Investment and financing for cash flow discounted with group diversity

• Published date: 01 September 2021
• Author: Pengfei Luo,Zhaojun Yang
• Date: 01 September 2021
• DOI: http://doi.org/10.1111/irfi.12295

ORIGINAL ARTICLE

Investment and financing for cash flow discounted

with group diversity

Pengfei Luo

1

| Zhaojun Yang

2

1

School of Finance and Statistics, Hunan

University, Changsha, China

2

Department of Finance, Southern University

of Science and Technology, Shenzhen, China

Correspondence

Zhaojun Yang, Department of Finance,

Southern University of Science and

Technology, Shenzhen, China.

Email: yangzj@sustech.edu.cn

Funding information

Special Innovation Projects of Universities in

Guangdong of China, Grant/Award Number:

2018WTSCX131; Guangdong Planning Office

of Philosophy and Social Science for the 13th

Five-Year Plan, Grant/Award Number:

GD19CYJ23

Abstract

We consider a firm's investment and financing decisions

made by a group of agents on behalf of shareholders, of

which each individual utilizes a different discount rate fol-

lowing a given probability distribution for the valuation of

equity. We measure group diversity by the variance of the

distribution. The price of debt is determined by an equilib-

rium method in a competitive market. We show that a

greater group diversity increases the project value, acceler-

ates investment and postpones default. The value of the

investment option increases but the optimal leverage

decrease with the group diversity. The inefficiency from

asset substitution increases but that from debt overhang

decreases with the group diversity. Our predictions are

documented by empirical evidences.

KEYWORDS

agency costs, group diversity, investment and financing, time

inconsistent, weighted discounting

JEL CLASSIFICATION

G11; G32

1|INTRODUCTION

The asset pricing theory stems from the simple concept that price equals expected discounted payoff and the main

task of the theory is to identify the discount factor or equivalently the instantaneous discount rate which takes into

account both the time and risk discount. Many papers in the literature assume that the instantaneous discount rate

is constant all the time. However, a lot of experimental and empirical studies on time preferences suggest that the

Received: 18 May 2019 Revised: 12 December 2019 Accepted: 23 December 2019

DOI: 10.1111/irfi.12295

© 2020 International Review of Finance Ltd. 2020

International Review of Finance. 2021;21:769–785. wileyonlinelibrary.com/journal/irfi 769

assumption of time consistency is unrealistic. For example, Frederick, Loewenstein, and O'donoghue (2002) review

the experimental literature on time preferences and Falk, Becker, Dohmen, Enke, and Huffman (2018) present survey

evidence representing 90% of the world population. Both studies report substantial heterogeneity in discounting

behavior. Actually, time inconsistency has recently attracted a lot of research in the literature, say Grenadier and

Wang (2007) and Tian (2016) among others.

Recently, Ebert, Wei, and Zhou (2018) argue that many decisions are made by a group of people, say in a large

company, and each member would use a different discount factor to value a project. Interestingly, Ebert et al. (2018)

show that even if all the members of a group are time consistent, the group must be generally time inconsistent in

making decisions and the group gets more and more patient with the lapse of time, that is, the group has the

decreasing impatience. Actually, at a much earlier time, Weitzman (2001) proposed to incorporate the different dis-

count factors decided by a group into making one-time irreversible investment decisions, and argued that it must be

a challenging direction for future research.

Along this research line, we consider the following problems. What is the impact of group diversity, that is, the

variance of all the discount rates used by the group, on investment for cash flow under the pure equity case? When

should investment be funded by issuing equity, debt, or their mix? What is the optimal capital structure? How does

the group diversity impact on investment timing, option value, and default threshold? What is the relationship among

the group diversity and leverage? How does the group diversity affect agency problem of debt (e.g., asset substitu-

tion and debt overhang)? We emphasize that in sharp contrast to equity of a private firm, the debt in our model

should be priced still in a competitive market. This is because the amount of money financed by issuing debt must be

equal to the market value of the debt in a public competitive market, which, of course, will not be influenced by the

group diversity. For this reason, we should utilize two different methods in pricing corporate securities: Equity is

priced by the group diversity method we discussed here while debt is valued by the classical equilibrium pricing

method. Naturally, we are curious about what a different capital structure and agency conflicts between bondholders

and shareholders would be if the two different pricing methods are used in valuing the same firm's claims. The

above-mentioned problems are not studied by previous papers and we therefore aim to fill this gap.

1.1 |Our contributions

We consider a firm's investment and financing decisi ons made by a group of agents on behalf of shareholders, of

which each individual utilizes different discoun t rates following a given probability distribution for the valuation of

equity. We measure group diversity by the variance of the distr ibution and the price of debt is determined by an

equilibrium method in a competitive market. We provide the cl osed-form prices for the firm's securities and the

pricing and timing of the option to invest for cash flow. We study the impact sof the group diversity on the invest-

ment and financing policies. We predict that a greater group div ersity increases the project value, accelerates

investment, and postpones default. The value of the investment opt ion increases with the group diversity. The opti-

mal leverage decreases with the group diversity. The inefficienc y from asset substitution increases but that from

debt overhang decreases with the group diversity. Our pr edictions are documented by empirical evidences. For

example, our prediction that the focused firms inves t significantly less than the diversified ones is in line with the

empirical findings of Singhal and Zhu (2013), Raja n, Servaes, and Zingales (2000), and Shin and Stulz (1998). Our

model predicts that the diversification reduces the likelih ood of bankruptcy, which is empirically documented by

Singhal and Zhu (2013), and that the diversification gi ves rise to carrying relatively less debt, which is consis tent

with an empirical evidence discovered by Singh, David son, and Suchard (2003), Margaritis and Psillaki (2 010), and

Lim, Das, and Das (2009). Our result explains the empirical findings by Faccio, Marchica, and Mura (2011) tha t the

firms controlled by the diversified large shareholder s have a stronger risk-shifting motive than those controlle d

by the nondiversified large shareholders. In additi on, we produce a financial explanation for the Prel ec's (2004)

measure of decreasing impatience.

770 LUO AND YANG