# Silicon Water Company currently pays a dividend of $1 per share and has a share price of$20. If...

## Question:

Silicon Water Company currently pays a dividend of $1 per share and has a share price of$20. If the dividend was expected to grow at 20%t for five years and at 10% per year thereafter.

Now, what is the firm's expected or required return on equity?

## Required Return on Equity:

To estimate the required return on equity, the dividend discount approach tries to find the discount rate such that current stock price is justified. That is, given the stream of dividends, the required return is the discount rate that equates the present value of dividends to the current stock price.

## Answer and Explanation:

According to the dividend discount model, the price of a stock is the discounted present value of future dividends. Therefore, to find the required return on the stock, we need to find the discount rate that equates the present value of future dividends to the stock's current price, i.e., the solving the following equation:

• {eq}\displaystyle \sum_{t=1}^{5}{\frac{1*(1 + 20\%)^t}{(1 + r)^t}} + \sum_{t=6}^{\infty}{\dfrac{1*(1 + 20\%)^5*(1 + 10\%)^{t-5}}{(1 + r)^t}} = 20 {/eq}

and the solution to the above equation, using trial and error, is:

• {eq}r = 21\% {/eq}

Therefore, the required return on the stock is 21%.