The Free-Float Company, a company in the 36% tax bracket, has riskless debt in its capital structure which makes up 40% of the total capital structure, and equity is the other 60%. The beta of the assets for this business is. 8 and the equity beta is:

This question is asking for unlevered beta given the levered beta;

Levered beta = Unlevered beta[ 1 + (1-tax) * D/E]

Levered beta = 0.8

tax = 36%

D/E = 0.40 / 0.60 = 0.6667

Next, plug in the numbers to the formula;

0.8 = Unlevered beta [ 1 + (1-0.36) * 0.6667]

0.8 = Unlevered beta [1.426688]

Divide both sides by 1.426688 to solve for unlevered beta;

0.8 / 1.426688 = Unlevered beta

0.56 = Unlevered beta; this is the beta without debt, hence the equity beta.