-sheet figure that Buffett said in 2007 is the underlying basis for the company's value.

Even refusing to part with the cash at any given time, "it's the ability to distribute cash that gives Berkshire its value." Though Buffett also has said in the past at times when Berkshire has more difficulty in figuring out how to invest its cash, it does become more difficult to calculate the intrinsic value. Berkshire ended September with close to $104 billion in cash.

He warned any investor who cannot come to conclusions about future cash flows of businesses in which they invest.

"There are all kinds of businesses that Charlie and I don't think we have the faintest idea what that future stream will look like. And if we don't have the faintest idea what the future stream is going to look like, we don't have the faintest idea what it's worth. ... Now, if you think you know what the price of a stock should be today but you don't think you have any idea what the stream of cash will be over the next 20 years, you've got cognitive dissonance. ... We are looking for things where we feel — fairly high degree of probability — that we can come within a range of looking at those numbers out over a period of time, and then we discount them back. ... We are more concerned with the certainty of those numbers than we are with getting the one that looks absolutely the cheapest."

### 4. You Have to Discount the Future.

To "discount" the numbers back, as Buffett remarked, is the third question that proceeds from Aesop's original "mathematics of investment":

What's the right discount rate?

That question is the key to evaluating the value of a company's cash generation, and it circles back around to Buffett's example of an investor expecting a farm to generate a 7 percent return, and basing a purchase decision on that return assumption and the current business price. There are essentially two components to the discount rate-based risk modeling: the concept of time value of money, and the additional risk premium for the investment.

The time value of money is typically accounted for using the long-term government rate. It is the way investors contend with the fact that the value of a dollar today will be lower in the future. The additional risk premium, because an investor buying a stock is taking risk versus the purchase of a bond, can be modeled by using a higher, customized discount rate, or by building what Benjamin Graham called a "margin of safety" directly into the cash flows (a concept we will come back to in the next section). For example, an investor believes there is a 90 percent probability of receiving the cash flow, they multiply the cash flow by 90 percent.

In the 1992 Berkshire Hathaway annual shareholder letter, Buffett turned to another writer, and a five-decade old business text, to explain stock value better than he thought he could himself. The text was "The Theory of Investment Value" written by John Burr Williams, a prominent figure in the history of fundamental analysis.

"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 "remaining life of the asset" makes it difficult to specify an exact period of time for this calculation, though in an example laid out by a Berkshire Hathaway shareholder to Buffett in an exchange back in 1999 (and which we will come to later) Buffett did say that the shareholder's model for intrinsic value looking out 20 years into the future was stated well.

Buffett went on to explain a few key differences between a discount rate for bonds and stocks. Bonds have a coupon and maturity rate that define its future cash flows. Stocks, on the other hand, are subject to cash flow estimates that even the best analysts can mess up, and, in addition, the performance of company management.

Buffett has been clear about the discount rate he prefers to use, saying at the 1996 shareholder meeting that he doesn't think he can be very good at predicting interest rates and so he thinks in terms of "the long-term government rate," as long as the business being considered first meets another requirement: it is one that the investor can understand. A higher discount rate is justified for riskier businesses, he said. Pertinent to the current market environment, he added: "And there may be times, when in a very — because we don't think we're any good at predicting interest rates, but probably in times of very — what would seem like very low rates — we might use a little higher rate."

But this doesn't mean Buffett is not also factoring a risk premium into his models. A "margin of safety" is likely built directly into his models so the additional risk premium is not required as a separate discount modeling rate.

### 5. It Is Important to Act as If You Won't Get It Exactly Right.

Buffett added to the definition provided by John Burr Williams in his own 1992 text that, "The investment shown by the discounted-flows-of-cash calculation to be the cheapest is the one that the investor should purchase - irrespective of whether the business grows or doesn't, displays volatility or smoothness in its earnings, or carries a high price or low in relation to its current earnings and book value."

But he made it clear that getting this right is a lot more difficult in practice. If the mathematical calculations required to evaluate equities are not difficult, Buffet still said that experienced and intelligent analysts can "easily go wrong in estimating future 'coupons.'"

Expecting to get things wrong about future cash flow is why Berkshire places so much emphasis on investing in businesses that the buyer understands, and only buying the businesses at prices which are reasonable — low enough to withstand mistakes in the model's assumptions.

"If a business is complex or subject to constant change, we're not smart enough to predict future cash flows. Second, and equally important, we insist on a margin of safety in our purchase price. If we calculate the value of a common stock to be only slightly higher than its price, we're not interested in buying. We believe this margin-of-safety principle, so strongly emphasized by Ben Graham, to be the cornerstone of investment success."

The margin of safety is not a single ratio or percentage that can be used across the board. It is a concept — some in the market have referred to it as more of an art than a science — and its methods can vary. It can be evaluated based the difference between the calculation of a company's intrinsic value and its trading price; it could also be evaluated based on the stock's return potential versus the risk-free rate (government bond rate).

### 6. Don't Think in Terms of Growth Stocks vs. Value Stocks.

One thing is certain: Intrinsic value is not to be confused with the way the word "value" is used to denote an entire class of stocks. In fact, even as many pundits position Buffett as one of the greatest "value" investors of all time, he dismissed the entire stock-picking industry that has been built around choosing between growth and value stocks in his 1992 letter to shareholders.

Buffett said the difference between companies judged to be growing faster than the market even if trading at relatively high prices (growth stocks) and those priced lower than peers based on measures like price to earnings ratio but with strong earnings potential than the market consensus believes (value stocks) is no way to pick stocks.

"Most analysts feel they must choose between two approaches customarily thought to be in opposition: 'value' and 'growth.' ... We view that as fuzzy thinking … Growth is always a component in the calculation of value, constituting a variable whose importance can range from negligible to enormous and whose impact can be negative as well as positive. ... In addition, we think the very term 'value investing' is redundant. What is 'investing' if it is not the act of seeking value at least sufficient to justify the amount paid? Consciously paying more for a stock than its calculated value — in the hope that it can soon be sold for a still-higher price — should be labeled speculation (which is neither illegal, immoral nor, in our view, financially fattening)."

Buffett added that a low ratio of price to book value, a low price- earnings ratio, or a high dividend yield, "even if they appear in combination, are far from determinative as to whether an investor is indeed buying something for what it is worth and is therefore truly operating on the principle of obtaining value in his investments."

### 7. The Berkshire Hathaway Shareholder Who (Sort Of) Got It Right.

At the 1999 Berkshire annual meeting, a shareholder from Bonita Springs, Florida, took the risk of asking Buffett and Munger whether his attempt to model Berkshire's intrinsic value was on target.

"You've given many clues to investors to help them calculate Berkshire's intrinsic value. I've attempted to calculate the intrinsic value of Berkshire using the discount of present value of its total look-through earnings. I've taken Berkshire's total look-through earnings and adjusted them for normalized earnings at GEICO, the super-cat business, and General Re. Then I've assumed that Berkshire's total look-through earnings will grow at 15 percent per annum on average for 10 years, 10 percent per annum for years 11 through 20. And that earnings stop growing after year 20, resulting in a coupon equaling year 20 earnings from the 21st year onward. Lastly, I've discounted those estimated earnings stream at 10 percent to get an estimate of Berkshire's intrinsic value. My question is, is this a sound method? Is there a risk-free interest rate, such as a 30-year Treasury, which might be the more appropriate rate to use here, given the predictable nature of your consolidated income stream?"

Buffett's response: "Investment is the process of putting out money today to get more money back at some point in the future. And the question is, how far in the future, how much money, and what is the appropriate discount rate to take it back to the present day and determine how much you pay? ... And I would say you've stated the approach — I couldn't state it better myself. The exact figures you want to use, whether you want to use 15 percent gains in earnings or 10 percent gains in the second decade, I would — you know, I have no comment on those particular numbers. But you have the right approach."

Buffett stressed again that getting to an intrinsic value that an investor can be comfortable with doesn't ever mean paying that price.

"Now, that doesn't mean we would pay that figure once we use that discount number. But we would use that to establish comparability across investment alternatives. So, if we were looking at 50 companies and making the sort of calculation that you just talked about, we would use a — we would probably use the long-term government rate to discount it back. But we wouldn't pay that number after we discounted it back. We would look for appropriate discounts from that figure. But it doesn't really make any difference whether you use a higher figure and then look across them or use our figure and look for the biggest discount. You've got the right approach. And then all you have to do is stick in the right numbers."

### The Pros and Cons of Building Your Own Valuation Model

Tim Vipond, CEO of the Corporate Finance Institute (CFI), said in an email to CNBC that there are three primary models of valuation it teaches. There is the cost model, which is predicated on the cost to build a business or its replacement cost. Then there are the more common approaches for valuing corporations, which are the relative value and intrinsic value models. Relative value relies on public company comparables and transactions that set a precedent in the market. In order to perform an intrinsic valuation analysis, an investor needs to build a discounted cash flow (DCF) model.

Start by thinking of how you would build a DCF model for a bond. "It would be relatively straightforward. ... You know the timing of when all the cash flows (interest and principle) will be paid, and you know exactly how much they will be (assuming the company doesn't default)," Vipond explained.

That's not the case for equities. "To build a DCF model for an equity investment is the same concept, however, it is much more complicated to estimate how much cash flow there will be for equity investors. How much will revenue grow? What will the expenses be? How much capital investment is required? etc. etc."

CFI does not provide investment advice and would not instruct an investor to give up, or go ahead, with building their own intrinsic value model. But Vipond did offer a note of caution as to a disadvantage most investors might face: "To build a 'good' model may require access to management, the CEO, CFO (interviews, essentially, which institutional investors like Warren Buffett can do, but retail investors cannot."

On the plus side, it also requires access to materials that many investors can get: equity research reports, lots of reading over 10-Ks and other company filings.

Buffett reads voraciously about companies, as many as 500 pages a week during his career, and reading is what he once told Columbia University students — including current Berkshire stock-picker Todd Combs — was his "secret."

From his earliest days as a student investor with Moody's securities manuals, through his married, family life when he would hole up in a home office at night, to his current octogenarian stock-picking, his life has been consumed by that practice.

"Read everything you can," he told shareholders in 2007, and be prepared to feel lucky if only 1 percent of it leads to a great investment idea.

An investor would be wise to start by reading a lot more about intrinsic value, as this barely scratches the surface. Or, if it all seems like too much, stick with an index fund.