Respuesta :
Answer:
Current Price = $39.79275 rounded off to $39.79
Explanation:
Using the constant growth of dividend model, we can calculate the price of the stock at any time. The formula for price today under this model is,
P0 = D0 * (1+g) / (r - g)
Where,
- Do is dividend today
- g is the growth rate
- r is the required rate of return
As we have P1, D1 and r available, we can use this to calculate the growth rate in dividends. We will use the following formula to calculate the price today.
Price today = Future price * (1 - g)
First we calculate the growth rate using P1, D1 and r in the constant growth rate formula.
42.5 = 1.85 * (1+g) / (0.11 - g)
42.5 * (0.11 - g) = 1.85 + 1.85g
4.675 - 42.5g = 1.85 + 1.85g
4.675 - 1.85 = 1.85g + 42.5g
2.825 = 44.35g
2.825 / 44.35 = g
g = 0.063697 or 6.3697% rounded off to 0.0637 or 6.37%
Now we calculate the current price of the stock to be,
Current Price = 42.5 * (1 - 0.0637)
Current Price = $39.79275 rounded off to $39.79
The dividend is the amount paid to the shareholders in the form of returns paid for the per number of shares held by the shareholders. The rate of dividend is fixed for preference shareholders, while it depends on the profit earned during the particular period.
The current value of the stock is $39.79
The current value of the stock will be computed by using the dividend growth model.
Computation:
Current value:
[tex]\begin{aligned}\text{Current Stock Value}&=\text{Future Price}\times\left(1-\text{growth rate} \right )\\&=\$42.50\times\left(1-0.0637 \right )\\&=\$39.79\end{aligned}[/tex]
Working Note:
Computation of growth rate:
[tex]\begin{aligned}\text{P0}&=\text{D0}\times\frac{\left(1+\text{g} \right )}{\left(\text{r-g} \right )}\\\$42.50&=\$1.85\times\frac{1+\text{g}}{\left( 0.11-\text{g}\right )}\\\$42.50\times\left( 0.11-\text{g}\right )&=\$1.85+\$1.85\text{g}\\\$4.675+\$42.5\text{g}&=\$1.85+\$1.85\text{g}\\ \$4.675-\$1.85&=\$1.85\text{g}+\$42.50\text{g}\\ \$2.825&=\$44.35\text{g}\\ \frac{\$2.825}{\$44.35}&=\text{g}\\ \text{g}&=0.06369\;\text{or}\;6.37\%\end{aligned}[/tex]
were,
P0 is the market price
D0 is the current dividend
g is the growth rate
r is the required rate of return
To know more about the dividend growth model, refer to the link:
https://brainly.com/question/24044979
