Having introduced this kind of cashflow evaluation, let's now implement it. First, the cashflows. Discounted cashflow analysis requires estimates of future cashflows. So consider shareholders interested in the value of their investments. The value of the firm as it is traded on the stock exchange today. So firm value, the present value today, is defined here as the sum of future cash flows discounted to the present. But you can see that these cash flows in this formula, assume that we know what they are in one year's time, two year's time, any year's time. We don't know that, so for that reason, we need to form expectations about those entitlements. So we need to forecast cash flows over the firm's expected lifetime. In this case, n years. We know a few things. We know for example, that future cash flows very quickly diminish in present value depending on the discount rate. So future cash flows, the further they are into the future, the less they contribute to the present firm value. So where do we draw the line? Well, first we've replaced the observed cashflows with expectations for those cash flows in the formula that you see on the screen. What we will do is distinguish between short-term predictable cash flows. Where analysts have got something meaningful to say about what the cash flow will be at the end of that financial year. As distinct from the much longer term cash flows where the best an analyst can do is just make an assumption of a sustainable business operation. So in fact, that means for our purpose of valuation that the lengths of time, the number of periods into the future. That we can meaningfully predict cash flows will depend on the size or the maturity of the firm. The more mature the firm, the larger the firm, the longer it's been around. The more sustainable the cash flows typically will be. The less variability there might be in those cash flows, the level of competition. The fears of the competition for a particular firm, the less certainty an analyst will have about future cash flows. The fears of the competition. They're more likely it is that the company will ran out of lifetime and will become shorter. Because it will be competed away by effective competition. And lastly on this list, current growth rates will have a bearing on the predictability of near term cash flows over longer term cash flows. So how do we estimate for our firm future earnings? Well typically we start with history. History tends to be a reasonably good guide for the future. Of course, with those provisos that we just saw, like competition. So for the valuation of large established mature corporations, this tends to work pretty well. We can simply extrapolate what we have seen in the recent past. But for new investment projects, well they're new, they don't have a lot of history. So we can't expect to get a lot of guidance by what has recently happened with those investment projects. Worse than that, their cash flow pattern also tends to be a lot more variable. Making it very difficult to get meaningful extrapolation into the future. Same story applies to growth, what we label as growth firms. So firms growing very rapidly and therefore, very quickly move from small businesses to mature large businesses. Past growth, large high growth rates, that we've observed in the past, will no longer be a guide for the more mature firm. What some analysts do is rely on management of the corporation, whose valuation they try to establish. But is that necessarily a good idea? Wouldn't that be a potential conflict of interest for management to give earnings forecast which are much more rosy than they really are expected to be? So analysts use a variety of approaches to estimating future cash flows. Expected cash flow is the single best estimate that an analyst can come up with for a particular cash flow for a particular period of occurrence. It captures the likelihood of both good and bad outcomes over that time span until the cash flow is realized. Scenarios on the other hand, rather than trying to establish in one hit what the best expected cash flow value is. Scenarios lead to a number of possible cash flows and then weigh each of those forecast scenarios by the likelihood of that scenario to get to the expected cash flow. And lastly simulation, leads to many different cash flow forecasts. A simple average of those cash flow forecasts will then just be taken as the expected cash flow to insert into the discounted cash flow evaluation. So a single point estimate with variability around it, a set of scenarios, a small number of plausible outcomes versus an enormous number of possible outcomes. And then simply taking the average of those outcomes are three different ways that analysts approach this problem. So remember the graph where I gave you the recent dividend payments by Kellog's for the past 15 years or so. Well, that looks like an easy one. The stepwise increase, I could easily extrapolate that. You can see that here for the next three years. Where the blue line is extended by the red forecast. But as I mentioned before, it's not always that easy. So how do we establish the added value that analysts bring to the analysis? So the quality of analyst's earnings forecast over simply extrapolating historical information, as I just did in that graph of dividends. What analysts do, is very carefully interpret what happened historically. But you could argue that you can do the same. You've got access to the financial statements and the balance sheets. For years past, you can do the extrapolation. But then the next thing that analysts bring to the table is environmental information. And in environmental, we mean the level of competition in the industry. Consumer confidence surveys will have a bearing on consumer demand for cereals. Macroeconomic news might have an impact on wages. A variety of let's call them, macro factors will have an impact on forecast earnings for our corporation. And then there's private information that is germane to the corporation itself, but as I put in bold here, be careful. Because private information is easily misconstrued as using inside information. That of course, is not legally allowed. So what we mean here with private information is publicly available data about the operations of the corporation that is accessible to the analyst. And lastly, it is the quality of the analysts' model. Analysts are not all using the same identical model. There are various modifications to discounted cash flow and the quality. Or the appropriate nature of a particular model will have a bearing on the accuracy of the earnings forecast.