Calculating Unlevered Beta and Adjusting for a Private Company
As a financial analyst, you are tasked with estimating the appropriate beta for a private company that is being valued for an acquisition. Since the company is not publicly traded, you will derive its Levered Beta by first calculating the Unlevered Beta from a set of comparable public companies (peers) and then adjusting it to the private firm's target capital structure.
1. Task Overview
Task: Using the provided financial data from five publicly traded companies, compute the Unlevered Beta for the industry and adjust it to reflect the private company’s capital structure.
Step 1: Given Data for Peer Group
The following table presents the Levered Beta, Debt/Equity (D/E) ratio, and Tax Rate for five comparable companies.
| Company | Levered Beta (βL) | Debt/Equity (D/E) | Tax Rate (T) |
|---|---|---|---|
| A | 1.3 | 50% (0.50) | 25% (0.25) |
| B | 1.5 | 80% (0.80) | 30% (0.30) |
| C | 1.2 | 40% (0.40) | 28% (0.28) |
| D | 1.6 | 100% (1.00) | 32% (0.32) |
| E | 1.4 | 60% (0.60) | 27% (0.27) |
Step 2: Calculating Unlevered Beta (βU)
The formula for Unlevered Beta is:
Show Unlevered Beta Formula
βU = βL / [1 + (1 - T) × (D/E)]
Using this formula, compute the Unlevered Beta for each company.
Step 3: Compute the Average Unlevered Beta
After calculating βU for each company, determine the industry average:
Show Industry Average Formula
Industry βU = (Σ βU of all companies) / Number of companies
Step 4: Adjusting to Target Capital Structure
The private company has a target D/E ratio of 70% and a tax rate of 30%. Adjust the Unlevered Beta using the following formula:
Show Relevered Beta Formula
βL = βU × [1 + (1 - T) × (D/E)]
Step 5: Compute the Cost of Equity Using CAPM
Once you have the new Levered Beta, compute the Cost of Equity using the CAPM formula:
Show CAPM Formula
Re = Rf + βL × Market Risk Premium
Assume:
- Risk-Free Rate (Rf) = 3%
- Market Risk Premium = 6%
Using these inputs, compute the Cost of Equity.
Solution
Step 1: Calculating Unlevered Beta
Applying the Unlevered Beta formula to each company:
| Company | Unlevered Beta (βU) |
|---|---|
| A | 1.03 |
| B | 1.02 |
| C | 1.00 |
| D | 1.05 |
| E | 0.98 |
Step 2: Compute the Industry Average Unlevered Beta
The average Unlevered Beta across all five companies is:
Industry βU = (1.03 + 1.02 + 1.00 + 1.05 + 0.98) / 5 = 1.016
Step 3: Adjusting for Target Capital Structure
Applying the formula for Relevered Beta using D/E = 70% and Tax Rate = 30%:
βL = 1.016 × [1 + (1 - 0.30) × 0.70]
βL = 1.016 × [1 + (0.70 × 0.70)]
βL = 1.016 × 1.49 = 1.51
Step 4: Compute the Cost of Equity Using CAPM
Using the CAPM model:
Re = 3% + 1.51 × 6%
Re = 3% + 9.06% = 12.06%
Final Results
- Industry Average Unlevered Beta: 1.016
- Relevered Beta for Private Company: 1.51
- Cost of Equity (Re) Using CAPM: 12.06%
This newly derived Levered Beta (1.51) is now used in further valuation models, such as Discounted Cash Flow (DCF), to estimate the intrinsic value of the private company.
Would you like to explore further adjustments, such as different capital structures or stress testing the beta assumptions?