Accounting quality, debt covenant design, and the cost of debt

Abstract

We examine whether debt covenant design (threshold tightness, covenants frequency, covenant interdependence, and overall covenant strictness) reduces the adverse effect of poor accounting quality on the cost of debt in the private lending market. We predict and find that when borrowing firms exhibit low accounting quality, lenders tend to increase debt contract strictness through debt covenant design (e.g., increasing the number of covenants, decreasing covenant interdependence or including covenants with greater threshold tightness). Moreover, our results indicate that the cost of debt for borrowers with low accounting quality is significantly influenced by the covenant strictness. Further evidence shows that, although debt covenant designs help mitigate adverse information risk, financial reporting quality is more important than strict debt covenants in lowering the cost of debt, a matter of concern for firm managers and lenders.

Appendices

Appendix 1

See Table 8.

Table 8 Variable descriptions

Appendix 2: Types of debt covenant restriction in loan contracts

The following table shows the type (in the first column) and distribution (in the second column) of covenants in our sample of loan packages. We take the loan package 100,472 (package ID) as an example to illustrate the debt covenant design. The lender of the loan is a syndicate group of banks. The loan amount was $25 million and would become mature in 12 months. The borrowing company of this loan contract is AAR Corporation, a company providing products and services to aviation, government, and defense markets worldwide. The loan contract is activated on Apr. 11, 2001 and includes four covenants (the number of covenants is above 80 % of the sample): Max. Leverage ratio covenant (the threshold is 0.6), Min. Current Ratio covenant (the threshold is 1.5), Min. Fixed Charge Coverage covenant (the threshold is 1.2), and Min. Tangible Net Worth covenant ($240 million). When the loan contract is activated, the company’s financial ratios or amounts are: leverage ratio is 0.3, current ratio is 2.7, fixed Charge Coverage is 1.4, and tangible net worth is about $341. The company was basically in a healthy financial condition as the loan was contracted. The company’s accruals quality (AQ) near the loan activated date (at the end of 2000 fiscal year) is 0.024, which is around the median of the sample; it’s earnings surprise (ES) is 0.058 and special items (SI) is 0.007, both of which are above 75 % of the sample. The covenant strictness (CovStrict) is 0.629, which is above the median of the sample; the covenant inter-dependence index (CovIntdep) of the loan is 0.453, which is below the median of the sample; among the four debt covenants, there is one debt covenant displaying covenant threshold tightness. As we can see, the borrowing company has relatively poor accounting quality and hence the loan contract was fairly strict.

Type of covenants	Numbers/percentages of packages that contain the covenant
Covenants for financial ratio
Max. Debt to EBITDA	4843 (47.50 %)
Min. Fixed Charge Coverage	3417 (33.51 %)
Min. Interest Coverage	3413 (33.47 %)
Max. Leverage ratio	1796 (17.61 %)
Min. Current Ratio	1044 (10.24 %)
Max. Debt to Tangible Net Worth	989 (9.70 %)
Min. Quick Ratio	293 (2.87 %)
Max. Debt to Equity	71 (0.70 %)
Covenants for financial amount
Max. Capex	2109 (20.68 %)
Min. Total Net Worth	1936 (18.99 %)
Min. Tangible Net Worth	1901 (18.65 %)
Min. EBITDA	714 (7.00 %)

Appendix 3: Theoretical explanation of debt covenant interdependence

For the following correlation matrix for n debt covenants in a loan package

$$\varSigma_{n} = \left[ {\begin{array}{*{20}c} 1 & {\rho_{12} } & \cdots & {\rho_{1n} } \\ {\rho_{21} } & 1 & {} & \vdots \\ \vdots & {} & \ddots & {} \\ {\rho_{n1} } & \cdots & {} & 1 \\ \end{array} } \right]$$

(6)

where $0 \le \rho_{ij} = \rho_{ji} \le 1,(i,j = 1, \cdots ,n)$. Let $\lambda_{1} ,\lambda_{2} , \ldots ,\lambda_{n}$ be the n eigenvalues of the correlation matrix $\sum_{n}$. When all the covenants are mutually independent, the off-diagonal elements, $\rho_{ij} ,(i \ne j)$, of $\sum_{n}$ become zero. Then all n eigenvalues equal to 1.0. However, when the covenants are inter-dependent, the nonzero $\rho_{ij} ,(i \ne j)$ make the eigenvalues different from each other. Take two dimension correlation matrix $\sum_{2} = \left[ {\begin{array}{*{20}c} 1 & \rho \\ \rho & 1 \\ \end{array} } \right]$ as an example. We compute the eigenvalues of $\sum_{2}$ for $\rho =$ 0, 0.5, and 1.0 respectively. When $\rho = 0$, both the eigenvalues are equal to 1.0; when $\rho = 0.5$, the eigenvalues are 1.5 and 0.5; when $\rho = 1.0$, the eigenvalues are 2.0 and 0. As we can see, when correlation $\rho$ increases, the difference between the eigenvalues increases. Thus it is the correlation that makes the eigenvalues heterogeneous. The more heterogeneous the eigenvalues, the high the inter-dependence among covenants.

We hence define CovIntdep as the standard deviation of the n eigenvalues

$$CovIntdep = Std(\hat{\lambda }) = \sqrt {Var(\hat{\lambda })}$$

(7)

where $\hat{\lambda } = [\lambda_{1} ,\lambda_{2} , \ldots ,\lambda_{n} ]$ and $Var(\hat{\lambda })$ is

$$\text{var} (\hat{\lambda }) = \frac{1}{n - 1}\sum\limits_{i = 1}^{n} {(\lambda_{i} - \bar{\lambda })^{2} } = \frac{1}{n - 1}\left( {\sum\limits_{i = 1}^{n} {\lambda_{i}^{2} } - 2\sum\limits_{i = 1}^{n} {\lambda_{i} \bar{\lambda }} + n\bar{\lambda }^{2} } \right)$$

(8)

where $\bar{\lambda } = \frac{1}{n}\sum\nolimits_{i = 1}^{n} {\lambda_{i} }$. Since $\lambda_{1} ,\lambda_{2} , \cdots ,\lambda_{n}$ are the n eigenvalues of $\sum_{n}$, they are the roots of the following characteristic polynomial of $\sum_{n}$

$$\lambda (\sum_{n} ) = \left| {\lambda I - \sum_{n} } \right| = \left| {\begin{array}{*{20}c} {\lambda - 1} & { - \rho_{12} } & \cdots & { - \rho_{1n} } \\ { - \rho_{21} } & {\lambda - 1} & {} & \vdots \\ \vdots & {} & \ddots & {} \\ { - \rho_{n1} } & \cdots & {} & {\lambda - 1} \\ \end{array} } \right| = \lambda^{n} - n\lambda^{n - 1} + a_{n - 2} \lambda^{n - 2} + \cdots + a_{1} \lambda + a_{0}$$

(9)

According to the relationship between the roots and the coefficients of a polynomial, we have $\sum\nolimits_{i = 1}^{n} {\lambda_{i} } = n$ and $\sum\limits_{i < j} {\lambda_{i} \lambda_{j} } = a_{n - 2}$. Therefore Eq. (8) can be simplified and expressed in terms of the coefficients of polynomial in the following Eq. (10).²²

$$\begin{aligned} \text{var} (\hat{\lambda }) & = \frac{1}{n - 1}\left( {\sum\limits_{i = 1}^{n} {\lambda_{i}^{2} } - n} \right) = \frac{1}{n - 1}\left[ {\left( {\sum\limits_{i = 1}^{n} {\lambda_{i} } } \right)^{2} - 2\sum\limits_{i < j} {\lambda_{i} \lambda_{j} } - n} \right] \\ & = \frac{1}{n - 1}\left( {n^{2} - 2a_{n - 2} - n} \right) = n - \frac{{2a_{n - 2} }}{n - 1} = \frac{{\sum\limits_{i \ne j} {\rho_{ij}^{2} } }}{n - 1} \\ \end{aligned}$$

(10)

Therefore our measure

$$CovIntdep = \sqrt {\text{var} (\hat{\lambda })} = \sqrt {\frac{{\sum\limits_{i \ne j} {\rho_{ij}^{2} } }}{n - 1}}$$

(11)

captures the correlations, i.e., $\rho_{ij} ,(i \ne j)$ between every two debt covenants included in the loan package.

For a 2-D correlation matrix $\sum_{2} = \left[ {\begin{array}{*{20}c} 1 & \rho \\ \rho & 1 \\ \end{array} } \right]$, we can calculate CovIntdep ₂ from equation C(6),

$$CovIntdep_{2} = \sqrt {\frac{{\sum\limits_{i \ne j} {\rho_{ij}^{2} } }}{n - 1}} = \sqrt {\frac{{2\rho^{2} }}{2 - 1}} = \sqrt 2 \left| \rho \right|$$

(12)

and obviously, CovIntdep ₂ increases as the correlation (the absolute value) of the two debt covenants increases.

Similarly we can calculate our measure for 3-D correlation matrix from Eq. (10) in terms of three unique off-diagonal elements, i.e., $\rho_{12} ,\,\rho_{23} ,$ and $\rho_{23}$

$$CovIntdep_{3} = \sqrt {\frac{{\sum\limits_{i \ne j} {\rho_{ij}^{2} } }}{n - 1}} = \sqrt {\frac{{2(\rho_{12}^{2} + \rho_{13}^{2} + \rho_{23}^{2} )}}{3 - 1}} = \sqrt {\rho_{12}^{2} + \rho_{13}^{2} + \rho_{23}^{2} }$$

One concern of our measure is that it is more likely to have inter-dependent debt covenants as the number of debt covenants increases, weakening the results. However, this is not a concern since, in our sample, about 80 % of the loan packages have fewer than 4 debt covenants and 95 % of the loan packages have fewer than 5 debt covenants.