# 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}

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