Question

As an analyst at Chitalu Securities, you are responsible for making recommendations to your firm’s clients regarding common stocks. After gathering data on CEC, you have found that their dividends have been growing at a rate of 10% per year to the current (D0) rate of K6 per share. The stock is currently selling for K78 per share, and you believe that an appropriate rate of return for this stock is 15% per year.

a) If you expect that the dividend will continue to grow at a 10% rate into the foreseeable future, what is the highest price at which you would recommend purchasing this stock to your clients?
b) Suppose now that you determine that the company’s new product line will cause much higher growth in the near future. Your revised estimate is for a three-year period of 20% annual growth, which will be followed by a return to the historical 10% growth rate. Under these new assumptions, what is the current value of the stock using the two-stage dividend growth model?
c) After considering your assumptions from part b, you realize that it is likely that the growth will gradually transition from 20% down to 10% rather than instantaneously. If you believe that this transition will take five years, what is the value that you place on the stock today? Use the three-stage dividend growth model. Provide answers using Excel.

Answer 1

The highest recommended purchase price for CEC stock with a constant 10% growth rate is K132. The value of the stock, considering a two-stage growth model with 20% growth for three years followed by a 10% constant rate, and a three-stage model with a gradual transition from 20% to 10% over five years, need to be calculated using the respective dividend growth models. These calculations consider present values of expected future dividends at a 15% required rate of return.

Step-by-step explanation:

To evaluate the appropriate purchase price and value of CEC stock, one must apply different dividend valuation models considering the expected growth rates. For part a), we would use the Gordon Growth Model (also known as the Dividend Discount Model) which assumes a constant growth rate in dividends. The model's formula is P = D1 / (k - g), where P is the price, D1 is the expected dividend next year, k is the required rate of return, and g is the growth rate. With a current dividend (D0) of K6 and a growth rate of 10%, the dividend in the next year (D1) would be K6 * 1.10 = K6.60. Given a required return (k) of 15%, the highest price you would recommend for purchasing the stock (P) would be K6.60 / (0.15 - 0.10) = K132. For part b), applying the two-stage dividend growth model involves calculating the present value of dividends during the high growth phase and then using the Gordon Growth Model to find the present value of dividends after this period transitions into constant growth. Finally, for part c), the three-stage dividend growth model acknowledges a transitioning growth, which has to be reflected in the calculation of present values of dividends across different stages before reaching perpetual growth. All these models require calculating present values of expected dividends at different points in time, considering the 15% required return, to arrive at the stock's current value. It is important to note that projected profits and growth rates are estimates and carry uncertainty. Hence, the valuation provides a guideline rather than a precise price point.