Aurora Borealis
1 May 2013 CFA Institute Journal Review

Pitfalls in Levering and Unlevering Beta and Cost of Capital Estimates in DCF Valuations (Digest Summary)

  1. Marla Howard, CFA

The standard weighted average cost of capital estimations in discounted cash flow (DCF) valuations cause some problems. The authors offer alternative formulas for leveraging and unleveraging beta and cost of capital to provide more accurate DCF valuations for growing companies. They include equity-linked securities in their formulas and show the importance of making adjustments when accounting treatment is different between companies.

What’s Inside?

The authors address pitfalls in assumptions used in the Modigliani and Miller (M&M) model for estimating the weighted average cost of capital (WACC) with taxes (American Economic Review 1963). They present a framework for adjusting the cost of capital formulas that are used in discounted cash flow (DCF) valuations to consider growth and nonpermanent debt levels and to estimate an implied beta for debt and preferred stock in the leveraging and unleveraging of beta.

They show the potential impact on the WACC and company valuation (1) when equity-linked securities are ignored and (2) when accounting treatment for long-term leases and other quasi-financing instruments is different between companies.

How Is This Research Useful to Practitioners?

The M&M model for estimating the WACC with taxes assumes a constant capital structure, no growth, and fixed perpetual debt. By using the cost of debt to discount all interest tax shields, the M&M model mitigates the impact of debt on the cost of equity for companies that refinance and increase their debt. The authors suggest that for growing companies in which new debt is issued and existing debt is refinanced, the interest tax shields are riskier than the company’s cost of debt. With continuous refinancing, the interest tax shields are assumed to have the same risk as the unleveraged assets and are thus discounted at the cost of unleveraged assets instead of at the cost of debt. A continuous refinancing assumption yields a cost of equity similar to an annual refinancing assumption. Therefore, the authors’ model discounts all interest tax shields at the unleveraged cost of capital.

They use CAPM-implied betas for debt and other nonequity securities in the leveraging and unleveraging of betas. The use of the implied betas leads to a lower cost of equity and WACC than the common practice of assuming zero betas for nonequity securities.

The authors demonstrate the importance of adjusting accounting information used in the WACC calculations when leases are not accounted for consistently between companies. They also encourage practitioners to include the effect of options and other equity-linked securities in the capital structure.

How Did the Authors Conduct This Research?

The authors review the general framework for how the WACC is determined by first leveraging the equity cost of capital by adding together the return on unleveraged assets and the effect of financial leverage (which takes into account the difference in risk of the interest tax shields and the company’s assets). Next, they unleverage the cost of capital, which equals the WACC of the company’s securities adjusted for the interest tax shields. They show how the WACC equals the unleveraged cost of capital adjusted for the value and risk of debt financing; that is, it reflects the tax deductibility of interest and the value of interest tax shields discounted at a different rate from the unleveraged cost of capital.

Using a hypothetical example, the authors show a 10% variation in relative discount rates (and thus a 10% difference in firm valuation) between the M&M model with taxes and the alternative formula that assumes continuous or annual debt refinancing. The difference results from discounting the interest tax shield at the unleveraged cost of capital instead of at the cost of debt as in the M&M model.

The authors also provide hypothetical examples to show the impact on DCF valuations for assuming zero betas for debt and preferred stock, as well as from using inconsistent accounting methods for leases.

Abstractor’s Viewpoint

The authors’ extensions to the M&M model for estimating the WACC with taxes may be beneficial for practitioners in estimating discount rates for DCF valuations. They also show a significant difference in valuation between similar companies when one is capitalizing and the other is expensing lease payments. I would caution that accounting in GAAP requires capitalization when the substance is a financed purchase; that is, the accounting treatment is not a choice. Nevertheless, practitioners should be aware of accounting differences and how they impact the WACC estimates and valuations.

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