Anderson Inc.’s current dividend is $2.40 per share. The dividend is expected to grow at a rate of 6 percent per year. The risk free rate is 5 percent and the return on the market is 9 percent. If the company’s beta is 1.3, what is the price of the stock today?
To calculate the price of the stock today, we can use the dividend discount model (DDM) or the Gordon growth model. The Gordon growth model is used when dividends are expected to grow at a constant rate indefinitely. Here's how you can apply the Gordon growth model:
Step 1: Calculate the required rate of return using the CAPM (Capital Asset Pricing Model):
The CAPM formula is:
Required Rate of Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)
In this case, the risk-free rate is given as 5%, the market return is 9%, and the beta is 1.3. Let's calculate the required rate of return:
Required Rate of Return = 5% + 1.3 * (9% - 5%)
Required Rate of Return = 5% + 1.3 * 4%
Required Rate of Return = 5% + 5.2%
Required Rate of Return = 10.2%
Step 2: Apply the Gordon growth model:
The Gordon growth model formula is:
Stock Price = Dividend / (Required Rate of Return - Dividend Growth Rate)
In this case, the dividend is $2.40 per share and the dividend growth rate is 6%. Let's calculate the stock price:
Stock Price = $2.40 / (10.2% - 6%)
Stock Price = $2.40 / 4.2%
Stock Price = $57.14
Therefore, the price of the stock today is $57.14 per share.