Unlevering and Relevering Beta, Explained
The question
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.
General educational practice only. This is not an actual, confidential, leaked, or firm-provided interview question. Check important technical details against primary learning materials.
Study explanation
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.
DCF timeline
| Line item | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Free cash flow | 50 | 54 | 58 | 63 | 68 |
| PV of free cash flow | 45 | 45 | 44 | 43 | 42 |
| Terminal value (Year 5 exit) | 1,001 |
| PV of terminal value | 621 |
| Implied enterprise value | 840 |
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The rest of this topic
Beta: levered, unlevered, relevered