Getting the valuation formulas right when it comes to annuities

What is it about?

The purpose of this paper is to mathematically establish the equity method, the free-cash-flow method, the adjusted-present-value method, and the relationships between these methods when the free cash flow appears as an annuity. More particularly, we depart from the two most widely used evaluation settings. The first setting is this of Modigliani and Miller (1958, 1963) in which the free cash flow is stationary. The second setting is this of Miles and Ezzell (1980, 1985) where the free cash flow represents an autoregressive possess of first order. In the previous literature, few attempts have been made to mathematically state these methods and their relationships for the case of annuities. However, until now the complete set of formulas has not been developed yet. Particularly, the following relationships are not established: (a) the correct discount rate of the tax shield when the free cash flow takes the form of a first-order autoregressive annuity, (b) the direct valuation of the tax shield from the free cash flow for a first-order autoregressive annuity, (c) the correct translation from the required return on unlevered equity to the levered equity, when the free cash flow is a stationary annuity, and (d) direct calculations of the unlevered and levered firm values, and the value of the tax-shield for a stationary annuity. In this paper, these relationships will be established.

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Photo by Giorgio Trovato on Unsplash

Photo by Giorgio Trovato on Unsplash