Let me define multiples. Multiples, this is not always the case, but in general a multiple is, price divided by some fundamental variable. Fundamental variable are basically the drivers of the value of a company, could be dividend, it could be cash, it could be the risk of the company, it could be many different things and we need to collapse that of course into a number. So the most general way of thinking about a number, again, there are a few exceptions, but the most general way would be price divided by some fundamental variable. Now those fundamental variables, again, could be a whole bunch of things. It could be earnings and then you have the price earnings ratio. It could be dividends, and then you would have the price to dividends ratio. It could be book value and then you would have the price to book ratio. Could be cash flow and then you have the price to cash flow ratio, and on, and on, and on. So typical is, again, price divided by some fundamental measure of the value of a company. And of course, this doesn't mean that you have to use one and for get about all the others, maybe properly applied multiples valuation is to look at more than one multiple so as to determine whether all of them point in the same direction or some of them point in a different direction that you may want to explore why that is the case. Now I'm going to focus the rest of the discussion on the PE ratio, and I think that you will be able to draw the parallels to any of the other ratios, any other multiples that we mentioned before. So it's easier for us to focus on one and then maybe export a lot of what we say into any of the other multiples that we may need to or that we may want to discuss. So when you think about the PE ratio, point number one, the P. The P is very simple. The P is the price of the company today. If you're valuing a market and multiples are very widely used to value markets, the P maybe the value of an index. But let's focus on a company to make it a little bit easier, now that P is how much do I have to pay today to buy a share of this company? The part that comes in the denominator, the fundamental variable in the PE ratio is earnings per share. So because prices expressed as what you have to pay per share, then all the fundamental variables that may we may want to put on the denominator of a multiple are also on a per share basis, so earnings per share. But that doesn't actually conclude the discussion of what earnings could be. One of the things that I always emphasize when I teach corporate finance is, there's never any discussion with P is, but there may be a lot of discussion what E happens to be because E could be many things. We can calculate those earnings looking back, looking ahead. We can actually take one time expenses that we think they're not going to happen again. We can think about operating earnings. We can define earnings in all sorts of different ways, and unless if you're having a discussion on valuation, unless you know that everybody is talking about the same E, then you may be in trouble. You may end up comparing apples and oranges. We're going to be discussing devaluation of Marriott, we're going to take that as an example. So here is what you found by Marriott at the end of the second quarter, that is, but the end of June. And there's a lot of numbers here, and I just want you to focus on these two, which are the trailing PE and the forward PE. These are just two perfectly acceptable definitions of PE, one that is looking at trailing earnings, that is, earnings that we've observed in the past, and the other is looking at expected earnings, forward earnings, that is earnings that we expect in the future. Now the P is the same, but notice that the difference between the two numbers, one the trailing PE gives me 39, the other the forward PE gives me 23. Obviously, if you get the same price and two different earnings dividing the same P and the numbers are different, when would expect in the forward earnings to be higher than the expected earnings. So, basically, what we have here is suppose you're in evaluation discussion and in that valuation discussion you're talking about, well, I think that Marriott has a PE of 39 and someone tells you well, but it by think that PE should be a lot lower than that or a lot higher than that. If you don't know whether you're talking about trailing earnings or forward earnings, then you could be comparing apples and oranges. So it's very important when you use PEs that you know what is the E that you're using to have a discussion about the evaluation of this company on the basis of those PEs.
