### CFA Practice Question

Charles Ray, a portfolio manager with Bay Side Brokerage, is examining shares of a large money center bank. In his analysis, Mr. Ray has determined that the \$1.20 per share dividend of this company is anticipated to grow at 14.5% annually. Additionally, Charles Ray has calculated his required rate of return as 16% per year. Assuming that Charles Ray can sell his shares of this bank for \$85 at the end of three years, what is the value of this common stock?
A. \$57.96
B. \$54.82
C. \$92.45
Explanation: 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 the investor's holding period. Had the investor in this example forecasted selling the shares at the end of the 9th year, then "n" would be the ninth 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 = [(\$1.20 * 1.145) / (1 + 0.16)^1] + [(\$1.374 * 1.145) / (1 + 0.16)^2] + [(\$1.57323 * 1.145) / (1 + 0.16)^3] + [\$85 / (1 + 0.16)^3]}

which can be further reduced to the following: {V = [\$1.184483 + \$1.169166 + \$1.154048 + \$54.455902] = \$57.96}