Ecolap Inc. (ECL) recently paid a $0.42 dividend. The dividend is expected to grow at a 10.50 percent rate. The current stock price is $47.32.
What is the return shareholders are expecting? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
Shareholders return %
To calculate the return shareholders are expecting, we need to determine the present value of the dividends and the future price of the stock.
First, let's calculate the present value of the dividends using the dividend growth model:
PV = D / (r - g)
Where:
PV = Present value of dividends
D = Dividend
r = Required rate of return
g = Dividend growth rate
In this case, the dividend is $0.42 and the dividend growth rate is 10.50%. However, we do not have the required rate of return. So let's calculate it using the formula:
r = (Dividend / Stock Price) + g
The current stock price is $47.32, so now we can calculate the required rate of return:
r = ($0.42 / $47.32) + 10.50%
Calculating the required rate of return gives us:
r = 0.0089 + 0.1050 = 0.1139 or 11.39%
Now that we have the required rate of return, we can calculate the present value of the dividends:
PV = $0.42 / (0.1139 - 0.1050)
Calculating the present value gives us:
PV = $0.42 / 0.0089 = $47.19
Next, we calculate the future stock price using the formula:
Future Stock Price = Dividend * (1 + g) / (r - g)
Future Stock Price = $0.42 * (1 + 10.50%) / (11.39% - 10.50%)
Calculating the future stock price gives us:
Future Stock Price = $0.4641 / 0.0089 = $52.13
Finally, we can calculate the return shareholders are expecting using the formula:
Return = (Future Stock Price - Current Stock Price + Dividend) / Current Stock Price
Return = ($52.13 - $47.32 + $0.42) / $47.32
Calculating the return gives us:
Return = $5.23 / $47.32 = 0.1105 or 11.05%
Therefore, shareholders are expecting a return of 11.05%.
To calculate the expected return for shareholders, we need to use the dividend growth model. The dividend growth model is given by the formula:
Expected Return = (Dividend / Stock Price) + Dividend Growth Rate
Given that the dividend is $0.42, the stock price is $47.32, and the dividend growth rate is 10.50%, we can substitute these values into the formula:
Expected Return = ($0.42 / $47.32) + 10.50% = 0.00888 + 10.50% = 0.10118
Converting this into a percentage, the expected return for shareholders is 10.12%. Rounded to two decimal places, the shareholders are expecting a return of 10.12%.