Mary Short is a retail investor. During the course of the last several weeks, Ms. Short has been examining shares of Tellcorr Industries, a large telecommunications firm. In her examination, Mary has determined that Tellcorr's $1.05 per share dividend is anticipated to grow 20% annually. Assuming that
Mary can sell her shares of Tellcorr for $70 per share at the end of three years, and that her required rate of return is 22% per year, what is the value of Tellcorr's common stock?
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A. B. C. D. E.A
The Multiple Holding Period form of the Dividend Discount Model takes the following form: {V = {[d1 / (1 + k)] + [d2 / (1 + k)^2] + ... .[dn / (1 + k)^n] + [Pn / (1 + k)
^n]}
Where: V = the price of the common stock at t0, d1 = the annual dividend at t1 (this is found by multiplying the annual dividend at t0 by (1 + the anticipated growth rate), d2 = the annual dividend at t2 (this is found by multiplying the dividend at t1 by (1 + the anticipated growth rate), k = the required rate of return, n = period
"n", and Pn = the sale price of the common stock at time "n".
In this example, time "n" is the third year, as this is the end horizon for Mary's holding period. Had the investor in this example forecasted selling the shares at the end of the 10th year, then "n" would be the tenth year.
Now that the formality of expressing the equation for this form of the DDM has been carried through, we can move toward a calculation of the value of this common stock. In this example, all of the necessary information has been provided, and the calculation of the value of this retail stock is as follows:
{V = [($1.05 * 1.20) / (1 + 0.22)^] + [($1.26 * 1.20) / (1 + 0.22)^2] + [($1.512 * 1.20) / (1 + 0.22)^3] + [$70 / (1 + 0.22)^3]}
Which can be further broken down into the following:
{V = [$1.032787 + $1.015856 + $0.999203+ $38.549482] = $41.60}