Beta and Cost of Capital of a Project

When estimating the cost of equity using the Capital Asset Pricing Model (CAPM), a reliable estimate of beta must be used.

The beta for a company that is not publicly traded may be estimated using the pure-play method. In the pure-play method, the starting point is the beta for a comparable publicly traded company, i.e., one which has similar business risk or risk relating to revenue uncertainty. This beta is then adjusted for differences in financial leverage to derive an estimate of beta for the company. Adjusting beta for financial leverage differences requires a process of “unlevering” and “levering” the beta.

Steps in the Pure-play Method for Calculating Beta

Step 1: A comparable company is selected.

Step 2: The equity beta of the comparable company, B_L,comparable is estimated.

Step 3: The comparable company’s beta is then unlevered by removing the effects of its financial leverage and leaving its business risk. The unlevered beta, B_U,comparable, is known as the asset beta.

The equation to represent this is:
$$ { \beta }_{ \text{U,comparable} }=\frac { \beta _{ \text{L,comparable} } }{ \left[ 1+\left( 1-{ t }_{ \text{comparable} } \right) \frac { { D }_{ \text{comparable} } }{ { E }_{ \text{comparable} } } \right] } $$

Where:

B_U,comparable = the asset beta for the comparable company

B_L,comparable = the equity beta for the comparable company

t_comparable = the marginal tax rate

D_comparable = the debt of the comparable company

E_comparable = the equity of the comparable company

Step 4: The comparable company’s asset beta is then adjusted or levered to arrive at an estimate of the equity beta for the company, B_L,company.

The equation to represent this is:

$$ \beta _{ \text{L,comparable} }={ \beta }_{ \text{U,comparable} }\left[ 1+\left( 1-{ t }_{ \text{comparable} } \right) \frac { { D }_{ \text{comparable} } }{ { E }_{ \text{comparable} } } \right] $$

Question

Company PQR is in the telemarketing business. The asset beta for a comparable company in the same industry is 1.3. If company PQR’s debt-to-equity ratio is 1.2, and the corporate tax rate is 35%, what is company QPR’s equity beta?

1. 1.65
2. 2.31
3. 2.58

Solution

The correct answer is B.

The comparable company’s asset beta, B_U,comparable, is given as 1.3. You are also provided with information which indicates that t_comparable= 35% and

$$ \frac { { D }_{ \text{companyPQR} } }{ { E }_{ \text{companyPQR} } } =1.2 $$

Solving for B_L,company = 1.3 × [1 + ((1-0.35) × 1.2)] = 1.3 × (1 + 0.78) = 2.314.