Capital Structure and Debt Priority

• DOI: http://doi.org/10.1111/fima.12011
• Author: Patrice Poncet,Sami Attaoui
• Published date: 01 December 2013
• Date: 01 December 2013

Capital Structure and Debt Priority

Sami Attaoui and Patrice Poncet∗

We study a defaultable firm’s debt priority structure in a simple structural model where the firm

issues senior and junior bonds and is subject to both liquidity and solvency risks. Assuming that

the absolute priority rule prevails and that liquidation is immediate upon default, we determine

the firm’s interior optimal priority structure along with its optimal capital structure. We also

obtain closed-form solutions for the market values of the firm’s debt and equity. We find that the

magnitude of the spread differential between junior and senior bond yields is positively, but not

linearly related to the total debt level and the riskiness of assets. Finally, we providean in-depth

analysis of probabilities of default and the term structure of credit spreads.

In a seminal work, Merton (1974) derived the first structural model for corporate debt pricing.

Relying on the contributions of Black and Scholes (1973) and Merton (1973), he obtained the

price of a zero coupon defaultable bond in the context of a terminal default boundary and

investigated the behavior of the ensuing credit spread term structure. Abundant literature has

since been developed to investigate the pricing of corporate bonds in more general frameworks

and, more broadly, to analyze capital structure decisions.1

This is an important area of study. The simplifying assumption of a homogeneousdebt str ucture

made in the prior literature contradicts firms’ actual practice of issuing debt of different priorities.

For instance, Barclay and Smith (1995) find that most of the firms in their sample rely on

senior and junior (subordinated) classes of bonds. Billett, King, and Mauer (2007) confirm that

subordinated debt accounts for approximately 25% of the total debt issuance in their sample.2

Rauh and Sufi (2010) observe that rated f irms simultaneouslyissue debt with different types and

priorities and that the number of debt classes depends markedly upon these firms’ credit standing.

Additionally, in a large data set of rated and unrated publicly listed firms, Colla, Ippolito, and

Li (2013) report that the sample mean ratios for senior and subordinated bonds over total debt

are approximately 40% and 10%, respectively. Moreover, a growing body of theoretical research

acknowledges and attempts to explain debt heterogeneity and priority structure. One strong

argument is that credit quality is a major force driving the firm’s debt structure. For example,

high quality firms can borrow directly from arm’s length (junior) creditors and reduce the costs

of (senior) bank debt associated with monitoring. Slightly more generally, the type and priority

Weare grateful to Raghu Rau (Editor) for his insightful comments and to an anonymous refereefor very useful comments

and suggestions that have substantially improved the overall quality of the paper. We also thank Sridhar Arcot, Florina

Silaghi, and participants at the EUROFIDAI—AFFI 9th International Paris Finance Conference for their discussions.

Weare solely responsible for any remaining errors.

∗Sami Attaoui is an Associate Professor of Finance in the Economics and FinanceDepartment, at the Rouen Business

School in Mont Saint Aignan, France.Patrice Poncet is a Distinguished Professorof Finance in the Finance Department

at ESSEC Business School in Cergy-Pontoise,France.

1See, for instance, Kim, Ramaswamy, and Sundaresan (1993), Longstaff and Schwartz (1995), Briys and de Varenne

(1997), Collin-Dufresne and Goldstein (2001), Leland (1994), Leland and Toft(1996), Goldstein, Ju, and Leland (2001),

Ju et al. (2005) and Ju and Ou-Yang(2006). See also useful surveys by Bielecki and Rutkowski (2002), Uhrig-Homburg

(2002), and Franc¸ois (2005).

2See their TableII on p. 705.

Financial Management •Winter 2013 •pages 737 - 775

738 Financial Management rWinter 2013

of debt is designed optimally to mitigate managerial and creditor agency issues (Diamond, 1991;

Bolton and Freixas, 2000). The existence of senior and junior debt has also been attributed to

covenantsthat prohibit f irms from issuing further senior debt. However,recent empirical evidence

contradicts this argument. For instance, Billet, King, and Mauer (2007) report only a few cases

of debt issuance restriction in their sample. Senior debt issuance including restrictions on issuing

further senior debt or subordinated debt is only observed in 0.4% and 0.7% of cases, respectively.

When subordinated debt is issued, these percentages increase but remain marginal (4.5% and

22.4%, respectively).3Overall, both the empirical evidence and the theoretical argument above

make the optimality of the debt mixture outside of financial distress a relevant problem to study.

In our paper, we consider two classes of bonds, senior and junior. We contribute to the literature

in four related ways.

Our first contribution is an interior optimal priority structure. This results from the trade-

off between bankruptcy costs and tax deductions. For a given level of total debt, increas-

ing the proportion of (more costly) junior bonds increases the firm’s probability of default

hence the present value of bankruptcy costs, but it also increases the present valueof tax deductions

the larger coupons provide. The optimal debt priority structure is reached when these two effects

cancel out at the margin.

Our second contribution is to account explicitly for two sources of risk. We are motivated

by Davydenko (2010), who investigates the nature of the default boundary for distressed firms

empirically. He finds that default is triggered either by a negative net worth at some prin-

cipal payment date (the firm is insolvent) or by a cash flow shortage (the firm is illiquid).

Thus, our model embeds these two risks in the following manner. First, default (or bankruptcy,

the two terms being used in this paper interchangeably) occurs if at any date the firm does

not generate enough cash flow to fund its debt coupons (liquidity risk). Then, provided that

bankruptcy due to illiquidity has not occurred before the firm’s debt maturity, default may still

occur at maturity if the firm’s assets are not sufficient to back the full amount of the debt

principals (solvency risk). This distinction between liquidity and solvency risks has also been

emphasized in theoretical models by Gryglewicz (2011) and von Thadden, Bergl¨

of, and Roland

(2010).4The existence of these two kinds of risk has considerable bearing on default probabil-

ities and, consequently, on bond values and yield spreads and on the firm’s optimal financing

policy.5

Our next contribution is the simultaneous analyses of the optimal debt priority mix and the

optimal capital structure. The valuation of senior and junior debt has been investigated by Black

and Cox (1976) and Geske (1977). Whereas Black and Cox (1976) analyze zero coupon bonds

maturing on the same date, Geske’s (1977) model allows for bonds with different maturities.

However, these papers are silent as to the optimality of the exogenous priority structure. Our

work is also related to two recent studies by Hackbarth, Hennessy, and Leland (2007) and

Hackbarth and Mauer (2012), but differs in several respects. First, in both papers, the debt is

infinitely lived. In contrast, our debts are (relatively) short-lived (from 2 to 20 years in the

simulations) so that we can highlight the role of debt maturity in determining both the op-

timal priority structure and the optimal leverage. Second, Hackbarth, Hennessy, and Leland

3See their TableIII on p. 707.

4For example, von Thadden, Bergl¨

of, and Roland (2010) write “firms default either because they lack liquidity, but are

fundamentally sound or because they have liquidity but little long-term value” (p. 2651).

5In an earnings before interest and taxes (EBIT)-based setting with a homogeneous debt, Gryglewicz (2011) determines

that the interaction between liquidity and solvency has an impact on leveragepolicies and credit spreads.

Attaoui & Poncet rCapital Structure and Debt Priority 739

(2007) posit a strategic default setting to investigate the debt priority structure between a bank

debt and a market debt, while Hackbarth and Mauer (2012) analyze the role that priority debt

structure plays in resolving conflicts between stakeholders over investment policy. We abstract

from these complications and assume immediate liquidation in the case of bankruptcy. In par-

ticular, both liquidity and solvency defaults are triggered by bond covenants and, as such, are

considered to be passive, as opposed to strategic, defaults (Fan and Sundaresan, 2000). Accord-

ing to the absolute priority rule under Chapter 7 liquidation, junior debtholders are paid some

amount upon default only if senior bondholders have received full payment. Empirical results

obtained by Bris, Welch, and Zhu (2006) confirm the absence of violations of the absolute

priority rule under Chapter 7. A final and crucial distinction from both Hackbar th, Hennessy,

and Leland (2007) and Hackbarth and Mauer (2012) is that their firms face solvency risk

only.

Our model predicts that lowleverage f irms rely more on junior debt than do more indebted firms.

In addition, high leverage firms increase their proportion of senior debt as their assets become

riskier. These results follow from the trade-off between the tax benefits the fir m receives from

the deduction of larger coupons on its junior debt and the expected bankruptcy costs generated by

a higher probability of intermediate or terminal default. In addition, a weakly levered firm relies

heavilyon junior bonds, with a smaller role played by either the volatility of its operational income

or the maturity of its debt. On the contrary, the high levered firm’s optimal policy depends upon

the riskiness of its assets. If the latter is low, the proportion of senior debt becomes significant only

at long maturities and then rises sharply as the debt maturity increases even more. If asset return

volatility is high, the proportion of senior debt becomes significant at much shorter maturities

and rockets to 100% for maturities that are even slightly longer. Additionally, we obtain realistic

values for the firm’s leverage ratio, measured as D/V where Dis the bonds’ market value and

Vis the firm’s market value. The ratio ranges from 49.9% (for very short debt maturity and

low asset volatility) to 20.6% (for long-term debt and high asset volatility). For instance, D/V

may be as small as 27.7% for a 30% asset volatility and a 10-year bond maturity. This result

is consistent, in particular, with the prediction of Ju, Parrino, Poteshman, and Weisbach (2005)

and the empirical findings of Faulkender and Petersen (2006). To achieve this optimal leverage,

the firm relies essentially on junior debt to take full advantage of the tax deductions. The firm’s

optimal leverage decreases with debt maturity and asset return volatility, as the probability of

premature or terminal default increases on both counts.

Finally, we contribute to the literature by determining the default probabilities for senior and

junior debt and by analyzing the ensuing senior and junior credit spreads. Credit spreads for

senior bonds range from zero to 52 basis points (bps) and widen as either the volatility of the

assets or the proportion of the assets financed through debt increases. Credit spreads for junior

bonds are naturally much higher and may reach 600 bps for highly volatile and strongly levered

firms. We find that the spread differential is also positively related to the total amount of debt

and the riskiness of the assets. These relationships, however, are not linear. We attribute this

result to the differences in the expected recovery rates of the senior and junior bonds that stem

from the debt priority structure, the level of leverage, and the type of default risk that may

materialize.

The remainder of the paper is organized as follows. Section I introduces our model setting and

assumptions. Section II provides the pricing formulas for both senior and junior bonds. Section

III derives the firm and equity values. In Section IV, we perform a numerical analysis of the

debt priority structure, the optimal capital structure, the debt values and credit spreads, and the

probabilities of default. Section V provides our conclusions.