Question

explain how to estimate the cost of capital.

How to adjust for the effect of leverage on the cost of equity (unlevered Beta)?

Should we use book or market value to determine the weights?

Answer 1

1.The cost of equity is more complicated, since the rate of return demanded by equity investors is not as clearly defined as it is by lenders. Theoretically, the cost of equity is approximated by the Capital Asset Pricing Model (CAPM) = Risk-free rate + (Company’s Beta x Risk Premium).

The firm’s overall cost of capital is based on the weighted average of these costs.the cost of capital that would be used to discount future cash flows from potential projects and other opportunities to estimate their Net Present Value (NPV) and ability to generate value.

2.To obtain the equity beta of a particular company, we start with portfolio of assets of that company or alternatively a sample of publicly traded firms with a similar systematic risk. We will first derive the betas of these individual assets or firms from market prices. The derived betas are levered betas as they would reflect the capital structure of the respective firms. They would need to be un-levered so as to only reflect their business risk components.

From the unlevered betas a weighted average unlevered beta will be obtained using as weights the proportions of the assets in the company’s asset portfolio or an average across all comparable firms will be derived. The weighted unlevered beta thus obtained would now be re-levered based on the capital structure of the company in order to determine the equity or levered beta for the company, a beta that reflects not only the business risk but also the financial risk of the company.

Un-levering and re-levering beta may be done in a number of ways. A method employed by practitioners gives the relationship between un-levered and re-levered beta as follows:

Levered Beta = Unlevered Beta * (1+D/E), where D/E = Debt-to-Equity Ratio of the company.

The practitioner’s method makes an assumption that the corporate debt is risk free. If corporate debt is considered risky then another possible formulation is:

Levered Beta = Asset Beta + (Asset Beta – Debt Beta) * (D/E) where Debt Beta is estimated from the risk free rate, bond yields and market risk premium.

Under the risky-debt formulation:

Levered Beta = Asset Beta + (Asset Beta – Debt Beta) * (D/E)*(1-T).

And WACC would be equal to E/(D+E)*Cost of Equity + D*(1-T)/(D+E) * Cost of Debt.

3.Analysts prefer a Market Value WACC because an investor would demand today’s market-required rate of return on the market value of the capital and not on its book value