IFT Notes for Level I CFA^® Program

R33 Cost of Capital

Part 3

4. Topics in Cost of Capital Estimation

A firm’s beta is used to estimate its required return on equity. Beta is a measure of risk; riskier firms will have higher betas, whereas less risker firms will have lower betas. Beta is estimated by regressing a stock’s returns with overall market returns.

At times, we need to estimate the beta for a project or a company that is not publicly traded. In this case we use the pure-play method.

Pure-Play Method

This method has three steps:

Step 1: Shortlist comparable publicly traded companies.

Step 2: Derive unlevered beta or comparable asset beta for the project using comparable company’s D/E and tax rates:
${{\beta }_{asset}=\beta }_{equity}*\frac{1}{1+\frac{\left(1-t\right)D}{E}}$
Step3: Get the equity levered beta for the project using project specific D/E and tax rate:
${\beta }_{equity}=\ {\beta }_{asset}*\left(1+\frac{\left(1-t\right)D}{E}\right)$
Example

AA Corp. is a large conglomerate and wants to determine the equity beta of its food division. This division has a D/E ratio of 0.7. The tax rate is 40%. A comparable publicly traded food company has an equity beta of 1.2 and a D/E ratio of 0.5. What is the equity beta of AA’s food division?

Solution:

Using the pure play method, we can calculate the equity beta of AA’s food division as:

Unlevered beta of publicly traded food company = 1.2 * $\frac{1}{1\ +\ 0.6\ \left(0.5\right)}$ = 0.923
Levered equity beta of AA’s food division = 0.923 [1 + 0.6 x 0.7] = 1.31

Inference: Since AA’s food division has more debt than the publicly traded company, it is riskier and has a higher beta value.

4.2. Country Risk

The general assumption so far has been that an investor is investing in a developed country. But what happens when an investor invests in emerging economies? Here the CAPM is modified to adjust for additional risk in a developing market by adding country risk premium (CRP) to market risk premium.
$r_e=RFR+\beta \ \left[E\ \left(R_m\right)-RFR+CRP\right]$
The country risk premium is computed as:

Country ERP = Sovereign yield spread * $\frac{{\sigma }_{equity}}{{\sigma }_{sovereign\ bond}}$
where:
${\sigma }_{equity} =$ Annualized standard deviation of equity index
${\sigma }_{sovereign\ bond}$ = Annualized standard deviation of the sovereign bond market in terms of the developed market currency

For example, assume you are a U.S. based investor investing in Indian securities. The risk-free rate is 3% and the beta for a stock is 1.5. The market risk premium is 6% and CRP for India is 3%. The cost of equity is 3 + 1.5[6+3] = 16.5%.