Consistent valuation of project finance and LBOs using the flows‐to‐equity method

• Author: Ian A. Cooper,Kjell G. Nyborg
• DOI: http://doi.org/10.1111/eufm.12136
• Date: 01 January 2018
• Published date: 01 January 2018

DOI: 10.1111/eufm.12136

ORIGINAL ARTICLE

Consistent valuation of project finance and LBOs

using the flows-to-equity method

Ian A. Cooper

1

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Kjell G. Nyborg

2,3,4

1

Department of Finance, London

Business School, Regent’s Park, London

NW1 4SA, UK

Email: icooper@london.edu

2

Department of Banking and Finance,

University of Zurich, Plattenstrasse 14,

8032 Zurich, Switzerland

Email: kjell.nyborg@bf.uzh.ch

3

Swiss Finance Institute,Walchestrasse 9,

8006 Zurich, Switzerland

4

Centre for Economic PolicyResearch, 33

Great Sutton Street, London EC1V0DX,

UK

Funding information

This research has benefited from a grant

from the Research Council of Norway

[grant number 1798866/S20]. We also

thank NCCR-FINRISK for financial

support.

Abstract

The flows-to-equity method is used to value transactions

where debt amortizes according to a fixed schedule,

requiring a formula that links the changing leverage with a

time-varying equity discount rate. We show that extant

formulas yield incorrect valuations because they are

inconsistent with the basic assumptions of this method.

The error from using the wrong formula can be large,

especiallyat currently low interest rates.We derive a formula

that captures the effects of a fixed debt plan, potentially

expensivedebt, and costs of financial distress. We resolve an

important issue about what to use as the cost of debt.

KEYWORDS

cost of debt, cost of equity, equity cash flow, flows to equity, LBO,

project finance, valuation

JEL CLASSIFICATION

G12, G24, G31, G32, G33, G34

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INTRODUCTION

The general topic of this paper is the valuation of investments that have fixed debt plans. In other words,

at the time the valuation is made the future amount of debt is expected to be a function of time alone.

The amount of debt is not expected to fluctuate with the future value of the investment. This type of

situation arises in leveraged buyouts (LBOs) (Baldwin, 2001a), project finance (Esty, 1999), and other

We are grateful to an anonymous referee and the editor, John Doukas, for helpful comments. This research has benefited from a

grant from the Research Council of Norway [grant number 1798866/S20]. We also thank NCCR-FINRISK for financial support.

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© 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/eufm Eur Financ Manag. 2018;24:34–52.

highly leveraged transactions (HLTs) where the future amortization of the debt has been agreed at the

time of the investment. Our focus is especially on valuing the equity in such investments directly

through the ‘flows-to-equity’method, whereby the project’s free cash flow to equity is discounted at a

leveraged equity rate.

The topic is important because the flows-to-equity method is often used in practice in cases in

which debt plans are fixed. However, as we show, standard formulas to calculate the equity discount

rate result in equity values that are incorrect when debt levels evolve according to a predetermined

schedule. They differ from the values one obtains from applying the fundamental idea of adjusted

present value (APV) that leveraged value equals unleveraged value plus the present value of financing

side effects. The main contribution of this paper is to derive a formula for the equity discount rate that

when applied in the flows-to-equity method under fixed debt plans, yields correct equity values. In

short, the paper can be viewed as reconciling the flows-to-equity method with APV for projects with

fixed debt plans. Our approach builds on the no-arbitrage valuation approach to valuing interest tax

shields in Cooper and Nyborg (2008). We also expand on the basic analysis by incorporating the

possibilities of mispriced debt and costs of financial distress in the equity discount rate formula.

A key challenge withusing the flows-to-equity method to value projectswith fixed debt plans is that

the equity discount rate will be time-varying as leverage, and thus alsothe risk of equity, changes over

time as the debt plan unfolds. Calculating leverage and equity discount rates at different pointsin time,

therefore, requires estimates of equity and debt values for each year, or date, of the project’slife.As

shown by Esty (1999), the apparentcircularity in this is dealt with through iteration, untilwhat one puts

in, in terms of initial values, is what one gets out. Thus, the final estimates of values and time-varying

discount rates mustsatisfy a simple consistency condition. Valuationusing iteration is common in other

applications in finance, for example, to value new issues of corporate securities with options features

such as warrants. The formula we derive in this paper links the equity discount rate to leverage and

generatescorrect valuations using Esty’s (1999) iterativeimplementation of the flows-to-equitymethod.

The flows-to-equity method has several features that may help explain its popularity in practice,

despite the relative complexity of an iterative procedure. For example, as emphasized by Esty (1999)

and Baldwin (2001a), the flows-to-equity method:

focuses directly on the cash flows that accrue to equity holders;

can allow for time-varying leverage, which is inconsistent with using a constant weighted average

cost of capital (WACC);

can allow for a time-varying cost of equity;

can allow for time-varying effective tax rates;

can allow for several rounds of financing.

These benefits of the approach are particularly relevant in HLTs such as LBOs and project finance.

However, the flows-to-equity approach also has some potential difficulties that may be especially

pertinent in the context of HLTs. In particular, these transactions tend to use high-yield structured debt,

which raises three important issues:

Should one use the debt’s promised yield or expected rate of return as the ‘cost of debt’when

calculating the equity discount rate for use in the flows-to-equity method?

The cost of debt may contain an element that reflects factors other than credit risk, such as illiquidity.

How should these non-risk elements of the cost of debt be incorporated in the valuation?

HLTs bring a significant chance of financial distress. Is there a simple way of including the effect of

this in the valuation?

COOPER AND NYBORG

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