Operating Leverage and Underinvestment: Theory and Evidence 1

Transcription

1 Operating Leverage and Underinvestment: Theory and Evidence 1 Chuanqian Zhang Cotsakos College of Business, William Paterson University, New Jersey zhangc4@wpunj.edu Feng Jiao University of Lethbridge, Canada feng.jiao@uleth.ca Xiaoyu Zhang Shanghai University of Economics and Finance, China Shanghai Pudong Development Bank (SPDB) xyz_sufe@126.com Michi Nishihara Graduate School of Economics, Osaka University, Toyonaka, Osaka , JAPAN nishihara@econ.osaka-u.ac.jp 1 We thank Marc Arnold for his constructive suggestions. Part of this work was conducted when Zhang visited Osaka University and he thanks for their accommodation. 1

2 Operating Leverage and Underinvestment: Theory and Evidence Abstract Operating leverage, caused by fixed operating cost, is normally considered as an internal debt of corporates. We explore its implication on firms investment decision. A simple contingent-claims model delivers an appealing fact that although operating leverage alone deters investment, it can, jointly with financial leverage, accelerate investment timing. In Myers (1977) theory, the default risk caused by existing corporate bond induces the underinvestment (or debt overhang) problem because a fraction of new project value will be transferred from equity holders to debt holders. We show that the fixed operating cost mitigates such agency conflicts via a reverse wealth transfer and improves investment efficiency. Using a proportional hazard model implemented on a large sample of publicly traded U.S. firms over the period , the results offer strong support to our modelbased predictions. These empirical findings still hold when various measures of operating leverage are taken care. JEL Classification: G31 Keywords: Structural model, Operating leverage, Corporate investment, Debt overhang 2

3 1. Introduction It has been well established that financial leverage can cause debt overhang problem because equity holders worry a wealth transfer from themselves to debt holders at investment. However, though in a similar payment pattern, operating leverage has been drawn far less attentions in its relationship to a firm s investment decision. Perhaps it is due to conventional wisdom that fixed operating cost erodes prospective profit margin thus it should reduce investment activities. We, despite its simplicity, argue that such intuition is unable to disclose the full story since it neglects an interaction between these two types of leverages, given the fact that both of them usually co-exist during firms operation. Thus in this article we prepare to bridge this gap by addressing the following question: How will the joint effect of operating and financial leverages shape a firm s investment decision? To this end, we build a structural model in a real options setting. The model is fully dynamic since the firm s value and decisions are governed by a single variable, market demand, which evolves in a diffusive process. The firm has an expansion opportunity to increase its current production capacity to a higher level. An operating cost is necessitated to sustain the production. It is quasi-fixed because it grows in proportion to the size of capital stock while be independent of the sales, giving rise to operating leverage as market demand fluctuates. Prior to investment, the equity holders have an existing console bond which incurs period constant coupon. Debt renders the firm risky since if the firm were unable to generate enough cash flows, either by profitable production or issuing new equity, to cover the interest payment, it will go bankruptcy. Once the bankruptcy trigger is hit before investment happens, the debt holders are assumed to taken over all unlevered assets, whose value largely depend on future sales and operating cost. When the market demand is sufficiently low, the debt holders have to liquidate the capital stock with zero value. The equity holders goal is to choose optimal investment and default thresholds to maximize their ex ante market value. 3

4 In line with Myer s (1977) theory, exercising growth options lead to augmented revenue flow and reduced uncertainty 2 that renders existing debt safer and introduces wealth transfer from equity holders to debt holders. Expecting this, equity holders will bypass some projects with positive NPV causing underinvestment. Therefore underinvestment problem only matters for unsecured debt. On the other hand, the fixed operating cost, largely overlooked by current literatures, also increases the burden on shareholders liability side especially when economy is at downturn, inducing a higher bankruptcy threshold. However, the operating leverage differs from financial leverage in the sense that the former introduces liquidation risk to unlevered asset while the later causes bankruptcy or credit risk for levered assets. At the time of default, the liquidation risk will be delegated to debt holders when they take over the production capital, namely, a risk-shifting effect which neutralize underinvestment problem. With that being said, the operating leverage can be considered as an internal debt. In summary, our model produces following testable outcomes. First, similar to financial leverage, operating leverage also has negative impact on corporate investment to the extent that investment timing increases with the fixed operating cost. Second, the joint effect of the two types of leverages has positive impact on investment. To be specific, when the operating cost is relatively low, the investment trigger increases monotonically with financial leverage; when the operating cost is relatively high, the investment trigger presents a slightly U-shaped or even decreasing relationship with financial leverage. To aid the analysis, we also quantify the corresponding agency conflicts between debtholders and shareholders. It shows that the magnitude greatly declines as operating leverage increases. Guided by model generated predictions, we test them empirically. It is noteworthy that although operating leverage is straightforward in terms of definition, it is probably less straightforward to proxy in empirics since quasi-fixed operating cost is difficult to observe. Therefore we employ three typical measures of operating leverage from García Feijóo and Jorgensen s (2010), Novy-Marx(2011) and Chen, Harford and Kamara (2017) respectively. Then we carry out empirical test using a large panel data covering 16,169 publicly traded firms over 2 Growth options represent contingent claims to future payoffs thus they are exposed to more uncertainty than the present value of those payoffs (i.e. post-investment asset-in-place). 4

5 the period from 1966 to After estimating a mixed proportional hazard model, as in Leary and Roberts (2005), Whited (2006) and Morellec, Valta, and Zhdanov (2015), we demonstrate that either financial leverage or operating leverage does hinder corporate investment, and operating leverage weakens the negative relationship between financial leverage and investment, consistent with our model predictions. These findings still hold when alternative measures of operating leverage and financial leverage are employed. In addition, we also consider potential endogeneity pertaining to the financial leverage and the operating leverage: 1) we attempt to address the endogenous concern between financial leverage and investment by using the instrumental variable approach (Tchetgen et al.,2015; Sunder et al, 2017); 2) we perform industry-level estimations as a robustness check, since the potential for endogeneity of operating leverage is much less severe at the industry level. Our paper is related two strands of literatures. First, we contribute to related theoretic works on identifying determinants of underinvestment problem due to agency cost of debt overhang. For example, previous works have investigated an array of financial leverage-side (or external debt) factors such as debt renegotiation by Pawlina (2010), debt priority structure by Hackbarth and Mauer (2012), short-term debt by Diamond and He (2014). We complement their work by revoking the impact of operating leverage (or internal debt) which is ignored by those papers. Arnold et al. (2017) find that investment financed by asset sales can mitigate debt overhang within aggregate dynamics. Hirth and Uhrig-Homburg (2010) reveal that cash financed investment can completely eliminate debt overhang problem. Both of them essentially show a reverse wealth transfer process due to exchanging riskless asset for risky assets upon investment. Our model reveal a similar result but distinguishes from them in terms of mechanism, namely, a liquidation risk transition from equity holders to debt holders through operating cost embedded in unlevered assets. Second, our paper contributes to the research field related to operating leverage or cost structure in both theory and empirics. The operating leverage has been extensively investigated in asset pricing literatures 3 in recent years while only a few relates it to corporate policies. Among them Chen et al (2017) explore the 3 See Carlson, Fisher and Giammarino (2004), Hackbarth and Johnson (2015), Gu, Hackbarth and Johnson (2018), Bustamante and Donangelo (2016), Novy-Marx (2011), García-Feijóo and Jorgensen (2010) 5

6 substitution and interaction effect between operating leverage and financial leverage on the components of profitability. Kulchania (2016) explores the impact of cost structure on firms payout policy. We complement their work by focusing on the interplay between the two leverages on corporate investment. Perhaps the closest one to ours, Kumar and Yerramilli (2017) study the substitution between the two types of leverages on endogenous capital structure and capacity choice. We complement their work by concentrating on investment timing and providing intriguing empirical evidence. The rest of paper proceeds as follows: Section 2 develops model frameworks as well as their numerical solutions. Then we derive testable hypothesis based on the results. Section 3 introduces data and empirical design. Section 4 presents empirical findings. Section 5 concludes the paper. 2. Model settings 2.1 Two-period Example We set up a static model bearing resemblance to Diamond and He (2014) within a context of capacity expansion. However, we augment their work by considering quasi-fixed operating cost, which only varies in a proportion to the size of installed capital instead of sales. At the beginning t = 0 the firm has already installed capital stock of K and it will not generate cash flows until the ending period t = G p K(x m), investment K(x m), no investment 1 2 B p K(y m), investment K(y m), no investment t = 0 issue debt t = 1 t = 2, debt matures The equity holders will immediately liquidate their production capital with zero value if the profit flow is negative. The firm has already raised zero-coupon bond with face value F at t = 0 and the debt will be retired at t 6

7 = 2. Managers will also need to make investment decision right after debt issuance. The economy can be evolved to two status at t = 1, namely, Good (G) and Bad (B) with equal opportunity ½. Without any investment, the deployed assets could generate revenue per capital x and y with x > y in either economic status. The asset in place is procyclical in the sense that p > 1/2. That is to say chances are higher for firms generate high sales than generate low sales at good time. Note we also could generalize the setting by differentiating p G and p B but it will complicate the analysis while deliver same results. Once the firm conducts investment the capital size increases from K to K in exchange for cost k, with Δ = K K. The debt is risky such that K(x m) F K(y m). When profit flows are not enough to pay back to debt holders, the equity holders declare bankruptcy. The Absolute Priority Rule is implemented hence equity holders seize zero value while debt holders receive all realized cash flows. The discount rate is set to zero. In what follows we analyze investment criteria as well as associated agency cost given the assumption that the investment is made at t = 0 thus the firm is unaware of future economic status and cash flow distributions. Later on we redo the analysis for investment decision being made at t = 1, at which the economic status is disclosed. Since we wish to explore the interactive effect of operating leverage and financial leverage, the analysis is separated two cases: low and high operating cost. For each case, we derive solution for both low and high debt levels. Case A: when the quasi-fixed operating cost is relatively low m < y and (1) If financial leverage is relatively low, K(y m) F, the value of equity holders who make investment will be E H = 1 K(y m) + 1 K(x m) k F; 2 2 (2) If financial leverage is relatively high, K(y m) F, the equity value of firm who makes investment will be E L = 1 2 K(x m) k 1 2 F. On the other hand, if the firm doesn t undertake any investment the equity value will become E = 1 K(x m) 1 F. Thus the investment criteria will be: 2 2 (1) For low financial leverage, the investment will be initiated only if E H > E or x 2k + m + F K(y m). Note the last item on the right hand side is negative. 7

8 (2) For high financial leverage, the condition for investment is E L > E or x 2k + m It can be easily detected that investment is more likely for low-debt firm since the criteria is less binding. In addition, as operating cost m increases, the investments for both scenarios are harder to realize, consistent with conventional wisdom. In terms of agency cost, we measure it as the foregone investment opportunities. For instance, at low debt level, the agency cost is zero while at high debt level, the agency cost will be AC = 1 2 (x m k), which declines with m. Case B: when the operating leverage is relatively high m y, the equity holders will close production with scrap value of zero at bottom knot of t = 2, regardless of debt amount. Therefore the equity value of firms undertaking investment will be E H = E L = 1 K(x m) k 1 F. Thus the corresponding threshold is always 2 2 hold at x 2k + m, namely, there is no underinvestment problem. In summary the model illustrates that operating leverage can mitigate underinvestment problem, especially for firms financed with relatively high debt. In the next, we corroborate the main implication by assuming an alternative scenario that the firm makes investment decision at t = 1. The stepwise derivation will not be shown since it is same as previous case. At point G, when operating cost is low m < y, the investment conditions are x k/p + m for high financial leverage and x k 1 p 1 p + m [K(y m) F] for low financial leverage. It can be easily observed that the p latter is less binding than former one. Alternatively, when operating leverage is high m > y the two investment criteria are identical. The agency cost (only applicable for low operating leverage) is = p (x m k). At point B, all results are same as in point G, except for replacing p with 1 p. Again, the solutions to the second investment pattern lend further support to our main result. In what follows, we generalize the setting in a dynamic world. 2.2 Dynamic model 8

9 Consider a firm operates in a continuous-time, infinite-horizon, and partial-equilibrium economy with decreasing to scale technology 4 incorporated in the Cobb-Douglas production function. The installed capital stock generates the profit flow which can be expressed as π t = x t K t γ mk t In this equation, γ < 1 denotes the return to economic scale and m represents cost of operating the production capital K. Since we assume the capital is at steady state and depreciation is excluded thus we have K t K. The variable x concisely captures market demand level which evolves Geometric Brownian Motion (GBM) process in a risk-neutral measure, namely dx = μxdt + σxdz where μ and σ are positive constants, and (Z t) t 0 is a standard Brownian Motion Process. Time is continuous and varies over [0, ). Uncertainty is represented by the filtered probability space (Ω, F, (F t ) t 0, P) over which all stochastic processes are defined. The firm is subjected to a constant corporate tax rate of τ (0< τ <1). Investment Opportunity: At any time, the firm may exercise expansion option to increase its capital stock. Define the constant capital level before investment as K and the augmented capital level as K which obeys K > K. To implement it, the firm will pay an investment cost k(k K) in exchange for receiving enhanced assets scale and k can be viewed as purchasing price of unit capital. We assume this investment cost is financed by common equity and abstract from debt financing, in line with recent related works such as Arnold et al. (2017) and Chen and Manso (2017) 5 because the main topic of our paper is investigating the underinvestment problem. As mentioned in Arnold et al. (2017), this assumption is justifiable for firms that have existing debt embedded a covenant prohibiting them to raise new debt. 4 The decreasing to scale technology has been widely applied such as Chen, Harford and Kamara (2016), Hackbarth and Johnson (2015), etc. 5 Other underinvestment models such as Mauer and Ott (2000), Pawlina (2010) and Hirth and Uhrig-Homburg (2010) apply similar assumption. 9

10 Bankruptcy: The firm may declare bankruptcy either before or after the investment decision is made. If default occurs prior to investment, debt holders will receive the firm s assets in place and the unexercised investment option subtracted by a fractional bankruptcy cost of φ, and equity holders will receive nothing (i.e., absolute priority rule, or APR, is enforced). If the firm declares bankruptcy after the investment, the debt holders will also similarly receive present value of unlevered assets, subtracting the same bankruptcy cost φ. We assume debt holders are not allowed to lever up the residual assets afterwards, consistent with the contingent-claim literature (Leland, 1994, Mauer and Ott, 2000). The alternative bankruptcy process such as debt renegotiation/ restructure can also be applied but it will not change the conclusion while complicate the analysis. Operating leverage: As in Novy-Marx (2011) we directly adopt unit operating cost m as a measure of operating leverage in our model since it not only concisely reflects the quasi-fixed nature but also relates closely to our empirical measures. Notably, in related literatures, the operating leverage might be expressed in other alternative ways. For example, Gu, Hackbarth and Johnson (2018) defines operating leverage as operating cost over sales revenue. Bustamante and Donangelo (2017) interpret operating leverage as operating cost divide operating profit. We believe those variations are of minor importance since they are monotonic functions of m. The empirical proxies of m will be introduced in section 3.2. The model is solved in two parts: we first derive the unlevered firm value and associated investment decision then we solve the levered firm value and corresponding investment and bankruptcy decisions. For each part, the model is solved in a backward manner. That is, we first solve each contingent claims given investment has been exercised than we solve their counterparts prior to investment Unlevered firm: After investment, the unlevered firm's asset value is no more than a present value of discounted cash flow plus a contraction option V 1 u (x) = (1 τ) ( x tk γ r μ mk r ) + Bxβ (1) 10

11 in which parameter β is the negative root of the quadratic equation: 1/2σ 2 β(β 1) + μβ r = 0. To solve eq (1) we need extra conditions V 1 u (x L ) = 0 and V 1 u (x L ) x form solution for both liquidation threshold and firm value x L = β β 1 V 1 u (x) = (1 τ) [ x tk γ Before investment the firm value can be written as = 0, where x L is the liquidation threshold. There is a closed r μ mk r mk r μ r K γ (2) γ (x LK mk ) ( x ) β ] (3) r μ r x L V 0 u (x) = (1 τ) ( x tk γ r μ mk r ) + H 1x α + H 2 x β (4) where H 1 and H 2 are unknown constants, α is the positive root of the quadratic equation: 1/2σ 2 β(β 1) + μβ r = 0. To solve the optimal investment trigger x * we need following conditions (similar to static model, we use Δ = (K K) to represent increased amount of capital) V(K, x ) = V(K, x ) kδ (5) V(K,x) x at x=x = V(K,x) x at x=x (6) Eq (5) is value matching condition to ensure value equivalence at investment and eq (6) is smooth pasting condition that guarantees optimality of investment timing. Since the firm could exit at distress prior to investment we have boundary conditions at pre-investment liquidation trigger V u 1 (x IL ) = 0 and V 1 u (x IL ) = 0. Now we present valuation and investment decisions for firms with debt financing: x Levered firm In this section, we assume the managers act in the interest of equity holders and make investment decision to maximize pre-investment equity value. We call it second-best strategy as opposed to first-best strategy, in which managers make investment decision to maximize firm value. Using similar technique, the post-investment equity and debt value can be derived as follows 11

12 E 1 (x) = (1 τ) [ x tk γ mk+c r μ r ( x b1k γ r μ mk+c ) ( x ) β ] (7) r x b1 D 1 (x) = c r + [(1 φ)v 1 u c r ] ( x x b1 ) β (8) in which the optimal post-investment default trigger is analytically obtained x b1 = Then we present pre-investment firm value: E 0 (x) = A 1 x α + A 2 x β + (1 τ) ( x tk γ mk+c r μ r β β 1 r μ r mk+c K γ ) (9) D 0 (x) = B 1 x α + B 2 x β + c r (10) where A 1, A 2, B 1, B 2 are constants to be solved. We also need to address optimal default x b0 and investment threshold x *. To do this, we recall both value matching (eq 11) and smooth pasting (eq 12) conditions at investment threshold x * E 0 (x ) = E 1 (x ) kδ (11) E 0 (x) x = E 1 (x) (12) at x=x x at x=x Note the eq (12) captures the idea of second-best policy that firms follow equity-maximizing investment decision. To solve bankruptcy threshold prior to investment, we need following conditions at default threshold To solve B 1 and B 2 we use conditions: E 0 (x b0 ) = 0 and E 0 (x) x at x=x b0 = 0 (13) D 0 (x ) = D 1 (x ) (14) D 0 (x b0 ) = (1 φ)v 0 u (x b0 ) (15) Both eq (14) and (15) are value matching conditions: the first one demonstrates that the pre- and post-investment debt value should be identical since there is no new debt issued. The second one is from assumption that debt holders get unlevered assets subtracted from bankruptcy cost Results of benchmark model 12

13 We define the benchmark model as the one that abstracts from corporate tax and bankruptcy cost. It serves two purposes. First, we aim to make it fully comparable with that of static model which ignores two of them. Second, it is attractive since the severity of underinvestment will be purely driven by agency conflicts. However, this assumption might also make the incentive to issue debt ungrounded thus we relax it in the next section. Notice that given there is no tax and bankruptcy cost, the optimal investment of an unlevered firm is equivalent to that of debt-financed firms pursuing first-best strategy (a formal proof is shown in Appendix A). The economic-wide parameter values are used in line with Hackbarth and Mauer (2012): the risk-free interest rate r = 6%, volatility of market demand σ = 25%, expected growth rate of demand μ = 1%. For the economic return to scale, we set γ = 0.8, which is in between Whited (2006, γ = 0.75) and Gu et al. (2017, γ = 0.85). The purchasing cost per unit capital k = 3 without loss of generality. The initial market demand x 0 = 0.87 which ensures the firm is alive but has not invested at t = 0, the initially installed capital K = 1 and augmented capital K = 2. Figure 1(a) illustrates relationship between investment trigger and coupon payments. The solid line represents firms operating with low cost (m = 0.2) in which the investment trigger increases from 0.77 to 0.93 as coupon increases from 0 to 1.2. The dash dotted line graphs firms operating with medium cost (m = 0.5) and the investment trigger decreases from 1.42 to 1.36 and then increases to The dotted line is meant to firms operating with high cost (m = 1.2) and the investment trigger decreases monotonically from 2.89 to In real option terms, a higher trigger implies low possibility that the investment will be conducted. In line with this logic, Fig 1(b) graphs ex ante investment probability given no bankruptcy has yet to come 6. It can be observed that the probability for lowest operating cost decreases by 26.5% (from 93.5% to 67%) while for highest operating cost decreases by 19.5% (from 20% to 0.05%). In summary the numerical results demonstrate that the negative impact of financial leverage on investment is greatly mitigated and even reversed as the operating cost increases. 6 The probability of investment given no bankruptcy has not happened can be written as p(x 0 ) = x 2λ/σ 2 2λ/σ 0 x 2 b0 2λ/σ 2 with λ = (μ σ 2 /2), the detailed derivations are in Hackbarth and Mauer (2012) x I 2λ/σ 2 x b0 13

14 [Figure 1 insert here] The suboptimal investment implied from Fig 1 indicates an agency cost between equity and debt holders. To visualize the magnitude, Figure 2 demonstrates further the relationship between agency cost and coupon payments for a range of operating leverage. The agency cost is calculated by quantifying difference of pre-investment firm values pursuing first-best and second-best strategies. The solid line represents firms operating with low cost (m = 0.2) in which the agency cost increases from 0 to 0.4% as coupon increases from 0 to 1.2%. The dotted line and dashed line graphs for firms with medium operating cost (m = 0.4) and high operating cost (m = 1.2) respectively, however, their magnitude declines significantly compared to that of low operating cost. [Figure 2 insert here] To lend more support to our model-based results, we also perform several comparative studies. Specifically, we investigate if the main results are still valid by varying key parameters such as return to scale γ, cash flow volatility σ, and growth multiple K/K. Because they are normally believed to impact debt overhang problems. For example, a higher return to scale and cash flow volatility or lower growth option will mitigate debt overhang, which might contaminate our operating leverage channel. The results are depicted at Appendix B Impact of Tax and Bankruptcy cost In this section we continue to follow Hackbarth and Mauer (2012) to adopt tax rate τ = 15% and bankruptcy filing cost φ = 25%. The investment decision for firms pursuing first-best strategy can be computed from an alternative smooth pasting condition (E 0 (x)+d 0 (x)) x at x=x = (E 1 (x)+d 1 (x)) x at x=x (16) All other boundary conditions are same as in aforementioned. We first analyze investment decision through comparing high (m = 1.2) and low (m = 0.3) operating costs. Specifically, the dotted line captures investment trigger for first-best (FB) scenario while the solid line represents second best (SB) scenario. To highlight their numerical significance, we report following result: for high operating cost, the FB investment trigger keeps relatively flat (ranges from 3.18 to 3.17) whereas the SB trigger decreases monotonically from 3.18 to 3.02; for 14

15 low operating cost, the FB investment trigger decreases from 1.25 to 1.13 whereas the SB trigger increases from 1.25 to Converting to probabilities, fig 4(b) shows that, when firms pursue SB strategy, the high operating cost case decreases by around 26% (from 72.3% to 46.6%) whereas the low operating cost case declines by around 19% (from 19.6% to 0.04%). Notice that the investment probabilities are almost same for FB and SB decisions for firms with high operating cost case, indicating a disappearing agency cost as financial leverage increases. [Figure 4 inserts here] Figure 5 illustrates agency cost for those two different operating leverage cases. The agency cost is obtained by valuing AC% = VFB (x 0 ) V SB (x 0 ) 100, in which V FB and V SB represent the firm value under first and second V FB (x 0 ) best investment policy. For high operating cost case the agency cost increases from 0 to 0.41% while for low operating cost case the agency cost shows a slightly bump shape with significantly smaller magnitude. The classic tradeoff theory indicates that there exists an optimal debt level given tax and default cost. Thus we also calculate the optimal coupon as well as agency cost by varying a range of operating costs. However, it deserves attention that the optimal financial leverage ratio is less relevant in empirics since the debt ratio usually deviates from the optimal level due to either adjustment cost or agency cost of debt overhang (Chen and Manso 2017),, Thus in our paper we believe an exogenous range of debt level connects model setting with empirics in a better way. Fig 6 (a) plots the optimal coupon with a variety of operating cost. It shows that the results for FB and SB have been converged when the operating cost is approximately larger than 0.3 and their difference is enlarged as operating cost decreases when debt overhang effect dominates. Fig 6(b) calibrates agency cost by assuming an optimal coupon has been embodied in both FB and SB cases. It shows that agency cost could be completely eliminated when operating cost is around In summary, a full-fledged numerical computation indicates following testable hypothesis H1: All else being equal, a firm s optimal investment timing will be postponed with either financial leverage or operating leverage. H2: The joint effect of the two leverages has positive impact on the investment timing or probability. 15

16 Statistically, to test the investment timing is equivalent to test the associated hazard rate of an investment, namely the probability of exercising an investment today as a function of the time since the last project. On the contrary, accounting data always presents a continuous investment pattern across periods. Thus we follow Whited (2006) 7 to count project investment only if a firm invests as twice as much the historic mean. 3. Empirical Design 3.1. Data Our primary data comes from Standard & Poor s COMPUSTAT database available on the Wharton Research Data Services server. We draw a sample of firm-year observations for the period 1966 to We include firms that are located and incorporated in the United State. To maintain consistency with previous empirical literature, we exclude regulated utility firms (SIC codes between 4900 and 4999) and financial firms (SIC codes between 6000 and 6999), as well as government entities (SIC codes greater than or equal to 9000). We exclude all observations for which the total book value of assets or net sales is either missing or negative. After excluding missing observations for all related variables, we get the final data set with 143,109 unique firm-years for 16,169 publicly traded firms. For robustness check, we use book leverage as an alternative measure of firm leverage. This results in a smaller dataset with 138,497 firm-year observations. Appendix B contains definitions of the variables used in the analysis Measures of Operating Leverage and Other Variables Although operating leverage is straightforward in terms of definition, it is probably less straightforward to proxy in empirics since quasi-fixed operating cost is difficult to observe. So far there are several proxies for operating leverage in the extant studies. We measure operating leverage by adopting three typical variables respectively. First, we follow the empirical approach of García Feijóo and Jorgensen s (2010) who estimate the annually timevarying degree of operating leverage (DOL) by running the time-series regressions at five-year overlapping 7 In recent literatures the hazard function has been applied to empirical test of investment timing in a real options framework such as Morellec et al (2015) and Akdoğu and Mackey (2008), etc. 16

17 intervals at firm-level. We estimate the DOL using a two-step time-series regression approach. First, we run regressions below over five-year overlapping intervals for each individual-firm: LnEBIT t = g ebit t + LnEBIT i0 + δ ebit,t LnSales it = g sales t + LnSales i0 + δ sales,t where EBIT 0 and Sales 0 are the beginning levels of earnings before interest and taxes (EBIT) and Sales, respectively. Next, we run the following regression on the residuals δ ebit,t and δ sales,t : δ ebit,t = γ 0i + γ 1i δ sales,t + u it Where the regression coefficient γ 1i is the estimator of DOL for company i. u it is error term. The time period for the regression runs from 1966 to Here to deal with negative values in the above estimation, we use the transformation technique adopted by García Feijóo and Jorgensen s (2010), which is also common in accounting research (Ljungqvist and Wilhelm, 2005). The transformation is given in the below. Y=Ln(1+X), if X 0 and Y=-Ln(1-X), if X<0 Where X stands for EBIT, Sales and Y is the value of the natural logarithm of the two variables after the transformation 9. Next, we adopt the proxy used by Novy-Marx(2011), which is calculated as the sum of cost of goods sold (COGS) and selling, general, and administrative expenses (XSGA) scaled by total assets. This measure can capture the variable production costs well. In addition, similar to the empirical proxy used by Novy-Marx(2011), we adopt the proxy used in Chen, Harford and Kamara (2016) and calculate operating leverage as selling, general, and administrative expenses (XSGA) divided by total assets. Different from Novy-Marx(2011), they don t include cost of goods sold (COGS) 8 For example, the DOL for year 1966 is estimated by time- series regression over fiscal years ; the DOL for year 1967 is estimated by time- series regression over fiscal years so on so forth. Thus the real time window for the data is 1962 to The adjusted value of LnEBIT and LnSales are used hereafter thus these are values after the adjustment rather than the natural logarithm of original data. 17

18 in the numerator for two reasons. First, XGSA is much stickier than COGS. Compared with XSGA, it is much more responsive to fluctuations in sales and so is better characterized as variable costs. Second, the exclusion of COGS helps mitigate potential endogeneity concerns. COGS depends on the production of goods and therefore, the inclusion of COGS makes firm s operating leverage dependent on production. As for financial leverage, we firstly compute it as the ratio of total debt scaled by the sum of total debt and total shareholders equity at the end of the year (see Fang, Huang and Karpoff (2015)). In order to show that these results are not driven by specific measure of this variable, we also compute financial leverage as book leverage, that is, the ratio of total debt divided by total assets for robustness (Valta, 2012). As for the measure of investment, most studies measure firm-specific investment intensity by capital expenditures scaled by either total assets (Mayers, 1998, Korkeamaki and Moore, 2004), or property, plant, and equipment (PP&E) (Fazzari, Hubbard, and Petersen, 1988, Hoshi, Kashyap, and Scharfstein, 1991). We focus on capital expenditures divided by PP&E at the beginning of the year. Since a majority of firms in our sample invests at least a small amount every year, the definition of a large project investment requires future adjustment (Whited, 2006). Low observed level of investment intensity might occur simply because of maintenance. Following Whited (2006) and Morellec, Valta, and Zhdanov (2015), we adopt the measure of investment spike as our primary dependent variable. An investment spike occurs if the ratio of investment to total assets is two times greater than the firm median. In our sample, we observe 20,606 investment spikes, approximately 14.4% of our total observations. The proportion is similar to those reported by Morellec, Valta, and Zhdanov (2015) and Whited (2006). We include several control variables in our estimations that were proven to affect firm investment in the literature. They include Tobin s Q, size, cash flow, sales growth rate, tangibility, R&D, cash flow volatility, dividend, and cash holdings. The variable definitions are provided in Appendix B, and Table 1 provides summary statistics for all the variables Empirical Specification 18

19 We estimate a mixed proportional hazard model, as in Leary and Roberts (2005), Whited (2006) and Morellec, Valta, and Zhdanov (2015), to examine the effects of operating leverage on investment. The hazard function at time t for firm i with covariates X i(t) is γ i (t) = ω i γ 0 (t)exp (X i (t) β) where t is the time to investment, γ 0 (t) is the baseline hazard, w i is a random variable that represents unobserved cross-sectional heterogeneity. X i(t) is a vector of covariates, is the corresponding vector of coefficients we need to estimate. The X i(t) and allow the hazard to shift up and down depending on their values (Whited, 2006). We estimate the mixed proportional hazard model using maximum likelihood. We consider two specifications of covariates. First we set the term X i(t) as in equation (1) to test the impact of operating leverage on firm investment for the full sample: X i (t ) β= b 1 OperLev i,t-1 + b 2 Controls i,t-1 + v t (1) The subscripts i and t represent firm and year, respectively. OperLev i,t-1 is firm i s operating leverage in year t-1. Our control variables for firm investment are motivated by prior literature, which includes Tobin s Q, size, cash flow, sales growth rate, tangibility, R&D, cash flow volatility, dividend, and cash holdings (Aivazian et al., 2005; Chen, Harford, and Kamara, 2017; Foucault and Frésard, 2014; Morellec, Valta, and Zhdanov, 2015). The industry level controls include a valuation ratio (Price/Book ratio), a capital structure ratio (Debt/Equity Ratio), and a profitability ratio (Gross profit margin) aggregated by the median for each of the Fama-French 49 industries. v t is year fixed effects, used to control for common time trends in investment expenditure across all firms. Table 2 gives the estimation results. For robustness, the standard errors are clustered at firm level. We then investigate the joint impact of operating leverage and leverage on firm investment for the full sample using specification (2). 19

20 X i (t ) β= b 1 FinLev i,t-1 OperLev i,t-1 + b 2 FinLev i,t-1 + b 3 OperLev i,t-1 + b 4 Controls i,t-1 + v t (2) The subscripts i and t represent firm and year, respectively. FinLev i,t-1 is firm i s financial leverage in year t- 1.OperLev i,t-1 is firm i s operating leverage in year t-1. Control variables are the same as in specification (1). v t is year fixed effects. The standard errors are clustered at firm level. Table 3 presents the estimation results. For robustness purposes, we also employ the book leverage as an alternative proxy for financial leverage. The book leverage is defined as the sum of debt in current liabilities and total long-term debt scaled by total book assets (Ozdagli, 2012). 4. Empirical Results 4.1. Descriptive Statistics Our basic sample consists of an unbalanced panel with 143,109 firm-year observations with 16,169 unique firms. We winsorize all ratios at the 1st and 99th percentiles to mitigate the impact of outliers. Table 1 shows means, medians, 25th and 75th percentiles, and standard deviations for firm characteristics in the sample. Panel A of Table 1 presents summary statistics for firm operating leverage. The mean of DOL is while that of OL NM is And the mean of OL CHK is All of them are similar to those reported in related studies (García Feijóo and Jorgensen s, 2010; Novy-Marx, 2011; Chen, Harford and Kamara, 2016). Panel B of Table 1 presents summary statistics for other firm characteristics. The firm investment (capital expenditures divided by lagged property, plant, and equipment PPE) has an average of and a median Around 14.4% of our total observations are identified as investment spikes. This proportion is similar to those reported by Morellec, Valta, and Zhdanov (2015) and Whited (2006). Summary statistics for firm characteristics resemble those reported in related studies (Foucault and Frésard, 2014, Valta, 2012, Chava and Roberts, 2008). The average (median) financial leverage (defined as total debt scaled by the sum of total debt and total shareholders equity at the end of the year (see Fang, Huang and Karpoff, 2015)), is (0.295) while that of book leverage (defined as total debt divided by total assets, see Valta, 2012) is (0.215) There is a large heterogeneity in Tobin's q in our sample: It ranges from to with a mean of and a median of The average size is and the median is

21 Table 1 about here 4.2. Operating leverage and corporate investment To test the first prediction of our model, we study the effect of operating leverage on firm investment by estimating the mixed proportional hazard with specification (1) using maximum likelihood method. Operating leverage is measured by different proxies in three columns and denoted as DOL, OL NM, OL CHK respectively. Table 2 presents the coefficient estimates. In column (1), the coefficient of operating leverage is with t- statistics of -4.23, significant at the 1% confidence level, which shows that operating leverage has negative impact on firms investment expenditure. In column (2), the estimated coefficient of operating leverage measured by OL NM is with t-statistic of while that of operating leverage measured by OL CHK is with t- statistic of in column (3). The magnitude of economic effect is sizable too. For example, in specification (1) the coefficient has a value of , which entails that a one-standard-deviation rise in operating leverage decrease the investment hazard rate by 4.1% (exp( )-1). All these results indicate that firm investment hazard decreases with operating leverage, consistent with the prediction of the model. Note that the coefficients of the control variables have the expected signs. Specifically, we control for Tobin q, size, sales growth rate and cash flow. The signs of the estimated coefficients are consistent with related studies (Chava and Roberts, 2008, Aivazian et al., 2005). High-Tobin q firms are likely to invest more than low-tobin q firms, because High- Tobin q implies good growth opportunity. Cash flow and cash holding are positively related to firm investment, while dividend and R&D activities have the opposite effects.. Table 2 about here 4.3. Operating leverage and debt overhang Evidence from Investment Hazard Model Estimates To test the second prediction of the model, we study the effect of financial leverage on firm investment and more importantly test the joint effect of operating leverage and financial leverage on investment hazard by estimating the mixed proportional hazard model using specification (2). Here, financial leverage is measured as 21

22 the sum of debt in current liabilities and total long-term debt scaled by the sum of debt in current liabilities, total long-term debt and total shareholders equity (SEQ) at the end of the year. Operating leverage is measured by DOL, OL NM, OL CHK and the results when these three measures are used are shown in column (1)-(3) respectively. Meanwhile Tobin s q, firm size, sales growth rate, cash flow among others are included as control variables as they may affect the firm s investment policy. From the columns (1) (3), we can see that estimated coefficients of FinLev are all negative ranging from to and all significant at the 1% confidence level. A one standard deviation increase in financial leverage implies about a drop of investment hazard rate, ranging from 5.7% (e ) to 15.6% (e ). Therefore we can conclude that the financial leverage has negative impacts on firm s investment hazard. Further, we focus on the estimated coefficient of FinLev OperLev to test how operating leverage influences the financial leverage-investment relationship. In column (1) where DOL is employed, the estimated coefficient of the interactive term between financial leverage and operating leverage is 0.04 with t-statistic of 4.96, and with t-statistic of 7.14 in column (2) when OL NM is adopted to measure operating leverage. When we use OL CHK to measure operating leverage, the estimated coefficient of FinLev OperLev is with t-statistic of All are significantly positive at the 1% level. The results indicate that operating leverage generally weakens the negative relationship between financial leverage and investment hazard. The economic effect is substantial too. For example, when the operating leverage (measured by DOL) increases by one standard deviation, the marginal effect of financial leverage is expected to be weaken by 16.43% (e ). In addition, the estimated coefficients of control variables are comparable to those in related literature as well (Foucault and Frésard, 2014, Valta, 2012, Chava and Roberts, 2008). In sum, these empirical results imply that financial leverage has negative impacts on firm s investment, however, such impact is diminishing as the operating leverage increases, consistent with the prediction of the model Book Leverage: Alternative Financial Leverage 22

23 In this section, we corroborate the main result using alternative proxies for financial leverage. As in Ozdagli (2012), we adopt book leverage as an alternative proxy for financial leverage, which is measured as the sum of debt in current liabilities and total long-term debt scaled by total book assets. The regression results are summarized in columns (4) (6) in Table 3. Here, three different proxies for operating leverage are used. Column (4)-(6) report estimated results when DOL, OL NM, OL CHK are used respectively. Meanwhile Tobin s q, firm size, sales growth rate and all other control variables are included as before. Industry level controls and year fixed effects are also included. From the three columns, we can see that estimated coefficients of Bklev presenting financial leverage are all negative, with the value of and t-statistics of in column (4), with the value of and t-statistics of in column (5), with the value of -0.7 and t-statistics of in column (6), and all significant at the 1% confidence level. A one standard deviation increase in book leverage implies a drop of investment hazard rate, ranging from 10.1% (e ) to 17.3% (e ). Therefore the conclusion that the financial leverage has negative impacts on firm s investment is independent of measures of financial leverage. Further, we focus on the estimated coefficient of BkLev*OperLev to identify how operating leverage influence the book leverage-investment relationship. In column (3) where DOL is employed, the estimated coefficient of the interactive term between book leverage and operating leverage is with t-statistic of 4.36, and with t-statistic of 4.77 in column (4) when OL NM is adopted to measure operating leverage. In column (5) OL CHK is used to measure operating leverage and the estimated coefficient of BkLev*OperLev is with t- statistic of All are significantly positive. These results indicate that operating leverage generally weakens the negative relationship between book leverage and investment. In addition, the estimated coefficients of control variables are comparable to those in previous results. The estimated coefficients imply that a one standard deviation increase in operating leverage, measured by the DOL, would lead to a reduction in the marginal effect of book leverage by 29.02% (e ). Overall, these additional results imply that book leverage has negative impacts on firm s investment, however, such impact is diminishing as the operating leverage increases, consistent with the prediction of the 23

24 model. In other words, the predictions are robust to alternative measure of financial leverage and operating leverage. Table 3 about here 4.4 Potential Endogeneity Issues Operating leverage: Industry Level Estimations To qualify as a valid regressor accounting for investment expenditure, firm leverage should be exogenous to firm investment choices. Based on the related definition, operating leverage is ex-ante determined depending on the technology and cost structure. In this section, we perform industry-level exercise to re-examine our hypotheses as the potential for endogeneity is much less severe at the industry level. Chen, Harford and Kamara (2017) argues that even if one accepts that individual firms have the ability to deviate endogenously somewhat from the production technology driven operating leverage, the industry average will not. We repeat our estimates in Tables 2 and 3 at the industry level. All the variables in Table 2 and 3 are constructed as their equally-weighted mean in each industry. The industry classification follows the Fama-French 49 industry classification approach. We remove all industry level controls. We adopt the industry level Fama- MacBeth regression approach in Chen, Harford and Kamara (2017). In other words, we first estimate hazard models cross-sectional for each year between 1966 and 2016, and then report the average estimated coefficients. The t-statistic are adjusted using the Newey-West (1987) method with four lags. Table 4 reports the results. The industry level estimates of Table 2 are presented in Panel A of Table 4, while Panel B corresponds to the industry level estimates of Table 3. Overall, the results in Table 4 are similar to our main results. Due to the smaller sample size, the statistical significance is moderately weaker compared to our firm level estimations. Panel A shows that firm investment hazard declines with operating leverage. The results in Panel B suggest that operating leverage weakens the negative relation between financial leverage and investment hazard. Table 4 about here 24