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How to Calculate The Cost of Equity with CAPM Method

Equity in addition to debt, is one of the sources of capital of a company.

For every source of capital, both equity and debt, of course there are costs. If the cost of debt is interest, then the cost of equity is the required return that shareholders expect as compensation from bearing the risk of their investment into the stock.

Of course, the higher the risk of an investment, the higher the return expected by investors.

The Capital Assets Pricing Model (CAPM) is a model used to calculate the cost of equity.  This model connects the required return on an investment with the level of risk to the investment.

The level of risk on an investment (including stocks) is represented by a coefficient (beta).

For more details, here is the formula from CAPM:

formula CAPM

 

Let’s review one by one the components of the Capital Assets Pricing Model (CAPM):

 

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Risk Free Rate of Return (Rf)

Risk free investment is usually measured by the yield of a 10-year fixed rate government bond.  This is because government bonds are a type of investment that is (almost) completely risk-free.

For the Case of Indonesia, the data rate of government bonds can among others be seen on the website “Penilai Harga Efek Indonesia“, as I quote below:

Risk Free Indonesian Government Bonds
Risk Free (yield of goverment bond 10 Y)
Source : www.ibpa.co.id

As we can see in the picture above, the rate of Government Bonds with a tenor of 10 years (at the time this article was written – February 26, 2021) is 6.774%.

This rate can be used as a reference for Risk Free (Rf) in Indonesia.

Beta Coefficient

Beta coefficient is a relative measure of the level of risk on a particular asset (which is not diversified) to the average risk level of another asset.

In the case of shares this can be interpreted as the level of volatility or sensitivity of a stock to market movements. In Indonesia, market movements are represented by IHSG (Indeks Harga Saham Gabungan or also known as Jakarta Composite Index- JCI)

    • The value of the beta coefficient 1 means that the stock has a positive correlation and moves exactly the same as the market movement (IHSG), if let’s say IHSG moves up 1%, then a stock with a beta value of 1 also (tends) to move up 1% and vice versa. 
    • A beta coefficient value smaller than 1 (one) means the stock is less volatile than the market (IHSG). This type of stock is less risk than the market, but because the risk is directly proportional to return, then of course the potential return of a stock with a beta smaller than one is also smaller than the average market return.

An example for a stock that has a beta value of 0.75, if for example IHSG is down 1%, then this stock (tends to) only fall by 0.75% and conversely if IHSG moves up 1%, then this stock (tends to) only go up 0.75% (I use the word “tends” to remind that this is statistically, does not mean all the time exactly so)

    • A beta coefficient greater than 1 (one) means that the stock is more volatile than the market (IHSG). This type of stock is more risk than the market. The principle is the same in high risk high return investments, so in addition to higher risk, the potential return of stocks with beta greater than one is also greater than the average market return.

For example, for a stock that has a beta value of 2, if for example the IHSG drops 1%, then this stock will tend to fall twice (2%) and vice versa if the IHSG moves up 1%, then this stock will also (potentially) increase twice as well. (2%)

    • “What if the beta coefficient is negative (smaller than 1) ?”,

It means that the stock has a negative correlation (opposite) compared to market movements, for example if there is a stock with a beta value of -2, when the IHSG rises 1%, then the stock (tends) to fall 2%, and vice versa if IHSG for example drops 1%, then the stock (tends) to rise 2%.

Here is the formula or formula of the beta coefficient:

Beta Coefficient Formula

or

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beta_coefficient_slope

This beta coefficient reflects the level of risk and expected return of an investment. The higher the beta value means the higher the risk of investing in the asset / company, so investors will demand a higher return on equity as compensation from bearing the risk.

Beta coefficient data for various stocks can be obtained from several sources that provide financial data such as Yahoo Finance, Bloomberg or Reuters, but in order to more easily understand where the number comes from, let’s try to calculate the coefficient itself.

For example, I will show you how to calculate the beta of two stocks, namely TELKOM (TLKM) and ANTAM (ANTM).

Disclaimer: The selection of these two issuers as examples in this article is only random, just to further clarify and apply theory into practice. I do not intend to recommend or not recommend the purchase or sale of the two stocks that serve as examples.

As a data source, in this example we use Yahoo Finance, we can download historical data on transactions of various stocks and also their market indices, (including IHSG) here.

For more details I show in the image below:

TLKM Stock Historical Data on Yahoo Finance
TLKM Stock Historical Data on Yahoo Finance
Source : Yahoo Finance

First, for Telkom, type the Telkom issuer code (TLKM) in the search field. Then in the Historical Data Tab, in the time period we determine the data retrieval period.

We take data for 5 years, (you can choose “5 Y”, but I suggest to choose the date manually). In this case, I do data retrieval at the end of Feb 2021, I choose the data retrieval period of 5 years which is 1 Feb 2016 – 1 Feb 2021).

Then in the Frequency column select the “Monthly

Then click “Apply” then “download“, the data will be downloaded to our computer in .csv format. We can convert it to excel format (in Microsoft Excel select import, and follow the steps). Below is an example of the display of data that has been converted to excel:

Historical TLKM data from Yahoo Finance
Excel display of TLKM Historical Data downloaded from Yahoo Finance

Antam Stock Historical Data (ANTM) as well as other stocks can be downloaded on Yahoo Finance in the same way.

Here we need a comparison of market data, please also download historical data IHSG – Jakarta Composite Index (code ^JKSE on Yahoo Finance)

We process the data, take the close data only in each month, then calculate the retun.

To calculate the return in a given month, say month n, use the following simple formula:

Formula for calculating stock returns
Formula for calculating stock returns

Arrange the data side by side between the stock return data that we will calculate the beta value with the market return data (IHSG), then we calculate the beta coefficient using the formula above. For more details, here we show the data that I have compiled and calculated:

Calculating TLKM beta coefficient from historical data
Calculating TLKM beta coefficient from historical data

because the data is long (up to 60 rows), for ease of view I only show the first three rows and the last three rows of data.

Calculations with both formulas above (covariance formula or slope formula) show more or less the same result.

Telkom’s beta value at the time of data was obtained (February 2021), with the covariance formula is 0.80, and with slope formula is 0.81

In the same way, we calculate the beta coefficient for Antam, the results I show as the picture below:

Calculating ANTM beta coefficient from historical data
Calculating ANTM beta coefficient from historical data

Antam’s beta value at the time the data was obtained (February 2021), with the covariance formula is 2.25 and with slope formula is 2.28

Okay, now try to compare the calculation above with beta coeffcient data from other sources that provide financial data.

In this case, I compare it to Reuters. Here I quote the beta values of Telkom (TLKM) and Antam (ANTM) from the Reuters website on the same date as the calculations above:

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TLKM beta coefficient data from Reuters 26 Feb 2021
TLKM beta coefficient data from Reuters 26 Feb 2021
Source : Reuters

 

ANTM beta coefficient data from Reuters 26 Feb 2021
ANTM beta coefficient data from Reuters 26 Feb 2021
Source : Reuters

 

We can see that the beta value for both companies is the same as the manual calculations we do (with the slope formula), which is 0.81 for Telkom (TLKM) and 2.28 for Antam (ANTM).

Beta values for companies engaged in commodities (mining or plantations for example) tend to be high, because commodity prices are volatile.

This beta value may vary between several sources, this may be due to differences in the duration of the data used for calculations and/or the data/ assumptions used.

If you are a stock investor. You can apply an understanding of this beta coefficient in compiling a stock investment portfolio, adjusting to your characteristics in taking risks. 

Try to find the beta value of the stock you own, then calculate the weighted average against the value of each stock. Is it worth more than 1 or less than 1?  

(there is nothing wrong or right), if you are a risk taker who is determined to beat the market return, then it does not matter if you prefer stocks with a beta of more than 1. However, if you are a safety player, you should average the weighted beta coefficient of your stock portfolio to range in number one.

Market Return (rm)

Market Retun is the rate of return of the Market, in the case of Indonesia, is the return of the Composite Stock Price Index (IHSG) or also known as the Indonesia Composite Index (ICI).

Let’s see how much the annual return of IHSG in the last 21 years in the table below:

IHSG (JCI) Return Period 1999-2021
IHSG (JCI) Return Period 1999-2021
Source : Pusatis.com

On an arithmetic average, the annual return of IHSG (1999-2020) is 15.8%.

This gives a rough idea of market return of stocks in Indonesia.

To calculate the average return of an investment is usually used geometric average (which takes into account the factor of interest interest or compounding effect).

The geometric mean formula is as follows:

geometric mean formula

“Is that difficult?”

but don’t worry with the help of spreadsheet programs like Microsoft excel we can calculate geometric flats easily, 

just enter the formula     =GEOMEAN(range-data).

Let’s try to calculate the Market Return of IHSG with geometric averages

First, we download first in Yahoo Finance monthly historical data of IHSG in the desired period, for example the period 1999-2020 (so that we can compare with the average arithmetic of annual return as tabled above).

How to download the data is the same as described above.

Then we do the following:

    • from close data every month, we calculate the return (close data of the month is reduced the previous month’s close data and then divided by the previous month’s close data)
    • To calculate the geometric average, the data must be positive, therefore we add 1 to all the data return per month that we have calculated.
    • we calculate using a geometric mean formula, in excel just type =GEOMEAN(range-data)
    • Because in the previous step of the data we added 1, we return the result by subtracting 1. This is the average monthly gemometric return from IHSG in the period 1999-2020 (i.e. 1.02%)
    • Then we annualized with the following formula:
Annualized_return_formula
Formula for annualized monthly returns from geometric mean

thus producing an annual geometric average of IHSG of 12.98%

More details can be seen in the picture below:

IHSG_market_return_calculation
Calculation of the Market Return of the IHSG (JCI) for the 1999-2000 period with a geometric average

 

Security Market Line

From the calculations that we have done, we get the following numbers:

    • Risk Free (Rf) = 6.774%
    • Market Return = (rm) = 12.98%

If we enter the two data above in the CAPM formula:

formula_CAPM

And we draw on a graph with required return (rs) as the y axis and beta coefficient as the x-axis, then we will get a graph called Security Market Line (SML), with Risk Free (Rf) as the intercept (cut point of the graph with y axis).

Difference between Market Return = (rm) and Risk Free (Rf) = 12.98 % – 6.774% = 6.21 % called Market Risk Premium

For more details, let’s look at the graph below:

Indonesian Security Market Line Chart (as of February 2021)
Indonesian Security Market Line Chart (as of February 2021)

Because we use Risk Free Indonesia data (from the 10-Year Government Bond rate as of Feb 26, 2021) and Market Return data from IHSG (geometric average period 1999-2021), the security market line (SML) above applies to all stocks listed on the Indonesia Stock Exchange (IDX).

note, this graph is valid for a limited period of time (data calculated in Feb 2021). The graph will change if the rate of government bonds changes and also if the assumptions, data retrieval periods and methods used in calculating market return from its IHSG are also different.

So if you are reading this article in 2025 for example, please recalculate Risk Free (Rf) and Market Return (rm) in Indonesia according to the conditions at that time 🙂

With this Risk Free (Rf) and Market Return (rm) Indonesia data, we can calculate the required return or cost of equity from various Companies (listed on the IDX).  

Simply get the beta value of the stock you want to find the cost of equity in a source that provides financial data such as Reuters, Bloomberg or Yahoo Finance, or calculate it yourself in a way as I explained earlier. Then enter it into the cost of equity formula with Risk Free (Rf) and Market Return (rm) values as mentioned above.

For example, let’s try to calculate the cost of equity Telkom and Antam from beta data that we have calculated before it.

beta coeefficient for Telkom (TLKM) = 0.81, and for Antam (ANTM) = 2.28

We enter the data in the FORMULA CAPM (Capital Assets Pricing Model), then we will get:

    • rs (required return or cost of equity) Telkom (TLKM) = 6.774% + [0.81*(12.98%-6,774%)} = 11.80%
    • rs (required return or cost of equity) Antam (ANTM) = 6.774% + [2.28*(12.98%-6,774%)} = 20.92%

To be clearer, we can also enter the two values on the Security Market Line (SML) chart, as shown below:

Grafik Security Market Line Indonesia (per Februari 2021)
Grafik Security Market Line Indonesia-dengan data TLKM & ANTM (per Februari 2021)

From the chart above we can also conclude, if the beta coefficient of a company is equal to 1 (one), then the cost of equity will be exactly the same as the Market Risk Premium (6.21% in this case), while if the beta coefficient is greater than one then the cost of equity will also be greater than the Market Risk Premium and vice versa.

As explained earlier, the cost of equity from companies with high beta coefficients will certainly be higher than companies with stocks that have a smaller beta value, this is because the expected return is directly proportional to risk (remember the basic principle in investing: high risk high return).

Furthermore, the cost of equity that we calculate with this CAPM method, has further benefits because it is part of the Weighted Average Cost of Capital (WACC).

This WACC is a weighted average of a company’s capital costs that is very beneficial in determining the investment decisions and valuation of company shares.

Also read my article that explains the cost of debt (other components forming WACC), WACC calculations and Stock Valuation :

 

If you have any questions, or suggestions, feel free to write them down in the comments section at the bottom of this article.

 

Source :

This post is also available in: Indonesian

Daniel
Danielhttps://danieel.id
Lahir di Palembang pada bulan November 1981, saya menyelesaikan S1 di Jurusan Teknik Kimia Universitas Sriwijaya, dan S2 Master of Business Administration (MBA) di Sekolah Bisnis Management Institut Teknologi Bandung (SBM-ITB). Bekerja di salah satu BUMN dan tinggal di daerah Jakarta Selatan.

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