The Bravo Company just paid an annual dividend of $4.00 per share. Due to a need to conserve...

Question:

The Bravo Company just paid an annual dividend of {eq}\$4.00 {/eq} per share. Due to a need to conserve cash, the dividend in one year will be cut to zero. Dividends per share are forecasted to be {eq}\$1.50 {/eq} in two years, {eq}\$2.50 {/eq} in three years, and {eq}\$3.50 {/eq} in four years. After four years, dividends are expected to grow at a constant rate forever. Investors in Bravo Company require a return of {eq}12 \% {/eq}. The current market price of Bravo s stock is {eq}\$30.66 {/eq} per share. Determine the constant growth rate in dividends after four years that would justify the current market price.

Dividend Growth Model:

The dividend growth model is used to priced a stock with perpetual growth in dividends. The price of such a stock is the next dividend per share divided by the difference between the required rate of return and the dividend growth rate.

Answer and Explanation:

We can use the dividend discount model to compute the price of the stock. According to this model, the price of a stock is the discounted present value of future dividends. Let the growth rate of the dividend after year 4 denoted by {eq}g {/eq}, then we have:

  • {eq}\dfrac{1.5}{(1 + 12\%)^2} + \dfrac{2.5}{(1 + 12\%)^3} + \dfrac{3.5}{(1 + 12\%)^4} + \dfrac{3.5*(1 + g)}{(12\% - g)(1 + 12\%)^4} = 30.66\\ 5.20 + \dfrac{3.5*(1 + g)}{(12\% - g)(1 + 12\%)^4} = 30.66\\ g = 3\% {/eq}

That is, the expected growth rate after year 4 is 3%.


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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