## Friday, October 21, 2011

### Security Market Line and Beta Basics

CFA Level 1 - Corporate Finance

The security market line(SML) is simply a plot of expected returns of investments with respect to its beta, market risk. Expected values are calculated with the following equation:

Formula 11.15

Es = rf + Bs(Emkt - rf)
Where:
rf = the risk-free rate
Bs = the beta of the investment
Emkg = the expected return of the market
Es = the expected return of the investment

The beta is thus the sensitivity of the investment to the market or current portfolio. It is the measure of the riskiness of a project. When taken in isolation, a project may be considered more or less risky than the current risk profile of a company. Through the use of the SML as a means to calculate a company's WACC, this risk profile would be accounted for.

Example:When a new product line for Newco is considered, the project's beta is 1.5. Assuming the risk-free rate is 4% and the expected return on the market is 12%, compute the cost of equity for the new product line.

Cost of equity = rf + Bs(Emkt - rf) = 4% + 1.5(12% - 4%) = 16%
The project's required return on retained earnings is thus 16% and should be used in our calculation of WACC.

Estimating Beta
In risk analysis, estimating the beta of a project is quite important. But like many estimations, it can be difficult to determine.

The two most widely used methods of estimating beta are:

1.Pure-play method
2.Accounting-beta method

1. Pure-Play Method
When using the pure-play method, a company seeks out companies with a product line that is similar to the line for which the company is trying to estimate the beta. Once these companies are found, the company would then take an average of those betas to determine its project beta.

Suppose Newco would like to add beer to its existing product line of soda. Newco is quite familiar with the beta of making soda given its history. However, determining the beta for beer is not as intuitive for Newco as it has never produced it.

Thus, to determine the beta of the new beer project, Newco can take the average beta of other beer makers, such as Anheuser Busch and Coors.

2.Accounting-Beta Method
When using the accounting-beta method, a company would run a regression using the company's return on assets (ROA) against the ROA for market benchmark, such as the S&P 500. The accounting beta is the slope coefficient of the regression.

The typical procedure for developing a risk-adjusted discount rate is as follows:

1. A company first begins with its cost of capital for the firm.
2.
The cost of capital then must be adjusted for the riskiness of the project, by adjusting the company's cost of capital either up or down depending on the risk of the project relative to the firm.

For projects that are riskier, the company's WACC would be adjusted higher and if the project is less risky, the company's WACC is adjusted lower. The main issue in this procedure is that it is subjective.

Capital Rationing
Essentially, capital rationing is the process of allocating the company's capital among projects to maximize shareholder return.

When making decisions to invest in positive net-present-value (NPV) projects, companies continue to invest until their marginal returns equal their marginal cost of capital. There are times, however, when a company may not have capital to do this. As such, a company must ration its capital among the best combination of projects with the highest total NPV.
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