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Getting the valuation formulas right when it comes to annuities

Denis Mike Becker (NTNU Business School, Norwegian University of Science and Technology, Trondheim, Norway)

Managerial Finance

ISSN: 0307-4358

Article publication date: 6 January 2022

Issue publication date: 15 February 2022

295

Abstract

Purpose

The purpose of this paper is to establish the flow-to-equity method, the free cash flow (FCF) method, the adjusted present value method and the relationships between these methods when the FCF appears as an annuity. More specifically, we depart from the two most widely used evaluation settings. The first setting is that of Modigliani and Miller who based their analysis on a stationary FCF. The second setting is that of Miles and Ezzell who worked with an FCF that represents an autoregressive possess of first order.

Design/methodology/approach

Inspired by recent observations in the literature concerning cash flows, discount rates and values in discounted cash flow (DCF) methods, we mathematically derive DCF valuation formulas for annuities.

Findings

The following relationships are 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 calculation of the unlevered and levered firm values and the value of the tax shield for a stationary annuity.

Originality/value

Until now the complete set of formulas for the valuation of stochastic annuities by different DCF methods has not been established in the literature. These formulas are developed here. These formulas are important for practitioners and academics when it comes to the valuation of cash flows of finite lifetime.

Keywords

Citation

Becker, D.M. (2022), "Getting the valuation formulas right when it comes to annuities", Managerial Finance, Vol. 48 No. 3, pp. 470-499. https://doi.org/10.1108/MF-03-2021-0135

Publisher

:

Emerald Publishing Limited

Copyright © 2021, Emerald Publishing Limited

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