How do we calculate cost of equity when shareholders’ capital does not carry interest like a bank loan? I usually start with a simple question: what return should investors require for taking on the risk of owning that stock?
Equity still has a cost: the required return, or the return shareholders demand. One way to estimate it is the Capital Asset Pricing Model (CAPM). This model links returns to systematic risk—the market risk that diversification alone cannot eliminate.
Disclaimer: all figures for Company X and Company Y in this article are dummy data for learning purposes. They do not represent listed companies or current market conditions. The choice of examples does not constitute advice to buy, sell, or hold shares, or a positive or negative judgment about any company. CAPM results are estimates based on assumptions, not promises of investment gains.
The formula to calculate cost of equity with CAPM
Ke is the cost of equity; Rf is the risk-free rate; β is the stock’s beta; and E(Rm) is the expected market return. The difference E(Rm) − Rf is the equity risk premium (ERP), also called the market risk premium. We can therefore also write the formula as Ke = Rf + β × ERP.
When you calculate cost of equity, use a single currency and a consistent time basis. Do not mix an annual Rf with a monthly premium. Beta has no units, but you should record the observation period and the frequency of the data used to estimate it.
Risk-free rate: choose a consistent benchmark
For valuations in Indonesian rupiah, the yield on rupiah-denominated government bonds is often used as an initial proxy. Choose a maturity close to the cash flow horizon. Ten-year bonds are commonly used for long-term valuations, but they are not a rule for every situation. Use the yield to maturity rather than the coupon rate, and specify the valuation date.
You can check yield curve data at Penilai Harga Efek Indonesia (PHEI). . Record the source, date, currency, and maturity whenever you update the model.
Government bonds are not automatically free of every risk, either. Their prices can change as interest rates move, and the issuer may still face default risk. In a valuation approach that adjusts for country risk, the risk-free rate can be estimated by subtracting an appropriate sovereign default spread from the government bond yield. Keep this approach consistent with the ERP framework so that country risk is not counted twice. You can find a discussion in Aswath Damodaran’s discount rate materials at NYU Stern.
Beta coefficient: understand the risk it measures
Beta measures how sensitive a stock’s return is to market returns. A beta of 1 means its average sensitivity to the market is roughly one-to-one, not that the correlation is perfect. A beta of 0.8 indicates lower sensitivity, while a beta of 1.5 indicates higher sensitivity. A negative beta means less than zero, not merely less than one.
However, a low beta does not automatically make a stock safe. A company may still face debt, liquidity, governance, or business risks. Beta also does not measure all of a stock’s volatility. Likewise, a high beta does not guarantee high realized returns or success in beating the market.
A portfolio’s beta is the weighted average of its stocks’ betas, with weights based on the market value of each position:
A portfolio beta of around one indicates market sensitivity of around one; it does not automatically mean the portfolio is safe. Read this figure alongside concentration, liquidity, and the risks of each business.
Calculating beta from paired returns
Ri is the stock return, and Rm is the benchmark index return. For a more rigorous CAPM estimate, regress the stock’s excess returns against the market’s excess returns: subtract the risk-free rate for the same period from each return. If the risk-free rate per period is constant, subtracting that constant does not change the slope.
Use stock and index prices from matching dates. Five years of monthly data can be a starting point, but a longer period is not always better when the business structure changes. To obtain 60 monthly returns, we need 61 price observations. Do not use data after the valuation date to estimate historical beta.
P is the price, and D is the dividend during the period. If the price rises from 1,000 to 1,030 and the dividend is 20, the price return is 3%, while the total return is 5%. Adjust for stock splits and corporate actions. If you use an adjusted close series that already accounts for dividends, do not add the dividends again. Aim to use comparable return measures for the stock and the index.
To learn about benchmark indices, see the Indonesia Stock Exchange’s information on stock indices. The IHSG, or Jakarta Composite Index, is a proxy for the domestic market, not the entire theoretical market portfolio in CAPM. You can also use vendor data, but check definitions, price adjustments, access permissions, and the beta methodology. Download options may change.
A dummy example and Excel formulas
The table below uses six fictional monthly return observations to make the calculation easy to check. This is an arithmetic exercise, not an adequate sample size for estimating a real company’s beta.
| Dummy period | Market (column B) | X (column C) | Y (column D) |
|---|---|---|---|
| M1 | −4% | −2.4% | −6.5% |
| M2 | 2% | 2.4% | 2.5% |
| M3 | 5% | 4.8% | 7% |
| M4 | −1% | 0% | −2% |
| M5 | 3% | 3.2% | 4% |
| M6 | −3% | −1.6% | −5% |
If the header is in row 1, calculate X’s beta with =SLOPE(C2:C7,B2:B7), which returns 0.8. For Y, use =SLOPE(D2:D7,B2:B7), which returns 1.5. The first argument contains stock returns; the second contains market returns.
For X, =COVARIANCE.S(C2:C7,B2:B7)/VAR.S(B2:B7) gives the same beta as SLOPE. The COVARIANCE.P and VAR.P pair also works. Do not mix population covariance with sample variance, because their denominators differ. If the results do not match, check the dates, number of observations, empty cells, and rounding. Replace commas with semicolons if your Excel settings require it; see Microsoft’s SLOPE documentation.
Market return and the market risk premium
CAPM requires an expectation of future returns. Historical returns help us develop assumptions, but they do not automatically become expected returns. Also remember that a price index does not include dividends in the way a total return index does.
The arithmetic average is often used to estimate a single-period return. The geometric average summarizes historical compound growth. For example, a return of +20% followed by −20% gives an arithmetic average of 0%, but a geometric average of approximately −2.02% per period. The geometric average is therefore not automatically the best input for CAPM.
In Excel, create a gross return column containing 1 + return, then use =GEOMEAN(range_gross_return)-1. Do not apply GEOMEAN directly to raw returns. All factors entered must be positive.
This formula annualizes the monthly geometric result; it does not turn it into a forecast. An alternative way to estimate ERP is the implied premium approach. For updates, read NYU Stern’s country risk premium data and methodology. Match the date, market, and risk framework before using the figures. Do not add a country risk premium again if it is already included.
The Security Market Line and examples for Company X and Company Y
Now let’s calculate cost of equity using dummy annual assumptions: Rf = 5% and ERP = 6%, so E(Rm) = 11%. The betas come from the earlier exercise. These figures do not represent the Indonesian market on any particular date.
The Security Market Line (SML) plots beta on the horizontal axis and required return on the vertical axis. In this example, the line starts at 5% when beta is zero, with a slope equal to the ERP of 6%.
When beta = 1, the cost of equity = 11%, which is the expected market return, not the 6% ERP. With a positive ERP and other assumptions unchanged, a beta greater than one produces a required return above the expected market return. The SML describes a relationship within the model, not a guarantee of returns for every stock on the Indonesia Stock Exchange.
Try a sensitivity check: if ERP rises to 7%, the result for X becomes 10.6%, and Y becomes 15.5%. Changes in assumptions can materially affect valuation. When you calculate cost of equity for a real company, document the inputs and check several scenarios.
Applying the result to WACC and wrapping up
Cost of equity is a component of WACC, alongside the after-tax cost of debt. For a simple capital structure without preferred stock:
E and D are the market values of equity and debt; Kd is the pre-tax cost of debt; and T is the relevant tax rate. The tax benefit of interest depends on the applicable rules and the company’s ability to use it. We can continue with how to calculate cost of debt and read about company financial ratios to understand the business’s financial condition.
For me, the value of learning to calculate cost of equity is that it makes risk assumptions clear and testable. Choose consistent benchmarks, estimate beta using well-organized data, and distinguish historical returns from expectations. Use the result as an analytical tool, then check actual data and the nature of the business before drawing investment conclusions.
Sources
- Lawrence J. Gitman & Chad J. Zutter, Principles of Managerial Finance, 13th edition.
- Yahoo Finance, the financial data reference in the original article; access and methodology should be checked again.
- Investopedia — Capital Asset Pricing Model, a reference for explaining the concept.
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