LEVERED BETA VS UNLEVERED BETA
Beta or levered beta is a measure of systematic risk of a firm in relation to the market. Systematic risk is the risk which affects the overall market. Beta does not take into account the unsystematic risk. Unsystematic risk is the risk which specifically affects a stock so it can be reduced by diversifying the portfolio.
Some industries or companies have a high level of debt on their balance sheet. This leverage makes their earnings volatile and investment in this company becomes risky. Levered beta considers the risk of leverage and its impact on company’s performance. So, levered beta is not an ideal measure to compare two companies with different debt proportions. In such scenario, you will have to remove the effect of debt by “unlevering” the beta. Unlevered beta will facilitate a better comparison for such companies than levered beta.
UNLEVERED BETA FORMULA
Unlevered Beta | = | Levered Beta (β) |
1 + [(1- Tax) (Debt/Equity)] |
Unlevered beta or asset beta can be found by removing the debt effect from the levered beta. The debt effect can be calculated by multiplying debt to equity ratio with (1-tax) and adding 1 to that value. Dividing levered beta with this debt effect will give you unlevered beta.
PURE PLAY METHOD
Capital asset pricing model (CAPM) can be used for publicly listed companies. Finding beta of projects or companies that are not publicly listed is not possible through CAPM due to the lack of data. Pure play method is used in such cases. Unlevered and levered beta are used in this method to estimate the beta.
Let’s take an example to understand this process. Company X is a non-listed private company. Here are some details available with you:
Description | Company X |
Total Debt | $ 2 million |
Total Equity | $ 5 Million |
Debt to Equity ratio | 40% |
Tax rate | 30% |
You want to find out the beta for the Company X. Firstly, you need to find out a comparable company which is similar in nature to the Company X. Also, the comparable company must be publicly listed so that its beta can be calculated. You found a Company A which is very similar in nature with Company X. Company A is operating in the same industry and it has the same product line and risk profile as Company X. So, you have collected the following data about the comparable company:
Description | Company A
(Comparable Company) |
Calculated Beta | 1.2 |
Total Debt | $ 4 million |
Total Equity | $ 8 Million |
Debt to Equity ratio | 50% |
Tax rate | 35% |
The second step is to calculate beta of the comparable company. Here, Company A has a beta of 1.2. Now, you will have to unlever the beta of Company A. in simple language, you have to remove the effect of leverage from the beta of company A. By applying the formula, we find the unlevered beta value to be 0.91.
Unlevered Beta (β_{Company A}) | = | Levered beta (β_{Company A}) |
1 + [ (1- Tax) (Debt/Equity) ] |
Unlevered Beta (β_{Company A}) | = | 1.2 | = | 0.91 |
1 + [ (1- 0.35) (0.5) ] |
The last step is to adjust Company A’s (comparable company) unlevered beta for the capital structure of Company X. We will assume the unlevered beta of Company A will be same as Company X because they are similar in nature. By adjusting the unlevered beta of Company X for its leverage, we will find the beta of Company X to be 1.17.
Levered beta (β_{Company X}) | = | Unlevered Beta (_{Company X}) | * | 1 + [ (1- Tax) (Debt/Equity) ] |
Levered beta (β_{Company X}) | = | 0.91 | * | 1 + [ (1- 0.3) (0.4) ] = 1.17 |
References:
- CFA Level 1 Curriculum 2016