You need to unlever a company's equity beta of 1.5. Its market value of debt is $400 million, market cap is $600 million, and the marginal tax rate is 30%. Compute the unlevered beta. Then re-lever it for a target D/E ratio of 0.8. Show all steps.

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Model answer

Current D/E = $400M / $600M = 0.6667. Unlever: βu = 1.5 / (1 + (1 - 0.30) × 0.6667) = 1.5 / (1 + 0.4667) = 1.5 / 1.4667 = 1.0227. Target D/E = 0.8. Re-lever: βl = 1.0227 × (1 + 0.7 × 0.8) = 1.0227 × (1 + 0.56) = 1.0227 × 1.56 = 1.595. This higher beta reflects the increased financial risk from the higher target leverage.

Follow-up pressure:

  • If you mistakenly used book values instead of market values, and book D/E was 0.4, how would that change the unlevered beta and the re-levered result?
  • The tax rate in the unlevering formula uses the marginal rate. Explain why you would not use the effective tax rate.

This is an advanced Superday-level question with a full model answer, part of IB Atlas's practice bank.

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