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.

Question

Accepted Answer

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.

Company	Unlevered Beta (β_U)
A	1.03
B	1.02
C	1.00
D	1.05
E	0.98

Calculating Unlevered Beta and Adjusting for a Private Company

📋 What you're given

1. Task Overview

Step 1: Given Data for Peer Group

Step 2: Calculating Unlevered Beta (β_U)

Step 3: Compute the Average Unlevered Beta

Step 4: Adjusting to Target Capital Structure

Step 5: Compute the Cost of Equity Using CAPM

💡 Model answer

Step 1: Calculating Unlevered Beta

Step 2: Compute the Industry Average Unlevered Beta

Step 3: Adjusting for Target Capital Structure

Step 4: Compute the Cost of Equity Using CAPM

Final Results

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Company	Levered Beta (β_L)	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)