Estimating Cost of Equity

In financial theory and practice one of the key fundamental metrics is the discount rate. Investors use discount rates in multiple contexts. In equity valuation there two main applications of discount rates - correcting cash flows for the concept of “Time Value of Money” and some models use discount rates as the expected performance of the financial asset. The most widely used discount rate is the cost of equity because it reflects the minimal required rate of return by investors and also it embedded with all risks from investing in the particular stock. There is a wide variety of models that can be used to estimate the cost of equity. In our practice we use the Capital Asset Pricing Model extended to include Country risk.

1.  Extended CAPM

Capital Asset Pricing Model is a market equilibrium model that describes the relationship between risk and return. Basically with CAPM we are able to give price to the risk and this price is our minimal required rate of return by investors a.k.a. cost of equity and can be used as a discount rate. Since CAPM is describing the relationship between risk and return and the discount rate must “include all risks to the company” therefore we are calculating the risk and using this relationship we get the premium (compensation) that investors require. The traditional equation for CAPM is (1):

One of the best parts of CAPM is the decomposition of risk into systematic and unsystematic:

Unsystematic risk is also known as stock-specific risk. On a portfolio level it can be diversified by including more assets into your portfolio. However unsystematic risk cannot be diversified since it is inherent in all securities. Therefore systematic risk must be included in the estimation of CAPM. Furthermore we divide the systematic risk into three groups:

·       Equity market risk – it comes from the investing in the stock market and it is inherent to all stocks

·       Country specific risk – stock on a local market are faced with similar risks that arise from the economy of the country. Therefore this is also systematic risk. In theory it can be diversified by investing in global portfolio (exposure to many markets is require) however this is rarely the case for both institutional and individual investors

·       Industry specific risk – operating risks may vary across different types of business, but for the companies that operate in given sector are facing common challenges, therefore this risk can also be categorized as systematic. However it is practically possible for the investor to build a portfolio that doesn’t have industry risk by managing the exposures to different industries. Furthermore this is more likely rather than diversifying across different markets. Therefore we exclude the industry risk in the estimation of CAPM.

It is evident that the CAPM must be extended to include Country-specific risks since the latter cannot be diversified by investors. Therefore the practical equation for cost of equity becomes (2):

The cost of equity for any company is a function of the risk free rate, country risk premium and equity market risk premium corrected with the stock’s exposure to market risk. Now in the next section we are going see how to estimate each component in MS Excel.

1.  Estimating Cost of equity

Risk-free rate

In practice the risk free asset does not exist. However we can use proxy. The closes asset class to the concept of risk-free are the government bonds and specifically those of developed economies. Therefore for risk-free rate we take the average yield of USA 10-Y T-bills. If we want to improve the accuracy of this estimation we can also employ some statistical model[1] to forecast the future yield of the USA government bonds. For this example using the historical average is sufficient.

Beta

Next step is calculate the exposure to the market risk which also known as beta. The most common approach to estimate beta is to use statistical regression between asset returns vs. the market excess return. However it is proven that this estimate is noisy since it has rather large error. Therefore we are going to use different approach to estimate betas. In economic terms the exposure to market risk is the level of risk that the business has in relation to the market. Therefore if we use the average beta coefficient for similar types of companies in the sector then the statistical errors from the regression will average out and we are going to get clearer estimate. However different companies use different leverage and therefore have different financial risk. To tackle this issue we have to unlever the betas before averaging using (3):

As you see we have created a peer group of 5 companies that operate in the Consumer electronics sector in Taiwan. Next we have their market betas and data on the D/E coefficient. Using (3) we get the unleveraged betas column J:

Next step is to find the central moment of this sample of unlevered betas. We use the median as a measure of the central moment and we get the average beta to be 0.64 for this peer group. Final step is to account the financial risk of Foxconn using the D/E ratio and the inverse equation:

Finally we arrive at the beta for Foxconn of 0.72 and this number is very usable since it almost does not have any assumption behind it and the errors from the statistical regression is minimized.

Equity Risk Premium (ERP)

Finding the required premium for investing in the equity market is a tricky task. Before we start discussing how to do it technically lets first make clear that in our model the best way to do it is to approximate it to the premium of matured equity market. In this case we are using the USA capital market represented by the broad market index S&P 500. Technically we can use the historical difference between the index returns and the risk-free rate but this would have high estimation error. Therefore we adopt a forward-looking approach using the implied equity risk premium:

Implied Equity Risk Premium (ERP) – average rate that all investors use to discount the expected earnings of the market portfolio in order to set the current price of the market portfolio.

TO make this work we need first a proxy for the market portfolio and S&P 500 is used. Next we need a valuation model. For simplicity lets use the one period GGM method:

Finding the inputs is relatively easy. For the expected earnings of the S&P 500 portfolio we can use readily available estimates found on internet (depends how much you trust given source!). As for the perpetual growth it is assumed to be the long term inflation. Finally we for which value of ERP the estimated value is equal to the price of S&P 500. On fig. 3 we have set up the valuation model and the necessary inputs:

To find the implied ERP that equates the value and price of S&P 500 we can use the Goal Seek tool in MS Excel. It can be found by “Data>What-if Analysis> Goal Seek”

This tool optimizes function (in a target cell) to certain value by changing some of the inputs. Therefore we set the difference between Value and Price of S&P 500 as a target cell, and then by changing the cell of Implied ERP we get the result of 6.52% which is quite logical result. Keep in mind that currently FED is raising the interest rates and this has impact on the equity risk premium.

Country Risk Premium (CRP)

Since we used the equity risk premium for a developed market we have to add the specific country risk for the economy where the company operates. In this example we are going to use the credit rating approach to find the country risk premium. Foxconn is a Taiwanese company therefore we have to check what is the credit rating of Taiwan and see what premium is for such rating in the table below:

Using Moody’s scale we see that the credit rating for Taiwanese government bonds is Aa3 that relates to 68 basis points of premium. This scale has been created by regression defaulted securities and the credit rating in order to determine how much should be the premium for risk of the rated securities. As you see such scales are readily available on internet and supported by academics and analysts. Depending on the sample and the exact methodology these premiums may vary in different sources, therefore you should check at least two different sources on internet.

Putting all together

Once we have all elements for the extended CAPM we can use the equation and calculate the cost of equity for Foxconn. The final result is presented: