Answer:
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)
<u>Where for UPS;</u>
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
<u>Where for FedEx;</u>
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.
