Under the risk premium approach, a risk premium is added to the yield (YTM) on the company's bonds (to reflect the higher risk borne by shareholders) to estimate cost of equity.

That is, cost of equity = Bond yield + risk premium.

The equity risk premium can be calculated in two ways - historic yield spread method and ex-ante yield spread based on DCF analysis.

The historic risk premium is the difference between the average of annual returns on a stock index in the past (say 10 years) and the average of annual returns on a bond index over the same period.

Historic yield spread = Average return on stock index - Average return on bond index.

The normal practice is to use geometric return on the indices. The historic premium is then added to company's bond yield to obtain an estimate of cost of equity. The shortcoming of this method is that the estimate is affected by the period chosen and end points of the period.

Under the ex-ante (expected) risk premium method, the average expected future return on a group of stocks, say index stocks, is calculated and the concurrent risk free rate is subtracted from it. The yield on long term T-Bond could be taken as Rf.

The DCF model may be used to estimate expected return on stocks. A survey of analysts' forecast of growth rate in dividends may be used as surrogate for 'g' in the equation.

The simple logic underlying risk premium approach is that if the premium is expected to remain constant overtime, then the constant premium may be added to the prevailing interest rate to obtain cost of equity. The risk premium should be estimated for fairly long periods of time. Academic studies make use of data for few decades.

5.7 Industry Beta

The beta of any individual asset is

Now consider a portfolio with weights Wp. The beta of the portfolio is

The betas of individual stocks tend to be fickle. They change quite rapidly. Portfolio betas, on the other hand, are more stable. Their standard errors are generally lower than that of individual betas. The weighted average of betas of stocks in the same industry group, say Pharma, is called industry beta, the weights are market capitalization (number of shares outstanding multiplied by market price) of individual companies. What purpose does industry beta serve? Let's suppose a company is in the process of appraising a banking project. So its executives are interested in estimating cost of equity for the project. They can use the parent company's beta or the banking industry beta. Common sense tells us that the banking industry beta is more indicative of what investors expect from that project. In other words, expected return is project specific. Exhibit 5.6 presents the cost of capital for several industry groups in the USA.

### 5.8 Fundamental Beta

Since firm characteristics change over a period of time we would expect beta to change. So putting too much emphasis on history might be unwise. Consequently, some academicians like Beaver, Ketler and Scholes (1970) and Rosenberg and Marathe (1975) have attempted to establish relationship between systematic risk and its determinants like payout ratio, growth, leverage, liquidity ratio, size of the firm,

 Industry Industry lev. Cost of equity Cost of debt Debt/capital Cost of capital

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