So in this section, we will cover equity valuation. The first topic we will cover is why it is that we can use the present value formulas to value equity in the first place. We are going to be valuing equity based on its dividend payments. This is a counterintuitive notion these days as many stocks don't pay dividends. So I'll explain why our present value formulas are still useful in this setting. In the next topic, we will use our infinite horizon formulas developed in the present value section. So these are the formulas for the perpetuity, the growing perpetuity, and the delayed perpetuity. These are very useful for valuing equity. One of the inputs into these formulas is the growth rate of dividends. So our last topic will be where does this growth rate of dividends come from? We will see that we can break the growth rate of dividends into the amount reinvested and the productivity of the firm. That has some really striking conclusions in terms of what a firm should invest and when it should disinvest. For instance, we will see that not all growth is created equal. Sometimes growing a company can actually destroy value. In the previous section, we determine the value of fixed income securities using present value methods. Now we're going to apply the same to stocks. So what is equity? Equity, Is the residual claim, On the assets of the corporation. So equity is what is left over after the bondholders have been repaid. So if you own equity in a company you are a partial owner of that company. Another word for equity is common stock. So the return to equity comes in two forms. One is a dividend and the other is, The capital gain. So equity holders receive, Dividends, And capital gains. So what is my return if I hold shares in the stock? Well, of course, we're going to use the definition of holding period return same definition as we used before. My value one year from now minus the value today divided the value today percent change in the value of my investment. So what's my value one year from now? Well, it's the price per share one year from now. Price per share one year from now. Plus the dividend per share one year from now. We always calculate prices after the dividend has been paid, its called the ex-dividend price. Now we subtract out what we paid which was the price at 0 and divided by what we paid which is the price at 0. So this is the holding period return, and we can manipulate it a bit to read something like this. So this first term here is the percent capital gain. It's the change in price divided by previous price. And this guy right here it's the dividend yield. So, Let's just use the notation r for holding period return. So then note we have r we just wrote equals D1 + P1- P0 over P0. If we do a little bit of algebra that tells us that 1 + r = D1 + P1 over P0. A little more algebra will get us to P0 = D1 + P1 over 1 + r. So this is our first valuation formula for a stock. It says what's the price of the stock today? Well, it's the discounted value of our cash flow tomorrow which is the dividend plus tomorrow's price or rather next year's dividend plus next year's price. That's may be kind of interesting but not super helpful because who knows what next year's price is? Well, after all we can use the same method to tell us when next year's priceis. After all P1 should be by the same reasoning D2 + P2. So the dividend 2 years from now plus the price 2 years from now, Discounted back. Okay, so substituting that in we get P0 = D1 over 1 + r, + D2 over 1 + r squared + P2 over 1 + r squared. Well, now we're basically in the same boat because we have a present value formula, but it's still got the price in it the price 2 years from now. So what do we do? Well, if we continue to apply the same reasoning, You can see what we're going to get. P0 is the dividend 1 year from now plus the dividend 2 years from now, Plus the dividend 3 years from now and so on and so forth until we feel like stopping when we get the dividend t years from now, and then we get this terminal price t years from now. Now we can keep going and going. And as long as the price grows more slowly than this discount factor can shrink it long as that's the case we can keep going and get what's called an infinite horizon formula. The price, Is the present discounted value of the future dividends out to infinity. And that is the basis for how we value equity. We value it just like we value anything else namely based on its cash flows. And what are the cash flows? They are the dividends or really any cash flow that you get sometimes it may not be called a dividend. For example, if the company is taken over and investors are bought out with cash that's essentially a dividend. Any cash payment coming to investors that's one of these Ds. But you might say wait a minute a lot of companies don't pay dividends, but their value is not 0. So can we maybe just not believe these formulas? Well, the answer is that just because they don't pay dividends now doesn't mean that they will never ever pay dividends, so perhaps the dividend is coming sometime in the future. So whatever we think those cash flows are going to be we put them in our present value formula. These dividends could be 0 for quite some time and then become non-zero.
