If the annual EPS of a company is $4.50 and its earnings yield is 5%, what is its stock price?
The correct answer and explanation is:
To find the stock price, we can use the relationship between Earnings Yield and Earnings Per Share (EPS): Earnings Yield=EPSStock Price×100%\text{Earnings Yield} = \frac{\text{EPS}}{\text{Stock Price}} \times 100\%
We are given:
- EPS = $4.50
- Earnings Yield = 5%
Let’s plug into the formula and solve for Stock Price: 0.05=4.50Stock Price0.05 = \frac{4.50}{\text{Stock Price}}
Now, solve for Stock Price: Stock Price=4.500.05=90\text{Stock Price} = \frac{4.50}{0.05} = 90
✅ Correct Answer: $90
📘 Explanation (300 words):
Earnings Per Share (EPS) represents the portion of a company’s profit allocated to each outstanding share of common stock. It is a key indicator of a company’s profitability. Earnings Yield is the inverse of the Price-to-Earnings (P/E) ratio and shows how much a company earns relative to its stock price. It is calculated as: Earnings Yield=(EPSStock Price)×100\text{Earnings Yield} = \left(\frac{\text{EPS}}{\text{Stock Price}}\right) \times 100
In this problem, we know the company earns $4.50 per share per year (EPS), and the earnings yield is 5%. This means that for every dollar invested in the company’s stock, the investor is earning 5 cents annually in terms of earnings.
To find the stock price, we simply rearrange the formula: Stock Price=EPSEarnings Yield (decimal)\text{Stock Price} = \frac{\text{EPS}}{\text{Earnings Yield (decimal)}}
Substituting values: Stock Price=4.500.05=90\text{Stock Price} = \frac{4.50}{0.05} = 90
This tells us that the market is valuing each share of the company at $90, given that it earns $4.50 per share and the yield expected by investors is 5%. A lower earnings yield (e.g., 2%) would imply a higher stock price for the same EPS, while a higher earnings yield would mean a lower price, all else equal. Investors use this relationship to assess whether a stock is fairly valued.