If a firm has a levered beta of .9 and a debt to equity ratio of 1, what is the unlevered beta assuming a tax rate of 30%? (Round to the nearest hundredth)

Unlevered beta = 0.53

Explanation:

Beta is a measure of systematic risk. Systematic risk is further divided into business and financial.

Business risk and financial risk. Business risk is that associated with the nature of the business operations that causes variability in the operating income of the business.

This is measured by the unlevered beta where the company has no debt finance.

Financial risk, on the other hand, is associated with use of debt finance . A company that uses a form of debt would face such risk . The systematic risk of such business would be measured using the levered beta.

The formula below shows the relationship:

βa = βe ×  Ve/ (Ve + Vd(1-T) )

βa -Unlevered beta

βe - Levered beta

Ve- Equity weight

Vd- Debt weight

T- Tax rate

DATA

βe- 0.9

βa- ?

Ve-  1

Vd- 1

T- 0.3

βa = 0.9 ×  1/(1 + 1×(1-0.3)=0.529

βa - 0.53

Unlevered beta = 0.53

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