# Pure Play Method

Pure play method is an approach used to estimate beta coefficient of a company whose stock is not publically traded. It involves finding beta coefficient of a pure play, a public listed company having single business focus; unlevering it and then relevering it at the first company's capital structure to find the beta coefficient.

Pure play method is also used to find cost of capital for a project that is different from the company's mainstream business. For example, if a power engineering company is interested in creating a search engine and providing associated services, it should evaluate the project using the cost of capital determined by un-levering and re-levering beta coefficient of a pure play engaged in search engine business such as Google, etc.

## Formula

In order to estimate (equity) beta coefficient of (a private) company A, you need to find (equity) beta coefficient of (a public ) company B by regressing return on its stock on the return on the relevant stock index and then carry out the following calculations.

$$ Unlevered\ Beta\ of\ B \\ = \frac{(Equity)\ Beta\ Coefficient\ of\ B}{1 + DE_B × (1 − Tax\ Rate_B)} $$

(Equity) Beta A = Unlevered Beta of B × (1 + DE_{A} × (1 − Tax Rate_{A}))

Where *DE _{A}* and

*DE*are the debt to equity ratios of company A and B respectively.

_{B}## Example

You are an assistant to the corporate finance director at Lomoro Systems Inc. (LS), a privately-owned defense contractor. The group is interested in investment in electric vehicles. The director is working out the appropriate discount rate to use in the analysis and has asked you to find the relevant beta coefficient. LS has a debt to equity ratio of 1.5 and applicable tax rate of 25%.

**Solution:**

Investment in development of electric vehicles is drastically different from Lomoro Systems current business. It would be inappropriate to use its current cost of capital to value the project with significantly different type and level of risk. The pure play approach is appropriate.

Tesla Motors Inc. (TSLA) is a pure play in the business in which LS is interested. Its beta coefficient is 0.7, its debt to equity ratio is 2 and relevant tax rate is 35%.

The (equity) beta coefficient is unlevered as follows:

Unlevered Beta of TSLA

= 0.7 ÷ (1 + 2 × (1 − 35%))

≈ 0.3

Which in turn is relevered as follows:

(Equity) Beta for LS Project

= 0.3 × (1 + 1.5 × (1 − 20%))

= 0.66

1.0.66 is the appropriate beta coefficient to be used in calculation of appropriate cost of equity for LS which in turn is used in calculation of appropriate WACC.

Written by Obaidullah Jan, ACA, CFA and last modified on