What is the value of a common stock if:
a) If earnings and dividends are growing annually at 10%, the current dividend is $1.32 and investors require a 15% return on investmenets in common stock?
b)What is the value of this stock if you add risk to the analysis and the firm's beta coefficient is 0.8, the risk-free rate is 9%, and the return on the market is 15%?
Thank you so much, I have lost my book and I need help with this one.
You've given us data about this stock -- but not the current selling price. You need to know that to determine its present value. But -- with earnings and dividends (sales, too?) growing annually at 15%, it's likely that the price will grow at something considerably less than 15%. This is also shown by the low beta coefficient of 0.8.
Bayside Inc plans to pay annual dividends for five more years. The last dividend paid was $1.40 a share. Dividends are increased by 2 percent each year. What is the current value of this stock at a discount rate of 9 percent?
To determine the value of a common stock, you can use a few different methods. Two common approaches are the Dividend Discount Model (DDM) and the Capital Asset Pricing Model (CAPM). I will explain both methods so you can understand how to calculate the value of the stock in each scenario.
a) Using the Dividend Discount Model (DDM):
The Dividend Discount Model values a stock based on the present value of its expected future dividends. The formula is as follows:
Value = Dividend / (Required Rate of Return - Dividend Growth Rate)
In this case, the current dividend is $1.32 and the investors require a 15% return on investments in common stock. Earnings and dividends are growing annually at 10%.
Let's plug the numbers into the formula:
Value = $1.32 / (0.15 - 0.10)
Value = $1.32 / 0.05
Value = $26.40
Therefore, the value of the stock based on the Dividend Discount Model is $26.40.
b) Using the Capital Asset Pricing Model (CAPM):
The Capital Asset Pricing Model takes into account the stock's risk level by using its beta coefficient, the risk-free rate, and the expected return on the market.
The formula for the expected return on a stock using CAPM is:
Expected Return = Risk-Free Rate + (Beta * (Market Return - Risk-Free Rate))
In this case, the stock's beta coefficient is 0.8, the risk-free rate is 9%, and the return on the market is 15%.
Let's calculate the expected return:
Expected Return = 0.09 + (0.8 * (0.15 - 0.09))
Expected Return = 0.09 + (0.8 * 0.06)
Expected Return = 0.09 + 0.048
Expected Return = 0.138 or 13.8%
Now, we can use the expected return in the Dividend Discount Model to calculate the value of the stock:
Value = Dividend / (Required Rate of Return - Dividend Growth Rate)
Value = $1.32 / (0.138 - 0.10)
Value = $1.32 / 0.038
Value = $34.74
Therefore, the value of the stock based on the Capital Asset Pricing Model is $34.74.
I hope this helps you calculate the value of the common stock in both scenarios. Remember, these models are just tools for estimation and the actual market value of the stock can differ.