We run a delivery service, and we believe our firm has market risk equally between that of UPS and FedEx. We know the following about these 2 firms:. Stock Price per share # shares outstanding Market Value of Debt
UPS $65 0.7 billion $ 5 billion
FedEx $55 250 million $ 3 billion
We also have the following data on the securities of these firms:.
Beta E Beta D
UPS 0.8 0
FedEx 1.1 0.1
Assume that our firm has risk-free debt with market value $20 million and equity with market value $450 million. Assume that taxes are not relevant. Please estimate our firm’s equity beta

The firm’s equity beta is therefore equal to 0.85.

Explanation:

Note: The data in the question are merged together. They are therefore sorted before answering the question. See the attached pdf file for the complete question with the sorted data.

The explanation of the answer is now provided as follows:

The equity beta refers to a beta that considers different levels of debt of a firm. The equity beta is also known as the levered beta or the project beta. The equity beta is therefore different from the asset beta.

Asset beta refers to a beta does not consider debt and assume that the firm uses only equity financing. Asset beta is known as unlevered beta.

The Firm’s equity can be calculated using the following steps:

Step 1: Calculation of average unlevered beta of the firm

Unlevered beta = Levered beta / (1 + ((1 - Tax rate) * (Debt / Equity ratio))) ……… (1)

Where for UPS;

Levered beta = Beta E = Beta of Equity = 0.80

Tax rate = 0

Debt = Market value of debt = $5 billion

Equity = Market value of equity = Stock Price per share * Number of shares outstanding = $65 * 0.7 billion = $45.50 billion

Substituting the values into equation (1), we have:

UPS unlevered beta = 0.80 / (1 + ((1 - 0) * (5 / 45.50))) = 0.720792079207921 = 0.72

Where for FedEx;

Levered beta = Beta E = Beta of Equity = 1.10

Tax rate = 0

Debt = Market value of debt = $3 billion

Equity = Market value of equity = Stock Price per share * Number of shares outstanding = $55 * 250 million = $13.75 billion

Substituting the values into equation (1), we have:

FedEx unlevered beta = 1.10 / (1 + ((1 - 0) * (3 / 13.75))) = 0.902985074626866 = 0.90

Therefore, firm’s averaged unlevered beta can be calculated as follows:

Firm’s averaged unlevered beta = (UPS unlevered beta + FedEx unlevered beta) / 2 = (0.72 + 0.90) / 2 = 0.81

Step 2: Calculation of firm’s levered beta

Firms’ levered beta = Firm’s averaged unlevered beta * (1 + ((1 - Tax rate) * (Debt / Equity ratio))) …….. (2)

Where;

Firm’s averaged unlevered beta = 0.81

Tax rate = 0

Debt = Market value of risk-free debt = $20 million

Equity = Market value of equity = $450 million

Substituting the values into equation (2), we have:

Firms’ levered beta = 0.81 * (1 + ((1 - 0) * (20 / 450))) = 0.846 = 0.85

Since from the definitions above, the equity beta is also known as the levered beta, the firm’s equity beta is therefore equal to 0.85.

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