Answer:
stock price = (Div 1 / r - g1) x {1 - [(1 + g1) / (1 + r)]ⁿ} + (Div 1 / r - g2) x [(1 + g1) / (1 + r)]ⁿ⁻¹
Explanation:
since the company will first grow at g1 for n years, and then at g2 forever, we need to first determine the present value of the dividends growing at g1 for n years:
present value of the dividends during n = (Div 1 / r - g1) x {1 - [(1 + g1) / (1 + r)]ⁿ}
e.g. div = $2, n = 5 years, g1 = 8%, r = 12%
(2 / 12% - 8%) x {1 - [(1 + 8%) / (1 + 12%)]⁵} = 50 x 0.166263 = $8.31
now we find the formula to calculate the present value for the growing perpetuity g2 at n - 1 years:
= (Div 1 / r - g2) x [(1 + g1) / (1 + r)]ⁿ⁻¹
following the same example but changing g1 for g2, and g2 = 5%
= (2 / 12% - 5%) x [(1 + 5%) / (1 + 12%)]⁵⁻¹ = 28.5714 x 0.772476 = $22.07
we now add both parts to finish our example = $8.31 + $22.07 = $30.38