Consider the following annual growth forecasts for a common stock:
Growth in years 1-2 = 50%
Growth in years 3-4 = 25%
Growth after year 4 = 10%
Assuming that the last dividend was $0.45 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.D
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. where
In this example, there is a transitional growth period of two years, during which the growth rate is expected to grow at 25% annually. This period will follow the two- year supernormal growth period, and would be denoted as "g subset t" if we were to reproduce the equation illustrated above. The calculation of the value of this common stock is illustrated as follows:
{V = {[$0.45 * (1.50)^1] / (1.20)} + {[$0.45 * (1.50)^2] / (1.20)^2} + {[$0.45 * (1.50)^2 * (1.25)^1] / (1.20)^3} + {[$0.45 * (1.50)^2 * (1.25)^2] / (1.20)^4} + {{[$0.45 *
(1.50)^2 * (1.25)^2 * (1.10)^1]/ (0.20 - 0.10)}/ (1.20)^4}
which can be deduced to the following:
{V = [$0.5625 + $0.703125 + $0.732422 + $0.762939 + $8.392334] = $11.15}