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
the question is to proof/Derive the above rofmula
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 | |||||||
From Textbook: Brooks, R.M., 2012, Financial Management: Core Concepts, 2nd ed., Pearson Education- Chapter 7(Stocks and...