I will preface this to say that yes of course I researched my face off for hours. And while the equation itself is explained (give me numbers and I can do it) all over the internet, the WHY of what is included is not clicking.
WHY on the bottom part of the equation am I subtracting the growth rate from the expected rate of return? The words “that is the effective discounting factor” mean nothing to me. I understand the “time value of money” concept (and suspect it has something to do with this); I do not understand how these two *particular* factors are the ones you need (to be divided by dividend price of course) to help determine the stock’s appropriate pricing.
What do those two amounts have to do with anything? Please help!
Edit: By explaining simply, I mean very very simply, like the link below, in an analogy, not using any financial terms. I am not a finance student.
https://www.reddit.com/r/explainlikeimfive/comments/kji6n/eli5_compound_interest/?utm_source=share&utm_medium=ios_app&utm_name=iossmf
In: 2
An easy way to see it better is to rearrange it with algebra. D/p + g = r. That is to say the return is the dividend divided by the price plus how much the company grows. Companies growing fast can have high returns even without a dividend. Likewise larger older companies often have low growth but high dividends. These two combined are how much you gain. When you rearrange it you use the others to find the price. So if d is 2 and p is 100 then d over p is .02 and if growth is 6 percent or .06 then r is .08. Expected returns are 8 percent.
A company does stuff. After they pay their bills, invest in R&D, blah blah blah, they have money left over. They can directly pay some of it to shareholders as a dividend. They can plow some of it back into the company (and theoretically increase the value of the company…i.e. the share price). It’s got to go to one of the two.
The part I think you might be missing is the larger definition for the terms on the bottom. It’s the growth rate *of the dividend* and the expected rate of return *of the equity*. Those two terms are how the company is dividing their profit between dividend and re-investment. They *both* provide return to shareholders, but in different ways. If you look at the derivation of the model, they’re not directly subtracting from each other, that’s just where the math lands when you clean everything up.
Intuitively, if they paid zero dividends, all profit would go into equity returns (share price increase). Paying dividends lowers the reinvestment in the company (cash out) so lowers the effective reinvestment in the company, lowers equity return, lowers share price.
Two things aren’t being spelled out here. The value of a perpetuity (pays 1 periodically forever) is 1/i, the discount interest rate. So, the model values a stock price as if it were a perpetuity. The remaining question is What is the appropriate discount rate. The model claims that it is cost of capital less the expected growth rate of the company and by implication the dividend. Subtracting the dividend growth rate is a shortcut to discounting a series of payments growing at that rate
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What you want is this – see link below.
Tldr is that when you sum up a series that grows at “g” and discounts at “r” every year the mathematics works out such that the convenient “r-g” factor goes in the denominator.
See this below:
https://medium.com/@matthew.wilkinson.mw/proving-the-gordon-growth-model-geometric-series-and-their-applications-c156a4ca0b3d
Or you can look up how geometric series are summed.
1. Future cash flows are discounted to 0 period to find the security’s value today
2. If growth rate is constant and cash flow is perpetual we reduce the growth from discounting factor as a way to incorporate growth in cash flows while using only 1st year cash flow through D1/Ko
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