Welcome to the Cost of Equity!
Hello there! We are diving into one of the most important parts of Section A: Financing Capital Projects. If you’ve ever wondered how a company decides if a project is "worth it," the answer often starts here.
The Cost of Equity (\(K_e\)) is essentially the return that shareholders expect to receive for investing their money in a company. Since shareholders take the most risk (they are the last to get paid if things go wrong), they expect a decent reward. For the company, this "reward" is a cost. Don't worry if this seems a bit abstract at first—we’re going to break it down into simple, manageable steps!
1. Understanding the Cost of Equity (\(K_e\))
Think of the Cost of Equity as a "hurdle rate." If a company wants to start a new project using money from shareholders, the project must earn at least the \(K_e\) to keep those shareholders happy. If the project earns less, the shareholders might take their money elsewhere.
Key Concept: The cost of equity is not a fixed legal obligation like interest on a bank loan. It is an "opportunity cost"—the return shareholders could have earned elsewhere for the same level of risk.
Quick Review: Why do we need \(K_e\)?
1. To calculate the Weighted Average Cost of Capital (WACC).
2. To use as a discount rate for evaluating new investment projects.
2. Method 1: The Dividend Valuation Model (DVM)
The DVM assumes that the value of a share today is the present value of all future dividends. We can rearrange this logic to find the cost of equity.
A. DVM with Constant Dividends (No Growth)
If a company pays the same dividend every year forever, the formula is very simple:
\( K_e = \frac{D}{P_0} \)
Where:
\(D\) = The constant annual dividend
\(P_0\) = The current market price of the share (ex-dividend)
B. DVM with Constant Growth (The Gordon Growth Model)
In the real world, shareholders usually expect dividends to grow over time. This makes the formula slightly more detailed:
\( K_e = \frac{D_1}{P_0} + g \) or \( K_e = \frac{D_0(1+g)}{P_0} + g \)
Where:
\(D_0\) = The dividend just paid (today)
\(D_1\) = The dividend expected in one year's time
\(g\) = The constant annual growth rate of dividends
\(P_0\) = The current market price (ex-dividend)
Common Mistake to Avoid:
Always check if the price given is "cum-div" or "ex-div". If it is "cum-div" (with dividend), you must subtract the upcoming dividend from the price before putting it into the formula. We only use the "ex-div" price in our calculations!
3. How do we find the Growth Rate (\(g\))?
If the exam doesn't give you "\(g\)" directly, you have two ways to find it:
Method A: The Retention Method (Gordon’s Growth)
This method assumes growth is fueled by the profits a company keeps and reinvests.
\( g = b \times r \)
Where:
\(b\) = The retention ratio (the % of profits kept in the business)
\(r\) = The return on new investment (often given as the return on capital employed)
Example: If a company keeps 40% of its profits and earns 10% on its projects, \(g = 0.40 \times 0.10 = 0.04\) or 4%.
Method B: The Extrapolation Method (Historical Growth)
This looks at what happened in the past to predict the future. The formula is:
\( g = \sqrt[n]{\frac{\text{Current Dividend}}{\text{Dividend } n \text{ years ago}}} - 1 \)
Step-by-Step for Extrapolation:
1. Count the number of growth periods (\(n\)). (Tip: If you have dividends for 2019 and 2023, \(n\) is 4).
2. Divide the latest dividend by the oldest dividend.
3. Take the \(n^{th}\) root of that result.
4. Subtract 1 to get the percentage.
4. Method 2: The Capital Asset Pricing Model (CAPM)
While the DVM focuses on dividends, CAPM focuses on risk. It says that shareholders need a basic "safe" return plus a "bonus" for taking on risk.
The CAPM Formula:
\( K_e = R_f + \beta(R_m - R_f) \)
Where:
\(R_f\) = Risk-free rate (e.g., return on government bonds)
\(\beta\) (Beta) = A measure of how risky the specific company is compared to the whole market
\(R_m\) = Market return (the average return of the stock market)
\((R_m - R_f)\) = The Equity Risk Premium (the extra return for moving from safe bonds to risky stocks)
Understanding Beta (\(\beta\)):
Beta tells us how sensitive a share is to market movements:
- \(\beta = 1.0\): The share moves exactly like the market.
- \(\beta > 1.0\): The share is riskier (more volatile) than the market.
- \(\beta < 1.0\): The share is safer (less volatile) than the market.
Analogy: Think of the stock market as a big ocean wave. A surfer with a Beta of 2.0 will go twice as high on the crest and twice as low in the trough. A surfer with a Beta of 0.5 will just bob up and down gently.
Did you know?
CAPM assumes that investors can "diversify" away specific risks (like a strike in one factory) by owning many different stocks. Therefore, they only expect to be rewarded for Systematic Risk (market-wide risks like inflation or interest rate changes) that cannot be diversified away.
5. DVM vs. CAPM: Which one to use?
In your F2 exam, you might be asked to discuss which method is better. Here is a quick comparison:
Dividend Valuation Model (DVM):
- Pro: Easy to understand; uses actual cash (dividends).
- Con: Hard to use if a company doesn't pay dividends; assumes growth is constant forever (which is rarely true!).
Capital Asset Pricing Model (CAPM):
- Pro: Considers the specific risk of the company relative to the market.
- Con: Relies on historical data to find Beta, and it’s hard to find a truly "risk-free" rate.
Summary and Key Takeaways
1. \(K_e\) is the return shareholders demand. It is a cost to the company when financing projects.
2. DVM Method: Use it when you have dividend data. Remember to use ex-div prices and \(D_1\) (next year's dividend).
3. Growth (\(g\)): Can be calculated via the retention method (\(br\)) or historical extrapolation.
4. CAPM Method: Use it when you have Beta and market risk data. It rewards investors for Systematic Risk only.
5. \(K_e\) Formula Recap:
- \( K_e = \frac{D_1}{P_0} + g \) (DVM)
- \( K_e = R_f + \beta(R_m - R_f) \) (CAPM)
Keep practicing these formulas! At first, they might look like "alphabet soup," but the more you use them, the more they will feel like second nature. You've got this!