The equations given for levered and unlevered betas are not so tough, once you have all the right information.

For example, say you have a levered beta of 1.5 for a company's stock, and that company has a debt-to-equity ratio of 0.25. The relevant tax rate is 21.0%. What is the unlevered beta?

Question

The equations given for levered and unlevered betas are not so tough, once you have all the right information.

For example, say you have a levered beta of 1.5 for a company's stock, and that company has a debt-to-equity ratio of 0.25. The relevant tax rate is 21.0%. What is the unlevered beta?

BlackTom AI · Accepted Answer

We begin by identifying the relationship between levered beta and unlevered beta. In capital structure theory, Beta_L = Beta_U × [1 + (1 − T) × (D/E)], where T is the tax rate, D/E is the debt-to-equity ratio, Beta_L is the levered beta, and Beta_U is the unlevered beta.

Option-by-option analysis:

- Option: about 0,.67
  This option appears to mix or misreport the expected quantitative result. If one tried to compute Beta_U from the formula, the result should be around 1.25, not less than 1. Clearly this candidate does not align with the standard calculation, and the decimal formatting (0,.67) suggests a typographical error rather than a meaningful estimate.

- Option: about 1.25
  This is the value you get when you plug the numbers into the formula correctly. Compute the denominator: 1 + (1 − 0.21) × 0.25 = 1 + 0.79 × 0.25 = 1 + 0.1975 = 1.1975. Then Beta_U = 1.5 / 1.1975 ≈ 1.251, which rounds to about 1.25. This matches the standard unlevering process and the given inputs.

- Option: about 3.35
  This would imply a much larger unlevered beta than the levered beta, which would occur if the debt multiplier were extremely high or tax effects were misapplied. Since the debt-equity ratio here is modest and the tax shield reduces the levered effect, 3.35 is inconsistent with the computation and with intuition about a modest leverage scenario.

- Option: about 1.12
  This value is close but not matching the precise calculation. It would correspond to either a slightly different D/E, a different tax rate, or a rounding difference. However, with D/E = 0.25 and T = 21%, the exact unlevered beta rounds to about 1.25, not 1.12.

In summary, applying the standard unlevering formula yields a result near 1.25, while the other options either reflect a miscalculation, a formatting issue, or values that are not consistent with the inputs.

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