# k-g intuition

Help me out here. The DDM formula is now beaten into my head, but I am having some trouble wrapping my brain around why it works. That is, what is the intuition behind why the difference between required rate of return and dividend growth (k-g) is the appropriate discount rate? They just don’t seem to have a close/dependent enough relationship to me…

The formula D(1)/(keg) is actually the limit of an infinite series. So, it just falls out fromm the math. But the way I intuit it is that since dividends are growing at a constant rate, you use the “growth adjusted” discount rate. This also covers the case where dividends are constant (in this case, dividends are also growing at a constant rate – it’s tust that the constant growth rate is zero).

^ Agree - is is because of a simplification of a infinite geometric series. You can take our word for it or you can have a look at some of the proofs that are around. http://www.investopedia.com/articles/fundamental/04/041404.asp http://en.citizendium.org/wiki/Gordon_model If you are interested in the math that is Busprof - Are you actually a Business Prof??

I suggest deriving the formula once. Here is my simple derivation: D1/(1+k) + D1*(1+g)/(1+k)^2+ … +D1*(1+g)^{n-1}/(1+k)^n = (D1/(1+k))*(1+(1+g)/(1+k)+((1+g)/(1+k))^2+…)= now notice that 1+a+a^2+ … = 1/(1-a) if abs(a) < 1, here a = (1+g)/(1+k) (D1/(1+k))*(1/(1-(1+g)/(1+k))=(D1/(1+k))*((1+k)/(k-g))=D1/(k-g)