[MUSIC PLAYING] Just as we found the value of bonds by calculating the yield to maturity, the present value of future coupon and maturity payments, the value of a stock is also found by examining the present value of expected future cash flows.
Stocks vary in attractiveness to different investors. This is called the clientele effect. At the end of an accounting period a business can do one of two things with its net income. It can pay out dividends to the shareholders, or it can reinvest it in the business.
Growth companies, often younger organizations, generally do not pay out dividends, reinvesting all of their profits into future growth. More mature companies will pay dividends because they no longer are growing at the same earlier rate. In either case, we could still project the value of a stock based on the expectation of future dividends, even if they are not being paid now.
One familiar model that lets us look at this is the constant growth model. Let's have a look. Here is the formula for the present value of a stock today that is a long series of present value calculations for the expected future dividends.
Now it certainly looks like this calculation could be very tedious depending on how long in the future we're expecting to receive dividends. But we could simplify this calculation into something called the constant growth model.
The constant growth model allows us to value the price of a stock today on the basis of its next dividend divided by the required rate of return minus the growth rate. So let's take a look at this.
D sub 0 is the last dividend that was paid, with a growth rate of g. So if we multiply D sub 0 times 1 plus D, we have the next dividend, or D sub 1. And it is compounded by the growth rate. r represents the required return on a stock with the same level of risk in the economy. Later, we'll talk about ways we can measure that risk. g is the expected growth rate that we expect to be constant into the future.
Now let's take a look at an example. What if we know the current annual dividend is $0.50 a share and the required rate of return is 6% and the growth rate is 5%? What current price should we expect?
Well, we can use a web app or a spreadsheet tool like Excel to calculate this. So with our current annual dividend of $0.50 a share and the required growth rate at 6% and the growth rate at 5%, what do you think the price might be? Well, the constant growth model says it will be $52.50.
So if we're investing in the market, if the constant growth model is saying the price should be 52.50, we might be looking at stocks with the same growth and required rate of return of dividends that might be undervalued and be better bargains for us.
But what happens in the constant growth model in a different situation? What if the board of directors votes to pay a $0.55 annual dividend up from $0.50? The required rate of return is still 6% and the constant growth rate is still 5%.
But now the current price is $57.75. Why is the price of this stock higher now? Because the annual dividend is greater. So it is worth more to us.
One more example. What if the economy goes into recession and the required return on the stock jumps to 8%? Rates increase in times of uncertainty. The growth rate is still 5.
Well, now the price falls, plummets to $19.25. Same dividend, same growth rate, but the required return is much higher. So the projected value for that stock is only $19.25.
So there should be a couple of questions that you're asking yourself. The first one, what about a company that doesn't pay dividends. Well, the answer is this-- their price is still dependent upon the expectation of future dividends.
Remember, a company could do one of two things with its net income-- it can be reinvested in the business, compared to or paid out to the owners as dividends. Companies that are new or in a very high growth cycle, will invest all of their net income back into the business.
To keep the stock attractive when their future growth is not so rapid, they'll have to pay a dividend. So when a company runs through all of its growth opportunities, it will start paying dividends. And the future value of those dividends is upon which the stock value is based.
What about a company that isn't growing at a constant rate? Well, over the long term life of the company, this is frequently the case. But what we could do with the model is allow us to estimate the value of a particular cycle.
For example, if a company starts off with a period of high growth of 10%, use that growth rate for that early period. And later if it flattens out for several years at 5%, use that as a growth rate for that period. And then at maturity later in the cycle if it only grows at 3%, use that as a rate, and then combine the valuation of those three periods together.
The important thing to remember is that the value of a share of stock is based on our expectation of future dividend payments in the present value of that cash flow.
This is Dr. Bob Nolley. And I'll see you in the next lesson.