D1/(Ke - g) is calcuated to create a terminal value (note that unlike bonds, equities don’t have a maturity value, so for the sake of valuation you need to limit your data analysis to say 10years, 5years or whatever in given in the problem).

So say at year 10 the company is mature enough and that it’s growth is already well-established ( i.e. could be fairly estimated). in addition, we are assuming that the company will continue to operate in the future. so at year 10 you calculate gordon growth to discount ALL future perpetual expected dividends to year 10. Now that you created a terminal value, then from year 10 to present you simply dscount that value using PV= P10/(1+Ke)^10.

Another example, when you have growth less than ke, simply use gordon formula. if growth > ke then use DDM.

when using DDM, you already have a terminal value say P2= 20$ so your formula will be:

P0 = D1/(1+Ke) + D2/(1+Ke)^2 + P2/(1+ke)^2 —> that is your terminal value

if P2 is not given, then surely you can calculate it using Gordon growth so P2 = D3/(ke-g)

So basically if we have Dividends for years , 2001 , 2002 and 2003 . while calculating the PV of the stock for 2002 , we should use the dividend expected to be paid in 2003 right ?

Now for example we have a question , Saying that :

Stock A has a current dividend of 2$ , we expect it to grow at 5% from year 4 and the expected cost on equity is 15% . what is thecurrent price of stock A ?

So this basically would be :

Pv of stock at year 4 = 2$/0.15-0.05 = 10$

and then PV at year 0/current PV would be = 2/(1+0.15) + 2/(1.15)^2+2/(1.15)^3+2/(1.15)^4+(10/1.15)^4 ?

The GGM is a series of PVs of future dividends, the proof of such should be in your textbook.

The idea is that the cost of equity is the expected yield of the price you pay. So a Ke of 8% on a $100 stock should give you $8 according to the formula D/Ke.

If the dividend is expected to constantly grow at a given growth rate, then you subtract the growth rate from the Ke for the coming period, and raising your investment price to adjust for the present value of growth opportunity. This should give you a PV simillar to another stock paying unchanging dividends, but at a lower expected yield.