Agency cost of debt overhang with optimal investment timing and size

• DOI: http://doi.org/10.1111/jbfa.12379
• Date: 01 May 2019
• Author: Chuanqian Zhang,Sudipto Sarkar,Michi Nishihara
• Published date: 01 May 2019

DOI: 10.1111/jbfa.12379

Agency cost of debt overhang with optimal

investment timing and size

Michi Nishihara1Sudipto Sarkar2Chuanqian Zhang3,4

1GraduateSchool of Economics, Osaka

University, Japan

2Michael Lee-Chin& Family Professor in

StrategicBusiness Studies, DeGroote School of

Business, McMaster University, Hamilton,

Canada

3YangtzeNormal University, Chongqing, P.R.

China

4CotsakosCollege of Business, William Paterson

University, New Jersey,USA

Correspondence

ChuanqianZhang, 1600 Valley Road, Wayne,

NJ07470, USA.

Email:zhangc4@wpunj.edu

Fundinginformation

NationalNatural Science Foundation of China,

Grant/AwardNumber: 71702013; JSPSKAK-

ENHI,Grant/Award Numbers: JP17H02547,

JP17K01254.

Abstract

The concept of debt overhang (that is, an equity-maximizing levered

firm will under-invest relative to a firm-value-maximizing firm) is

well established in the literature. A number of papers have demon-

strated it as delayed investment (when investmentsize is specified)

or smaller investment (when investmenttime is specified). However,

there is no work on the underinvestment effect when the firm

chooses both size and timing of investment, as it usually does in real

life. This is what our paper focuses on. When the firm has the flexibil-

ity to choose both size and time, the effect is complicated by the fact

that delayed investmentresults in larger investment, which suggests

that the underinvestment problem might be mitigated. We find,

however, that the effect depends on how underinvestment is mea-

sured. When measured by the expectedpresent value of investment,

flexibility can mitigate or exacerbate the underinvestmentproblem,

depending on the cost of installing capacity. But when measured by

the agency cost, flexibility always exacerbates the underinvestment

problem. It is shown numerically that, at the optimal leverage ratio,

the agency cost with plausible parametervalues can be economically

significant. Thus, with the flexibility of choosing both time and size

of investment, the debt overhang problem can be of significant

practical relevance in corporateinvestment decisions.

KEYWORDS

agency cost, contingent-claim model, debt overhang, investment

flexibility,investment trigger, underinvestment

1INTRODUCTION

This paper studies the debt overhang (or underinvestment) problem and the associated agency cost when a firm has

the flexibility to choose both the timing and the size of its investment. Although there is a sizeable literature on debt

overhang and its effect on corporate investment, the existing papers examine a firm’s investment decision when it

chooses either the investment timing (for given size) or the investment size (for given timing); examples are Chen

and Manso (2017), Childs, Mauer, and Ott (2005), Hennessy (2004), Manso (2008), Mauer and Ott (2000), Mello and

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2019 John Wiley & Sons Ltd wileyonlinelibrary.com/journal/jbfa JBus Fin Acc. 2019;46:784–809.

NISHIHARA ET AL.785

Parsons (1992), Pawlina(2010), Titman and Tsyplakov (2007), etc., for the former, and Jou and Lee (2004) and Moyen

(2007) for the latter.

In practice, though, the firm will generally have the ability to choose both the timing and size of its investment

(Bar-Ilan & Strange, 1999; Dangl, 1999; Huberts, Huisman, Kort, & Lavrutich, 2015; Jou & Lee, 2008), and it is not

clear how this flexibilitywill affect the underinvestment problem. As shown by the first set of papers above, for a given

investment size, shareholders of a leveredfirm will delay investment or under-invest; in other words, the second-best

investment trigger (that maximizes equity value) will exceed the first-best trigger (that maximizes total firm value).

Now, if the firm has the additional flexibility of choosing investment size as well, it will choose a larger size because

of the delayed investment (i.e., second-best investment size will exceedthe first-best size).1That is, if investment is

delayed (implying underinvestment),the investment size will also be larger (implying overinvestment), so it is not clear

whether the underinvestment problem will be mitigated, exacerbated or unchanged bythe investment flexibility (the

ability to choose both timing and size). For instance, the offsetting nature of the timing and size effects might suggest

that investment flexibilitywill mitigate the underinvestment incentive.

However,while this scenario should be of practical interest, it has not been examined to date. Our paper addresses

this gap in the literature,by extending the existing literature to study the debt overhang problem for a levered firm that

can choose both investment timing and investment size, using a ‘lumpyinvestment’ capacity model similar to Bar-Ilan

and Strange (1999) and Dangl (1999).

Ourmodel shows that the overall effect on the underinvestment incentive is ambiguous, and depends on how under-

investment is measured. When measured by investment dollars (in expected present value terms), underinvestment

might be mitigated or exacerbated by investment flexibility depending on the cost of productive capacity. However,

when measured by agency cost, the underinvestment problem is always exacerbatedby investment flexibility. In con-

trast to earlier studies, the agencycost of underinvestment can be economically significant with reasonable parameter

values.2Agency cost is generally substantially larger than previously thought, because of the interactionof timing and

scale choices in investment. The practical implication is that the debt overhang/underinvestmentproblem can have a

non-trivial impact on corporate investmentdecisions.

Although our conclusions are based on numerical results, they are robust to changes in parameter values; thus, we

are confident of the generality of the results. The rest of the paper is organized as follows. Section 2 summarizes the

findings in the existing literature, Section 3 develops the model, Section 4 illustrates the main results, and Section 5

concludes.

2LITERATURE

As mentioned above, a number of studies analyze the debt overhang problem when the investment size is specified

and the firm chooses investmenttiming optimally. These studies show that the second-best investment trigger exceeds

the first-best trigger,implying delayed investment or underinvestment. Mauer and Ott (2000) and Mello and Parsons

(1992) demonstrate underinvestment but report very small agency costs. Pawlina (2010) also finds extremely small

agency cost (except for the unusual scenario of negative growth), and shows that debt renegotiation in financial

1It has been shown that firms that investlater choose a larger size or capacity, thus it is important to study the capacity decision next to the timing decision

(Bar-Ilan& Strange, 1999; Dangl, 1999; Huberts, Huisman, Kort, & Lavrutich, 2015; Jou & Lee, 2008).

2Theexisting literature finds the agency cost of debt overhang to be generally negligible; according to Moyen (2007): ‘The existing literature,including Mauer

and Ott (2000), Mello and Parsons (1992) and Parrino and Weisbach (1999), already provides debt overhangcost estimates. Their estimates quantify the

overhangproblem to no more than 1.54% of firm value’. Mello and Parsons (1992) estimate agency cost at only 0.8% of firm value for the base case, and much

smaller at optimal leverageratio (varies between 0.031% and 0.313% for a reasonable range of commodity price (their Table VI)). Pawlina (2010) finds that,

for reasonable parametervalues (‘to reflect a typical US non-financial firm’, p. 687), the maximum agency cost is between 0.2% and 0.3% (their Figure 3, part

A). In fact, Parrinoand Weisbach (1999) demonstrate, using Monte Carlo simulations, that agency costs are unlikely to be important in corporate investment

decisions. This leads to the question: if the agency cost of debt overhang is so small, does the debt overhangproblem have a material effect on shareholder

well-being,or can it, for practical purposes, be ignored in corporate decisions?