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Firm Valuation: Tax Shields & Discount Rates
Abstract
This paper proposes a new discounted cash flows’ valuation setup, and derives a general expression for the tax shields’ discount rate. This setup applies to any debt policy and any cash flow pattern. It only requires the equality at any time between the assets side and the liabilities side of the market value balance sheet, which has been introduced by Farber, Gillet and Szafarz (2006). This concept is extensively developed in the paper. This model encompasses all the usual setups that consider a fixed discount rate for the tax shields and require a fixed level of debt or a fixed leverage ratio, in particular Modigliani & Miller (1963) and Harris & Pringle (1985). It proposes an endogenized and integrated approach and modelizes the different market value discount rates as functions of both their relevant leverage ratio and the operating profitability of the firm. Among these rates are the cost of debt and the tax shields’ discount rate, which are usually assume constant. In this model, all the discount rates are likely to vary as soon as perpetuity cases are not considered. This setup introduces a new rate for the cost of levered equity without tax shields and develops the relation between the present value of tax shields and the market value of equity since debt tax shields entirely flow to equity. It only requires the risk free rate and the unlevered cost of capital as inputs but not the capital structure of the firm, as it tackles the circularity problem by considering an iterative approach. This fully dynamic model yields both theoretical and economic sensible results, and allows straightforward applications. It apparently solves the discrepancies of the usual setups and hopefully paves the way for further research.
... Arzac and Glosten 2005;Cooper and Nyborg 2006;Fernandez 2004;Fieten et al. 2005). Depending on the assumed financing policy and the resulting risk structure of the tax shields, different valuation approaches have been developed (e.g. the overviews by Fernandez 2006or Ansay 2010. In wide parts of the literature, the two following idealised financing policies are used to reduce the discount rates of the tax shields either to the interest rate on debt or to the required return of an unlevered company: ...
... Possible solutions can again be found in iterative procedures, which can be realised manually or automatically (Pratt and Grabowski 2014). Due to the existing level of IT, spreadsheet solutions nowadays provide powerful tools to find asymptotic solutions for such circularity problems (Ansay 2010;Tham and Vélez-Pareja 2004;Vélez-Pareja and Tham 2009;Wood and Leitch 2004). Further, analytical solutions to that problem can be attained in a recursive way (Mejía-Peláez and Vélez-Pareja 2011) or simultaneously based on a matrix approach (Casey 2004). ...
... These planned debt values do not necessarily reflect a constant debtto-value proportion, which is necessary to use a constant WACC or constant cost of equity. Many practitioners and textbooks make this convenient assumption to avoid the difficulty of readjusting the cost of capital considering its circularity (Ansay 2010). In the base case of the numerical example, the correct cost of equity ranges from 13% in the first period to 18% in the fourth period given the assumed autonomous debt financing (see Table 9). ...
Two of the most important issues related to value-based management are a company’s value and the contribution made to it in a certain period. Variations in residual income have been discussed and used for such kinds of valuation purposes and performance measurement for many years to link the value of a company to traditional accounting data. Considering certain financing policies with changing levels of debt, the technical problem of circularity has to be solved concerning the readjustment of the cost of capital. As a practical way to handle that issue, a matrix-based approach is presented in this article. The result of this technique is a vector of the current and future expected amounts of a firm’s goodwill. This vector provides a useful base simultaneously for valuation purposes and for measuring the contribution made to the corporate value in a particular period. Thus, the method presented tackles these two main issues of value-based management at once solely by focusing on traditional accounting data.
The insights of Modigliani and Miller (Am Econ Rev 53:433–443, 1963) and Miles and Ezzell (15:719–730, https://doi.org/10.2307/2330405, 1980) on the cost of capital of firms rank among the most important results in financial theory. The underlying assumptions regarding the financial policy, however, can hardly be reconciled with empirical findings. We investigate the implications of an alternative approach that is characterized by a fixed payout ratio. By introducing additional assumptions about investment opportunities, we find relationships between the cost of equity of levered and unlevered firms. The results contribute to explaining empirical findings and open the possibility to base valuation techniques on realistic and yet practicable assumptions.
This chapter reviews tax research related to whether corporate and personal taxes affect domestic and multinational capital structure, debt maturity, payout policy, compensation policy, risk management, earnings management, leasing, pensions, R&D partnerships, tax shelters, transfer pricing, repatriation of foreign profits, and organizational form. For each topic, theory related to how taxes can affect corporate decision making and firm value is reviewed, followed by a summary of the related empirical evidence and a discussion of unresolved issues. Tax research generally supports the hypothesis that high-tax rate firms make policy choices in response to tax incentives. Many issues remain unresolved, however, including understanding whether tax effects are of first-order importance, why firms do not pursue tax benefits more aggressively, and measuring the effect of investor-level taxes on corporate actions.
In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We present a general formulation without circularity for the equity value (E), cost of levered equity (Ke), levered firm value
(V), and the weighted average cost of capital (WACC). We furthermore compare the results obtained from these formulas with the results of the application of the Adjusted Present Value approach (no circularity) and the iterative solution of circularity based upon the iteration feature of a spreadsheet, concluding that all methods yield exactly the same answer. The advantage of this solution is that it avoids problems such as using manual methods (i.e., the popular “Rolling WACC”) ignoring the circularity issue, setting a target leverage (usually constant) with the inconsistencies that result from it, the wrong use of book values, or attributing the discrepancies in values to rounding errors.
This note builds on the paper of Farber, Gillet and Szafarz (2006). The WACC is a discount rate widely used in corporate finance. However, the correct calculation of the WACC rests on a correct valuation of the tax shields. The value of tax shields depends on the debt policy of the company. Many authors, (e.g. Inselbag and Kaufold (1997), Booth (2002), Cooper and Nyborg (2006), Farber, Gillet and Szafarz (2006)) consider that debt policy may only be framed in terms of maintaining a fixed market value debt ratio (Miles-Ezzell assumption) or a fixed dollar amount of debt (Modigliani-Miller assumption).
I modify the uniform-price auction rules in allowing the seller to ration bidders. This allows me to provide a strategic foundation for underpricing when the seller has an interest in ownership dispersion. Moreover, many of the so-called "collusive-seeming" equilibria disappear.
If there has been a shift in corporate finance and valuation in recent years, it has been towards giving excess returns a more central role in determining the value of a business. While early valuation models emphasized the relationship between growth and value - higher growth firms were assigned higher values - more recent iterations of these models have noted that growth unaccompanied by excess returns creates no value. With this shift towards excess returns has come an increased focus on measuring and forecasting returns earned by businesses on both investments made in the past and expected future investments. In this paper, we examine accounting and cash flow measures of these returns and how best to forecast these numbers for any given business for the future.
Fernandez [2004b. The value of tax shields is not equal to the present value of tax shields. Journal of Financial Economics 73, 145–165] argues that the present value effect of the tax saving on debt cannot be calculated as simply the present value of the tax shields associated with interest. This contradicts standard results in the literature. It implies that, even though the capital market is complete, value-additivity is violated. As a consequence, adjusted present value formulae of a standard sort cannot be used. Also, Fernandez's argument implies that the value of the tax saving differs from conventional estimates by a considerable amount. We reconcile Fernandez's results with standard valuation formulae for the tax saving from debt. We show that, as one would expect, the value of the debt tax saving is the present value of the tax savings from interest. The apparent violation of value-additivity in the Fernandez paper comes from mixing the Miles and Ezzell and Miller and Modigliani leverage policies.
This paper presents the Capital Cash Flow (CCF) method for valuing risky cash flows. I show that the CCF method is equivalent to discounting Free Cash Flows (FCF) by the weighted average cost of capital. Because the interest tax shields are included in the cash flows, the CCF approach is easier to apply whenever debt is forecasted in levels instead of as a percent of total enterprise value. The CCF method retains its simplicity when the forecasted debt levels and the implicit debt-to-value ratios change throughout forecast period. The paper also compares the CCF method to the Adjusted Present Value (APV) method and provides consistent leverage adjustment formulas for both methods.