Cost of capital and valuation in the public and private sectors: Tax, risk and debt capacity

• Author: Richard A. Brealey,Michel A. Habib,Ian A. Cooper
• Date: 01 January 2020
• DOI: http://doi.org/10.1111/jbfa.12413
• Published date: 01 January 2020

DOI: 10.1111/jbfa.12413

Cost of capital and valuation in the public and

private sectors: Tax, risk and debt capacity

Richard A. Brealey1Ian A. Cooper1Michel A. Habib2

1LondonBusiness School, Sussex Place, Regent’s

Park,London, NWl 4SA, United Kingdom

2University of ZurichSwiss Finance Institute, and

CEPR

Correspondence

IanA. Cooper, London Business School, Sussex

Place,Regent’s Park, London, NWl 4SA, United

Kingdom.

Email:icooper@london.edu

Abstract

Cost of capital and valuation differ in the private and public sectors,

because taxes are a cost to the private sector but are only a transfer

to the public sector.We show how to transform the after-tax private

sector cost of capital into its pre-tax equivalent, for comparison with

the public sector cost of capital. We establish the existence of a tax

induced wedge between these two costs of capital. The wedge intro-

duces a preference on the part of the private sector for assets with

rapidtax depreciation, high debt capacity and low risk. We show that,

in circumstances where an asset has identical public and private sec-

tor valuation in the absence of taxes, the tax induced difference in

valuation is identical to the change in government tax receipts that

results from having the asset owned by the private rather than the

public sector. We provide some examples of distortions that result

from failure to adjust for changes in tax revenues, and show how to

effect such adjustment.

KEYWORDS

cost of capital, debt capacity,depreciation, outsourcing, private sec-

tor,privatization, public sector, regulation, risk, tax, valuation

JEL CLASSIFICATION

G18

1INTRODUCTION

Numerous assets and activities lie at the boundary between the private and public sectors; whether these should

belong to or be undertaken by a private sector firm or the government involvesthe comparison of the value of these

assets or activities under private and public sector ownership or provision. Forexample, decisions regarding the priva-

tization of public assets, the private financing of public infrastructure, the contracting out of governmentservices, the

granting of governmentguarantees, and the forward purchase of goods and services by the government all involve the

computation of the present value of the associated cash flows under public and private ownership or provision. They

therefore require the determination of public and private sector valuation procedures and costs of capital.

J Bus Fin Acc. 2020;47:163–187. wileyonlinelibrary.com/journal/jbfa c

2019 John Wiley & Sons Ltd 163

164 BREALEY ET AL.

These differ in the presence of taxes,even for the same asset or activity: taxes are a cost to the private sector but are

only a transfer to the public sector.We use a novel approach based on quasi-arbitrage to derive the discount rates and

determine the valuation procedures that should be used by the private and public sectors in the presence of corporate

and personal taxes. We show how to transform the after-tax private sector cost of capital into its pre-tax equivalent

for comparison with the public sector cost of capital. We establish the existenceof a tax induced wedge between these

two costs of capital. We show that, in circumstances where an asset has identical public and private sector valuation in

the absence of taxes, the tax induced difference in valuation is identical to the change in government tax receipts that

results from having the asset owned by the private ratherthan the public sector: a higher private sector valuation is at

the expense of the government, which sees its tax revenuesdecrease compared to the case in which the government

owns the asset; conversely,a lower private sector valuation benefits the government, which enjoys an increase in tax

revenues.

Taxesare a cost to private sector investors, who individually receive,in the form of government benefits, only a very

small fraction of the incremental tax payments that they make following investment in a givenproject.1The private

sector therefore adjusts for tax both in the cash flows that it receives from the project and in the discount rate which

reflects the opportunity cost of investingin that project. In contrast, taxes incurred as part of public investment are but

a transfer within the public sector,for example from the public sector corporation that has undertaken a given project

to the general governmentbudget.

The quasi-arbitrage approach we use is similar to that used by Modigliani and Miller (1958, 1963). Investmentin a

project sees both shareholders and citizens/taxpayersrebalance their portfolios away from equity and towards debt to

hedge the risk of the investment. The requirement that there be no arbitrageequates the return on the hedged invest-

ment to the risk free return; returns are expressed on an after-tax basis for shareholders and on a before-tax basis for

citizens/taxpayers.The resulting equilibrium conditions deliver the valuation procedures and the cost of capital for the

private and public sectors. Transformingthe private sector equilibrium condition from after- to pre-tax obtains the pre-

tax equivalent of the after-tax private sector cost of capital. Comparison with the public sector cost of capital reveals

the existence of a wedge between the private and public sector costs of capital, due to the different taxation of debt

and equity and of real and financial investment.

The wedge implies that a project will appear to have different values depending on whether it is undertakenby the

public or the private sector.Under conditions that characterize most tax systems, taxes induce a systematic preference

by the private sector for assets with rapidtax depreciation, high debt capacity, and low systematic risk. Yet, such differ-

ence is illusory,as a difference in valuation that is due entirely to tax considerations amounts only to a wealth transfer

between the public and the private sectors. Indeed, we show that the difference in valuation corresponds to the change

in tax payments that result from the transfer of the asset fromthe public to the private sector.

The apparent difference in valuation has possibly misleading implications for whether a project should be under-

takenby the public or the private sector. We analyze these implications for the choice between public and private own-

ership, transactionsbetween the public and the private sector, and regulation. We show how to evaluate such decisions

correctly.

For our analysis to matter,governments must use present value techniques for the purpose of evaluating projects.

Is that the case? The guidelines for investment of the Asian Development Bank (Asian DevelopmentBank, 2017), the

European Investment Bank (European Investment Bank, 2013), France’s Inspection des Finances (Charpin, Ruat, &

Freppel, 2016), the United Kingdom’s Treasury(HM Treasury, 2018), the United States’ Office of Management and

Budget (Office and Management and Budget, 2018), and the World Bank (Independent Evaluation Group, 2010), all

suggest such is indeed the case, for central governmentsand international organizations at least.2

Our analysis makesa number of assumptions. Toconcentrate on the effect of tax, we abstract from other important

considerations. Specifically, we abstract from differences in risk-bearing ability by assuming that both sectors have

1Alternatively,private sector investors may enjoy reduced tax payments; recall the discussion in the preceding paragraphand see the formal analysis below.

2Thecase of local government may be different; we thank an anonymous referee for alerting us to that difference.