Consider the following annual growth forecasts for a common stock:

Growth in years 1-3 = 25%
Growth after year 3 = 15%

Assuming that the last dividend was $2.25 per share, and the required rate of return is 20% per year, what is the value of this common stock?

Explanation: To determine the value of a common stock experiencing temporary supernormal growth, use the following equation: {V = {[d₀ x (1 + gs)¹] / k} + {[d₁ x (1 + gs)²} + ... {d_n x (1 + gs)ⁿ} + {[d_n x (1 + gs)ⁿ x (1 + gn] / (k - g)} / (1 + k)ⁿ}}
where: V = the value of common stock at t₀, d₀ = the dividend at t₀, d₁ = the dividend at t₁, d_n = the dividend at tn, g_s = the supernormal rate of growth, gn = the normal rate of growth, n = the time period "n", and k = the required rate of return.

In this example, there is a supernormal growth period of three years, during which the growth rate of this common stock is expected to grow at 25% annually. After this period of supernormal growth, the growth rate is anticipated to settle to a "normal" rate of 15%, and this rate is expected to remain stable indefinitely. The calculation of the value of this common stock is illustrated as follows: {V = {[$2.25 x (1.25)¹] / (1.20)} + {[$2.25 x (1.25)²] / (1.20)²} + {[$2.25 x (1.25)³] / (1.20)³}{{[$2.25 x (1.25)³ x (1.15)¹]/ (0.20 - 0.15)}/ (1.20)³} which can be deduced to the following: {V = [$2.34375 + $2.441406 + $2.543132 + $58.492025] = $65.82}