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

Date01 January 2018
Published date01 January 2018
DOI: 10.1111/eufm.12136
Consistent valuation of project finance and LBOs
using the flows-to-equity method
Ian A. Cooper
Kjell G. Nyborg
Department of Finance, London
Business School, Regents Park, London
Department of Banking and Finance,
University of Zurich, Plattenstrasse 14,
8032 Zurich, Switzerland
Swiss Finance Institute,Walchestrasse 9,
8006 Zurich, Switzerland
Centre for Economic PolicyResearch, 33
Great Sutton Street, London EC1V0DX,
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
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.
cost of debt, cost of equity, equity cash flow, flows to equity, LBO,
project finance, valuation
G12, G24, G31, G32, G33, G34
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.
© 2017 John Wiley & Sons, Ltd. Eur Financ Manag. 2018;24:3452.
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-equitymethod, whereby the projects 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 projectslife.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 Estys (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 debts promised yield or expected rate of return as the cost of debtwhen
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?

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