The Infinitum company's value of outstanding equity is USD 400 million, and you have estimated its beta to be 1.5. Infinitum has four-year zero-coupon debt outstanding with a face value of USD 100 million that currently trades for USD 80 million. The firm pays no dividends and reinvests all of its earnings. The risk-free rate of interest is currently 6.00% and is continuously compounded, while the standard deviation of the return on firm's assets is equal to 0.5. From the standard normal distribution table, please use the 4-digit value. Using the Black-Scholes formula, the estimated unlevered beta of the firm is closest to:

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BlackTom AI · Accepted Answer

First, identify the inputs we have: the market value of equity E is 400 million, and the market value of debt D is 80 million (from the given debt price of 80 for a 100 face value). The levered beta is given as 1.5. We will use the Hamada equation to extract the unlevered beta.

Hamada's formula (with zero taxes) relates levered beta (beta_L) to unlevered beta (beta_U) via: beta_L = beta_U * (1 + D/E).

Compute the debt-to-equity ratio using market values: D/E = 80 / 400 = 0.20.

Plug into the formula and solve for beta_U: beta_U = beta_L / (1 + D/E) = 1.5 / (1 + 0.20) = 1.5 / 1.20 = 1.25.

Rounding considerations: the result 1.25 is very close to 1.26, and among the options, 1.26 is the best match.

Option A (1.00): This would imply no leverage effect, which contradicts the given debt and the levered beta. The presence of debt and a levered beta of 1.5 means beta must be higher than beta_U, so 1.00 is incorrect.

Option B (1.26): This aligns with the calculation beta_U ≈ 1.25 and is the closest to the derived value when rounded to three significant figures. The reasoning path supports this as the correct choice.

Option C (0.25): A beta this low would imply extremely low risk relative to the market, which is inconsistent with the provided levered beta of 1.5 and the debt level. This is not plausible given the data.

Option D (1.78): This would suggest a much larger levered effect than what the input levered beta and debt-to-equity imply under the Hamada relationship; it conflicts with the computed 1.25 unlevered beta.

In summary, applying the standard Hamada adjustment with D/E = 0.20 yields beta_U = 1.25, and the closest provided option is B. 1.26.

Corporate Finance (WI000091) (11.08.2025) Lecture Hall Exam

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