Contingent Capital, Real Options, and Agency Costs

• Author: Zhaojun Yang,Dandan Song
• Published date: 01 March 2016
• DOI: http://doi.org/10.1111/irfi.12076
• Date: 01 March 2016

Contingent Capital, Real Options,

and Agency Costs*

DANDAN SONG

†

AND ZHAOJUN YANG

‡

†

School of Finance and Statistics, Hunan University, Changsha 410079, China and

‡

School of Business Administration, Hunan University, Changsha 410082, China

ABSTRACT

This paper aims to clarify how contingent convertible bond (CoCo) as a debt

financing instrument affects a firm’s investment policy, agency cost of debt, and

capital structure. We consider endogenous and exogenous conversion thresholds,

respectively. Under the exogenous case, there is an explicit optimal fraction of

equity allocated to CoCo holders upon conversion, such that the agency cost

reaches zero. Numerical analysis demonstrates that under an endogenous conver-

sion threshold, CoCo induces overinvestment, a higher leverage, a possible bigger

agency cost, and a stronger incentive to increase risk. But ifthe conversion thresh-

old is exogenously determined, almost the opposite holds true.

JEL classification: G13; G32

I. INTRODUCTION

In this paper, we provide an investment-based explanation for issuance of con-

tingent capital, that is, contingent convertible bond (CoCo, henceforth), into

the capital structure of a firm. To this end, we develop a continuous-time model

for a firm, which is initially endowed with a perpetual option to invest in a pro-

ject at any time by incurring an irreversible sunk cost. The firm must make two

decisions regarding the undertaking of the project at initial time: the investment

timing and optimal financing policies. We model the firm’s investment behavior

as a real option under the firm-value-maximizing and equity-value-maximizing

policies respectively and not a static (now or never) decision. Throughout the pa-

per, the firm makes its financing decision by determining the optimal issuing

amounts of equity and debt (straight bond and/or CoCo) at the moment when

the investment option is exercised. By providing a comparison with straight

bond financing (SB, henceforth), we attempt to shed some additional light on

the role of the issuance of CoCo to the firm’s investment policy, optimal capital

structure of the firm, and the problems of risk-shifting and agency costs.

* The authors are grateful to an anonymous referee and an associate editor for their helpful com-

ments. The research for this paper was supported by the National Natural Science Foundation of

China (project nos. 71171078, 71502054, 71371068, 71221001 and 71431008) and the China

Scholarship Fund for Studying Abroad (project no. 201506135009).

© 2016 International Review of Finance Ltd. 2016

International Review of Finance, 16:1, 2016: pp. 3–40

DOI: 10.1111/irfi.12076

In the recent financialcrisis, many financial institutions/firms have experienced

financial distress,under which the companieswere not able to raise significantnew

funds from themarket through conventionalassets and some banks had to depend

instead on governmentsto provide capital, that is, government bailouts.However,

emergency-type government bailouts can be controversial because the essence of

government bailout is to give the taxpayers’moneyto the troubled financial firms.

This action inevitably leads to serious moral hazard problems. For this reason, the

so called CoCo has drawn much attention of researchers and regulators because

CoCo is able to increase tax shields while keeping default risk in a given level.

CoCos, also known as contingent capital or CoCo notes, are specific type of

corporate hybrid bonds similar to traditional convertible bonds. However, in

contrast to the latter whose conversion thresholds are freely decided by the

bondholders, the time to convert CoCo into equity may be optimally determined

by the shareholders or contingent on a specified event, which can be different

depending on a particular goal.

It is well known in corporate finance that optimal capital structure depends on

the firm’sfinancial conditions, say the cash flow level generated by the firm or

the unlevered firm value. Generally speaking, the better the financial conditions,

the higher the leverage in capital structure should be. On account of that the fi-

nancial conditions usually change randomly all the time, and more often than

not, the optimal capital structure just established will become obsolete quickly.

To keep the capital structure optimal, we are able to do nothing but update the

capital structure dynamically and continuously. For example, if a firm gets into

(grows out of) trouble, the firm should retire (issue) debt to dynamically adjust

the firm’s leverage; see Titman and Tsyplakov (2007) among others. However,

in general, such update would incur considerable adjustment costs, and espe-

cially, it is nearly impossible under many situations. For instance, if the firm is

a small- and medium-sized enterprise, the adjustment is very difficult, or adjust-

ment costs are prohibitively expensive (Yang and Zhang, 2013). In sharp

contrast, if a firm includes CoCo into its capital structure, to some extent, such

adjustment is automatically realized and roughly incurs no extra cost.

Based on this, there are at least two merits if firms issue CoCo: Firstly, the firms

are relieved of serving their debt obligations in bad states of the economy, when

costly financial distress may occur and if creditors continue to demand their in-

terest and principal payments. Secondly, the equity buffer could increase, further

bolstering the firm’s capital as a result of the forced conversion of CoCo. Clearly,

if the firm takes CoCo as a debt financing instrument, the bankruptcy risk of the

firm will decrease considerably. Therefore, for a firm like a bank, which is too im-

portant to fail, it is very beneficial to issue CoCo as argued by many researchers

after the recent global financial crisis.

A. Our contributions

The contributions of this paper to the literature are summarized as follows. We

take into account the interaction between real options and the capital structure

International Review of Finance

© 2016 International Review of Finance Ltd. 20164

including CoCo, and especially investigate the effect of CoCo as a means of debt

financing instrument. We propose and examine an additional explanation why it

is important for CoCo to be included into capital structure. We investigate CoCo

under two different conversion rules: One is optimally endogenously determined

by shareholders, and the other is exogenously given. We find a new merit of

CoCo: If CoCo is well designed, it is able to considerably lessen the agency cost

of debt. In particular, we provide an explicit expression of the optimal fraction

of equity allocated to CoCo holders upon the conversion of CoCo to equity,

which makes sure that the agency cost of debt arrives at the minimum value zero

if the conversion barrier of CoCo is exogenously determined.

Our numerical analysis demonstrates that the issuance of CoCo not only

decreases the bankruptcy costs but also significantly increases the total firm value

because of the much larger leverage, which creates additional larger tax shields. If

the conversion threshold of CoCo is endogenously determined by shareholders,

our results state that a firm issuing CoCo exercises investment option earlier than

that issuing SB only. The former will have more incentive to increase risk and

incur a larger agency cost of debt. However, if the conversion threshold is exoge-

nously given, the risk-taking incentive, overinvestment problem, and the agency

cost of debt decrease significantly. In addition, the total firm value at initial time

is a concave function of the conversion ratio (ownership stake), and so, there is a

unique optimal conversion ratio under the equity-value-maximizing investment

policy, at which the agency cost reaches the minimum value zero.

B. Literature review

In their seminal work, Brennanand Schwartz (1985) uses option pricing theory to

fix the value and the optimal production policies of a naturalresource investment.

After that, real options theory, which captures the value of flexibility under uncer-

tainty, has attracted growing attention following McDonald and Siegel (1986).

Leland (1994) derives closed-form solutions for the value of debt, yield spreads,

and optimal capital structure in a unified analytical framework. Mauer and Sarkar

(2005) examine the impact of a stockholder–bondholder conflict over the optimal

investment policy for a project and provide a measure of the agency cost of debt.

The optimal capital structure is found, and also, the tax benefits of debt financing

are included in their analysis. Sundaresan et al. (2015) investigate the investment

problems fora firm with growth option, which is financed withequity and SB only.

Egami (2010)considers a firm that has an expansion optionto invest in a new plant

with convertible debt financing. They use options game techniques to analyze

optimal strategies. Yagi and Takashima (2012) develop a model to examine the

timing of investment decision in relation to the issuance of convertible debt by

firms. They analyze the optimal coupon payments that are determined by maxi-

mizing the firm value. But the literature is silent about how corporate investment

interacts with financing decision when CoCo is included in capital structure.

Lyandres and Zhdanov (2014) study an expansion problem with equity financing

for a firm having issued SB and ordinary convertible bond instead of CoCo.

Contingent Capital, Real Options, and Agency Costs

© 2016 International Review of Finance Ltd. 2016 5