Question

Fiddler Foundations has a tax rate of 40% and their stock has a beta of 1.2. The company has a capital structure of 45% debt and 55% common equity. Calculate the company's unlevered beta Calculate the company's levered beta if they changed their capital structure ton 40% debt and 60% common equity.

Answer 1

Unlevered beta compares the risk of an unlevered company to the risk of the market. The unlevered beta is the beta of a company without taking its debt into account. Unlevering a beta removes the financial effects of leverage. This number provides a measure of how much systematic risk a firm's equity has when compared to the market.

ẞu = ẞl/[1 + (1 - t) * (D/E)]

where,

                  ẞu is Unlevered Beta

                  Levered Beta (ẞl) = 1.2

                  Corporate tax rate = 40%

                  Debt to equity ratio = 0.82

Let's put all the values in the formula,

ẞu = 1.2/ [1 + (1 - 0.4)* 0.82]

    = 1.2/ [1 + 0.6* 0.82]

    = 1.2/ [1 + 0.492]

    = 1.2/ [1.492]

    = 0.8

Unlevered beta is 0.8

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If the capital structure changed to 40% debt and 60% equity

The debt to equity ratio = 40/60 = 0.6667

ẞu = ẞl/[1 + (1 - t) * (D/E)]

0.8 = Leveraged beta/[1+ (1 – 0.4)*(.6667)]

Leveraged beta = 0.8 * [1+ (0.6) * (0.6667)]

Leveraged beta = 0.8* [ 1 + 0.4]

Leveraged beta = 0.8* 1.4

                             = 1.12

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