Revenue-expense matching and performance measure choice

Abstract

Recent research shows that matching between contemporaneous revenues and expenses has declined over the past 40 years. We argue that this decline in matching reduces the contracting usefulness of earnings and affects managerial effort allocation and performance measure choice. Based on a theoretical model, we predict that firms with poor matching benefit from contracting on sales revenue instead of earnings. Using hand-collected CEO performance measure data from S&P 500 firms, we document a significant increase in the use of sales revenue coupled with a significant decline in the use of bottom line income as a performance measure over time. We confirm the model prediction that firms are more likely to explicitly employ sales revenue as a performance measure when matching is poor. We further show that this negative association between matching and the use of sales revenue performance persists after controlling for the use of other earnings measures and equity compensation. This study contributes to the literature by examining the effect of revenue-expense matching on compensation design and documenting the increasing trend of revenue-based compensation in recent years.

Appendices

Appendix 1

Variable definitions

Variable name	Definition
SALES	A dummy variable that equals one when a firm’s CEO annual bonus contract is explicitly tied to sales revenue performance metric and zero otherwise
MATCHING	A firm-year specific measure of revenue-expense matching obtained from estimating the following model using a seven-year rolling window (t-7 to t-1) (Dichev and Tang, 2008): Revenuesi,t = β0 + β1Expensesi,t-1 + β2Expensesi,t + β3Expensesi,t+1 + εi,t. Revenues is net revenues, and Expenses is the difference between revenues and earnings before extraordinary items; both are deflated by average total assets. MATCHING is the coefficient on current-period expense (β2)
SALESNOISE	Sales noise, measured as the standard deviation of sales over book value of equity for prior five years (t-5 to t-1)
EQ	A measure of earnings quality obtained from estimating the following model for each year and Fama and French (1997) industry (modified version of Dechow and Dichev 2002): ΔWCt = r0 + r1CFOt-1 + r2CFOt + r3CFOt+1 + r4ΔREVt + r5PPEt + εt. WC is working capital. CFO is cash flow from operations. REV is revenue, and PPE is gross value of property, plant, and equipment. We multiply the standard deviation of the residuals by -1 to obtain EQ so that a higher value of EQ indicates higher earnings quality
MB	Market-to-book ratio, calculated as market value of total assets over book value of total assets
INTAN	Intangible intensity, calculated as intangible assets over total assets
E-Score	The sum of the five indicator variables: Emp, Grow, MA, Disc, and Loss. Emp (Grow) is a dummy variable that equals one if the firm experienced negative employee (revenue) growth and zero otherwise; MA (Disc) is an indicator variable that equals one if the firm had a merger or acquisition (discontinued operations) and zero otherwise. Loss is a dummy variable that equals one if the firm experienced negative operating income after depreciation and zero otherwise
GDP	Real gross domestic product (GDP) growth rate, defined as the average of three years’ (i.e., year t-2, t-1, and t) real GDP growth rate
HHI	Herfindahl–Hirschman Index, defined as the sum of squares of market shares of all firms in an industry, where market share is firm revenue scaled by industry revenue based on Compustat data
HHI-Census	Herfindahl–Hirschman Index, defined as the sum of squares of market shares of all firms in an industry, where market share is firm revenue scaled by industry revenue based on U.S. Census Data
AGE	Firm age measured as total number of years a firm has appeared in the CRSP database
LEVERAGE	Long-term debt over total assets
LOGTA	Firm size defined as logarithm of total assets
ROA	Return on assets, defined as income before extraordinary items over total assets
OPINC	A dummy variable that equals one when a firm’s CEO annual bonus contract is explicitly tied to operating income and zero otherwise
OPINC2	A dummy variable that equals one when a firm’s CEO annual bonus contract is explicitly tied to earnings before special items (including operating income, earnings before taxes (EBT), earnings before taxes and interest (EBIT), or earnings before taxes, interest, depreciation, and amortization (EBITDA)) and zero otherwise
CF	A dummy variable that equals one when a firm’s CEO annual bonus contract is explicitly tied to cash flows and zero otherwise
COST	A dummy variable that equals one when a firm’s CEO annual bonus contract is explicitly tied to cost control and zero otherwise
NF	A dummy variable that equals one when a firm’s CEO annual bonus contract is explicitly tied to nonfinancial measures and zero otherwise
NINOISE	Net income noise, measured as the standard deviation of bottom line earnings over book value of equity for prior five years (t-5 to t-1)

Appendix 2: proofs

1.1 Proof of proposition 1:

Under the LEN framework, the principal’s payoff is maximized subject to the incentive compatibility (IC) and the individual rationality (IR) constraints. We obtain the solution of the optimal weights as shown on page 433 of Feltham and Xie (1994).

$${v}^{+}=Q\mu b$$

(12)

$$\mathrm{Q}\equiv {(\mu {\mu }^{+}+r\Sigma )}^{-1}$$

(13)

$${a}^{+}={\mu }^{+}v,$$

(14)

where v is the optimal compensation weight matrix,¹⁶ u is the marginal sensitivity of effort matrix for performance measures, b is the marginal productivity of effort matrix for the principal’s outcome, Σ is the variance–covariance matrix of performance measures, and a is the optimal effort matrix. For simplicity, we normalize the agent’s absolute risk-aversion parameter r to one. Based on the model setup described in Section 2.2, we obtain the following equations.

$$\mathrm{b}=\left[\begin{array}{c}1\\ 1\end{array}\right]$$

(15)

$$\upmu =\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$$

(16)

$$\Sigma =\left[\begin{array}{cc}{\upsigma }_{1}^{2}& {\upsigma }_{1}^{2}\\ {\upsigma }_{1}^{2}& {\upsigma }_{1}^{2}+{\upsigma }_{2}^{2}+{\upsigma }_{\mathrm{v}}^{2}\end{array}\right]$$

(17)

Plugging Eqs. (16)–(17) into Eq. (13), we obtain:

$$\mathrm{Q}={\left(\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]+\left[\begin{array}{cc}{\upsigma }_{1}^{2}& {\upsigma }_{1}^{2}\\ {\upsigma }_{1}^{2}& {\upsigma }_{1}^{2}+{\upsigma }_{2}^{2}+{\upsigma }_{\mathrm{v}}^{2}\end{array}\right]\right)}^{-1}.$$

(18)

$\mathrm{Let D}=\left(1+{\upsigma }_{1}^{2}\right)\left(1+{\upsigma }_{2}^{2}+{\upsigma }_{\mathrm{v}}^{2}\right)$, Eq. (18) becomes:

$$\mathrm{Q}=\frac{1}{D}\left[\begin{array}{cc}2+{\upsigma }_{1}^{2}+{\upsigma }_{2}^{2}+{\upsigma }_{\mathrm{v}}^{2}& -1-{\upsigma }_{1}^{2}\\ -1-{\upsigma }_{1}^{2}& 1+{\upsigma }_{1}^{2}\end{array}\right].$$

(19)

Plug equations (15), (16), and (19) into (12), we have:

$${v}^{+}=\frac{1}{D}\left[\begin{array}{cc}2+{\upsigma }_{1}^{2}+{\upsigma }_{2}^{2}+{\upsigma }_{\mathrm{v}}^{2}& -1-{\upsigma }_{1}^{2}\\ -1-{\upsigma }_{1}^{2}& 1+{\upsigma }_{1}^{2}\end{array}\right]\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]\left[\begin{array}{c}1\\ 1\end{array}\right].$$

(20)

Simplify equation (20), we obtain:

$${v}^{+}=\frac{1}{D}\left[\begin{array}{c}{\upsigma }_{2}^{2}+{\upsigma }_{\mathrm{v}}^{2}-{\upsigma }_{1}^{2}\\ 1+{\upsigma }_{1}^{2}\end{array}\right].$$

(21)

Equation (21) gives the compensation weights on revenue (${W}_{Rev}^{*}$) and earnings (${W}_{Earn}$) as follows.

$${W}_{Rev}^{*}=\frac{{\upsigma }_{2}^{2}+{\upsigma }_{\mathrm{v}}^{2}-{\upsigma }_{1}^{2}}{D}.$$

(22)

$${W}_{Earn}=\frac{{1+\upsigma }_{1}^{2}}{D}.$$

(23)

Taking partial derivatives of ${W}_{Rev}^{*}$ with respect to ${\upsigma }_{\mathrm{v}}^{2}$, we have:

$$\frac{\partial {W}_{Rev}^{*}}{\partial {\upsigma }_{\mathrm{v}}^{2}}=\frac{{({1+\upsigma }_{1}^{2})}^{2}}{{D}^{2}}>0.$$

(24)

Taking partial derivatives of ${W}_{Earn}$ with respect to ${\upsigma }_{\mathrm{v}}^{2}$, we have:

$$\frac{\partial {W}_{Earn}}{\partial {\upsigma }_{\mathrm{v}}^{2}}=-\frac{{\left({1+\upsigma }_{1}^{2}\right)}^{2}}{{D}^{2}}<0.$$

(25)

Equation (24) shows that the partial derivative of changes in compensation weight on revenue with respective to changes in the degree of mismatching is positive, in support of Proposition 1. In addition, Eq. (25) shows that the partial derivative of changes in compensation weight on earnings with respect to the degree of mismatching is negative.