Question

Great Pumpkin Farms just paid a dividend of $4.50 on its stock. The growth rate in dividends is expected to be a constant 7.5 percent per year indefinitely. Investors require an 18 percent return on the stock for the first three years, an 11 percent return for the next three years, and 12 percent return thereafter. What is the current share price of the stock?

Answer 1

Given, Dividen paid (D₀)=4.5

Growth Rate (g)=7.5%.

Therefore Subsequent Dividends (D_n) will be D₀*(1+g)^n=D₀*1.075^n. Where n denotes divident paid in year n.

Therefore D2=4.5*(1.075)^2=5.20 (e.g.)

Since the required rate of return is different over different time periods, we have to compund them to get the discounting factor. For 4th year, this will be (1.18^3)*(1.11), 5th year (1.18^3)*(1.11^2), and so on.

The Present Value of dividends will be D₁/1.18+D₂/1.18^2+D₃/1.18^3+D₄/(1.18^3*1.11)+D₅/(1.18^3*1.11^2) +D₆/(1.18^3*1.11^3)

=4.5*1.075/1.18+4.5*(1.075)^2/1.39+4.5*(1.075^3)/1.64+4.5*(1.075^4)/1.82+4.5*(1.075^5)/2.02+4.5*(1.075^6)/2.24

=20.81

From year 7, company will have have stable rate of return of 12%. We can use the Gordon Growth Model to find out the Terminal Value in Year 6, given by TV=D₇/(r-g). Where, r is 12% and g is the growth rate (7.5%)

TV= 4.5*(1.075^7)/(0.12-0.075)=165.9

Present Value of TV=TV/(1.18^3)(1.11^3) (We are discounting by 6 years)

=73.83

Value of the share=Present Value of T.V + Present Value of Dividends

=73.83+20.81=94.65 (Do not round intermediate calculations, if you need accurate answer)