Stormy Weather has no attractive investment opportunities. Its return on equity equals the discount rate, which is 10%. Its expected earnings this year are $2 per share. Find the stock price, P/E ratio, and growth rate of dividends for plowback ratios of
Plowback Ratio - 0
Plowback Ratio - 0.20
Plowback Ratio - .70
To find the stock price, P/E ratio, and growth rate of dividends for different plowback ratios, we need to use the formulas and information given. Let's go through each plowback ratio one by one.
1. Plowback Ratio of 0:
When the plowback ratio is 0, it means that the company pays out all its earnings as dividends and reinvests nothing.
The formula for the price-to-earnings (P/E) ratio is:
P/E ratio = Stock price / Earnings per Share
Since all earnings are paid out as dividends, the earnings per share (EPS) is equal to the expected earnings this year, which is $2 per share.
So, for a plowback ratio of 0:
P/E ratio = Stock price / $2
Given that Stormy Weather has no attractive investment opportunities, the return on equity (ROE) equals the discount rate, which is 10%. Therefore, we can calculate the stock price:
Stock price = ROE / P/E ratio
Stock price = 10% / P/E ratio
To find the actual stock price, we need a specific value for the P/E ratio. However, with only the information provided, we can't determine the exact stock price and P/E ratio for a plowback ratio of 0.
2. Plowback Ratio of 0.20:
When the plowback ratio is 0.20, it means that the company retains 20% of its earnings and pays out the remaining 80% as dividends.
The plowback ratio (b) can be calculated as:
b = (EPS - Dividends) / EPS
Given that EPS is $2 per share, and 80% is paid out as dividends:
0.20 = ($2 - Dividends) / $2
We can solve this equation to find the value of Dividends:
Dividends = ($2 - 0.20 * $2)
Dividends = ($2 - $0.40)
Dividends = $1.60 per share
Now, the formula for the stock price becomes:
Stock price = ROE / (Dividends / EPS)
Stock price = 10% / ($1.60 / $2)
Stock price = 10% / 0.80
Stock price = $12.50 per share
The P/E ratio for this plowback ratio would then be calculated as:
P/E ratio = Stock price / EPS
P/E ratio = $12.50 / $2
P/E ratio = 6.25
3. Plowback Ratio of 0.70:
When the plowback ratio is 0.70, it means that the company retains 70% of its earnings and pays out the remaining 30% as dividends.
Using the same approach as before, we can determine the Dividends:
0.70 = ($2 - Dividends) / $2
Dividends = ($2 - 0.70 * $2)
Dividends = ($2 - $1.40)
Dividends = $0.60 per share
Next, we can calculate the stock price:
Stock price = ROE / (Dividends / EPS)
Stock price = 10% / ($0.60 / $2)
Stock price = 10% / 0.30
Stock price = $33.33 per share
The P/E ratio for this plowback ratio would be:
P/E ratio = Stock price / EPS
P/E ratio = $33.33 / $2
P/E ratio = 16.67
To calculate the growth rate of dividends, we can use the Dividend Growth Model:
Growth rate of dividends = ROE x Plowback ratio
Growth rate of dividends = 10% x 0.70
Growth rate of dividends = 7%
In summary:
For a plowback ratio of 0, we can't determine the stock price and P/E ratio.
For a plowback ratio of 0.20, the stock price is $12.50 per share, the P/E ratio is 6.25, and the growth rate of dividends is 0% since all earnings are paid out.
For a plowback ratio of 0.70, the stock price is $33.33 per share, the P/E ratio is 16.67, and the growth rate of dividends is 7%.