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	<title>Indonesian Stock Market &#187; estimating intrinsic value</title>
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		<title>Understanding Intrinsic Value</title>
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		<pubDate>Mon, 17 Jan 2011 08:32:00 +0000</pubDate>
		<dc:creator>bullbear</dc:creator>
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		<description><![CDATA[Intrinsic Value versus Market PriceBuffett's core investment measure is finding the intrinsic value of a company and being certain the price he pays for the company is justified by that intrinsic value. &#160;The definition of intrinsic value is the di...]]></description>
			<content:encoded><![CDATA[<p></p><div class="separator" style="clear: both; text-align: center;"><a href="http://www.tritoncapmanagement.com/assets/images/value_investing_scale.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://www.tritoncapmanagement.com/assets/images/value_investing_scale.JPG" width="316" /></a></div>
<div class="separator" style="clear: both; text-align: center;">Intrinsic Value versus Market Price</div>
<div class="separator" style="clear: both; text-align: center;"></div>
<p><b><span class="Apple-style-span" style="color: yellow;">Buffett&#8217;s core investment measure is finding the <u>intrinsic value</u> of a company and being certain the price he pays for the company is justified by that intrinsic value. </span></b><span class="Apple-style-span" style="color: lime;"><b>&nbsp;The definition of intrinsic value is the discounted value of the cash that can be taken out of a business during its remaining life.</b></span></p>
<p>The key secret there is that the way to calculate intrinsic value is<b><u> not precise</u></b>. &nbsp;It&#8217;s based on a lot of <b><u>assumptions</u></b>, and those assumptions can be easily adjusted based on anticipated interest rate.</p>
<p>Buffett never gives investors the intrinsic value he has calculated for a company, but he will give details in his annual reports relating to the facts that he and Munger used to determine the intrinsic value of a company.</p>
<p>Buffett believes Berkshire Hathaway&#8217;s book value far understates its intrinsic value because many of the businesses Berkshire Hathaway controls are worth much more than their carrying value.</p>
<p>Also read:</p>
<h3 class="post-title entry-title" style="color: #ffeedd; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font: normal normal normal 30px/normal Georgia, Utopia, 'Palatino Linotype', Palatino, serif; line-height: 18px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; position: relative;"><a href="http://myinvestingnotes.blogspot.com/2011/01/fair-valuation-of-berkshire-hathaway.html"><span class="Apple-style-span" style="font-size: small;">Fair Valuation of Berkshire Hathaway</span></a></h3>
<div class="blogger-post-footer">Health is Wealth<br />
Bullbear Stock Investing Notes<img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2884768844412347068-3630768786917300703?l=myinvestingnotes.blogspot.com' alt='' /></div>
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		<title>Intrinsic Value &#8211; What a stock is worth?</title>
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		<pubDate>Sat, 31 Jul 2010 07:18:00 +0000</pubDate>
		<dc:creator>bullbear</dc:creator>
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		<description><![CDATA[<span>Intrinsic Value - What a stock is worth?</span><br /><div>Without knowing what a stock is worth- in other words its Intrinsic Value- how can you know how much you should pay for it? Stocks should be purchased because they are trading at some discount to their intrinsic value, not simply because they are priced at a higher or lower point than similar companies.</div><div></div><div>The big drawback of the ratios discussed in the&#160;<a href="http://www.stock-picks-focus.com/stock-valuation.html" target="_new" title="Learn the basics of stock valuation">Stock Valuation Basics</a>&#160;section is that they are all based on price - they compare what investors are currently paying for one stock to what they are paying for another stock. Ratios do not, however, tell you anything about value, which is what a stock is actually worth. Comparing ratios across companies and across time can help us understand whether our valuation estimate is close to or far from the mark, but estimating the intrinsic value of a company gives us a better target.</div><div></div><div>Pat Dorsey, Director of Stock Analysis, Morningstar Inc. in his very useful book -&#160;<a href="http://www.amazon.com/Five-Rules-Successful-Stock-Investing/dp/0471686174" title="Check out the most practical do-it-yourself book on learning successful investing">The 5 Rules for Successful Stock Investing</a>&#160;- tells us how we can go about calculating what a stock is really worth- in other words, its Intrinsic Value. His writings are the primary source for this article.</div><div>Having an intrinsic value estimate keeps you focused on the value of the business, rather than a piece of the stock - and that's what you want because, as an investor, you are buying a small piece of a business. Intrinsic valuation also forces you to think about the cash flows that a business is generating today and the cash it could generate in the future, as well as the returns on the capital that the firm creates. It makes you ask yourself, "If I could buy the whole company, what would I pay?</div><div></div><div>Second, having an intrinsic value gives you a stronger basis for making investment decisions. Without looking at the true determinants of value, such as cash flow and return on capital, we have no way of assessing whether a P/E of, for example 15 or 20 is too low, too high, or right on target. After all, the company with the P/E of 20 might have much lower capital needs and a less risky business than the company with the P/E of 15, in which case it might actually be the better investment.</div><h2>Cash Flow, Present Value, and Discount Rates</h2><span>What is a stock worth? Economists Irving Fisher and John Burr Williams answered this question for us more than 60 years ago. The value of a stock is equal to the present value of its future cash flows. No more and no less.</span><br /><div></div><div>Companies create economic value by investing capital and generating a return. Some of that return pays operating expenses, some get re-invested in the business, and the rest is&#160;<a href="http://www.stock-picks-focus.com/free-cash-flow.html" target="blank">free cash flow</a>. Remember we care about the free cash flow because that's the amount of money that could be taken out of the business each year without harming its operations. A firm could use free cash flow to benefit shareholders in a number of ways. It can pay a dividend, which essentially converts a portion of each investor's interest in the firm to cash. It can buy back stock, which reduces the number of shares outstanding and thus increases the percentage ownership of each shareholder. Or, the firm can retain the free cash flow and re-invest it in the business.</div><div></div><div>These free cash flows are what give the firm its investment value. A present value calculation simply adjusts those future cash flows to reflect the fact that money we plan to receive in the future is worth less than money we receive today.</div><div></div><div>Why are future cash flows worth less than the current ones? First, money that we receive today can be invested to generate some kind of return, whereas we cant invest future cash flows until we receive them. This is the time value of money. Second, there is a chance that we may never receive those future cash flows, and we need to be compensated for that risk, called the risk premium.</div><div></div><div>The time value of money is essentially the opportunity cost of receiving money in the future versus receiving it today, and is often represented by the interest rates being paid on government bonds. Its pretty certain that the government will be around to pay us our interest in a few years.</div><div></div><div>Of course, not many cash flows are as certain as those from the government, so we need to take an additional premium to compensate us for the risk that we may never receive the money we have been promised. Add the government bond rate to the risk premium, and we have what's known as a discount rate.</div><div></div><div>Now you can start to see why stocks with stable, predictable earnings often have such high valuations - investors discount their future cash flows at a lower rate, because they believe that there's a lower risk attached to the likelihood that those future cash flows will actually show up. Conversely a business with an extremely uncertain future should logically have a lower valuation because there is a substantial risk that the potential future cash flows will never materialise.</div><div></div><div>You can see why a rational investor should be willing to pay more for a company that's profitable now relative to one that promises profitability only at some point in the future. Not only does the latter carry a higher risk (and thus a higher discount rate), but the promised cash flows won't arrive until some years in the future, diminishing their value still further.</div><div></div><div>Changing discount rates and the timing of cash flows can have a telling effect on present value. In all three examples, below -StableCorp, CycliCorp, and RiskCorp -the sum of the undiscounted cash flows is about $32000.</div><span><img alt="" border="0" height="308" src="http://www.stock-picks-focus.com/images/Changing-discount-rates.png" width="400" /></span><span>&#160;</span><span><br /></span><span><br /></span><span><br /></span><span>However, the value of the discounted cash flows is quite different from company to company. In present value terms, CycliCorp is worth about $2700 less than StableCorp. That's because StableCorp is more predictable, which means that investors' discount rate isn't high. CycliCorp's cash flow increases by 20 percent some years and shrinks in some years, so investors perceive it as a riskier investment and use a higher discount rate when they are valuing its shares. As a result the present value of the discounted cash flows is lower.</span><br /><div></div><div>The difference in the present value of the cash flows is even more acute when you look at RiskCorp, which is worth almost $8300 less than StableCorp. Not only are the bulk of RiskCorp's cash flows far off in the future, bu also, we are less certain that they will come to pass, so we assign an even higher discount rate.</div><div></div><div>This is the basic principle behind a discounted cash flow model. Value is determined by the amount, timing, and riskiness of a firm's future cash flows, and these are the three items you should always be thinking about when deciding how much to pay for a stock. That's all it really boils down to.</div><h2><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="present-value"></a>Calculating Present Value</h2><span>To find the present value of a $100 future cash flow, divide that future cash flow by 1.0 plus the discount rate. Using a 10% discount rate, for example, a cash flow of $100 one year in teh future is worth $100/1.10. or $90.91. A $100 cash flow two years in the future is worth $100/(1.10x1.10), or $82.64. In other words, $82.64 invested at 10% becomes $90.91 in a year and $100 in 2 years. Discount rates are really just interest rates that go backwards through time instead of forwards.</span><br /><div></div><div>Generalising the previous formula, if we represent the discount rate as R, the present value of a future cash flow (CF) in year N equals</div><span><img alt="" border="0" height="16" src="http://www.stock-picks-focus.com/images/Present-Value-Formula.png" width="400" /></span><br /><h3><br /><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="discount-rate"></a>Fun with discount rates</h3><span>Now that we have the formula down, we need to figure out what factors determine discount rates for use in Intrinsic Value calculations. How do we know whether to use 7 percent or 10 percent?</span><br /><div></div><div>Unfortunately, there is no precise way to calculate the exact discount rate that you should use in discounted cash flow (DCF) model, and academicians have filled entire journals with nothing but discussions on the right way to estimate discount rates for Intrinsic value calculations.</div><div></div><div>Here's what you want to know for practical purposes. As interest rates rise, so will discount rates. As a firm's risk level increases, so will its discount rate. Let's put these two together. For interest rates you can use the long-term average of treasury rates as a reasonable proxy. (Remember we use interest rate on treasuries to represent opportunity costs because we are pretty certain that the government will pay us our promised interest).</div><div></div><div>Now for risk, which is an even less exact factor to measure. Here are some factors that should be taken into account when estimating discount rates.</div><div></div><div><b>Size</b></div><div>Smaller firms are generally riskier than larger firms because they're more vulnerable to adverse events. They also usually have less diversified product lines and customer bases.</div><div></div><div><b><a href="http://www.stock-picks-focus.com/financial-leverage.html" target="blank">Financial Leverage</a></b></div><div>Firms with more debt are generally riskier than firms with less debt because they have a higher proportion of fixed expenses (debt payments) relative to other expenses. Earnings will be better in good times, but worse in bad times, with an increased risk of financial distress. Look at a firm's debt-to-equity ration, interest coverage, and a few other factors to determine the degree of a company's risk from financial leverage.</div><div></div><div><b>Cyclicality</b></div><div>Is the firm in a cyclical industry (such as commodities or automobiles) or a stable industry (such as breakfast cereal or beer)? Because the cash flows of cyclical firms are much tougher to forecast than stable firms, their level of risk increases.</div><div></div><div><b>Management/Corporate Governance</b></div><div>This factor boils down to a simple question: How much do you trust the folks running the shop? Although its rarely black or white, firms with promotional managers (who leave no opportunity to drum up stock prices through their media appearances), managers who draw egregious salaries, or who exhibit any of the other red flags are definitely riskier than companies with managers who do not display these traits.</div><div></div><div><b>Economic Moat</b></div><div>Does the firm have a wide moat, a narrow moat, or no economic moat? The stronger a firm's competitive advantage -that is, the wider its moat- the more likely it will be able to keep competitors at bay and generate a reliable stream of cash flows.</div><div></div><div><b>Complexity</b></div><div>The essence of risk is uncertainty. And its tough to value what you can't see. Firms with extremely complex businesses or financial structures are riskier than simple, easy-to-understand firms because there's a greater chance that something unpleasant is hiding in a footnote that you missed. Even if you think management is as honest as the day is long and that the firm does a great job running its operations, its wise to incorporate a complexity discount into your mental assessment of risk.</div><div></div><div>How should you incorporate all of these risk factors into a discount rate? There is no right answer.</div><div>Morningstar uses 10.5 percent as the discount rate for an average company based on the above factors and creates a distribution of discount rates based on whether firms are riskier or less risky than the average. A so mid-2003, firms such as Johnson and Johnson, Colgate and Wal-Mart fall at the bottom of the range at around 9 percent, whereas riskier firms such as Micron technology, JetBlue Airways, and E*Trade -top out at 13 percent to 15 percent.</div><div></div><div>The key is to pick a discount rate you are comfortable with. Don't worry about being exact -just think about whether the company you are evaluating is riskier or less risky than the average firm, along with how much riskier or less risky it is, and you will be fine.</div><div></div><div><b><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="indian-market-discount-rate"></a>Discount rates for the Indian market context</b></div><div>In the Indian market context we may use 15% as the discount rate for an average company (8 percent risk-free rate + 7 percent risk-premium). High-Quality companies may be discounted at a low rate of 12%, above-average companies at 13%, and poor quality companies may be discounted at a high of 18%.</div><h2><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="perpetuity-value"></a>Calculating Perpetuity Values</h2><span>We have cash flow estimates, and we have a discount rate. We need one more element called a perpetuity value. We need a perpetuity because it's not feasible to project a company's future cash flows out to infinity, year-by-year, and because companies have theoritically finite lives.</span><br /><div></div><div>The most common way to calculate a perpetuity is to take the last cash flow (CF) that you estimate, increase it by the rate at which you expect it to grow over the very long term (g), and divide the result by the discount rate (R) minus the expected long-term growth rate.</div><span><img alt="" border="0" height="31" src="http://www.stock-picks-focus.com/images/Perpetuity-Value.png" width="400" /></span><span>&#160;</span><span><br /></span><span><br /></span><span>The result of this calculation than must be discounted back to present, using the method discussed for calculating present value. For example, suppose we are using a 10-year DCF model for a company with an 11 percent discount rate. We estimate that the company’s cash flow in year 10 will be $1 billion and its cash flow will grow at a steady 3 percent annual rate after that. (Three percent is generally a good number to use as your long-run growth rate because it’s roughly the U.S. gross domestic product [GDP] growth. If you are valuing a firm in a declining industry, you might use 2 percent).</span><br /><div></div><div></div><div>Perpetuity Value = $ 1 billion x (1+ 0.03) / (0.11-0.03)</div><div>= $ 1.03 billion/ 0.08</div><div>= $ 12.88 billion</div><div>To get the present value of these cash flows, we need to discount them using the formula</div><span><img alt="" border="0" height="16" src="http://www.stock-picks-focus.com/images/Present-Value-Formula.png" width="400" /></span><span>&#160;</span><span><br /></span><span><br /></span><span>where n is the number of years in the future, CFn is the cash flow in year n, and R is the discount rate. Plugging these numbers, N = 10, CFn = $12.88 billion, R= 0.11</span><br /><div></div><div></div><div>Discounted Perpetuity Value = $12.88 bn/ (1+0.11)^10 = $12.88 bn/2.839 = $4.536 bn</div><h2><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="intrinsic-value"></a>Calculating Intrinsic Value</h2><span>Now all that we need to do is add this discounted perpetuity value to the discounted value of our estimated cash flows in years 1 through 10, and divide by the number of shares outstanding.</span><span><br /></span><span><br /></span><span><img alt="" border="0" height="310" src="http://www.stock-picks-focus.com/images/simple-10yr-DCF-model2.png" width="400" /></span><span>&#160;</span><span><br /></span><span><br /></span><span>That was a brief outline of the process. You can follow along by matching the following steps:</span><br /><div></div><div></div><div></div><div>1. Estimate free cash flows for the next 4 quarters. This amount will depend on all of the factors discussed earlier -how fast the company is growing, the strength of its competitors, its capital needs, and so on. Using Clorox as an example, our first step is to see how fast free cash flow has grown over the past decade, which turns out to be 9% when we do the math. We could just increase the $600 million in free cash flow that Clorox generated in 2003 by 9 percent, but that would assume the future would be as rosy as in the past. Mega retailers like Wal-Mart -which now accounts for almost a quarter of Clorox sales -has hurt the bargaining power of consumer-product firms. So, let's be conservative and assume free cash flow increases by only 5 percent over the last year, which would work out to $630 million.</div><div></div><div>2. Estimate how fast you think free cash flow will grow over the next 5 to 10 years. Remember, only firms with very strong competitive advantages and low capital needs are able to sustain above-average growth rates for very long. If the firm is cyclical don't forget to throw in some bad years. We won't do this for Clorox because selling bleach and Glad bags is a very stable business. We will however be conservative on our growth rate because of the "Wal-Mart factor", and will assume free cash flow increases at 5 percent annually over the next decade.</div><div></div><div>3. Estimate a discount rate. Financially Clorox is rock-solid, with little debt, tons of free cash flow, and a non-cyclical business. So we will use 9% for our discount rate, which is meaningfully lower than the 10.5 percent average we discussed earlier. Clorox, is a predictable company, after all.</div><div></div><div>4. Estimate a long-run growth rate. Because people will still need bleach and trash bags in the future, and its a good bet that Clorox will continue to get a piece of that market, we can use the long-run GDP average of 3 percent.</div><div></div><div>5. That's it! We discount the first 10 years of cash flows, add that value to the present value of the perpetuity, and divide by the shares outstanding.</div><div></div><div>This is a very simple DCF model. The one used at Morningstar has about a dozen excel tabs, adjusts for complicated items such as pensions and operating leases, and explicitly models competitive advantage periods, among many other things. But a model doesn't need to be super complex to get you most of the way there and help you clarify your thinking.</div><div></div><div>The important thing is that we forced ourselves to think through these kinds of issues as discussed earlier, which we wouldn't have if we had just looked at Clorox's stock chart or if we had just said, "Sixteen times earnings seem reasonable". By thinking about the business, we arrived at a better valuation in which we have more confidence.</div><h3>Valuing Clorox using a Discounted Cash Flow model</h3><span><img alt="" border="0" height="390" src="http://www.stock-picks-focus.com/images/Valuing-Clorox-using-DCF2.png" width="400" /></span><br /><h2><br /><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="margin-of-safety"></a>Margin of Safety</h2><span>We have analysed a company, we have valued it - now we need to know when to buy it. If you really want to succeed as an investor, you should seek to buy companies at a discount to your estimate of their intrinsic value. Any valuation and any analysis is subject to error, and we can minimise the effect of these errors by buying stocks only at a significant discount to our estimated intrinsic value. This discount is called the Margin of Safety, a term first popularised by investing great Benjamin Graham.</span><br /><div></div><div>Here is how it works. Let's say we think Clorox's intrinsic value is $54, and the stock is trading at $45. If we buy the stock and we're exactly right about our analysis, the return we receive should be the difference between $45 and $54 (20 percent) plus the discount rate of about 9 percent. That would be 29 percent, which is a pretty darn good return, all things considered.</div><div></div><div>But what if we are wrong? What if Clorox grows even more slowly than we had anticipated -may be a competitor takes market share - or the firm's pricing power erodes faster than we had thought? If that's the case, then Clorox's intrinsic value might actually be $40, which means we would have overpaid for the stock by buying it at $45.</div><div></div><div>Having a margin of safety is like an insurance policy that helps prevent us from overpaying - it mitigates the damage caused by overoptimistic estimates. If, for example, we had required a margin of safety of 20 percent before buying Clorox, we wouldn't have purchased the stock until it fell to $43. In that case, even if our initial analysis had been wrong and the fair value had really been $40, the damage to our portfolio wouldn't have been as severe.</div><div></div><div>Because all stocks aren't created equal, not all margins of safety should be the same. It's much easier to forecast the cash flows of, for example, Anheuser-Busch over the next 5 years than the cash flows of Boeing. One company has tons of pricing power, dominant market share, and relatively stable demand, whereas the other has relatively little pricing power, equal market share, and highly cyclical demand. Because I am less confident about my forecasts for Boeing, I'll want a larger margin of safety before I buy the shares. There's simply a greater chance that something might go wrong, and that my forecasts will be too optimistic.</div><div></div><div>Paying more for better businesses makes sense, within reason. The price you pay for a stock should be closely tied to the quality of the company, and great businesses are worth buying at smaller discounts to intrinsic value. Why? Because high-quality businesses - those that have wide economic moats - are more likely to increase in value over time, and it's better to pay fair price for a great business than a great price for a fair business.</div><div></div><div>How large should your margin of safety be? It ranges all the way from just 20 percent for very stable firms with wide economic moats to 60 percent for high-risk stocks with no competitive advantages. For above-average firms we would require a 25 percent margin of safety, while on average, we require a 30 percent to 40 percent margin of safety for most firms.</div><div></div><div>Having a margin of safety is critical to being a disciplined investor because it acknowledges that as humans, we are flawed. Simply investing in the stock market requires some degree of optimism about the future, which is one of the biggest reasons that buyers of stocks are too optimistic far more often than they're too pessimistic. Once we know this, we can correct for it by requiring a margin of safety for all of our share purchases.</div><div></div><div>Every approach to equity investing has its own warts. Being disciplined about valuation may mean that you will miss out on some great opportunities because some companies wind up performing better for longer periods of time than almost anyone could have anticipated. Companies such as Microsoft looked very pricey back in their heyday, and its unlikely that many investors who were very strict about valuation would have bought it early in their corporate lives.</div><div></div><div>Being disciplined about valuation would have meant missing those opportunities, but it also would have kept you out of many investments that were priced like Microsoft, but which wound up disappointing investors in a big way. Although we acknowledge that some high-potential companies are worth a leap of faith and a high valuation, on balance, we think its better to miss a solid investment because you are too cautious in your initial valuation than it is to buy stocks at prices that turn out to be too high.</div><div></div><div>After all, the real cost of losing money is much worse than the opportunity cost of missing out on gains. that's why the price you pay is just as important as the company you buy.<br /><br /><a href="http://www.stock-picks-focus.com/intrinsic-value.html">http://www.stock-picks-focus.com/intrinsic-value.html</a></div><div>Health is Wealth<img width="1" height="1" src="https://blogger.googleusercontent.com/tracker/2884768844412347068-4210045154360114652?l=myinvestingnotes.blogspot.com" alt="" /></div>]]></description>
			<content:encoded><![CDATA[<p></p><p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 26px; font-weight: bold;">Intrinsic Value &#8211; What a stock is worth?</span>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Without knowing what a stock is worth- in other words its Intrinsic Value- how can you know how much you should pay for it? Stocks should be purchased because they are trading at some discount to their intrinsic value, not simply because they are priced at a higher or lower point than similar companies.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">The big drawback of the ratios discussed in the&nbsp;<a href="http://www.stock-picks-focus.com/stock-valuation.html"  title="Learn the basics of stock valuation">Stock Valuation Basics</a>&nbsp;section is that they are all based on price &#8211; they compare what investors are currently paying for one stock to what they are paying for another stock. Ratios do not, however, tell you anything about value, which is what a stock is actually worth. Comparing ratios across companies and across time can help us understand whether our valuation estimate is close to or far from the mark, but estimating the intrinsic value of a company gives us a better target.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Pat Dorsey, Director of Stock Analysis, Morningstar Inc. in his very useful book -&nbsp;<a href="http://www.amazon.com/Five-Rules-Successful-Stock-Investing/dp/0471686174" title="Check out the most practical do-it-yourself book on learning successful investing">The 5 Rules for Successful Stock Investing</a>&nbsp;- tells us how we can go about calculating what a stock is really worth- in other words, its Intrinsic Value. His writings are the primary source for this article.</div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Having an intrinsic value estimate keeps you focused on the value of the business, rather than a piece of the stock &#8211; and that&#8217;s what you want because, as an investor, you are buying a small piece of a business. Intrinsic valuation also forces you to think about the cash flows that a business is generating today and the cash it could generate in the future, as well as the returns on the capital that the firm creates. It makes you ask yourself, &#8220;If I could buy the whole company, what would I pay?</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Second, having an intrinsic value gives you a stronger basis for making investment decisions. Without looking at the true determinants of value, such as cash flow and return on capital, we have no way of assessing whether a P/E of, for example 15 or 20 is too low, too high, or right on target. After all, the company with the P/E of 20 might have much lower capital needs and a less risky business than the company with the P/E of 15, in which case it might actually be the better investment.</div>
<h2 style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 22px; margin-bottom: 14px; margin-left: 0px; margin-right: 0px; margin-top: 8px;">Cash Flow, Present Value, and Discount Rates</h2>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">What is a stock worth? Economists Irving Fisher and John Burr Williams answered this question for us more than 60 years ago. The value of a stock is equal to the present value of its future cash flows. No more and no less.</span>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Companies create economic value by investing capital and generating a return. Some of that return pays operating expenses, some get re-invested in the business, and the rest is&nbsp;<a href="http://www.stock-picks-focus.com/free-cash-flow.html" >free cash flow</a>. Remember we care about the free cash flow because that&#8217;s the amount of money that could be taken out of the business each year without harming its operations. A firm could use free cash flow to benefit shareholders in a number of ways. It can pay a dividend, which essentially converts a portion of each investor&#8217;s interest in the firm to cash. It can buy back stock, which reduces the number of shares outstanding and thus increases the percentage ownership of each shareholder. Or, the firm can retain the free cash flow and re-invest it in the business.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">These free cash flows are what give the firm its investment value. A present value calculation simply adjusts those future cash flows to reflect the fact that money we plan to receive in the future is worth less than money we receive today.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Why are future cash flows worth less than the current ones? First, money that we receive today can be invested to generate some kind of return, whereas we cant invest future cash flows until we receive them. This is the time value of money. Second, there is a chance that we may never receive those future cash flows, and we need to be compensated for that risk, called the risk premium.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">The time value of money is essentially the opportunity cost of receiving money in the future versus receiving it today, and is often represented by the interest rates being paid on government bonds. Its pretty certain that the government will be around to pay us our interest in a few years.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Of course, not many cash flows are as certain as those from the government, so we need to take an additional premium to compensate us for the risk that we may never receive the money we have been promised. Add the government bond rate to the risk premium, and we have what&#8217;s known as a discount rate.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Now you can start to see why stocks with stable, predictable earnings often have such high valuations &#8211; investors discount their future cash flows at a lower rate, because they believe that there&#8217;s a lower risk attached to the likelihood that those future cash flows will actually show up. Conversely a business with an extremely uncertain future should logically have a lower valuation because there is a substantial risk that the potential future cash flows will never materialise.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">You can see why a rational investor should be willing to pay more for a company that&#8217;s profitable now relative to one that promises profitability only at some point in the future. Not only does the latter carry a higher risk (and thus a higher discount rate), but the promised cash flows won&#8217;t arrive until some years in the future, diminishing their value still further.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Changing discount rates and the timing of cash flows can have a telling effect on present value. In all three examples, below -StableCorp, CycliCorp, and RiskCorp -the sum of the undiscounted cash flows is about $32000.</div>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><img alt="" border="0" height="308" src="http://www.stock-picks-focus.com/images/Changing-discount-rates.png" width="400" /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">&nbsp;</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br clear="all" /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">However, the value of the discounted cash flows is quite different from company to company. In present value terms, CycliCorp is worth about $2700 less than StableCorp. That&#8217;s because StableCorp is more predictable, which means that investors&#8217; discount rate isn&#8217;t high. CycliCorp&#8217;s cash flow increases by 20 percent some years and shrinks in some years, so investors perceive it as a riskier investment and use a higher discount rate when they are valuing its shares. As a result the present value of the discounted cash flows is lower.</span>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">The difference in the present value of the cash flows is even more acute when you look at RiskCorp, which is worth almost $8300 less than StableCorp. Not only are the bulk of RiskCorp&#8217;s cash flows far off in the future, bu also, we are less certain that they will come to pass, so we assign an even higher discount rate.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">This is the basic principle behind a discounted cash flow model. Value is determined by the amount, timing, and riskiness of a firm&#8217;s future cash flows, and these are the three items you should always be thinking about when deciding how much to pay for a stock. That&#8217;s all it really boils down to.</div>
<h2 style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 22px; margin-bottom: 14px; margin-left: 0px; margin-right: 0px; margin-top: 8px;"><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="present-value"></a>Calculating Present Value</h2>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">To find the present value of a $100 future cash flow, divide that future cash flow by 1.0 plus the discount rate. Using a 10% discount rate, for example, a cash flow of $100 one year in teh future is worth $100/1.10. or $90.91. A $100 cash flow two years in the future is worth $100/(1.10&#215;1.10), or $82.64. In other words, $82.64 invested at 10% becomes $90.91 in a year and $100 in 2 years. Discount rates are really just interest rates that go backwards through time instead of forwards.</span>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Generalising the previous formula, if we represent the discount rate as R, the present value of a future cash flow (CF) in year N equals</div>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><img alt="" border="0" height="16" src="http://www.stock-picks-focus.com/images/Present-Value-Formula.png" width="400" /></span><br />
<h3 style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 14px; margin-left: 0px; margin-right: 0px; margin-top: 8px;"><br clear="all" /><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="discount-rate"></a>Fun with discount rates</h3>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Now that we have the formula down, we need to figure out what factors determine discount rates for use in Intrinsic Value calculations. How do we know whether to use 7 percent or 10 percent?</span>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Unfortunately, there is no precise way to calculate the exact discount rate that you should use in discounted cash flow (DCF) model, and academicians have filled entire journals with nothing but discussions on the right way to estimate discount rates for Intrinsic value calculations.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Here&#8217;s what you want to know for practical purposes. As interest rates rise, so will discount rates. As a firm&#8217;s risk level increases, so will its discount rate. Let&#8217;s put these two together. For interest rates you can use the long-term average of treasury rates as a reasonable proxy. (Remember we use interest rate on treasuries to represent opportunity costs because we are pretty certain that the government will pay us our promised interest).</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Now for risk, which is an even less exact factor to measure. Here are some factors that should be taken into account when estimating discount rates.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><b>Size</b></div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Smaller firms are generally riskier than larger firms because they&#8217;re more vulnerable to adverse events. They also usually have less diversified product lines and customer bases.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><b><a href="http://www.stock-picks-focus.com/financial-leverage.html" >Financial Leverage</a></b></div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Firms with more debt are generally riskier than firms with less debt because they have a higher proportion of fixed expenses (debt payments) relative to other expenses. Earnings will be better in good times, but worse in bad times, with an increased risk of financial distress. Look at a firm&#8217;s debt-to-equity ration, interest coverage, and a few other factors to determine the degree of a company&#8217;s risk from financial leverage.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><b>Cyclicality</b></div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Is the firm in a cyclical industry (such as commodities or automobiles) or a stable industry (such as breakfast cereal or beer)? Because the cash flows of cyclical firms are much tougher to forecast than stable firms, their level of risk increases.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><b>Management/Corporate Governance</b></div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">This factor boils down to a simple question: How much do you trust the folks running the shop? Although its rarely black or white, firms with promotional managers (who leave no opportunity to drum up stock prices through their media appearances), managers who draw egregious salaries, or who exhibit any of the other red flags are definitely riskier than companies with managers who do not display these traits.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><b>Economic Moat</b></div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Does the firm have a wide moat, a narrow moat, or no economic moat? The stronger a firm&#8217;s competitive advantage -that is, the wider its moat- the more likely it will be able to keep competitors at bay and generate a reliable stream of cash flows.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><b>Complexity</b></div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">The essence of risk is uncertainty. And its tough to value what you can&#8217;t see. Firms with extremely complex businesses or financial structures are riskier than simple, easy-to-understand firms because there&#8217;s a greater chance that something unpleasant is hiding in a footnote that you missed. Even if you think management is as honest as the day is long and that the firm does a great job running its operations, its wise to incorporate a complexity discount into your mental assessment of risk.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">How should you incorporate all of these risk factors into a discount rate? There is no right answer.</div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Morningstar uses 10.5 percent as the discount rate for an average company based on the above factors and creates a distribution of discount rates based on whether firms are riskier or less risky than the average. A so mid-2003, firms such as Johnson and Johnson, Colgate and Wal-Mart fall at the bottom of the range at around 9 percent, whereas riskier firms such as Micron technology, JetBlue Airways, and E*Trade -top out at 13 percent to 15 percent.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">The key is to pick a discount rate you are comfortable with. Don&#8217;t worry about being exact -just think about whether the company you are evaluating is riskier or less risky than the average firm, along with how much riskier or less risky it is, and you will be fine.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><b><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="indian-market-discount-rate"></a>Discount rates for the Indian market context</b></div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">In the Indian market context we may use 15% as the discount rate for an average company (8 percent risk-free rate + 7 percent risk-premium). High-Quality companies may be discounted at a low rate of 12%, above-average companies at 13%, and poor quality companies may be discounted at a high of 18%.</div>
<h2 style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 22px; margin-bottom: 14px; margin-left: 0px; margin-right: 0px; margin-top: 8px;"><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="perpetuity-value"></a>Calculating Perpetuity Values</h2>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">We have cash flow estimates, and we have a discount rate. We need one more element called a perpetuity value. We need a perpetuity because it&#8217;s not feasible to project a company&#8217;s future cash flows out to infinity, year-by-year, and because companies have theoritically finite lives.</span>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">The most common way to calculate a perpetuity is to take the last cash flow (CF) that you estimate, increase it by the rate at which you expect it to grow over the very long term (g), and divide the result by the discount rate (R) minus the expected long-term growth rate.</div>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><img alt="" border="0" height="31" src="http://www.stock-picks-focus.com/images/Perpetuity-Value.png" width="400" /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">&nbsp;</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br clear="all" /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">The result of this calculation than must be discounted back to present, using the method discussed for calculating present value. For example, suppose we are using a 10-year DCF model for a company with an 11 percent discount rate. We estimate that the company’s cash flow in year 10 will be $1 billion and its cash flow will grow at a steady 3 percent annual rate after that. (Three percent is generally a good number to use as your long-run growth rate because it’s roughly the U.S. gross domestic product [GDP] growth. If you are valuing a firm in a declining industry, you might use 2 percent).</span>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Perpetuity Value = $ 1 billion x (1+ 0.03) / (0.11-0.03)</div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">= $ 1.03 billion/ 0.08</div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">= $ 12.88 billion</div>
<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">To get the present value of these cash flows, we need to discount them using the formula</div>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><img alt="" border="0" height="16" src="http://www.stock-picks-focus.com/images/Present-Value-Formula.png" width="400" /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">&nbsp;</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br clear="all" /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">where n is the number of years in the future, CFn is the cash flow in year n, and R is the discount rate. Plugging these numbers, N = 10, CFn = $12.88 billion, R= 0.11</span>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Discounted Perpetuity Value = $12.88 bn/ (1+0.11)^10 = $12.88 bn/2.839 = $4.536 bn</div>
<h2 style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 22px; margin-bottom: 14px; margin-left: 0px; margin-right: 0px; margin-top: 8px;"><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="intrinsic-value"></a>Calculating Intrinsic Value</h2>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Now all that we need to do is add this discounted perpetuity value to the discounted value of our estimated cash flows in years 1 through 10, and divide by the number of shares outstanding.</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><img alt="" border="0" height="310" src="http://www.stock-picks-focus.com/images/simple-10yr-DCF-model2.png" width="400" /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">&nbsp;</span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br clear="all" /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><br /></span><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">That was a brief outline of the process. You can follow along by matching the following steps:</span>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">1. Estimate free cash flows for the next 4 quarters. This amount will depend on all of the factors discussed earlier -how fast the company is growing, the strength of its competitors, its capital needs, and so on. Using Clorox as an example, our first step is to see how fast free cash flow has grown over the past decade, which turns out to be 9% when we do the math. We could just increase the $600 million in free cash flow that Clorox generated in 2003 by 9 percent, but that would assume the future would be as rosy as in the past. Mega retailers like Wal-Mart -which now accounts for almost a quarter of Clorox sales -has hurt the bargaining power of consumer-product firms. So, let&#8217;s be conservative and assume free cash flow increases by only 5 percent over the last year, which would work out to $630 million.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">2. Estimate how fast you think free cash flow will grow over the next 5 to 10 years. Remember, only firms with very strong competitive advantages and low capital needs are able to sustain above-average growth rates for very long. If the firm is cyclical don&#8217;t forget to throw in some bad years. We won&#8217;t do this for Clorox because selling bleach and Glad bags is a very stable business. We will however be conservative on our growth rate because of the &#8220;Wal-Mart factor&#8221;, and will assume free cash flow increases at 5 percent annually over the next decade.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">3. Estimate a discount rate. Financially Clorox is rock-solid, with little debt, tons of free cash flow, and a non-cyclical business. So we will use 9% for our discount rate, which is meaningfully lower than the 10.5 percent average we discussed earlier. Clorox, is a predictable company, after all.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">4. Estimate a long-run growth rate. Because people will still need bleach and trash bags in the future, and its a good bet that Clorox will continue to get a piece of that market, we can use the long-run GDP average of 3 percent.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">5. That&#8217;s it! We discount the first 10 years of cash flows, add that value to the present value of the perpetuity, and divide by the shares outstanding.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">This is a very simple DCF model. The one used at Morningstar has about a dozen excel tabs, adjusts for complicated items such as pensions and operating leases, and explicitly models competitive advantage periods, among many other things. But a model doesn&#8217;t need to be super complex to get you most of the way there and help you clarify your thinking.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">The important thing is that we forced ourselves to think through these kinds of issues as discussed earlier, which we wouldn&#8217;t have if we had just looked at Clorox&#8217;s stock chart or if we had just said, &#8220;Sixteen times earnings seem reasonable&#8221;. By thinking about the business, we arrived at a better valuation in which we have more confidence.</div>
<h3 style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 18px; margin-bottom: 14px; margin-left: 0px; margin-right: 0px; margin-top: 8px;">Valuing Clorox using a Discounted Cash Flow model</h3>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;"><img alt="" border="0" height="390" src="http://www.stock-picks-focus.com/images/Valuing-Clorox-using-DCF2.png" width="400" /></span><br />
<h2 style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 22px; margin-bottom: 14px; margin-left: 0px; margin-right: 0px; margin-top: 8px;"><br clear="all" /><a href="http://www.blogger.com/post-create.g?blogID=2884768844412347068" name="margin-of-safety"></a>Margin of Safety</h2>
<p><span class="Apple-style-span" style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">We have analysed a company, we have valued it &#8211; now we need to know when to buy it. If you really want to succeed as an investor, you should seek to buy companies at a discount to your estimate of their intrinsic value. Any valuation and any analysis is subject to error, and we can minimise the effect of these errors by buying stocks only at a significant discount to our estimated intrinsic value. This discount is called the Margin of Safety, a term first popularised by investing great Benjamin Graham.</span>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Here is how it works. Let&#8217;s say we think Clorox&#8217;s intrinsic value is $54, and the stock is trading at $45. If we buy the stock and we&#8217;re exactly right about our analysis, the return we receive should be the difference between $45 and $54 (20 percent) plus the discount rate of about 9 percent. That would be 29 percent, which is a pretty darn good return, all things considered.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">But what if we are wrong? What if Clorox grows even more slowly than we had anticipated -may be a competitor takes market share &#8211; or the firm&#8217;s pricing power erodes faster than we had thought? If that&#8217;s the case, then Clorox&#8217;s intrinsic value might actually be $40, which means we would have overpaid for the stock by buying it at $45.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Having a margin of safety is like an insurance policy that helps prevent us from overpaying &#8211; it mitigates the damage caused by overoptimistic estimates. If, for example, we had required a margin of safety of 20 percent before buying Clorox, we wouldn&#8217;t have purchased the stock until it fell to $43. In that case, even if our initial analysis had been wrong and the fair value had really been $40, the damage to our portfolio wouldn&#8217;t have been as severe.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Because all stocks aren&#8217;t created equal, not all margins of safety should be the same. It&#8217;s much easier to forecast the cash flows of, for example, Anheuser-Busch over the next 5 years than the cash flows of Boeing. One company has tons of pricing power, dominant market share, and relatively stable demand, whereas the other has relatively little pricing power, equal market share, and highly cyclical demand. Because I am less confident about my forecasts for Boeing, I&#8217;ll want a larger margin of safety before I buy the shares. There&#8217;s simply a greater chance that something might go wrong, and that my forecasts will be too optimistic.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Paying more for better businesses makes sense, within reason. The price you pay for a stock should be closely tied to the quality of the company, and great businesses are worth buying at smaller discounts to intrinsic value. Why? Because high-quality businesses &#8211; those that have wide economic moats &#8211; are more likely to increase in value over time, and it&#8217;s better to pay fair price for a great business than a great price for a fair business.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">How large should your margin of safety be? It ranges all the way from just 20 percent for very stable firms with wide economic moats to 60 percent for high-risk stocks with no competitive advantages. For above-average firms we would require a 25 percent margin of safety, while on average, we require a 30 percent to 40 percent margin of safety for most firms.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Having a margin of safety is critical to being a disciplined investor because it acknowledges that as humans, we are flawed. Simply investing in the stock market requires some degree of optimism about the future, which is one of the biggest reasons that buyers of stocks are too optimistic far more often than they&#8217;re too pessimistic. Once we know this, we can correct for it by requiring a margin of safety for all of our share purchases.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Every approach to equity investing has its own warts. Being disciplined about valuation may mean that you will miss out on some great opportunities because some companies wind up performing better for longer periods of time than almost anyone could have anticipated. Companies such as Microsoft looked very pricey back in their heyday, and its unlikely that many investors who were very strict about valuation would have bought it early in their corporate lives.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">Being disciplined about valuation would have meant missing those opportunities, but it also would have kept you out of many investments that were priced like Microsoft, but which wound up disappointing investors in a big way. Although we acknowledge that some high-potential companies are worth a leap of faith and a high valuation, on balance, we think its better to miss a solid investment because you are too cautious in your initial valuation than it is to buy stocks at prices that turn out to be too high.</div>
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<div style="font-family: Verdana, Geneva, Arial, Helvetica, sans-serif; font-size: 13px;">After all, the real cost of losing money is much worse than the opportunity cost of missing out on gains. that&#8217;s why the price you pay is just as important as the company you buy.</p>
<p><a href="http://www.stock-picks-focus.com/intrinsic-value.html">http://www.stock-picks-focus.com/intrinsic-value.html</a></div>
<div class="blogger-post-footer">Health is Wealth<img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2884768844412347068-4210045154360114652?l=myinvestingnotes.blogspot.com' alt='' /></div>
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		<title>The company’s intrinsic value is the net present value of projected future cash flows.</title>
		<link>http://www.indonesianstockmarket.com/idx/the-company%e2%80%99s-intrinsic-value-is-the-net-present-value-of-projected-future-cash-flows/</link>
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		<pubDate>Thu, 29 Jul 2010 06:49:00 +0000</pubDate>
		<dc:creator>bullbear</dc:creator>
				<category><![CDATA[BEI Index]]></category>
		<category><![CDATA[discounted cash flow]]></category>
		<category><![CDATA[estimating intrinsic value]]></category>
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		<description><![CDATA[<img height="280" src="http://rcrawford.files.wordpress.com/2008/08/tevasu001.png?w=720&#38;h=325" width="500" /><br /><br /><a href="http://rcrawford.wordpress.com/2008/08/05/teva-pharma-teva-august-4-2008/">http://rcrawford.wordpress.com/2008/08/05/teva-pharma-teva-august-4-2008/</a><br /><span>The company’s intrinsic value is the net present value of projected future cash flows.</span><br /><span>We will take the free cash flow rate and project it out over the next decade, followed by an assumed 5% growth rate in the second decade.</span><br /><span><br /></span><br /><span><img height="331" src="http://www.21se.cn/images/articles/image/acca/acca0104biaoge6.jpg" width="500" /> </span><br /><span><span><b><a href="http://www.21se.cn/z/inc/print.php?aid=359">Valuing a firm using Free Cash Flows</a></b></span></span><br /><span></span><div>Health is Wealth<img width="1" height="1" src="https://blogger.googleusercontent.com/tracker/2884768844412347068-6197248125612449184?l=myinvestingnotes.blogspot.com" alt="" /></div>]]></description>
			<content:encoded><![CDATA[<p></p><p><img height="280" src="http://rcrawford.files.wordpress.com/2008/08/tevasu001.png?w=720&amp;h=325" width="500" /></p>
<p><a href="http://rcrawford.wordpress.com/2008/08/05/teva-pharma-teva-august-4-2008/">http://rcrawford.wordpress.com/2008/08/05/teva-pharma-teva-august-4-2008/</a><br /><span class="Apple-style-span" style="color: #222222; font-family: 'Lucida Grande', 'Lucida Sans Unicode', Helvetica, Arial, sans-serif; font-size: 13px; line-height: 19px;">The company’s intrinsic value is the net present value of projected future cash flows.</span><br /><span class="Apple-style-span" style="color: #222222; font-family: 'Lucida Grande', 'Lucida Sans Unicode', Helvetica, Arial, sans-serif; font-size: 13px; line-height: 19px;">We will take the free cash flow rate and project it out over the next decade, followed by an assumed 5% growth rate in the second decade.</span><br /><span class="Apple-style-span" style="color: #222222; font-family: 'Lucida Grande', 'Lucida Sans Unicode', Helvetica, Arial, sans-serif; font-size: 13px; line-height: 19px;"><br /></span><br /><span class="Apple-style-span" style="color: #222222; font-family: 'Lucida Grande', 'Lucida Sans Unicode', Helvetica, Arial, sans-serif; font-size: 13px; line-height: 19px;"><img height="331" src="http://www.21se.cn/images/articles/image/acca/acca0104biaoge6.jpg" width="500" /> </span><br /><span class="Apple-style-span" style="color: #222222; font-family: 'Lucida Grande', 'Lucida Sans Unicode', Helvetica, Arial, sans-serif; font-size: 13px; line-height: 19px;"><span class="Apple-style-span" style="color: black; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: x-large; line-height: normal;"><b><a href="http://www.21se.cn/z/inc/print.php?aid=359">Valuing a firm using Free Cash Flows</a></b></span></span><br /><span class="Apple-style-span" style="color: #222222; font-family: 'Lucida Grande', 'Lucida Sans Unicode', Helvetica, Arial, sans-serif; font-size: 13px; line-height: 19px;"></span>
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		<title>What is the correct company value?  Value versus Price</title>
		<link>http://www.indonesianstockmarket.com/idx/what-is-the-correct-company-value-value-versus-price/</link>
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		<pubDate>Mon, 26 Jul 2010 10:30:00 +0000</pubDate>
		<dc:creator>bullbear</dc:creator>
				<category><![CDATA[appraising value]]></category>
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		<description><![CDATA[<img src="http://www.strategy-at-risk.com/wp-content/uploads/2009/02/value-vs-price-table.jpg" /><br /><br /><b>What is the correct company value?</b><br /><br />Nobel Prize winner in Economics, Milton Friedman, has said;<span><b><span> “the only concept/theory which has gained universal acceptance by economists is that the value of an asset is determined by the expected benefits it will generate”.</span></b></span><br /><br /><b><span><span>Value is not the same as price. Price is what the market is willing to pay. Even if the value is high, most want to pay as little as possible.</span></span></b> One basic relationship will be the investor’s demand for return on capital – investor’s expected return rate. There will always be alternative investments, and in a free market, investor will compare the investment alternatives attractiveness against his demand for return on invested capital. If the expected return on invested capital exceeds the investments future capital proceeds, the investment is considered less attractive.<br /><br /><img alt="value-vs-price_chart1" height="310" src="http://www.strategy-at-risk.com/wp-content/uploads/2009/02/value-vs-price_chart1.jpg" width="400" /><br /><br /><a href="http://www.strategy-at-risk.com/2009/02/15/what-is-the-correct-company-value/">http://www.strategy-at-risk.com/2009/02/15/what-is-the-correct-company-value/</a><div>Health is Wealth<img width="1" height="1" src="https://blogger.googleusercontent.com/tracker/2884768844412347068-5085407197705754980?l=myinvestingnotes.blogspot.com" alt="" /></div>]]></description>
			<content:encoded><![CDATA[<p></p><p><img src="http://www.strategy-at-risk.com/wp-content/uploads/2009/02/value-vs-price-table.jpg" /></p>
<p><b>What is the correct company value?</b></p>
<p>Nobel Prize winner in Economics, Milton Friedman, has said;<span class="Apple-style-span" style="color: lime;"><b><span class="Apple-style-span" style="font-size: x-large;"> “the only concept/theory which has gained universal acceptance by economists is that the value of an asset is determined by the expected benefits it will generate”.</span></b></span></p>
<p><b><span class="Apple-style-span" style="color: yellow;"><span class="Apple-style-span" style="font-size: x-large;">Value is not the same as price. Price is what the market is willing to pay. Even if the value is high, most want to pay as little as possible.</span></span></b> One basic relationship will be the investor’s demand for return on capital – investor’s expected return rate. There will always be alternative investments, and in a free market, investor will compare the investment alternatives attractiveness against his demand for return on invested capital. If the expected return on invested capital exceeds the investments future capital proceeds, the investment is considered less attractive.</p>
<p><img alt="value-vs-price_chart1" height="310" src="http://www.strategy-at-risk.com/wp-content/uploads/2009/02/value-vs-price_chart1.jpg" width="400" /></p>
<p><a href="http://www.strategy-at-risk.com/2009/02/15/what-is-the-correct-company-value/">http://www.strategy-at-risk.com/2009/02/15/what-is-the-correct-company-value/</a>
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		<title>Estimating an investment&#8217;s value using DCF</title>
		<link>http://www.indonesianstockmarket.com/idx/estimating-an-investments-value-using-dcf/</link>
		<comments>http://www.indonesianstockmarket.com/idx/estimating-an-investments-value-using-dcf/#comments</comments>
		<pubDate>Sat, 17 Jul 2010 23:58:00 +0000</pubDate>
		<dc:creator>bullbear</dc:creator>
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		<description><![CDATA[<span></span><br /><h1><span>Using DCF Foolishly</span></h1><div><span>By David Meier&#160;</span><br /><span>March 28, 2005</span>&#160;<span></span></div><div><div><span><span><br /></span></span></div><div>I consider myself a value investor. To me, all that means is that I am price-conscious. It doesn't matter what type of company I look at or what its situation is. The bottom line is that I refuse to pay more than an investment is worth.</div><div>If I am not going to pay too much, then I have to make an estimate of an investment's value. There are different ways to calculate value; you have probably seen many of them in the&#160;<a href="http://www.fool.com/school.htm"><span>Fool's School</span></a><span>.</span> But today I want to focus on the<span>&#160;</span><a href="http://wiki.fool.com/Discounted_cash_flow?source=ihlsitlnk0000001" title="Get the definition on The Motley Fool Investing Wiki"><span>discounted cash flow</span></a>&#160;analysis.</div><div>John Burr Williams developed the idea in the '50s, and Warren Buffett has evangelized it in the years since. Despite its power and simplicity, there are areas where we need to tread carefully. Used Foolishly, DCF can be a great friend; used foolishly, DCF can be our worst enemy. So let's look at DCF carefully, because I don't want you to pay too much for an investment.</div><div><strong>Here's what we're up against</strong><br />First, we need the equation. You may already know it, but I'll present it here for reference:</div><blockquote><div>Value = Sum[<a href="http://wiki.fool.com/Cash_flow?source=ihlsitlnk0000001" title="Get the definition on The Motley Fool Investing Wiki"><span>Cash Flow</span></a>(t)/(1+k)^t] from t = 1 to infinity</div></blockquote><div>We'll call this the long form. All you need to do is predict all of the future cash flows and discount them back to the present at the rate of&#160;<i>k</i>. What could be easier? For simplicity, we'll define "cash flow" as cash flow from operations minus&#160;<a href="http://wiki.fool.com/Capital_expenditures?source=ihlsitlnk0000001" title="Get the definition on The Motley Fool Investing Wiki"><span>capital expenditures</span></a><span>.</span></div><div><strong><span><span>Pitfall No. 1: We don't know jack</span></span></strong><span><span>I</span></span> know that sounds harsh, but it's the truth. We cannot consistently predict the cash flows and their growth rates with any accuracy; the business environment is far too dynamic. Of course, we should try to make the best estimates we can. And that means being careful about our assumptions and predictions because we don't want to have the pitfalls of the equation work against us.</div><div><b>Merck</b>&#160;<span>(NYSE:<span>&#160;</span><a href="http://caps.fool.com/Ticker/MRK.aspx?source=isssitthv0000001"><span>MRK</span></a>)</span>&#160;has been getting the attention of many value investors lately. The Vioxx problems and the court ruling about early patent expirations have caused lots of&#160;<a href="http://wiki.fool.com/Uncertainty?source=ihlsitlnk0000001" title="Get the definition on The Motley Fool Investing Wiki"><span>uncertainty</span></a>, knocking down the stock price. Using our definition, Merck earned $7 billion in cash flow in 2004. Should that be the starting point? No. Do we know the cash flow reduction from the two issues stated above? I read one report that said the Vioxx lawsuit could cost $4 billion to $30 billion. No precision there. Will two people using the same information predict the same value? Not likely.</div><div>The equation is not for calculating precise answers, like in physics and engineering. I think it is Foolish for making estimates based on personal judgments. The better the judgment, the better the estimate.</div><div><strong><span><span>Pitfall No. 2: Stay away from critical mass situations</span></span></strong>There is a simplified form of this equation, assuming constant growth and a constant&#160;<a href="http://wiki.fool.com/Discount_rate?source=ihlsitlnk0000001" title="Get the definition on The Motley Fool Investing Wiki"><span>discount rate</span></a><span>.</span></div><blockquote><div>Value = Cash Flow(t = 0)*(1+g)/(k-g) where</div><div>g = growth<br />k = discount rate<br />t = 0 is the cash flow from the previous year</div></blockquote><div>One reason we cannot rely on the equation for precise answers is that there is a point of critical mass. In 1946, scientist Louis Slotin died from radiation poisoning after he accidentally let two half-spheres of beryllium-coated plutonium touch during an experiment. When the two halves touched, they reached the critical mass required to sustain a nuclear reaction.</div><div>The equation above is valid only if the discount rate is greater than the&#160;<a href="http://wiki.fool.com/Growth_rate?source=ihlsitlnk0000001" title="Get the definition on The Motley Fool Investing Wiki"><span>growth rate</span></a>&#160;(k &#62; g). If<i>k</i>&#160;is less than or equal to&#160;<i>g</i>, the equation is undefined. Our critical mass pitfall comes when&#160;<i>g</i>starts to get close to&#160;<i>k</i>. As this happens, value starts to get really big, really fast.</div><div>For illustration, let's look at&#160;<b>Google</b>&#160;<span>(Nasdaq:<span>&#160;</span><a href="http://caps.fool.com/Ticker/GOOG.aspx?source=isssitthv0000001"><span>GOOG</span></a>)</span>. My gut tells me that Google is overvalued. But my gut and a quarter won't get me a cup of&#160;<b>Starbucks</b>&#160;coffee. From 2004 financial statements, we know everything in the upper half of the table. We don't know the growth rate. So let's assume a discount rate and solve for growth.</div><table cellspacing="0"><thead><tr><th valign="top"><span>Google</span></th><th valign="top"></th><th valign="top"><span>(on 12/31/2004)</span></th><th valign="top"></th><th valign="top"></th><th valign="top"></th></tr></thead><tbody><tr><td valign="top"><strong>Diluted Shares</strong></td><td valign="top">272.8</td><td valign="top"><strong>Market Cap</strong></td><td valign="top">$52,590</td><td valign="top"><strong>CFFO</strong></td><td valign="top">$977</td></tr><tr><td valign="top"><strong>Price</strong></td><td valign="top">$192.78</td><td valign="top"><strong>Debt</strong></td><td valign="top">$0</td><td valign="top"><strong>CAPEX</strong></td><td valign="top">$319</td></tr><tr><td valign="top"></td><td valign="top"></td><td valign="top"><strong>Cash</strong></td><td valign="top">$2,100</td><td valign="top"><strong>FCF</strong></td><td valign="top">$658</td></tr><tr><td valign="top"></td><td valign="top"></td><td valign="top"><strong>Enterprise Value</strong></td><td valign="top">$50,490</td><td valign="top"></td><td valign="top"></td></tr><tr><td valign="top"></td><td valign="top"></td><td valign="top"></td><td valign="top"></td><td valign="top"></td><td valign="top"></td></tr><tr><td valign="top"></td><td valign="top"></td><td valign="top"></td><td valign="top"></td><td valign="top"></td><td valign="top"></td></tr><tr><td valign="top"></td><td valign="top"></td><td valign="top"><strong>Assume&#160;<em>k</em></strong></td><td valign="top">10%</td><td valign="top">25%</td><td valign="top">50%</td></tr><tr><td valign="top"></td><td valign="top"></td><td valign="top"><strong>Solve for&#160;<em>g</em></strong></td><td valign="top">8.60%</td><td valign="top">23.40%</td><td valign="top">48.10%</td></tr><tr><td valign="top"></td><td valign="top"></td><td valign="top"><strong>k - g</strong></td><td valign="top">1.40%</td><td valign="top">1.60%</td><td valign="top">1.90%</td></tr></tbody></table><span>Note: Dollar values in millions.</span><br /><br /><div>The results tell us that cash flow needs to grow at 23.4% per year from now until infinity to achieve a 25% annual return. So in year 19, Google will have to generate $35.7 billion in cash. For comparison,&#160;<b>Microsoft</b>&#160;<span>(Nasdaq:&#160;<a href="http://caps.fool.com/Ticker/MSFT.aspx?source=isssitthv0000001"><span>MSFT</span></a>)</span>&#160;generated $13.5 billion of cash in its 19th year as a publicly traded company. That's a lofty goal. Does it mean that Google is overvalued? I don't think we can say from this equation. The validity of the answer breaks down because we are too close to the critical mass point, where&#160;<i>k</i>&#160;equals&#160;<i>g</i>.</div><div><strong><span><span>Pitfall No. 3: Money for nothing.</span></span></strong>So if the simplified form of the equation is breaking down, what about using the long form? We can break the equation into parts: a fast-growth part and a slower-growth part. Let's assume that Google can grow cash flow at 100% per year for the next five years and at a slower rate after that. Again, let's use a discount rate of 25%. I know you Fools are wondering how I can have a growth rate higher than the discount rate. In the long form of the equation, there's nothing that says we can't. But let's think carefully about what that means.</div><div>Essentially, it means that we are getting money for nothing. It implies that the cash flows are more valuable simply because they are growing. It also implies that our investment has infinite value and that we are guaranteed a return no matter what price we pay. We both know those are foolish notions.</div><div>At the&#160;<b>Berkshire Hathaway</b>&#160;annual meeting, Warren Buffett referred to this as the St. Petersburg Paradox, based on a paper by David Durand. No investment has infinite value. So we have to be very careful using g &#62; k for extended periods of time.</div><div><b>Should we throw DCF out the window?</b>An emphatic&#160;<i>no</i>! We just need to use it Foolishly. Here's what I recommend:</div><div><span><b>1. Be conservative.</b></span><br />Aggressive analyses can lead to inflated values and cause you to pay too much. Pay too much, just like incurring high transaction costs, and you get lower returns.</div><div><b><span>2. Think about your assumptions and gather contrasting viewpoints.</span></b><br />Poor assumptions based on viewpoints that are the same as yours can lead to aggressive analysis. And we know where that can lead.</div><div><b><span>3. Use a&#160;</span></b><a href="http://wiki.fool.com/Margin_of_safety?source=ihlsitlnk0000001" title="Get the definition on The Motley Fool Investing Wiki"><b><span>margin of safety</span></b></a><b><span>.</span></b><br />Sorry. Despite the fact that you are conservative doesn't mean your answers are more accurate. Have the courage to pay significantly less than your estimate of value. Your family will thank you down the road.</div><div>At the<span>&#160;</span><a href="http://www.fool.com/shop/newsletters/14/decide.asp?source=iivedilnk825178"><em><span>Inside Value</span></em></a>&#160;website, Philip Durell has a wonderful DCF calculator to help you with your analyses.&#160;</div><div><i>Fool contributor&#160;<a href="mailto:dm_fool@charter.net" rel="nofollow"><span>David Meier</span></a><span>&#160;</span>learned to be price-conscious from his wife. He does not own shares in any of the companies mentioned in this article. The Motley Fool has a&#160;<a href="http://www.fool.com/help/index.htm?display=about02"><span>disclosure policy</span></a><span>.</span></i></div><div><i><span><br /></span></i></div><div><i><span><a href="http://www.fool.com/investing/value/2005/03/28/using-dcf-foolishly.aspx">http://www.fool.com/investing/value/2005/03/28/using-dcf-foolishly.aspx</a></span></i></div></div><div>Health is Wealth<img width="1" height="1" src="https://blogger.googleusercontent.com/tracker/2884768844412347068-9171917115694070646?l=myinvestingnotes.blogspot.com" alt="" /></div>]]></description>
			<content:encoded><![CDATA[<p></p><p><span class="Apple-style-span" style="color: #222222; font-family: Arial, Helvetica, sans-serif; font-size: 14px; line-height: 22px;"></span><br />
<h1 style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 28px; font-style: inherit; font-weight: bold; letter-spacing: -1px; line-height: 32px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="color: cyan;">Using DCF Foolishly</span></h1>
<div class="articleMeta" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #666666; font-family: Arial, Helvetica, sans-serif; font-size: 12px; font-style: inherit; font-weight: inherit; line-height: 1.3em; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="vcard byline" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 12px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">By David Meier&nbsp;</span><br /><span class="dateline" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 12px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">March 28, 2005</span>&nbsp;<span class="comments" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 12px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"></span></div>
<div class="entry-content" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<div style="text-align: center;"><span class="Apple-style-span" style="font-size: small;"><span class="Apple-style-span" style="font-size: 11px; line-height: 14px;"><br /></span></span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">I consider myself a value investor. To me, all that means is that I am price-conscious. It doesn&#8217;t matter what type of company I look at or what its situation is. The bottom line is that I refuse to pay more than an investment is worth.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">If I am not going to pay too much, then I have to make an estimate of an investment&#8217;s value. There are different ways to calculate value; you have probably seen many of them in the&nbsp;<a href="http://www.fool.com/school.htm" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline;"><span class="Apple-style-span" style="color: cyan;">Fool&#8217;s School</span></a><span class="Apple-style-span" style="color: cyan;">.</span> But today I want to focus on the<span class="Apple-style-span" style="color: cyan;">&nbsp;</span><a class="wikiTerm qsAdd qs-source-ihlsitlnk0000001" href="http://wiki.fool.com/Discounted_cash_flow?source=ihlsitlnk0000001" style="border-bottom-width: 1px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; white-space: nowrap;" title="Get the definition on The Motley Fool Investing Wiki"><span class="Apple-style-span" style="color: cyan;">discounted cash flow</span></a>&nbsp;analysis.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">John Burr Williams developed the idea in the &#8217;50s, and Warren Buffett has evangelized it in the years since. Despite its power and simplicity, there are areas where we need to tread carefully. Used Foolishly, DCF can be a great friend; used foolishly, DCF can be our worst enemy. So let&#8217;s look at DCF carefully, because I don&#8217;t want you to pay too much for an investment.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Here&#8217;s what we&#8217;re up against</strong><br />First, we need the equation. You may already know it, but I&#8217;ll present it here for reference:</div>
<blockquote dir="ltr" style="border-bottom-color: rgb(229, 229, 229); border-bottom-style: dotted; border-bottom-width: 1px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-color: rgb(229, 229, 229); border-top-style: dotted; border-top-width: 1px; font-family: Georgia, 'Times New Roman', Times, serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 15px; padding-left: 20px; padding-right: 20px; padding-top: 15px;"><div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Value = Sum[<a class="wikiTerm qsAdd qs-source-ihlsitlnk0000001" href="http://wiki.fool.com/Cash_flow?source=ihlsitlnk0000001" style="border-bottom-width: 1px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; white-space: nowrap;" title="Get the definition on The Motley Fool Investing Wiki"><span class="Apple-style-span" style="color: cyan;">Cash Flow</span></a>(t)/(1+k)^t] from t = 1 to infinity</div>
</blockquote>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">We&#8217;ll call this the long form. All you need to do is predict all of the future cash flows and discount them back to the present at the rate of&nbsp;<i style="font-style: italic;">k</i>. What could be easier? For simplicity, we&#8217;ll define &#8220;cash flow&#8221; as cash flow from operations minus&nbsp;<a class="wikiTerm qsAdd qs-source-ihlsitlnk0000001" href="http://wiki.fool.com/Capital_expenditures?source=ihlsitlnk0000001" style="border-bottom-width: 1px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; white-space: nowrap;" title="Get the definition on The Motley Fool Investing Wiki"><span class="Apple-style-span" style="color: cyan;">capital expenditures</span></a><span class="Apple-style-span" style="color: cyan;">.</span></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="color: lime;"><span class="Apple-style-span" style="font-size: x-large;">Pitfall No. 1: We don&#8217;t know jack</span></span></strong><span class="Apple-style-span" style="color: lime;"><span class="Apple-style-span" style="font-size: x-large;">I</span></span> know that sounds harsh, but it&#8217;s the truth. We cannot consistently predict the cash flows and their growth rates with any accuracy; the business environment is far too dynamic. Of course, we should try to make the best estimates we can. And that means being careful about our assumptions and predictions because we don&#8217;t want to have the pitfalls of the equation work against us.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><b style="font-weight: bold;">Merck</b>&nbsp;<span class="ticker" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">(NYSE:<span class="Apple-style-span" style="color: cyan;">&nbsp;</span><a class="qsAdd qs-source-isssitthv0000001" href="http://caps.fool.com/Ticker/MRK.aspx?source=isssitthv0000001" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline;"><span class="Apple-style-span" style="color: cyan;">MRK</span></a>)</span>&nbsp;has been getting the attention of many value investors lately. The Vioxx problems and the court ruling about early patent expirations have caused lots of&nbsp;<a class="wikiTerm qsAdd qs-source-ihlsitlnk0000001" href="http://wiki.fool.com/Uncertainty?source=ihlsitlnk0000001" style="border-bottom-width: 1px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; white-space: nowrap;" title="Get the definition on The Motley Fool Investing Wiki"><span class="Apple-style-span" style="color: cyan;">uncertainty</span></a>, knocking down the stock price. Using our definition, Merck earned $7 billion in cash flow in 2004. Should that be the starting point? No. Do we know the cash flow reduction from the two issues stated above? I read one report that said the Vioxx lawsuit could cost $4 billion to $30 billion. No precision there. Will two people using the same information predict the same value? Not likely.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">The equation is not for calculating precise answers, like in physics and engineering. I think it is Foolish for making estimates based on personal judgments. The better the judgment, the better the estimate.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="color: lime;"><span class="Apple-style-span" style="font-size: x-large;">Pitfall No. 2: Stay away from critical mass situations</span></span></strong>There is a simplified form of this equation, assuming constant growth and a constant&nbsp;<a class="wikiTerm qsAdd qs-source-ihlsitlnk0000001" href="http://wiki.fool.com/Discount_rate?source=ihlsitlnk0000001" style="border-bottom-width: 1px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; white-space: nowrap;" title="Get the definition on The Motley Fool Investing Wiki"><span class="Apple-style-span" style="color: cyan;">discount rate</span></a><span class="Apple-style-span" style="color: cyan;">.</span></div>
<blockquote dir="ltr" style="border-bottom-color: rgb(229, 229, 229); border-bottom-style: dotted; border-bottom-width: 1px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-color: rgb(229, 229, 229); border-top-style: dotted; border-top-width: 1px; font-family: Georgia, 'Times New Roman', Times, serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 15px; padding-left: 20px; padding-right: 20px; padding-top: 15px;"><div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Value = Cash Flow(t = 0)*(1+g)/(k-g) where</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 22px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">g = growth<br />k = discount rate<br />t = 0 is the cash flow from the previous year</div>
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<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">One reason we cannot rely on the equation for precise answers is that there is a point of critical mass. In 1946, scientist Louis Slotin died from radiation poisoning after he accidentally let two half-spheres of beryllium-coated plutonium touch during an experiment. When the two halves touched, they reached the critical mass required to sustain a nuclear reaction.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">The equation above is valid only if the discount rate is greater than the&nbsp;<a class="wikiTerm qsAdd qs-source-ihlsitlnk0000001" href="http://wiki.fool.com/Growth_rate?source=ihlsitlnk0000001" style="border-bottom-width: 1px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; white-space: nowrap;" title="Get the definition on The Motley Fool Investing Wiki"><span class="Apple-style-span" style="color: cyan;">growth rate</span></a>&nbsp;(k &gt; g). If<i style="font-style: italic;">k</i>&nbsp;is less than or equal to&nbsp;<i style="font-style: italic;">g</i>, the equation is undefined. Our critical mass pitfall comes when&nbsp;<i style="font-style: italic;">g</i>starts to get close to&nbsp;<i style="font-style: italic;">k</i>. As this happens, value starts to get really big, really fast.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">For illustration, let&#8217;s look at&nbsp;<b style="font-weight: bold;">Google</b>&nbsp;<span class="ticker" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">(Nasdaq:<span class="Apple-style-span" style="color: cyan;">&nbsp;</span><a class="qsAdd qs-source-isssitthv0000001" href="http://caps.fool.com/Ticker/GOOG.aspx?source=isssitthv0000001" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline;"><span class="Apple-style-span" style="color: cyan;">GOOG</span></a>)</span>. My gut tells me that Google is overvalued. But my gut and a quarter won&#8217;t get me a cup of&nbsp;<b style="font-weight: bold;">Starbucks</b>&nbsp;coffee. From 2004 financial statements, we know everything in the upper half of the table. We don&#8217;t know the growth rate. So let&#8217;s assume a discount rate and solve for growth.</div>
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<th style="background-attachment: initial; background-clip: initial; background-color: #eeeeee; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: center; vertical-align: middle;" valign="top"><span class="Apple-style-span" style="color: cyan;">Google</span></th>
<th style="background-attachment: initial; background-clip: initial; background-color: #eeeeee; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: center; vertical-align: middle;" valign="top"></th>
<th style="background-attachment: initial; background-clip: initial; background-color: #eeeeee; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: center; vertical-align: middle;" valign="top"><span class="Apple-style-span" style="color: cyan;">(on 12/31/2004)</span></th>
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<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Diluted Shares</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">272.8</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Market Cap</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">$52,590</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">CFFO</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">$977</td>
</tr>
<tr style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Price</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">$192.78</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Debt</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">$0</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">CAPEX</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">$319</td>
</tr>
<tr style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Cash</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">$2,100</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">FCF</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">$658</td>
</tr>
<tr style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Enterprise Value</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">$50,490</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
</tr>
<tr style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
</tr>
<tr style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
</tr>
<tr style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Assume&nbsp;<em style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: italic; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">k</em></strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">10%</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">25%</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">50%</td>
</tr>
<tr style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Solve for&nbsp;<em style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: italic; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">g</em></strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">8.60%</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">23.40%</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">48.10%</td>
</tr>
<tr style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">k &#8211; g</strong></td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">1.40%</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">1.60%</td>
<td style="border-bottom-color: rgb(187, 187, 187); border-bottom-style: solid; border-bottom-width: 1px; border-color: initial; border-left-color: rgb(187, 187, 187); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: solid; border-right-width: 1px; border-style: initial; border-top-color: rgb(187, 187, 187); border-top-style: solid; border-top-width: 1px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 5px; padding-left: 7px; padding-right: 7px; padding-top: 5px; text-align: left; vertical-align: baseline;" valign="top">1.90%</td>
</tr>
</tbody>
</table>
<p><span class="smalltext" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #999999; display: block; font-family: inherit; font-size: 12px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: -20px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Note: Dollar values in millions.</span></p>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">The results tell us that cash flow needs to grow at 23.4% per year from now until infinity to achieve a 25% annual return. So in year 19, Google will have to generate $35.7 billion in cash. For comparison,&nbsp;<b style="font-weight: bold;">Microsoft</b>&nbsp;<span class="ticker" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">(Nasdaq:&nbsp;<a class="qsAdd qs-source-isssitthv0000001" href="http://caps.fool.com/Ticker/MSFT.aspx?source=isssitthv0000001" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline;"><span class="Apple-style-span" style="color: cyan;">MSFT</span></a>)</span>&nbsp;generated $13.5 billion of cash in its 19th year as a publicly traded company. That&#8217;s a lofty goal. Does it mean that Google is overvalued? I don&#8217;t think we can say from this equation. The validity of the answer breaks down because we are too close to the critical mass point, where&nbsp;<i style="font-style: italic;">k</i>&nbsp;equals&nbsp;<i style="font-style: italic;">g</i>.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><strong style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-style: inherit; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="color: lime;"><span class="Apple-style-span" style="font-size: x-large;">Pitfall No. 3: Money for nothing.</span></span></strong>So if the simplified form of the equation is breaking down, what about using the long form? We can break the equation into parts: a fast-growth part and a slower-growth part. Let&#8217;s assume that Google can grow cash flow at 100% per year for the next five years and at a slower rate after that. Again, let&#8217;s use a discount rate of 25%. I know you Fools are wondering how I can have a growth rate higher than the discount rate. In the long form of the equation, there&#8217;s nothing that says we can&#8217;t. But let&#8217;s think carefully about what that means.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Essentially, it means that we are getting money for nothing. It implies that the cash flows are more valuable simply because they are growing. It also implies that our investment has infinite value and that we are guaranteed a return no matter what price we pay. We both know those are foolish notions.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">At the&nbsp;<b style="font-weight: bold;">Berkshire Hathaway</b>&nbsp;annual meeting, Warren Buffett referred to this as the St. Petersburg Paradox, based on a paper by David Durand. No investment has infinite value. So we have to be very careful using g &gt; k for extended periods of time.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><b style="font-weight: bold;">Should we throw DCF out the window?</b>An emphatic&nbsp;<i style="font-style: italic;">no</i>! We just need to use it Foolishly. Here&#8217;s what I recommend:</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="color: yellow;"><b>1. Be conservative.</b></span><br />Aggressive analyses can lead to inflated values and cause you to pay too much. Pay too much, just like incurring high transaction costs, and you get lower returns.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><b><span class="Apple-style-span" style="color: yellow;">2. Think about your assumptions and gather contrasting viewpoints.</span></b><br />Poor assumptions based on viewpoints that are the same as yours can lead to aggressive analysis. And we know where that can lead.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><b><span class="Apple-style-span" style="color: yellow;">3. Use a&nbsp;</span></b><a class="wikiTerm qsAdd qs-source-ihlsitlnk0000001" href="http://wiki.fool.com/Margin_of_safety?source=ihlsitlnk0000001" style="border-bottom-color: rgb(0, 102, 204); border-bottom-style: dashed; border-bottom-width: 1px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; white-space: nowrap;" title="Get the definition on The Motley Fool Investing Wiki"><b><span class="Apple-style-span" style="color: yellow;">margin of safety</span></b></a><b><span class="Apple-style-span" style="color: yellow;">.</span></b><br />Sorry. Despite the fact that you are conservative doesn&#8217;t mean your answers are more accurate. Have the courage to pay significantly less than your estimate of value. Your family will thank you down the road.</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">At the<span class="Apple-style-span" style="color: cyan;">&nbsp;</span><a href="http://www.fool.com/shop/newsletters/14/decide.asp?source=iivedilnk825178" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline;"><em style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: italic; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="color: cyan;">Inside Value</span></em></a>&nbsp;website, Philip Durell has a wonderful DCF calculator to help you with your analyses.&nbsp;</div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><i style="font-style: italic;">Fool contributor&nbsp;<a href="mailto:dm_fool@charter.net" rel="nofollow" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline;"><span class="Apple-style-span" style="color: cyan;">David Meier</span></a><span class="Apple-style-span" style="color: cyan;">&nbsp;</span>learned to be price-conscious from his wife. He does not own shares in any of the companies mentioned in this article. The Motley Fool has a&nbsp;<a href="http://www.fool.com/help/index.htm?display=about02" style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: inherit; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline;"><span class="Apple-style-span" style="color: cyan;">disclosure policy</span></a><span class="Apple-style-span" style="color: cyan;">.</span></i></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><i style="font-style: italic;"><span class="Apple-style-span" style="color: cyan;"><br /></span></i></div>
<div style="border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 14px; font-style: inherit; font-weight: inherit; margin-bottom: 22px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><i style="font-style: italic;"><span class="Apple-style-span" style="color: cyan;"><a href="http://www.fool.com/investing/value/2005/03/28/using-dcf-foolishly.aspx">http://www.fool.com/investing/value/2005/03/28/using-dcf-foolishly.aspx</a></span></i></div>
</div>
<div class="blogger-post-footer">Health is Wealth<img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2884768844412347068-9171917115694070646?l=myinvestingnotes.blogspot.com' alt='' /></div>
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		<title>The Right Attitude to Value Investing</title>
		<link>http://www.indonesianstockmarket.com/idx/the-right-attitude-to-value-investing/</link>
		<comments>http://www.indonesianstockmarket.com/idx/the-right-attitude-to-value-investing/#comments</comments>
		<pubDate>Mon, 12 Jul 2010 08:33:00 +0000</pubDate>
		<dc:creator>bullbear</dc:creator>
				<category><![CDATA[BEI Index]]></category>
		<category><![CDATA[Benjamin Graham]]></category>
		<category><![CDATA[core tenets in value investing]]></category>
		<category><![CDATA[estimating intrinsic value]]></category>
		<category><![CDATA[IDX]]></category>
		<category><![CDATA[Indonesia Shares]]></category>
		<category><![CDATA[Indonesia Stock Market]]></category>
		<category><![CDATA[margin of safety principle]]></category>
		<category><![CDATA[value investing]]></category>
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		<description><![CDATA[Value investing is based more on philosophy than on theorems. &#160;Benjamin Graham's purpose was to make his students use the deductive process to think for themselves.<br /><br />The three key concepts of Benjamin Graham's value investing are:<br /><br /><ul><li>Having the right attitude</li><li>The importance of margin of safety</li><li>Knowing the Intrinsic value.</li></ul><br />To be successful, a value investor must adopt the right attitude toward investing in general, and an aversion to speculation in particular. &#160;A speculation is not an investment. &#160;Graham insisted, and it is crucial to be able to distinguish between the two.<br /><br />Graham frowned upon market timing. &#160;He insisted that any financial decision based solely on the prediction that the market will move up or down is a speculation.<div>Health is Wealth<img width="1" height="1" src="https://blogger.googleusercontent.com/tracker/2884768844412347068-5068736365741422227?l=myinvestingnotes.blogspot.com" alt="" /></div>]]></description>
			<content:encoded><![CDATA[<p></p><p>Value investing is based more on philosophy than on theorems. &nbsp;Benjamin Graham&#8217;s purpose was to make his students use the deductive process to think for themselves.</p>
<p>The three key concepts of Benjamin Graham&#8217;s value investing are:</p>
<ul>
<li>Having the right attitude</li>
<li>The importance of margin of safety</li>
<li>Knowing the Intrinsic value.</li>
</ul>
<p>To be successful, a value investor must adopt the right attitude toward investing in general, and an aversion to speculation in particular. &nbsp;A speculation is not an investment. &nbsp;Graham insisted, and it is crucial to be able to distinguish between the two.</p>
<p>Graham frowned upon market timing. &nbsp;He insisted that any financial decision based solely on the prediction that the market will move up or down is a speculation.
<div class="blogger-post-footer">Health is Wealth<img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2884768844412347068-5068736365741422227?l=myinvestingnotes.blogspot.com' alt='' /></div>
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		<title>Intrinsic Value is understood to be that value which is justified by the facts, e.g. the assets, earnings, dividends and definite prospects.</title>
		<link>http://www.indonesianstockmarket.com/idx/intrinsic-value-is-understood-to-be-that-value-which-is-justified-by-the-facts-e-g-the-assets-earnings-dividends-and-definite-prospects/</link>
		<comments>http://www.indonesianstockmarket.com/idx/intrinsic-value-is-understood-to-be-that-value-which-is-justified-by-the-facts-e-g-the-assets-earnings-dividends-and-definite-prospects/#comments</comments>
		<pubDate>Wed, 21 Apr 2010 08:06:00 +0000</pubDate>
		<dc:creator>bullbear</dc:creator>
				<category><![CDATA[BEI Index]]></category>
		<category><![CDATA[estimating intrinsic value]]></category>
		<category><![CDATA[IDX]]></category>
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		<category><![CDATA[Indonesia Stock Market]]></category>
		<category><![CDATA[intrinsic value]]></category>
		<category><![CDATA[BEI]]></category>
		<category><![CDATA[Indonesia Investment]]></category>

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		<description><![CDATA[Before you risk your hard-earned money on a stock, you probably want to know the value you can expect to get in return. &#160;The value you assign to a stock, or that stock's intrinsic value, is the maximum amount that you are willing to pay now for fu...]]></description>
			<content:encoded><![CDATA[<p></p><p>Before you risk your hard-earned money on a stock, you probably want to know the value you can expect to get in return. &nbsp;The value you assign to a stock, or that stock&#8217;s <i>intrinsic value</i>, is the <span class="Apple-style-span" style="color: lime;">maximum</span> amount that you are willing to pay now for<span class="Apple-style-span" style="color: lime;"> future benefits</span>, which could come from<span class="Apple-style-span" style="color: magenta;"> dividends </span>or the<span class="Apple-style-span" style="color: magenta;"> potential sale</span> of the stock at a<span class="Apple-style-span" style="color: magenta;"> realistic future price. &nbsp;</span></p>
<p>It makes no sense to buy a stock when its intrinsic value is smaller than the current price. </p>
<p>Buffett cautions: &nbsp;&#8221;The calculation of intrinsic value, though, is <span class="Apple-style-span" style="color: lime;">not so simple </span>&#8230;. intrinsic value is <span class="Apple-style-span" style="color: lime;">an estimate</span> rather than a precise figure.&#8221;</p>
<p><b>Computing Intrinsic Value</b></p>
<p><span class="Apple-style-span" style="color: lime;">Individuals differ from one another in assessing companies&#8217;</span><span class="Apple-style-span" style="color: yellow;"> future prospects. </span>&nbsp;They also differ in their <span class="Apple-style-span" style="color: yellow;">risk tolerance. </span>&nbsp;Hence, it should be no great leap to accept that there is no unique intrinsic value that can be assigned to a common stock upon which everyone will agree.<span class="Apple-style-span" style="font-size: x-large;"> &nbsp;In computing intrinsic value, you should start by examining a</span><span class="Apple-style-span" style="color: lime;"><span class="Apple-style-span" style="font-size: x-large;"> company&#8217;s balance sheet. </span></span></p>
<ul>
<li><span class="Apple-style-span" style="color: yellow;">Some assets,</span> such as <span class="Apple-style-span" style="color: yellow;">cash and investments in marketable securities</span>, are reported at market value. &nbsp;As a first approximation, the intrinsic value of such items can be taken to be the<span class="Apple-style-span" style="color: yellow;"> same </span>as their market values. &nbsp;</li>
<li>For<span class="Apple-style-span" style="color: yellow;"> most companies</span>, however, the <span class="Apple-style-span" style="color: yellow;">major component of intrinsic value</span> comes <span class="Apple-style-span" style="color: yellow;">from their future earnings</span>.</li>
</ul>
<p><b>Valuation of future earnings</b></p>
<p><span class="Apple-style-span" style="color: lime;"><span class="Apple-style-span" style="font-size: x-large;">For valuation of future earnings, </span></span>you can</p>
<ol>
<li>Start with <span class="Apple-style-span" style="color: orange;">estimating a growth rate</span> based on your evaluation of the company&#8217;s <span class="Apple-style-span" style="color: orange;">past performance. &nbsp;</span></li>
<li>Then you can <span class="Apple-style-span" style="color: orange;">apply the estimated growth rate to current earnings </span>to approximate expected earnings for a future year, say, 10 years from the current year. &nbsp;</li>
<li>Finally,<span class="Apple-style-span" style="color: orange;"> apply a P/E multiple to the future earnings per share</span> to estimate the value of those earnings in the future and<span class="Apple-style-span" style="color: orange;"> discount them to their present value. </span>&nbsp;</li>
<li>In addition, <span class="Apple-style-span" style="color: orange;">dividends</span> should be properly accounted for.</li>
</ol>
<p>While it is a simple approach, <span class="Apple-style-span" style="color: magenta;"><span class="Apple-style-span" style="font-size: x-large;">it requires many assumptions.</span></span> </p>
<ul>
<li>For example, you may have to <span class="Apple-style-span" style="color: lime;">adjust reported earnings </span>in an attempt to <span class="Apple-style-span" style="color: orange;">obtain underlying or sustainable earnings. &nbsp;</span></li>
<li>You also need to<span class="Apple-style-span" style="color: lime;"> assume </span>a <span class="Apple-style-span" style="color: orange;">growth rate, a P/E multiple, and a discount rate. &nbsp;</span></li>
</ul>
<p>With this approach, it is<span class="Apple-style-span" style="color: lime;"> <span class="Apple-style-span" style="font-size: x-large;">important to know the company&#8217;s business well for you to come up with reliable estimates.</span></span></p>
<p>For example:</p>
<p>It is important to learn a lot about the company so that you may consider the <span class="Apple-style-span" style="color: lime;">appropriate method for computing its intrinsic value. </span>&nbsp;You should invest only when the margin of safety is high.</p>
<p>Company A: &nbsp;This is easy to evaluate because <span class="Apple-style-span" style="color: lime;">most of its assets</span> are in marketable securities. &nbsp;Earnings play a <span class="Apple-style-span" style="color: magenta;">limited</span> role in this company&#8217;s intrinsic value.</p>
<p>Company B: &nbsp;This company&#8217;s value is <span class="Apple-style-span" style="color: yellow;">driven primarily by its earnings. &nbsp;</span></p>
<p>Read also:<br /><span class="Apple-style-span" style="color: #cceedd; font-family: 'Trebuchet MS', Verdana, Arial, sans-serif; font-size: 13px; line-height: 18px;"></span><br />
<h3 class="post-title entry-title" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: url(http://www2.blogblog.com/rounders4/icon_arrow.gif); background-origin: initial; background-position: 10px 0.5em; background-repeat: no-repeat no-repeat; border-bottom-color: rgb(187, 187, 187); border-bottom-style: dotted; border-bottom-width: 1px; border-left-color: rgb(187, 187, 187); border-left-style: dotted; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: dotted; border-right-width: 1px; border-top-color: rgb(187, 187, 187); border-top-style: dotted; border-top-width: 0px; color: white; display: block; font: normal normal bold 135%/normal 'Trebuchet MS', Verdana, Arial, sans-serif; line-height: 1.5em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 2px; padding-left: 29px; padding-right: 14px; padding-top: 2px;"><a href="http://myinvestingnotes.blogspot.com/2010/04/intrinsic-value-described-by-ben-graham.html" style="background-color: #bbbbbb; color: white; text-decoration: none;">Intrinsic value described by Ben Graham in Security Analysis.</a></h3>
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		<title>Computing Intrinsic Value</title>
		<link>http://www.indonesianstockmarket.com/idx/computing-intrinsic-value/</link>
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		<pubDate>Tue, 13 Apr 2010 12:27:00 +0000</pubDate>
		<dc:creator>bullbear</dc:creator>
				<category><![CDATA[BEI Index]]></category>
		<category><![CDATA[estimating intrinsic value]]></category>
		<category><![CDATA[graham's intrinsic value formula]]></category>
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		<description><![CDATA[Individuals differ from one another in assessing companies' future prospects. &#160;They also differ in their risk tolerance. &#160;Hence, it should be no great leap to accept that there is no unique intrinsic value that can be assigned to a common sto...]]></description>
			<content:encoded><![CDATA[<p></p><p>Individuals differ from one another in assessing companies&#8217; future prospects. &nbsp;They also differ in their risk tolerance. &nbsp;Hence, it should be no great leap to accept that<span class="Apple-style-span" style="color: lime;"><span class="Apple-style-span" style="font-size: x-large;"> there is no unique intrinsic value that can be assigned to a common stock upon which everyone will agree. &nbsp;</span></span></p>
<p>In computing intrinsic value <span class="Apple-style-span" style="color: yellow;"><span class="Apple-style-span" style="font-size: x-large;">you should start by examining a company&#8217;s balance sheet. &nbsp;</span></span></p>
<ul>
<li>Some assets, such as cash and investments in marketable securities, are reported at market value. &nbsp;</li>
<li>As a first approximation, the intrinsic value of such items can be taken to be the same as their market values. &nbsp;</li>
</ul>
<p>For most companies, however,<span class="Apple-style-span" style="color: yellow;"><span class="Apple-style-span" style="font-size: x-large;"> the major component of intrinsic value comes from their future earnings.</span></span><br />For valuation of future earnings:</p>
<ol>
<li><span class="Apple-style-span" style="color: lime;">You can start with estimating a growth rate based on your evaluation of the company&#8217;s past performance. &nbsp;</span></li>
<li><span class="Apple-style-span" style="color: lime;">Then you can apply the estimated growth rate to current earnings to approximate expected earnings for a future year, say, 10 years from the current year. &nbsp;</span></li>
<li><span class="Apple-style-span" style="color: lime;">Finally, apply a P/E multiple to the future earnings per share to estimate the value of those earnings in the future and discount them to their present value.</span></li>
<li><span class="Apple-style-span" style="color: lime;">In addition, dividends should be properly accounted for.</span></li>
</ol>
<div>While it is a simple approach,<span class="Apple-style-span" style="color: yellow;"><span class="Apple-style-span" style="font-size: x-large;"> it requires many assumptions.</span></span> &nbsp;For example,&nbsp;</div>
<div>
<ul>
<li>you may have to <span class="Apple-style-span" style="color: lime;"><span class="Apple-style-span" style="font-size: x-large;">adjust reported earnings </span></span>in an attempt to obtain <span class="Apple-style-span" style="color: lime;">underlying or sustainable earnings.&nbsp;</span></li>
<li>You also need to <span class="Apple-style-span" style="color: lime;"><span class="Apple-style-span" style="font-size: x-large;">assume a growth rate, a P/E multiple, and a discount rate. &nbsp;</span></span></li>
</ul>
<p>With this approach, it is <span class="Apple-style-span" style="color: yellow;"><span class="Apple-style-span" style="font-size: x-large;">important to know the company&#8217;s business well</span></span> for you to come up with <span class="Apple-style-span" style="color: yellow;"><span class="Apple-style-span" style="font-size: x-large;">reliable estimates.</span></span></div>
<div></div>
<p>Related posts:<br /><span class="Apple-style-span" style="color: #cceedd; font-family: 'Trebuchet MS', Verdana, Arial, sans-serif; line-height: 18px;"></span><br />
<h3 class="post-title entry-title" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: url(http://www2.blogblog.com/rounders4/icon_arrow.gif); background-origin: initial; background-position: 10px 0.5em; background-repeat: no-repeat no-repeat; border-bottom-color: rgb(187, 187, 187); border-bottom-style: dotted; border-bottom-width: 1px; border-left-color: rgb(187, 187, 187); border-left-style: dotted; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: dotted; border-right-width: 1px; border-top-color: rgb(187, 187, 187); border-top-style: dotted; border-top-width: 0px; color: white; display: block; font: normal normal bold 135%/normal 'Trebuchet MS', Verdana, Arial, sans-serif; line-height: 1.5em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 2px; padding-left: 29px; padding-right: 14px; padding-top: 2px;"><a href="http://myinvestingnotes.blogspot.com/2010/04/intrinsic-value-described-by-ben-graham.html" style="background-color: #bbbbbb; color: white; text-decoration: none;"><span class="Apple-style-span" style="font-size: medium;">Intrinsic value described by Ben Graham in Security Analysis.</span></a></h3>
<div><span class="Apple-style-span" style="color: #cceedd; font-family: 'Trebuchet MS', Verdana, Arial, sans-serif; line-height: 18px;"></span><br />
<h3 class="post-title entry-title" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: url(http://www2.blogblog.com/rounders4/icon_arrow.gif); background-origin: initial; background-position: 10px 0.5em; background-repeat: no-repeat no-repeat; border-bottom-color: rgb(187, 187, 187); border-bottom-style: dotted; border-bottom-width: 1px; border-left-color: rgb(187, 187, 187); border-left-style: dotted; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: dotted; border-right-width: 1px; border-top-color: rgb(187, 187, 187); border-top-style: dotted; border-top-width: 0px; color: white; display: block; font: normal normal bold 135%/normal 'Trebuchet MS', Verdana, Arial, sans-serif; line-height: 1.5em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 2px; padding-left: 29px; padding-right: 14px; padding-top: 2px;"><a href="http://myinvestingnotes.blogspot.com/2008/11/choosing-discount-assumption.html" style="background-color: #bbbbbb; color: white; text-decoration: none;"><span class="Apple-style-span" style="font-size: medium;">Choosing a Discount Assumption</span></a></h3>
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<div><span class="Apple-style-span" style="color: #cceedd; font-family: 'Trebuchet MS', Verdana, Arial, sans-serif; line-height: 18px;"></span><br />
<h3 class="post-title entry-title" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: url(http://www2.blogblog.com/rounders4/icon_arrow.gif); background-origin: initial; background-position: 10px 0.5em; background-repeat: no-repeat no-repeat; border-bottom-color: rgb(187, 187, 187); border-bottom-style: dotted; border-bottom-width: 1px; border-left-color: rgb(187, 187, 187); border-left-style: dotted; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: dotted; border-right-width: 1px; border-top-color: rgb(187, 187, 187); border-top-style: dotted; border-top-width: 0px; color: white; display: block; font: normal normal bold 135%/normal 'Trebuchet MS', Verdana, Arial, sans-serif; line-height: 1.5em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 2px; padding-left: 29px; padding-right: 14px; padding-top: 2px;"><a href="http://myinvestingnotes.blogspot.com/2008/11/intrinsic.html" style="background-color: #bbbbbb; color: white; text-decoration: none;"><span class="Apple-style-span" style="font-size: medium;">Intrinsic Value Model</span></a></h3>
</div>
<div><span class="Apple-style-span" style="color: #cceedd; font-family: 'Trebuchet MS', Verdana, Arial, sans-serif; font-size: 13px; line-height: 18px;"></span><br />
<h3 class="post-title entry-title" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: url(http://www2.blogblog.com/rounders4/icon_arrow.gif); background-origin: initial; background-position: 10px 0.5em; background-repeat: no-repeat no-repeat; border-bottom-color: rgb(187, 187, 187); border-bottom-style: dotted; border-bottom-width: 1px; border-left-color: rgb(187, 187, 187); border-left-style: dotted; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: dotted; border-right-width: 1px; border-top-color: rgb(187, 187, 187); border-top-style: dotted; border-top-width: 0px; color: white; display: block; font: normal normal bold 135%/normal 'Trebuchet MS', Verdana, Arial, sans-serif; line-height: 1.5em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 2px; padding-left: 29px; padding-right: 14px; padding-top: 2px;"><span class="Apple-style-span" style="font-size: medium;"><a href="http://myinvestingnotes.blogspot.com/2008/09/estimation-of-intrinsic-value.html" style="background-color: #bbbbbb; color: white; text-decoration: none;">Estimation of Intrinsic Value</a></span><span class="Apple-style-span" style="color: #cceedd; font-size: 13px; font-weight: normal; line-height: 18px;"> 
<div class="post-header">
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<p></span></h3>
<div><span class="Apple-style-span" style="color: #cceedd; font-family: 'Trebuchet MS', Verdana, Arial, sans-serif; font-size: 13px; line-height: 18px;"><br />
<h3 class="post-title entry-title" style="background-attachment: initial; background-clip: initial; background-color: initial; background-image: url(http://www2.blogblog.com/rounders4/icon_arrow.gif); background-origin: initial; background-position: 10px 0.5em; background-repeat: no-repeat no-repeat; border-bottom-color: rgb(187, 187, 187); border-bottom-style: dotted; border-bottom-width: 1px; border-left-color: rgb(187, 187, 187); border-left-style: dotted; border-left-width: 1px; border-right-color: rgb(187, 187, 187); border-right-style: dotted; border-right-width: 1px; border-top-color: rgb(187, 187, 187); border-top-style: dotted; border-top-width: 0px; color: white; display: block; font: normal normal bold 135%/normal 'Trebuchet MS', Verdana, Arial, sans-serif; line-height: 1.5em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 2px; padding-left: 29px; padding-right: 14px; padding-top: 2px;"><a href="http://myinvestingnotes.blogspot.com/2010/04/introduction-to-valuation-videos.html" style="background-color: #bbbbbb; color: white; text-decoration: none;">Introduction to Valuation &#8211; Videos</a></h3>
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		<title>Will Your Stock Hit Rock Bottom?</title>
		<link>http://www.indonesianstockmarket.com/idx/will-your-stock-hit-rock-bottom/</link>
		<comments>http://www.indonesianstockmarket.com/idx/will-your-stock-hit-rock-bottom/#comments</comments>
		<pubDate>Fri, 22 Jan 2010 23:59:00 +0000</pubDate>
		<dc:creator>bullbear</dc:creator>
				<category><![CDATA[BEI Index]]></category>
		<category><![CDATA[estimating intrinsic value]]></category>
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		<category><![CDATA[Indonesia Stock Market]]></category>
		<category><![CDATA[intrinsic value]]></category>
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		<description><![CDATA[Will Your Stock Hit Rock Bottom?By Jordan DiPietro January 22, 2010 Figuring out what you believe to be the intrinsic value of a stock is one of the most significant things you can do. If you bought shares of Sprint Nextel (NYSE: S) for more than $10 a...]]></description>
			<content:encoded><![CDATA[<p></p><p>Will Your Stock Hit Rock Bottom?</p>
<p>By Jordan DiPietro <br />January 22, 2010 </p>
<p><strong><span style="color: yellow;">Figuring out what you believe to be the intrinsic value of a stock is one of the most significant things you can do.</span></strong> If you bought shares of Sprint Nextel (NYSE: S) for more than $10 a pop, you better know at what price you&#8217;d be willing to sell, or you may find your stock hitting rock bottom.</p>
<div></div>
<p><strong><span style="color: orange;">How you define the floor</span></strong> <br />When investors try to determine a sales price, it seems as though we<strong><span style="color: lime;"> all too often let our emotions get the best of us.</span></strong> To illustrate this point, consider an experiment documented by behavioral economist and professor Dan Ariely.</p>
<div></div>
<p><strong><span style="color: magenta;">Duke students are fanatical about their basketball program, and they illustrate their passion when it comes to buying tickets. </span></strong>There is a strict procedure where students have to camp out intermittently for an entire semester, responding to arbitrary bull horns and missing classes and exams. These are die-hard fans. For big games, students at the front of the line aren&#8217;t even guaranteed a ticket &#8212; only a spot in a lottery system. A list is posted later with the winners of the lottery, and often those who have sacrificed the most find themselves without a ticket to the game.</p>
<div></div>
<p>Duke professors wanted to conduct an experiment, so they found students who received lottery tickets and those who did not, and tried to find an equilibrium price where a ticket could be bought and sold. Remember &#8212; both sets of students missed classes, spent evenings in tents, and went through the same rigorous process to obtain these cherished tickets.<span style="color: magenta;"><strong> When the lottery losers were asked how much they would pay for a ticket, the average price was $175. The lottery recipients, on the other hand, would not sell their tickets for anything less than an average of $2,400!</strong></span> <strong><span style="color: orange;">How could there be such a price discrepancy when both sets of students were willing to go through the same ordeal?</span></strong></p>
<div></div>
<p>We all love what we have &#8230; <br />The reason is that the lottery winners were victims of<span style="color: yellow; font-size: large;"><strong> ownership bias</strong></span>; that is,<span style="color: yellow;"><strong> they overvalued what they owned, simply because they owned it!</strong></span>
<ul>
<li>This helps explain why people may have <span style="color: lime;"><strong>held</strong> </span>on to shares of Cisco Systems (Nasdaq: CSCO) or Yahoo! (Nasdaq: YHOO), even when the dot.com bubble was bursting at the seams. </li>
<li>Or why people were still <span style="color: lime;"><strong>holding</strong></span> onto financials like Bank of America (NYSE: BAC) in 2007, when the subprime crisis was all but written on the wall.</li>
</ul>
<p>
<div></div>
<p><span style="color: orange;"><strong>When investors make a purchase, what Ariely calls <span style="color: yellow; font-size: large;">an emotional chasm is formed</span></strong></span> between the &#8220;old you&#8221; who didn&#8217;t own the stock and the &#8220;new you&#8221; who now owns some very precious shares. In the case of Duke basketball, it was an &#8220;empirical chasm as well &#8212; the average selling price (about $2,400) was separated by a factor of about 14 from the average buyer&#8217;s offer (about $175),&#8221; Ariely wrote in his book Predictably Irrational.</p>
<div></div>
<p><strong><span style="color: yellow; font-size: large;">I fall prey to this bias every time I buy a stock</span></strong>. 
<ul>
<li>In August of last year, I purchased shares of General Electric (NYSE: GE) when it was trading for about $11 and change. </li>
<li>Because there is constant controversy surrounding a conglomerate like GE, I find myself ignoring criticisms of the company or critiques about GE&#8217;s capital division &#8212; just because I own the stock. </li>
<li>I constantly have to remind myself to step back, impartially evaluate the company, and reassess my prospects for the industry. </li>
<li>The stock eventually fell as low as $6 (though it has since recovered to $16).</li>
</ul>
<p>
<div></div>
<p><strong><span style="color: orange;">And we never want to let it go &#8230;</span></strong> <br />Say you were bullish on the solar industry and owned shares of First Solar (Nasdaq: FSLR) and Suntech Power (NYSE: STP), and analysts were coming out with negative industry reports. Instead of listening to the scrutiny and reading the reports, many investors would simply ignore the contrary opinion and convince themselves that their original analysis was correct. Because if in fact the analysts were correct &#8212; and the solar industry was doomed &#8212; then you&#8217;d have to sell your shares, and we&#8217;ve already established how we feel about things we already own. <strong><span style="color: yellow; font-size: large;">We simply don&#8217;t like to let things go, whether it&#8217;s a basketball ticket or a share of stock.</span></strong></p>
<div></div>
<p>Do you know when to hold or sell that stock, because &#8212; let&#8217;s face it &#8212; conditions change?</p>
<p>Remember, there&#8217;s no greater way to avoid having your stock hit rock bottom than having received objective analysis and reasonable advice.</p>
<div></div>
<p>
<div><a href="http://www.fool.com/investing/general/2010/01/22/will-your-stock-hit-rock-bottom.aspx">http://www.fool.com/investing/general/2010/01/22/will-your-stock-hit-rock-bottom.aspx</a></div>
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