Question

From Textbook: Brooks, R.M., 2012, Financial Management: Core Concepts, 2nd ed., Pearson Education- Chapter 7(Stocks and Stock Valuation)- The Constant Growth Dividend Model with a Finite Horizon Formula

Pr Price = - X + (r-g

the question is to proof/Derive the above rofmula

Answer 1

As per the dividend growth model,
g	growth rate
r	return on equity
Po	Today's price
Pn	Price after n periods
Div0	Dividend today
The current price is the discounted value of the future cash flows
So Po =	Div0*(1+g)/(1+r) + Div0*(1+g)^2/(1+r)^2 +…+Pn/(1+r)^n
As per formula for sum of geometric progression
Po =	Div0*(1+g)/(1+r)*(1+(1+g)/(1+r)+…+ (1+g)^n/(1+r)^n) + Pn/(1+r)^n
Po =	Div0*(1+g)/(1+r)*(1-(1+g)^n/(1+r)^n)/(1-(1+g)/(1+r))+Pn/(1+r)^n
Po =	Div0*(1+g)/(1+r)*(1-(1+g)^n/(1+r)^n)/(1-(1+g)/(1+r))+Pn/(1+r)^n
Po =	Div0*(1+g)/(1+r)*(1-(1+g)^n/(1+r)^n)/(1-(1+g)/(1+r))+Pn/(1+r)^n
Po =	Div0*(1+g)/(r-g)*(1-((1+g)/(1+r))^n)+Pn/(1+r)^n