How to calculate Price/Earnings - Price/Sales - Price/Free Cash Flow for given stock
To calculate you take the Price and divide it by the Earnings, or by the Sales, or by the Free Cash Flow. Most of these calculations are done for you on a lot of finance sites if the data is available. Such sites as Yahoo Finance and Google Finance as well as my personal favorite: Morningstar
"Stock price is determined by the buyers and sellers, correct? Correct! ""Everything is worth what its purchaser will pay for it""-Publius Syrus What causes people to buy or sell? Is it news? earnings? stock analysis and techniques? All of these things influence investors' perception of how much a stock is worth. If AMZN makes a lot of money one quarter, then the price might go up. But maybe public perception of AMZN changes because of a large scandal. This could cause the share price to decline even with the favorable earnings report. Why do these 'good' or 'bad' news make people want to buy/sell a stock? People invest to make money. If it looks like a company is going to take a turn for the worst, people will sell. If it looks like the company has a bright, cash-laden future in front of them, people will buy. News is one of the many factors people use to determine how well a company will do. Theoretically could a bunch of people short AMZN and drive down the price regardless of how well it is doing? Say investors wanted to boycott AMZN in order to drive down the cost and get some cheap shares. This is pretty silly, but say for the sake of the argument that everyone who owned AMZN decided to sell their shares and no other investor was willing to buy the shares for less than $0.01, then AMZN shares would be ""worth"" $0.01 in that aspect. That is extremely unlikely to happen, though, for two reasons:" In this type of strategy profit is made when the shares go down as your main position is the short trade of the common stock. The convertible instruments will tend to move in about the same direction as the underlying (what it can be converted to) but less violently as they are traded less (lower volatility and lower volume in the market on both sides), however, they are not being used to make a profit so much as to hedge against the stock going up. Since both the bonds and the preference shares are higher on the list to be repaid if the company declares bankruptcy and the bonds pay out a fixed amount of interest as well, both also help protect against problems that may occur with a long position in the common stock.  Essentially the plan with this strategy is to earn fixed income on the bonds whilst the stock price drops and then to sell both the bonds and buy the stock back on the market to cover the short position. If the prediction that the stock will fall is wrong then you are still earning fixed income on the debt and are able to convert it into stock at the higher price to cover the short sale eliminating, or reducing, the loss made on the short sale. Effectively the profit here is made on the spread between the price of the bond, accounting for the conversion price, and the price of the stock and that fixed income is less volatile (except usually in the junk market) than stock. This is a great question for understanding how futures work, first let's start with your assumptions The most interesting thing here is that neither of these things really matters for the price of the futures.  This may seem odd as a futures contract sounds like you are betting on the future price of the index, but remember that the current price already includes the expectations of future earnings as well! There is actually a fairly simple formula for the price of a futures contract (note the link is for forward contracts which are very similar but slightly more simple to understand).  Note, that if you are given the current price of the underlying the futures price depends essentially only on the interest rate and the dividends paid during the length of the futures contract.  In this case the dividend rate for the S&P500 is higher than the prevailing interest rate so the futures price is lower than the current price.  It is slightly more complicated than this as you can see from the formula, but that is essentially how it works. Note, this is why people use futures contracts to mimic other exposures.  As the price of the future moves (pretty much) in lockstep with the underlying and sometimes using futures to hedge exposures can be cheaper than buying etfs or using swaps. Edit: Example of the effect of dividends on futures prices For simplicity, let's imagine we are looking at a futures position on a stock that has only one dividend (D) in the near term and that this dividend happens to be scheduled for the day before the futures' delivery date.  To make it even more simple lets say the price of the stock is fairly constant around a price P and interest rates are near zero.  After the dividend, we would expect the price of the stock to be P' ~ P - D as if you buy the stock after the dividend you wouldn't get that dividend but you still expect to get the rest of the value from additional future cash flows of the company. However, if we buy the futures contract we will eventually own the stock but only after the dividend happens.  Since we don't get that dividend cash that the owners of the stock will get we certainly wouldn't want to pay as much as we would pay for the stock (P).  We should instead pay about P' the (expected) value of owning the stock after that date.   So, in the end, we expect the stock price in the future (P') to be the futures' price  today (P') and that should make us feel a lot more comfortable about what we our buying.  Neither owning the stock or future is really necessarily favorable in the end you are just buying slightly different future expected cash flows and should expect to pay slightly different prices. "The formula for standard deviation is fairly simple in both the discrete and continuous cases. It's mostly safe to use the discrete case when working with adjusted closing prices. Once you've calculated the standard deviation for a given time period, the next task (in the simplest case) is to calculate the mean of that same period. This allows you to roughly approximate the distribution, which can give you all sorts of testable hypotheses. Two standard deviations (σ) away from the mean (μ) is given by:  It doesn't make any sense to talk about ""two standard deviations away from the price"" unless that price is the mean or some other statistic for a given time period. Normally you would look at how far the price is from the mean, e.g. does the price fall two or three standard deviations away from the mean or some other technical indicator like the Average True Range (an exponential moving average of the True Range), some support level, another security, etc.  For most of this answer, I'll assume we're using the mean for the chosen time period as a base. However, the answer is still more complicated than many people realize. As I said before, to calculate the standard deviation, you need to decide on a time period. For example, you could use S&P 500 data from Yahoo Finance and calculate the standard deviation for all adjusted closing prices since January 3, 1950. Downloading the data into Stata and applying the summarize command gives me: As you can probably see, however, these numbers don't make much sense. Looking at the data, we can see that the S&P 500 hasn't traded close to 424.4896 since November 1992. Clearly, we can't assume that this mean and standard deviation as representative of current market conditions. Furthermore, these numbers would imply that the S&P 500 is currently trading at almost three standard deviations away from its mean, which for many distribution is a highly improbable event. The Great Recession, quantitative easing, etc. may have changed the market significantly, but not to such a great extent.  The problem arises from the fact that security prices are usually non-stationary.. This means that the underlying distribution from which security prices are ""drawn"" shifts through time and space. For example, prices could be normally distributed in the 50's, then gamma distributed in the 60's because of a shock, then normally distributed again in the 70's. This implies that calculating summary statistics, e.g. mean, standard deviation, etc. are essentially meaningless for time periods in which prices could follow multiple distributions.  For this and other reasons, it's standard practice to look at the standard deviation of returns or differences instead of prices. I covered in detail the reasons for this and various procedures to use in another answer. In short, you can calculate the first difference for each period, which is merely the difference between the closing price of that period and the closing price of the previous period. This will usually give you a stationary process, from which you can obtain more meaningful values of the standard deviation, mean, etc.  Let's use the S&P500 as an example again. This time, however, I'm only using data from 1990 onwards, for the sake of simplicity (and to make the graphs a bit more manageable). The summary statistics look like this: and the graph looks like this; the mean is the central horizontal red line, and the top and bottom lines indicate one standard deviation above and below the mean, respectively.   As you can see, the graph seems to indicate that there were long periods in which the index was priced well outside this range. Although this could be the case, the graph definitely exhibits a trend, along with some seemingly exogenous shocks (see my linked answer).  Taking the first difference, however, yields these summary statistics: with a graph like this:  This looks a lot more reasonable. In periods of recession, the price appears much more volatile, and it breaches the +/- one standard deviation lines indicated on the graph.  This is only a simple summary, but using first differencing as part of the wider process of detrending/decomposing a time series is a good first step.  For some technical indicators, however, stationary isn't as relevant. This is the case for some types of moving averages and their associated indicators. Take Bollinger bands for instance. These are technical indicators that show a number of standard deviations above and below a moving average. Like any calculation of standard deviation, moving average, statistic, etc. they require data over a specified time period. The analyst chooses a certain number of historical periods, e.g. 20, and calculates the moving average for that many previous periods and the moving/rolling standard deviation for those same periods as well. The Bollinger bands represent the values a certain number of standard deviations away from the moving average at a given point in time. At this given point, you can calculate the value two standard deviations ""away from the value,"" but doing so still requires the historical stock price (or at least the historical moving average). If you're only given the price in isolation, you're out of luck.  Moving averages can indirectly sidestep some of the issues of stationarity I described above because it's straightforward to estimate a time series with a process built from a moving average (specifically, an auto-regressive moving average process) but the econometrics of time series is a topic for another day.  The Stata code I used to generate the graphs and summary statistics:" Broadly, there's a bunch of stuff you need to be accounting for that's not reflected in the above, which will impact the A/D profile of an acquisition:  * Consideration paid (all cash on substantially the same terms is going to be more accretive than an all-stock transaction...because in the latter, your denominator is much bigger)  * Shares outstanding (including repurchases, in-kind dividends and option exercise)  * Financing / interest expense  * Upside / base / downside case for all of your assumptions - best to have a toggle based on a CHOOSE function that will allow the user to easily toggle between these  I'm not sure what EBITDA is getting you. EPS accretion/dilution typically looks at earnings, but you could also look at Cash EPS A/D which measures OCF/shares outstanding.  The point is, this really depends on how back of the envelope you want the A/D computation to be. At a minimum, you need an earnings schedule projected over the next 2-3 years, and you need a schedule reflecting outstanding shares over the same time period.  Your earnings buildout can have varying degrees of granularity. You can project cost synergies over the forecast period, which most obviously is going to affect your earnings, but you can also drill down further. Financing, transaction fees, etc. Your writeups and writedowns from your B/S combination may result in certain deferred tax items that will affect your bottom line over the forecast period.  Your share schedule can also have varying degrees of complexity. One way to do it is to just presume that the company will not issue any more shares, and will not repurchase any shares, and that there will be no options exercised, over the forecast period. This is a bad series of assumptions. It is likely that as options vest, if in the money, they will be exercised, resulting in dilution for existing shareholders. It is also likely that certain preferred shareholders and optionholders are going to experience adjustments to the conversion prices based on antidilution provisions in their securities. These may be but are not always disclosed in the 10K.  Last point - models are tools. What are you trying to build an accretion/dilution model for? This will affect and determine the degree of granularity you'll want to go into. "First, note that a share represents a % of ownership of a company. In addition to the right to vote in the management of the company [by voting on the board of directors, who hires the CEO, who hires the VPs, etc...], this gives you the right to all future value of the company after paying off expenses and debts. You will receive this money in two forms: dividends approved by the board of directors, and the final liquidation value if the company closes shop. There are many ways to attempt to determine the value of a company, but the basic theory is that the company is worth a cashflow stream equal to all future dividends + the liquidation value. So, the market's ""goal"" is to attempt to determine what that future cash flow stream is, and what the risk related to it is. Depending on who you talk to, a typical stock market has some degree of 'market efficiency'. Market efficiency is basically a comment about how quickly the market reacts to news. In a regulated marketplace with a high degree of information available, market efficiency should be quite high. This basically means that stock markets in developed countries have enough traders and enough news reporting that as soon as something public is known about a company, there are many, many people who take that information and attempt to predict the impact on future earnings of the company. For example, if Starbucks announces earnings that were 10% less than estimated previously, the market will quickly respond with people buying Starbucks shares lowering their price on the assumption that the total value of the Starbucks company has decreased. Most of this trading analysis is done by institutional investors. It isn't simply office workers selling shares on their break in the coffee room, it's mostly people in the finance industry who specialize in various areas for their firms, and work to quickly react to news like this. Is the market perfectly efficient? No. The psychology of trading [ie: people panicking, or reacting based on emotion instead of logic], as well as any inadequacy of information, means that not all news is perfectly acted upon immediately. However, my personal opinion is that for large markets, the market is roughly efficient enough that you can assume that you won't be able to read the newspaper and analyze stock news in a way better than the institutional investors. If a market is generally efficient, then it would be very difficult for a group of people to manipulate it, because someone else would quickly take advantage of that. For example, you suggest that some people might collectively 'short AMZN' [a company worth half a trillion dollars, so your nefarious group would need to have $5 Billion of capital just to trade 1% of the company]. If someone did that, the rest of the market would happily buy up AMZN at reduced prices, and the people who shorted it would be left holding the bag. However, when you deal with smaller items, some more likely market manipulation can occur. For example, when trading penny stocks, there are people who attempt to manipulate the stock price and then make a profitable trade afterwards. This takes advantage of the low amount of information available for tiny companies, as well as the limited number of institutional investors who pay attention to them. Effectively it attempts to manipulate people who are not very sophisticated. So, some manipulation can occur in markets with limited information, but for the most part prices are determined by the 'market consensus' on what the future profits of a company will be.  Additional example of what a share really is: Imagine your neighbor has a treasure chest on his driveway: He gathers the neighborhood together, and asks if anyone wants to buy a % of the value he will get from opening the treasure chest. Perhaps it's a glass treasure chest, and you can mostly see inside it. You see that it is mostly gold and silver, and you weigh the chest and can see that it's about 100 lbs all together. So in your head, you take the price of gold and silver, and estimate how much gold is in the chest, and how much silver is there. You estimate that the chest has roughly $1,000,000 of value inside. So, you offer to buy 10% of the chest, for $90k [you don't want to pay exactly 10% of the value of the company, because you aren't completely sure of the value; you are taking on some risk, so you want to be compensated for that risk].  Now assume all your neighbors value the chest themselves, and they come up with the same approximate value as you. So your neighbor hands out little certificates to 10 of you, and they each say ""this person has a right to 10% of the value of the treasure chest"". He then calls for a vote from all the new 'shareholders', and asks if you want to get the money back as soon as he sells the chest, or if you want him to buy a ship and try and find more chests. It seems you're all impatient, because you all vote to fully pay out the money as soon as he has it. So your neighbor collects his $900k [$90k for each 10% share, * 10], and heads to the goldsmith to sell the chest. But before he gets there, a news report comes out that the price of gold has gone up. Because you own a share of something based on the price of gold, you know that your 10% treasure chest investment has increased in value. You now believe that your 10% is worth $105k. You put a flyer up around the neighborhood, saying you will sell your share for $105k. Because other flyers are going up to sell for about $103-$106k, it seems your valuation was mostly consistent with the market.  Eventually someone driving by sees your flyer, and offers you $104k for your shares. You agree, because you want the cash now and don't want to wait for the treasure chest to be sold. Now, when the treasure chest gets sold to the goldsmith, assume it sells for $1,060,000 [turns out you underestimated the value of the company]. The person who bought your 10% share will get $106k [he gained $2k]. Your neighbor who found the chest got $900k [because he sold the shares earlier, when the value of the chest was less clear], and you got $104k, which for you was a gain of $14k above what you paid for it. This is basically what happens with shares. Buy owning a portion of the company, you have a right to get a dividend of future earnings. But, it could take a long time for you to get those earnings, and they might not be exactly what you expect. So some people do buy and sell shares to try and earn money, but the reason they are able to do that is because the shares are inherently worth something - they are worth a small % of the company and its earnings." This link does it ok:  http://investexcel.net/1979/calculate-historical-volatility-excel/ Basically, you calculate percentage return by doing stock price now / stock price before.  You're not calculating the rate of return hence no subtraction of 100%.  The standard is to do this on a daily basis: stock price today / stock price yesterday. The most important and most misunderstood part is that you now have to analyze the data geometrically not arithmetically.  To easily do this, convert all percentage returns with the natural log, ln(). Next, you take the standard deviation of all of those results, and apply exp().  This answers the title of your question. For convenience's sake, it's best to annualize since volatility (implied or statistical) is now almost always quoted annualized.  There are ~240 trading days each year.  You multiply your stdev() result by (240 / # of trading days per return) ^ 0.5, so if you're doing this for daily returns, multiply the stdev() result by 240^0.5; if you were doing it weekly, you'd want to multiply by (240 / ~5)^0.5; etc.  This is your number for sigma.  This answers the intent of your question. For black-scholes, you do not convert anything back with exp(); BS is already set up for geometric analysis, so you need to stay there. The reason why analysis is done geometrically is because the distribution of stock returns is assumed to be lognormal (even though it's really more like logLaplace). Use the Black-Scholes formula. If you know the current price, an options strike price, time until expiration, and risk-free interest rate, then knowing the market price of the option will tell you what the market's estimation of the volatility is. This does rely on a few assumptions, such as Gaussian random walk, but those are reasonable assumptions for most stocks. You can also get a list of past stock prices, put them in Excel, and ask Excel to calculate the standard deviation with stdev.s(), but that gives you the past volatility. The market's estimate of future volatility is more relevant.