CAPM

The usage of CAPM requires us to estimate three things

* The value of rf
* The beta of the company
* The risk premium

Though empirical evidence suggests that CAPM does not give the correct expected returns and various models have been proposed over time in order to overcome the problems associated with the CAPM equation. But due to the simplicity associated with using CAPM it still is one of the widely used methodology in the industry.

Now coming to the questions that were raised, first let us answer the value of Rf. The value of Rf should be such that it matches the duration of the cash flows. Since we assume the business is going to last for perpetuity, the longest available Rf is used which in case of India is the 30 year government bond. For portfolio management on the other hand we can use 1 year Rf.

Now for calculation of beta we can either choose the Sensex or the Nifty for regressing with the stock price. It has been found empirically that both give the same result. Now what should be the duration for which we should consider the stock prices should we take the data for the past 2 years, 5 years, 10 years. The answer can be looked at from the factors affecting beta. If we can say that the operational risk and the financing risk of the company has remained constant over certain period then that should be the period that we should be considering.usually we take a period of 2-3 years for the calculation of beta.

Now second question is should you take the monthly return or the daily returns. If we go by larger the data better it is then we should be taking the daily returns only but this logic doesnot hold good if we consider the following two facts
* Daily prices are highly volatile
* Illiquid stocks(Stocks for which no trade has taken place) might be a problem because we will be underestimating the returns in this case.

Mathematically

Week day Price Price shown in databases Returns
F 50 50
M - 50 0%
T - 50 0%
W 51 51 some no
T 52 52 some no
F - 52 0%

So now the beta is the ratio of covariance of market with stock and variance of market. Covariance of market will come down as the correlation coefficient between the stocks would be less given that some values are 0. Therefore it would be an underestimation of the value of beta.

There can be situation when the beta might have changed significantly for the company in order to take care of the same, we can see the beta for the other firms in the industry and unlever them to get an average unlevered beta and then lever the beta again with the firm specific debt/equity ration and get the corresponding beta value.

Beta(levered)= Beta unlevered *(1+(1-tax rate)*D/E) - Beta debt *D/E(1-t)

Beta debt is calculated in a reverse process. We generally include the cost of debt first and then calculate the beta of the stock.

Now Rm-Rf has generally been found out to be 7% in case of US and 10% in case of India.

Operating Income

For the purpose of valuation, the most essential component that needs to be calculated(For present year) and estimated(For future years) is the operating income. The best way to decided the operating income is not through the sales figure given in the profit and loss account. The best way is to visualize the operating income as constituting of those parts which are recurrent in nature.

This classification has been proposed by Mckinsey. They classify the income as recurring and non recurring. The recurring part of the income is due to day2day operations where as the non-recurring part is generally a one time event. Let us say for example Bajaj Auto, the company has 50% of its assets in investments so not considering the income from these investments would not be a good option as the income would be earned each year.

In short the rule is "If it is recurring, it is operating income"