The price of a stock with dividends growing at a constant rate can be calculated using the Gordon Growth Model (Dividend Discount Model):

$P_0 = \frac{D_1}{K_e - g}$

where:

• $P_0$ = Price of the stock
• $D_1$ = Dividend expected in the next 12 months
• $K_e$ = Required rate of return
• $g$ = Constant growth rate of dividends

1. Compute the price of Ecology Labs' common stock.

Given values:

• $D_1 = 2.50$
• $K_e = 19\% = 0.19$
• $g = 8\% = 0.08$

Using the formula:

$P_0 = \frac{2.50}{0.19 - 0.08}$

Let's calculate this:

$P_0 = \frac{2.50}{0.11}$

$P_0 \approx 22.73$

2. Assume $K_e$ goes up to 23 percent. What will be the new price?

Given values:

• $K_e = 23\% = 0.23$
• $D_1 = 2.50$
• $g = 8\% = 0.08$

Using the formula:

$P_0 = \frac{2.50}{0.23 - 0.08}$

$P_0 = \frac{2.50}{0.15}$

$P_0 \approx 16.67$

3. Assume the growth rate ($g$) goes up to 10 percent. What will be the new price? $K_e$ goes back to its original value of 19 percent.

Given values:

• $K_e = 19\% = 0.19$
• $D_1 = 2.50$
• $g = 10\% = 0.10$

Using the formula:

$P_0 = \frac{2.50}{0.19 - 0.10}$

$P_0 = \frac{2.50}{0.09}$

$P_0 \approx 27.78$

4. Assume $D_1$ is $3.00. What will be the new price? Assume $K_e$ is at its original value of 19 percent and $g$ goes back to its original value of 8 percent.

Given values:

• $D_1 = 3.00$
• $K_e = 19\% = 0.19$
• $g = 8\% = 0.08$

Using the formula:

$P_0 = \frac{3.00}{0.19 - 0.08}$

$P_0 = \frac{3.00}{0.11}$

$P_0 \approx 27.27$

Summary of the Answers:

1. Price of the stock: $22.73
2. New price if $K_e = 23\%$: $16.67
3. New price if $g = 10\%$: $27.78
4. New price if $D_1 = 3.00$: $27.27

Would you like further explanation or have any questions? Here are some related questions:

1. How does the required rate of return affect stock price?
2. What happens to the stock price if the growth rate exceeds the required rate of return?
3. How can changes in dividends impact stock valuation?
4. What assumptions does the Gordon Growth Model make?
5. How would the price change if there were a higher dividend payout ratio?

Tip: When using the Gordon Growth Model, ensure the required rate of return is higher than the growth rate; otherwise, the model is not valid.