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City Foods, a rapidly growing convenience store, paid a dividend of $2.00 during 2003. They...

Question:

City Foods, a rapidly growing convenience store, paid a dividend of $2.00 during 2003. They expect to see their dividend grow at a twenty percent rate for the next two years and then level out at a continuous six percent growth rate. City Food's required rate of return is twelve percent. What is the value of City Foods' common stock?

Multi-Stage Dividend Discount Model:

The multi-stage dividend discount model is a variant of the dividend discount model in which we assume different growth phases for dividends of a stock. Therefore, as opposed to the Gordon growth model, in this model the dividend growth rate is not constant over the entire analyzed period.

Answer and Explanation:

Let's denote the dividend by D, the growth rate by g, and the required rate of return by r. Based on the simple present value formula and the Gordon growth model equation, the value of the City Foods' common stock can be calculated as follows:

{eq}Value = \dfrac{D_{1}}{(1+r)^{1}} + \dfrac{D_{2}}{(1+r)^{2}} + \dfrac{D_{3}}{r-g} \times \dfrac{1}{(1+r)^{2}} {/eq}

The dividends for the next three years are:

{eq}D_{1} = \$2.00 \times (1+0.20) = \$2.40 {/eq}

{eq}D_{2} = \$2.40 \times (1+0.20) = \$2.88 {/eq}

{eq}D_{3} = \$2.88 \times (1+0.06) = \$3.05 {/eq}

Assuming the continuous growth rate of 6% after the year 2, and the required rate of return of 12%, the value of the City Food's stock is:

{eq}Value = \dfrac{\$2.40}{(1+0.12)^{1}} + \dfrac{\$2.88}{(1+0.12)^{2}} + \dfrac{\$3.05}{0.12-0.06} \times \dfrac{1}{(1+0.12)^{2}} {/eq}

{eq}Value = \$44.96 {/eq}


Learn more about this topic:

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The Dividend Growth Model

from Finance 101: Principles of Finance

Chapter 14 / Lesson 3
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