Your company continuously adjusts its leverage to maintain a target D/V ratio of 50%. Its equity beta is 1.4, and its debt beta is 0.2. What would the company’s equity beta be if it did not have leverage?

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BlackTom AI · Accepted Answer

We start by restating the situation and the options to ensure clarity.
Question and options: A company targets a debt-to-value (D/V) ratio of 50%, has current equity beta 1.4 and debt beta 0.2. The question asks what the company's equity beta would be if it had no leverage (i.e., D = 0). Answer choices: 1) 1.4, 2) 0.8, 3) 0, 4) 0.2, 5) 1.1.

First, we compute the asset (unlevered) beta using the current levered structure. When the company has D/V = 0.5 and E/V = 0.5, the levered equity beta is a weighted combination of asset beta and debt beta: beta_equity = beta_asset * (E/V) + beta_debt * (D/V).

Plugging in the numbers with the current equity beta given as 1.4, we can solve for beta_asset:
beta_asset = [beta_equity − (E/V) * beta_debt] / (E/V) = [1.4 − 0.5 * 0.2] / 0.5 = [1.4 − 0.1] / 0.5 = 1.3 / 0.5 = 0.8.
This means the asset beta (the beta of the firm’s assets if it had no leverage) is 0.8.

Now, consider the unlevered scenario where the firm has no debt. In that case, the equity is effectively the firm’s assets, so the equity beta would equal beta_asset, which is 0.8.

Option-by-option analysis:
- Option 1: 1.4 — This matches the current levered equity beta, not the unlevered case. It ignores the impact of removing debt on the beta since debt contributes to overall risk, and removing debt should lower the equity beta below the current levered level. Therefore this option is incorrect.
- Option 2: 0.8 — This aligns with the computed asset beta. It represents the unlevered, or no-leverage, equity beta derived from the given levered beta and capital structure. This is a plausible and mathematically consistent value for the unlevered beta.
- Option 3: 0 — An unlevered beta of zero would imply the firm’s assets have no systematic risk, which contradicts the given information that even the debt and the firm’s current equity carry risk (beta values of 0.2 and 1.4). This makes the option incorrect.
- Option 4: 0.2 — This matches the debt beta, not the equity beta in an unlevered (debt-free) scenario. Since unlevered equity should reflect asset risk, not solely debt risk, this option is incorrect.
- Option 5: 1.1 — This value is higher than the calculated asset beta and does not reflect removing leverage. It might arise from misapplying weights or misunderstanding the leverage effect, but it does not fit the unlevered beta calculation here.

In summary, the key idea is that the levered equity beta combines asset risk with debt risk according to the current capital structure, and removing debt leaves you with the asset beta as the new equity beta. The asset beta computed from the given levered beta and capital structure is 0.8, which corresponds to the unlevered scenario.

Your company continuously adjusts its leverage to maintain a target D/V ratio of 50%. Its equity beta is 1.4, and its debt beta is 0.2. What would the company’s equity beta be if it did not have leverage?

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