Corporate investment and financing with uncertain growth opportunities

• Published date: 01 September 2021
• Author: Biao Chen,Jinqiang Yang,Chuanqian Zhang
• Date: 01 September 2021
• DOI: http://doi.org/10.1111/irfi.12298

ORIGINAL ARTICLE

Corporate investment and financing with

uncertain growth opportunities

Biao Chen

1

| Jinqiang Yang

1,2

| Chuanqian Zhang

3

1

School of Finance, Shanghai University of

Finance and Economics, Shanghai, China

2

Shanghai Key Laboratory of Financial

Information Technology, Shanghai Institute of

International Finance and Economics,

Shanghai, China

3

Department of Economics, Finance and

Global Business, William Paterson University,

Wayne, New Jersey

Correspondence

Chuanqian Zhang, Department of Economics,

Finance and Global Business, William

Paterson University, Wayne, NJ.

Email: zhangc4@wpunj.edu

Funding information

Innovative Research Team of Shanghai

University of Finance and Economics, Grant/

Award Number: #2016110241; National

Natural Science Foundation of China, Grant/

Award Numbers: 71772112, 71972122

Abstract

This paper develops a continuous-time model of a firm's

sequential investments. The firm has an option to expand rev-

enue after the initial investment. However, the timing of

exercising the growth option depends not only on the underly-

ing cash flows but also on the uncertainty of the growth

opportunity. We show that the uncertainty of growth oppor-

tunity has a positive effect on the initial investment. In particu-

lar, the investment threshold has a nonmonotonic (U-shaped)

relation with the arrival rate of the growth opportunity, in that

it starts to decrease and then increase with the arrival rate.

The outcome is driven by the tradeoff between benefit and

cost of the prospective expansion, and the magnitude of that

rests on the level of arrival rate. For optimally levered firm, the

financial leverage ratio displays a U-shaped relation with the

arrival rate. It is caused by the interaction between future

growth uncertainty and debt overhang problem. Furthermore,

we show that the optimal leverage, depending on the level of

growth uncertainty, may or may not display inverse relation

with the growth size. Our results shed valuable light on the

empirical implication of testing the existence of debt overhang.

KEYWORDS

capital structure, growth uncertainty, real options, sequential

investment

JEL CLASSIFICATION

G31

[Correction added on 14 February 2020, after first online publication: affiliation 1 has been amended.]

Received: 22 December 2018 Revised: 30 November 2019 Accepted: 23 December 2019

DOI: 10.1111/irfi.12298

© 2020 International Review of Finance Ltd. 2020

International Review of Finance. 2021;21:821–842. wileyonlinelibrary.com/journal/irfi 821

1|INTRODUCTION

Firm's investment and financing decisions are among the most important topics in corporate finance. These decisions

can be impacted by many factors such as agency conflict (Mauer & Sarkar, 2005; Grenadier & Wang, 2005; Xu & Xu,

2019), asset tangibility (Campello & Hackbarth, 2012), debt issuance constrain (Shibata &Nishihara, 2012), liquidity

constrain (Bolton, Wang, and Yang, 2014; Boyle and Guthrie, 2003), macroeconomic conditions (Hackbarth, Miao,

and Morellec, 2006), market competition (Grenadier, 2002; Mason and Weeds, 2010), etc.

In this paper, we consider a channel, the uncertainty of growth opportunities, through which the investment and

financing decisions are distorted. The reasons for uncertainty of a firm's growth opportunity are multiple. For exam-

ple, some firms need technology innovation to generate new products; the success of new technology is uncertain

and unknown to managers (R&D, new drug development, etc). Some firms may have trouble tackling with uncertain

policies, selection of factory location and upstream supplier when they decide to expand either domestically or inter-

nationally. Thus it will be quite useful for a firm to consider such future uncertainties when it prepares to make the

initial investment decision.

Despite the important effect of future growth uncertainty on the current investment decision, only a few papers

have examined such a phenomenon. While our treatment of growth uncertainty is similar to Anderson and Carverhill

(2011),

1

there are some differences in modeling the uncertainty. They assume the growth is fully stochastic, thus the

value of each contingent claim is the probability weighted average of the value assuming the growth does occur and

does not occur. We model the uncertainty by assuming it arrives with Poisson process, similar to Li and Mauer

(2016). However, they assume that the expansion option must be exercised immediately if at all,

2

while in our paper

the firm can time its exercise of the growth opportunity.

From the perspective of investing, our model assumes there are two investment options, namely, initial invest-

ment and growth opportunity. The firm has no assets before initial investment. After initial investment, the firm

obtains one unit of asset-in-place which generates continuous profit flow and a growth option claim to the second

investment, which will further enhance the profit level. From the perspective of financing, we first assume the firm

can fund the initial investment by issuing a mix of debt and equity. Only equity (or retained earnings) will be used to

finance the second investment (one-stage debt financing), then we consider the case that the firm can fund the initial

investment and the growth opportunity by issuing a mix of debt and equity (two-stage debt financing). All the invest-

ment and bankruptcy thresholds will be endogenously derived.

Suppose a firm has made the first investment and wishes to expand current revenue. However, such an expan-

sion cannot be realized without more advanced technology and some investment cost. The irreversible sunk cost

implies the firm has to wait until the price reaches a higher level to exercise the growth option. However, the new

technology will arrive with uncertainty. It may have always been accessible for the time being, or need some time to

develop and we do not know when it can be implementable. Consequently, if the technology exists before the opti-

mal expansion trigger, then the firm can expand at this trigger, in line with traditional real option model. If the oppor-

tunity has not arrived, then it will not expand until the technology is available. To our best knowledge, this paper is

the first to relate future expansion opportunity to current investment decision, through arrival uncertainty. We docu-

ment that the magnitude of the impact of future uncertainty (embodied in Poisson process) on firm's initial invest-

ment can be economically significant. The concise symbolization by Poisson parameter not only makes our model

more tractable, but also can capture a wide range of realities as described previously.Thus our model provides a use-

ful guideline on the firm's investment decisions.

Our paper reveals several new results. Firstly, without arrival uncertainty, we illustrate that the expansion option

will impact the initial investment for a levered firm, the magnitude of which depends on the interaction between

growth size and agency problem of debt overhang.

Secondly, if there is uncertainty of arrival, our analysis shows that the uncertain ty of growth opportunity

has a positive effect (accelerating investment) on the initial investment, regardless of one-stage debt financing

and two-stage debt financing. The mechanism through which the initial investment timing is impacted lies on

822 CHEN ET AL.