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Firm valuation: tax shields & discount rates

Ansay, Thomas (2009): Firm valuation: tax shields & discount rates.

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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.

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