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?
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A. B. C. D. E. F.Explanation
To determine the value of a common stock experiencing temporary supernormal growth, use the following equation:
{V = {[d0 * (1 + gs)^1] / k} + {[d1 * (1 + gs)^2} + ... {dn * (1 + gs)^n} + {[dn * (1 + gs)^n * (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, dn = the dividend at tn, gs = 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 * (1.25)^1] / (1.20)} + {[$2.25 * (1.25)^2] / (1.20)^2} + {[$2.25 * (1.25)^3] / (1.20)^3}{{[$2.25 * (1.25)^3 * (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}