Risk and Return Portfolio Diversification and the Capital Asset Pricing Model the Cost of Equity Case Study

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Finance

There are three different models that can be used to estimate a company's cost of capital. Basically, each of these three is used to estimate the cost of equity. The cost of debt is usually calculated on the basis of the current weighted average of the yield to maturity on the company's debt. Thus, it is the cost of equity that must be calculated. The cost of equity reflects the return that the shareholders need to be paid in order for them to own the stock. This have given us three major approaches to calculating the cost of equity.

The first of these is the capital asset pricing model. The formula for this is:

Investopedia (2013)

The cost of equity therefore reflects three major components. The first is the risk free rate, which is inherent in all securities. The second is the market risk premium, which is added to the risk free rate for any given market. Third is the firm-specific risk, which in this case is reflected by the beta. The beta is the correlation of the stock's price to the value of the market. Thus, it reflects the volatility level of a stock relative to the market, in essence the firm's risk beyond the market risk premium.

The underlying assumption of this model is that investors are essentially paying for past returns, of both the stock and the market, along with the current risk free rate.

The second model is the dividend growth model. This model assumes that investors are basically paying for the cash flows that come from the dividends. The dividends are the only cash flows that matter in this model, because they are the only ones that reliable. A rational investor, this model assumes, would not pay for capital gains. Those would be priced into the stock already so only the expected future cash flows from dividends are included in the value of the stock. This model is based on the following formula:

Source: Investopedia (2013)

So the value of the stock reflects the dividend today, the growth rate of the dividend going forward, and the firm's cost of capital.

The third model is the arbitrage pricing theory. This has the basic mathematical structure of the capital asset pricing model but it uses different inputs. Whereas the CAPM takes the cost of equity as relating to the correlation between the price of the stock and the general market, APT measures the price of the stock vs. multiple macroeconomic variables. The market can be one, but there are usually several others as well. The underlying logic of this methods is that there are macroeconomic predictors of success, so if those can be understood, one can determine a more accurate price for the security. This of course allows us to derive a cost of equity. So any number of different variables can be taken into consideration. Furthermore, because different variables are used, they need to be given a weighted average. The user can choose the variables and the weights for them, which means that any given person will do the APT calculation for a company differently, which is not the case with the CAPM or the dividend growth model.

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The accuracy of these models is up to debate, but it seems most likely that the smartest of these models is APT, because it is customizable. It has far more data points, which is likely to increase its accuracy over time.

However, the arbitrage pricing theory is not particularly easy to use. Those data points do not gather themselves. It takes a lot longer to do the APT calculation, a day or two per stock, in order to get the cost of capital. Also, because the APT calculation is subjective, it is also a garbage in, garbage out sort of equation. If the wrong variables and weights are chosen, the output is not going to be particularly useful. For this reason, caution must be exercised in using this model. CAPM and the dividend growth model are much easier to use, requiring very few data points and being based on metrics that are commonly available. This is another problem with APT -- you need to get the data yourself. So in CAPM, the beta is used as the correlation with the market, but the beta is available online. The equivalent correlation coefficient used in the multiple macroeconomic measures in APT would need to be calculated, making it a vastly more complex calculation.

Lastly, one must understand the assumptions built into each model. The dividend growth model has key assumptions, the biggest being that the investors are only investing for the dividends. This is entirely unrealistic. It rests on the idea of the perfectly rational investor. Such a person does not exist. The reality is that investors are not perfectly rational. Many invest strictly for capital gains. Ultimately, the dividend growth model explains this as people investing for future dividends, but there are company that are on record as having no intention of paying a dividend, and these companies still have stocks valued above zero. Thus, the key underlying assumption of the dividend growth model does not actually make sense. The key underlying assumptions of CAPM and APT actually make little sense as well. One of the first things you learn in investments is that past performance is not indicative of future performance. Yet, that is the underlying assumption of both of these models, where the cost of capital going forward is based on the past performance of the stock. So while these models are better than the DGM, they also have flawed assumptions.

My recommendation of a model to estimate our cost of equity is the capital asset pricing model. This is the model that represents the best balance between having reasonable assumptions and ease of use. The APT is fine, but it is risky in that it might not be any more effective than any other model, but it is very difficult to use. The dividend growth model might work for firms that are slow growing and have substantial dividends, but the underlying assumptions of that model….....

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