External Growth Opportunities and a Firm s Financing Policy Sigitas Karpavičius a and Fan Yu b a Flinders Business School, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia. E-mail: sigitas.karpavicius@flinders.edu.au. Phone: +61 8 8201 2707. b School of Management, Fudan University, 670 Guoshun Road, Shanghai 200433, China. E-mail: yu_fan@fudan.edu.cn. May 3, 2015 Abstract This paper provides a theoretical explanation for how a firm s external growth opportunities impact a firm s optimal financing policy and shareholder value. We find that equity value increases with a firm s external growth opportunities, supporting the Gordon dividend growth model. We also find that financial leverage is lower for high-growth firms, controlling for agency problem of excess free cash flow, firm age, and other alternative explanations. The results suggest that average coefficient of constant relative risk aversion of firms managers is less than their subjective discount factor, meaning that firms managers are either risk-seeking, risk-neutral, or weakly risk-averse, on average. Key words: Capital structure; Growth opportunities; Risk preferences. JEL classifications: D21; D22; D58; G32. The authors would like to thank Terry Walter and seminar participants at 2014 Annual Summer Meeting of Economists in Vilnius, Shanghai University of Finance and Economics, University of Adelaide, and University of South Australia for their helpful comments and suggestions. Corresponding author.
1 Introduction Do external growth opportunities such as general demand growth impact a firm s financing policy? The empirical studies suggest that a firm s financial leverage decreases with growth opportunities (see, for example, Frank and Goyal, 2009). The potential explanations for the negative relation between debt level and growth opportunities include the free cash flow hypothesis and underinvestment due to the conflict between shareholders and debtholders. Classical agency theory predicts that corporate managers with substantial free cash flow are more likely to invest in negative net present value (NPV) projects, even if paying out cash would be better for shareholders (Jensen, 1986; Stulz, 1990). Jensen (1986) suggests using debt to control the agency problem associated with excess cash flow. The increased interest payments reduce the cash flow accessible to managers. Firms with high growth opportunities are less likely to have excess cash; therefore, they should have less debt, ceteris paribus. Myers (1977) demonstrates that a firm, partially financed by risky debt, might reject positive NPV projects. Thus, it is optimal for a firm with growth opportunities to be financed by equity, implying the negative relation between debt and growth opportunity. 1 External growth opportunities tend to be negatively correlated to the firm s age (Autio et al., 2000). The existing corporate finance research argues that young firms tend to have less debt because they have limited collateral (Frank and Goyal, 2003), feature greater information asymmetry (Myers, 1984), and, thus, are riskier borrowers. This suggests that the relation between debt financing and growth opportunities might even be spurious, as the third factor firm age impacts both; thus, we observe that high-growth firms are less levered. This paper improves our understanding of how growth opportunities impact a firm s financing policy in three ways. Firstly, we analyze how external growth opportunities affect a firm s financing decisions, regardless of firm age, agency problems associated with excess 1 Lang et al. (1996) find that there is a negative relation between growth opportunities and debt level only for low Tobin s q firms; however, debt financing does not impact growth for firms with good investment opportunities. 1
cash flow, and underinvestment due to risky debt that is, if we assume that these three factors do not impact the relation between growth opportunities and capital structure. Secondly, the theory in Myers (1977) implies that leverage impacts a firm s growth, suggesting that leverage is an exogenous variable and growth is endogenous. However, from the firm s perspective, it is more likely that the direction of causality is just the opposite. Some firms operate in higher growth industries and some firms belong to lower growth industries; due to high switching costs, the latter firms cannot quickly switch industries. For example, the production of semiconductors and other electronic components industry (NAICS = 3344) increased by 11.7% and the newspaper publishing industry (NAICS = 51111) dropped by 9.3% in 2013. 2 As it is hard or nearly impossible for a newspaper publisher to immediately switch to the semiconductor industry, one can argue that firms are subject to growth opportunities that do not depend on the ability of their managers, as those opportunities depend on the industry. 3 In contrast, financing decisions are made by the managers of the firms rather than by the industries (unless a firm s manager, for whatever reason, mimics the capital structure decisions of competing firms (see Leary and Roberts (2014))). Thus, financing decisions are endogenous. In this paper, we follow this logic and analyze how growth opportunities impact firms capital structures but not vice versa. Thirdly, the theories and hypotheses in Jensen (1986) and Myers (1977) are of a dynamic nature (as they are related to future growth); however, they are based explicitly or implicitly on the static models that, by construction, ignore the risk and time preferences of the firm s manager that impact on how the firm s future cash flows will be distributed over time. To control for managerial preferences, we expand the dynamic partial equilibrium model developed in Karpavičius (2014b) to include external growth opportunities. The model assumes that a firm s manager maximizes a certain objective function that positively depends on shareholder value. In each time period, the firm s manager makes 2 Data source: Industrial Production and Capacity Utilization - G.17 Table at http://www. federalreserve.gov/econresdata/statisticsdata.htm (retrieved on 5 June 2014). 3 However, a firm should operate in the industry as long as the NPV of operations is positive, regardless whether the industry is declining or not. 2
several simultaneous decisions, specifically, how much capital to raise in the external equity and debt markets, how much to produce, and how much to invest in productive capital stock. A firm uses a mix of equity and debt to finance its activities; however, there are no agency costs of debt. A firm produces a single tradable final good that is sold in a competitive market. The relation among all endogenous variables and their dynamics are jointly determined in equilibrium. We assume that a firm evolves along a stable growth path that proxies the firm s external growth opportunities. The three innovations discussed above will lead to new insights on the relation between growth opportunities and optimal leverage of the firm. Growth opportunities of the firm can be either exogenous or endogenous. Exogenous (or external) growth opportunities are those which do not depend on the firm s activities and include general demand growth due to the change in consumers preferences and behavior. Endogenous (or internal) growth opportunities arise due to certain firm activities such as research and development or marketing. In this paper, we only focus on exogenous growth opportunities as they are easier to be modeled and measured. We expand the dynamic partial equilibrium model developed in Karpavičius (2014b) to include external growth opportunities. According to the model, equity value is directly affected by exogenous growth opportunities, whereas the impact on leverage is indirect. This paper shows that a dynamic model based on shareholder wealth maximization implies the Gordon dividend growth model which suggests that share price is equal to the discounted future dividend stream (see Williams (1938, p. 88) and Gordon (1959)). In contrast, previous studies usually assumed that share price is equal to the present value of future dividends (see, for example, Modigliani and Miller (1958)). This feature helps validate the model. Our model suggests that the impact of external growth opportunities on share price is not always positive as the Gordon dividend growth model implies. We show that the equity value increases (decreases) with a firm s external growth opportunities if the coefficient of constant relative risk aversion of firm s manager is less (more) than her subjective discount 3
factor. The threshold is driven by the growth factor of the manager s marginal utility. Our model predicts that a firm s external growth opportunities have a limited and nonmonotonic impact on optimal firm size or assets. Leverage is computed as the difference between firm s assets and equity over assets. If we assume that assets are constant then the predicted impacts on leverage are just the opposite to those on equity value. Thus, the model predicts that leverage should decrease (increase) with a firm s external growth opportunities if the coefficient of constant relative risk aversion of firm s manager is less (more) than her subjective discount factor. We test the model s implications using the sample of US industrial firms during the period 1985-2012. According to the model, growth opportunities impact the demand of the firm s products; therefore, we measure firms growth opportunities using industry 3-year sales growth. The results from panel data regressions show that equity value increases with a firm s external growth opportunities and that financial leverage is lower for highgrowth firms, controlling for agency problem of excess free cash flow, firm age, and other alternative explanations. The results are robust to alternative measures of firms growth opportunities. Therefore, the empirical results suggest that average coefficient of constant relative risk aversion of firms managers is less than their subjective discount factor which is a number close to one but smaller than one. Thus, firms managers are either risk-seeking, risk-neutral, or weakly risk-averse, on average. The results are consistent with Lambert and Larcker (1987) who use the Box-Cox estimation for the sample of 370 US firms from 1970 to 1984 and find that the mean (median) coefficient of relative risk aversion is 0.784 (0.400). The rest of the paper is structured as follows. Section 2 introduces a non-stationary dynamic stochastic partial equilibrium model. We develop and test our hypotheses in Section 3. Finally, Section 4 concludes. 4
2 The model We use the dynamic stochastic partial equilibrium (DSPE) model developed in Karpavičius (2014b). 4 The model replicates the performance of a representative firm in a dynamic world with a changing environment. We consider a firm with an infinite life span in discrete time. The firm s manager acts completely in the best interests of shareholders and has rational expectations about the future. In each time period, the firm s manager observes the changes in the environment that are defined by stock price and productivity shocks, and makes several decisions accordingly; namely, to choose how much capital to raise in the external equity and debt markets, how much to produce, and how much to invest in capital stock (i.e., fixed assets used in production). The firm s manager does not know the timing of future shocks but knows their distributional properties. Thus, the decisions of the manager are made knowing that the future value of innovations is random but will have zero mean. The model is non-stationary; that is, a firm is subject to exogenous growth opportunities. A firm produces a single tradable final good that is sold in a competitive market. 2.1 A firm The firm s manager has the following intertemporal objective function: ( ) E 0 β t U t, (1) t=0 where β is the subjective discount factor and reflects the time preferences of the firm s manager. We assume that the firm s manager acts in the best interests of current shareholders and maximizes a certain objective function that increases with shareholder value. 5 4 In this section, the description of the model is broadly similar to one in Karpavičius (2014b). 5 For more details, see the discussion on page 292 of Karpavičius (2014b). 5
Thus, the instantaneous objective function, U t, is given by: U t = (P t m N t ) 1 σ, 1 σ where P m t is market value of equity per share at time t and N t is the number of shares outstanding. σ is the coefficient of constant relative risk aversion (the inverse of elasticity of substitution). The firm s manager maximizes the objective function subject to the balance sheet equation and asset composition of the firm: Pt b N t = Pt 1N b t 1 + Pt 1N m t Pt 1N m t 1 +RE t (2) }{{} New share issue K t = κ(d t + P b t N t ). (3) P b t is book value of equity per share at time t. The left hand side of Equation (2) is the book value of equity. Therefore, ( P m t 1 N t P m t 1 N t 1) is the proceeds from issuance of common stock. 6 The relation between market value and book value of equity is given by: P m t = P b t e qt, (4) where q t is shock to market-to-book ratio and follows the AR(1) process: q t = ρ q q t 1 + η q t, (5) where η q t N(0, σ2 q), 0 ρ q < 1, and σ 2 q > 0. q t measures the deviation of market value of equity per share from the book value and proxies the information asymmetry between the firm s manager and investors. Positive q t means that stock is overvalued, and vice versa. 6 This term controls for market timing activities. For example, a high stock price might trigger an equity issue. Similarly, if the share price falls below its fair value, a firm might decide to repurchase some shares, as it would be in line with the interests of shareholders. If N t < N t 1 then (P m t 1N t P m t 1N t 1) is equal to the funds spent to repurchase shares. 6
RE t denotes retained earnings: RE t = π t d t N t 1, (6) where d t is dividends at time t. They are paid to those who owned shares at time (t 1). Thus, investors who purchase shares at time t are not entitled to receive dividends in this period. π t represents net income. K t is capital stock at time t. D t is new borrowing; thus, D t 1 is debt a firm pays back in period t. For simplicity, it is assumed that debt consists of one-period securities. Equation (3) implies that a firm can invest only the κ fraction of its financial assets into capital stock. This assumption is introduced in order to make the model more realistic. For example, a mean of fixed assets-to-total assets ratio is equal to 0.285 for the population of Compustat firms during 1980-2009. The rest of the financial capital, (1 κ) (D t + Pt b N t ), can be seen as working capital. Thus, κ is the outcome of firm s working capital management. Stock of physical capital, K t, evolves according to: K t = (1 δ)k t 1 + I t, (7) where δ is the capital depreciation rate. I t stands for investment. The firm s net income is given by: π t = (S t C t δk t 1 D t 1 r t 1 ) (1 τ), (8) where S t is sales revenue. C t is the amount of production input (for example, labor and raw materials). It is assumed that the unit cost of C t is one. τ is corporate income tax. r t is the interest rate for a debt obtained in time t, D t. The interest rate at which a firm can borrow funds evolves according to the following equation: ( ) r t = r D t 1 + Φ r D t + Pt bn, (9) t 7
where r is a constant and equal to the hypothetical interest rate on corporate bonds for firms with zero leverage. The last term in Equation (9) is the risk premium related to a firm s financial leverage. Φ r > 0 is the parameter of risk premium. The definition of interest rate implies that it is an increasing function of a firm s financial leverage. In the model, debt has advantages (such as tax deductibility of interest expenses and lower costs) and disadvantages (increased bankruptcy risk). Sales revenue, S t, is the product of output volume, Y t, and the price per output unit, p t : S t = Y t p t. (10) The price per output unit depends on demand for a firm s products and is given by the following equation: ) η (Ỹt p t = p t, (11) Y t where Ỹt and p t are respectively the stable-growth path values of demand for a firm s products and their market price at time t. 7 Parameter η is price elasticity of demand. To produce a single tradable good, a firm uses the following Cobb-Douglas technology: Y t = Ae At K α t 1C 1 α t, (12) where A is the total factor of productivity. A t is the productivity shock that follows the AR(1) process: A t = ρ a A t 1 + η a t, (13) where ηt a N(0, σa), 2 0 ρ a < 1, and σa 2 > 0. α is capital share. Equation (12) implies that production output is the increasing function of capital stock and other production inputs. We assume that it takes one period for a firm to install the newly acquired productive capital stock before it can be used in production. 7 Throughout this paper, variables with tildes denote stable-growth path values. 8
Dividends per share evolve according to the following equation: d t = ψ d t + (1 ψ) π t N t 1, (14) where d t is the stable-growth path value of dividends per share. ψ is subjective dividend smoothness parameter that reflects the manager s perception on the dividend policy. Equation (14) shows that dividends per share, d t, consist of constant and variable parts. The constant part is equal to the stable-growth path dividends per share, d t, multiplied by ψ. 8 It is equivalent to a certain amount of cash per share distributed to shareholders at the end of each period. The variable part is proportional to the firm s net income per share. 2.2 The equilibrium In each period, the firm s manager observes the values of the shocks and parameters and chooses strategy {C t, K t, N t, D t } t= t=0 to maximize her expected lifetime utility subject to constraints (Equations (2) and (3)), initial values of debt, capital stock, share price, the number of shares outstanding and a no-ponzi scheme constraint of the form: lim j E t D t+j j i=1 (1 + r i) 0. (15) To simplify the firm s manager s optimization problem, we assume that the firm s manager does not consider an option of strategic default while running a firm. We admit that, in some cases, it could be optimal from the shareholder perspective to liquidate a firm in order to avoid further losses. However, in reality, we do not observe (at least, we are not familiar with) cases where a manager liquidated a firm with positive net assets; that is, when a firm s assets exceeded its liabilities. Usually, managers try to run a firm as long as possible; thus, creditors initiate bankruptcy procedure. This occurs when a 8 The stable-growth path value of dividends per share, d t, can be seen as the long-term historical average dividends per share or the target dividends per share. In good times, actual dividends per share exceed the stable-growth path value but in bad times, actual dividends per share are lower than it. However, the average actual dividends per share are equal to the stable-growth path value. 9
firm s net assets are negative. The potential explanations for why managers do not file for bankruptcy when firms net assets are still positive include agency-related reasons (managers do not want to lose their jobs and thus salaries important source of their income), information asymmetry (managers are more likely to have better information regarding the firm s prospects than other stakeholders), and behavioral reasons (managers might be overconfident about their firm s prospects and their abilities). Thus, without loss of generality, we assume that the firm s manager does not foresee the possibility that a firm might default. Maximization of objective function (Equation (1)), subject to the evolution of shareholder value and asset composition of a firm (Equations (2) and (3)), yields the following first-order conditions: C t : C t = (1 α)(1 η)s t, (16) ( ) σ [ ( ) : (e qt ) 1 σ Kt K t κ D Nt+1 t λ t + βe t {λ t+1 1 + e qt 1 N t [ +κψ (1 τ) α(1 η) S ( ) ]]} 2 t+1 δ + Φ r r Dt κ = 0, (17) K t K t [ e q t 1 ( )] [ Kt 1 : λ t N t N t 1 κ D t 1 = βe t {λ t+1 e N ( ) ]} qt t+1 Kt (N t ) 2 κ D t + ψ d t, (18) [ ] σ : (e qt ) 1 σ Kt D t κ D t λ t { [ ( Nt+1 βe t λ t+1 1 + e qt 1 N t ) + ψe ψ t+1 (1 τ) r [ 1 + 2Φ r κ D ]]} t K t = 0, (19) where λ t is a Lagrange multiplier, that is the shadow price for capital, equity, and debt. It reflects the impact on the firm s manager s utility of an additional unit of capital, equity, or debt. Equation (16) defines the optimal level of production input, C t, and Equations (17)-(19) are Euler conditions. 10
The equilibrium of the model is defined by the evolution of shareholder value, asset composition constraint, first-order conditions, several variable definitions (in total 15 equations), and two shocks. 9 The number of endogenous variables is equal to the number of equations; thus, the model can be solved. To understand long-term equilibrium relations among the model s variables, we analyze the properties of the model assuming a nonstochastic environment. We solve for the non-stochastic steady state of the model by using the following procedure: we detrend non-stationarly variables, then all shocks are set to zero, the time subscripts are dropped, and the steady-state values of each endogenous variable are expressed in terms of parameters. 2.3 Stable growth path and steady state We assume that the majority of variables feature the following law of motion: X t = X 0 e gt, (20) e g = Γ t Γ t 1 1 + g, (21) where X t is any variable, g is a quarterly growth rate, and Γ t is growth factor. d t, p t, r t, P b t, and P m t are stationary variables. Euler conditions imply that a Lagrange multiplier, λ t, decreases at a σg rate (i.e., a Lagrange multiplier s growth factor is e σg ). 10 To obtain steady-state relations, we detrend non-stationary variables by dividing them by their growth factor. 11 When all shocks are set to zero and the time subscripts are dropped, the model reduces to 13 equations: Equation (11) cancels out and the steady-state expressions of Equations (2) and (14) are identical. To express the steady-state values of each endogenous variable in terms of parameters and constants, the number of endogenous variables must 9 Specifically, the equilibrium of the model is defined by Equations (2)-(4), (6)-(12), (14), (16)-(19) and two exogenous processes: Equations (5) and (13). 10 λ t grows at the same rate as the marginal utility. 11 The term steady state refers to the deterministic steady state. Throughout this paper, variables with bars denote steady-state values. 11
be equal to the number of equations. Thus, we assume that steady-state values of the number of shares outstanding, N, and dividends, d, are known. We re-arrange steady-state expressions of Equations (3) and (18) and ascertain that market value of equity per share in the steady state is as follows: 12 P m = βe σg ψ d 1 βe σg e g. (22) The effective discount factor of the stationary model should take into account the growth of variables and is defined as a product the subjective discount factor of the firm s manager, β, and the growth factor of the manager s marginal utility, e σg (i.e., βe σg ). Then the effective discount rate is as follows: R = 1 βe σg βe σg. (23) Growth factor, e g, can be expressed as (1 + g), assuming that g is a small number. Then Equation (22) can be rewritten as follows: P m = ψ d R g. (24) Equation (24) is similar to the Gordon dividend growth model, except that the latter considers whole dividends (i.e., constant and variable parts) and implies that firms with greater growth opportunities are more valuable (see Williams (1938, p. 88) and Gordon (1959)). Previous studies usually assume that share price is equal to the present value of future dividend stream. The fact that our model is consistent with Gordon dividend growth model helps validate our model. 12 See Appendix A for more details. 12
2.4 Calibration There is no consensus in the literature on the calibration of the coefficient of relative risk aversion. Some studies report or use the value of the coefficient equal to or less than one. Huddart (1994) sets the coefficient of relative risk aversion to 0.5 and 0.75. Oyer and Schaefer (2005) use a coefficient of relative risk aversion value of one. Bhagat et al. (2011) set the coefficient of risk aversion to 0.19. Lambert and Larcker (1987) use the Box-Cox estimation for the sample of 370 US firms from 1970 to 1984 and find that the mean (median) coefficient of relative risk aversion is 0.784 (0.400). Brown and Kim (2014) find that 95 out of 101 (or 94%) experiment participants have the coefficient of relative risk aversion smaller than 0.97 in Epstein and Zin s (1989) framework. However, the value of the coefficient of relative risk aversion of the representative agent used in macroeconomic literature is normally between one and two. For example, Khan and Tsoukalas (2012) estimate that it is 1.08, Smets and Wouters (2007) report a value of 1.38. 13 The recent survey by Graham et al. (2013) finds that CEOs are very different from the rest of the population. Graham et al. (2013) report that only 8.4% of CEOs have the coefficient of relative risk aversion greater than 3.76, in contrast to 64.6% of the general population of a similar age (Barsky et al., 1997). This suggests that CEOs are significantly less risk averse than ordinary individuals and could prompt their coefficient of relative risk aversion to be smaller than one, as assumed by the previous studies (for example, Huddart (1994)). We assume that the coefficient of manager s risk aversion, σ, is set to 0.97; that is, the value that is less than but close to one. The quarterly growth rate, g, is assumed to be 0.02 which is slightly lower than the average industry sales and assets growth rate. The quarterly discount factor, β, is set to 0.98. It corresponds to an 8% annual discount rate, consistent with Bhagat et al. (2011). The values of β and g imply that the coefficient of relative risk aversion, σ, should be somewhat smaller than one, as only then do the exogenous growth opportunities lead to higher shareholder value (see Equation (22)). 14 13 In addition, many studies (for example, Justiniano et al., 2010) use a log-utility function that assumes that the coefficient of relative risk aversion is equal to one. Others, for example, Gertler et al. (2012) set the coefficient of relative risk aversion as equal to two. 14 The exact relation among share price, σ, and g is derived in Section 3.1. 13
Table 1: Calibration of the parameters and steady-state values of some variables This table presents the calibrated parameter values and steady-state values of some variables. Coefficient Description Value N Shares outstanding in the steady state 1 d Dividends in the steady state 1 g Quarterly growth rate 0.02 κ Fixed assets-to-capital ratio 0.28 τ Corporate income tax rate 0.3 r Interest rate for unlevered firm 0.015 α Capital share 0.33 η Price elasticity of demand 0.15 β Subjective discount factor 0.98 ψ Weight of the constant part of dividends 0.7 Φ r Parameter of risk premium 1 δ Capital depreciation rate 0.025 σ Coefficient of constant relative risk aversion 0.97 This provides a further reason to set σ to 0.97. The rest of the model is calibrated similarly as in Karpavičius (2014b) (see Table 1). 15 We assume that the variables are measured quarterly. The steady-state values for the number of shares outstanding, N, and dividends, d, are normalized to one. Following macroeconomic literature, quarterly capital depreciation rate, δ, is set to 0.025 and capital share in the production function, α, is set to 0.33. Further, we assume that a firm can invest 28% of its financial resources in productive capital; that is, κ = 0.28). The value is similar to average net property, plant, and equipment scaled by total book value of assets for US public firms over the last two decades. The steady-state quarterly interest rate on corporate bonds, r, is set equal to 0.015. It implies that the hypothetical annual interest rate for unlevered firms is 6%. It is approximately equal to Moody s Seasoned Aaa Corporate Bond Yield during the 1993-2013 period. 16 The corporate income tax rate, τ, is 0.3, which is approximately equal to an average value of corporate marginal tax rate simulated in Graham and Mills (2008). To achieve reasonable leverage ratios, we calibrate the rest of the parameters respec- 15 In this paper, we do not run any simulations; therefore, we do not calibrate the parameters of the stochastic processes. 16 Source: http://research.stlouisfed.org. 14
tively. We assume that ψ is 0.7. It implies that the weight of the constant part of the dividends is 0.7. We assume that price elasticity of demand, η, is 0.15. It implies that if the production supply increases by 10%, the sale price decreases by 1.5%, and vice versa. The parameter of risk premium, Φ r, is set equal to one. It implies that if a firm s leverage increases by one percentage point, the quarterly interest rate will increase by 1.5 basis points if r is 0.015. The calibrated parameter values imply quite reasonable firm characteristics in the steady state. Book (market) leverage, L = D P b, is 0.23. N+ D Quarterly dividend yield is 0.029 and implying that shareholders earn 11.5% per year on their investment. 17 Thus, equity financing is more expensive than debt financing. Net profit margin (net income, π, over sales, S) is equal to 0.22. 18 3 Results In this subsection, we analyze the implications of the model, develop and test hypotheses concerning external growth opportunities and a firm s financing policy. 3.1 Implications of the model The expression of share price in the steady state (see Equation (22)) implies that a firm s stock price is impacted by the manager s time and risk preferences, growth opportunities, and dividend policy. To investigate the relation between share price, P m, and growth 17 Share price, P m t, is a stationary variable; therefore, capital gains are zero. 18 Table B.1 in Appendix B presents the steady-state values of all variables. 15
opportunities, g, we compute partial derivatives of share price, P m, with respect to g: P m g P m g [ βψ de σg βe (1 σ)g σ ] = [ ] 1 βe g(1 σ) 2, (25) > 0 if βe (1 σ)g > σ (or β > σ), < 0 if βe (1 σ)g < σ (or β < σ). Equation (25) implies that higher growth opportunities do not necessarily lead to higher share price. According to Equation (24), share price should increase with growth rate, g, assuming that R does not depend on g. However, this is not a case; that is, g impacts R. The effect of g on R is opposite to that on the effective discount factor, βe σg. The latter increases with g only if σ < 0 and vice versa, suggesting the negative relation between firm s growth opportunities and managerial risk aversion. This is consistent with Graham et al. (2013) who find that firms with high historical or future rates of growth are less likely to be run by highly risk-averse CEOs. Thus, R decreases with g if σ < 0. Lower R leads to higher stock valuations. Share price is impacted by g directly and indirectly (i.e., through R). The direct impact does not depend on σ whereas the indirect impact is positive only if σ < 0. In aggregate, this implies that share price increases with growth opportunities if σ < βe (1 σ)g rather than if σ < 0. According to the current calibration, this is true if σ 0.98. Assuming that (1 σ)g is a small number, e (1 σ)g 1, and the relation βe (1 σ)g > σ can be simplified as β > σ. If g > 0, the relation βe (1 σ)g > σ is always satisfied if σ < β. This leads to our first hypotheses: Hypothesis 1a: Share price increases with firm s growth opportunities (suggesting that σ < β). Hypothesis 1b: Share price decreases with firm s growth opportunities (suggesting that σ > β). Using Equations (22) and (A.3), one can derive the following expression for the firm s 16
financial leverage (debt-to-assets ratio), L: 19 L = 1 e σg κβψ d N K (1 βe σg e g, where (26) ) K = Λ 2 Λ 2 ± 2 4Λ 1 Λ 3, (27) 2Λ 1 2Λ 1 ] Λ 1 = η [δ + r κ (1 + φ r), (28) [ ] 1 Λ 2 = α(1 η) 1 τ + (1 + 2φ r)r βe σg ψ d N 1 βe (1 σ)g, (29) ( βe Λ 3 = r σg ) 2 ψ d N φ r κ[η + 2α(1 η)] 1 βe (1 σ)g. (30) Due to the complexity of the formula for leverage, we do not compute its partial derivatives. Instead, we perform sensitivity analysis of leverage with respect to σ and g. We calculate the leverage values for different values of the two parameters. 20 The sensitivity analysis suggests that the impact of g on leverage is, in most cases, just the opposite to its impact on stock price, P m (see Table 2). 21 That is, firm s leverage decreases (increases) with growth opportunities if the coefficient of relative risk aversion is less than or equal to (greater than) 0.97 (in Section 2.4, we discussed why it is likely that the coefficient of relative risk aversion is less than one). Figure 1 illustrates the intuition of this result. Unreported sensitivity analysis indicates that g has a limited and not monotonic impact on optimal firm size. Thus, for simplicity, one can assume that assets are constant when g changes (assets are set to 100 in Figure 1). Further, we assume that the next dividend per share is six, interest rate is 0.1, and (for Figure 1b only) growth rate is 0.02. Higher growth rate leads to greater equity value (if growth rate increases from zero to 0.02, equity value increases from 60 to 75 in Figure 1). As a result, leverage drops from 0.4 to 0.25. 19 See Appendix A for Equation (A.3). 20 The unreported sensitivity analysis shows that leverage decreases with the subjective discount factor, β. This is consistent with Karpavičius (2014a) who finds that firms with more patient managers (i.e., managers with a higher subjective discount factor) have proportionally less debt. 21 One can notice that the evolution of leverage is not always continuous in Table 2. For example, in Panel A, if g = 0.01 and if σ increases from 3 to 1.25, leverage increases from 1.212 to 1.320. However, if σ = 1, leverage is 0.516. And if σ increases to 3, leverage gradually reaches the value of 0.631. The non-continuous behavior of leverage is likely to be caused by its non-linear nature with respect to g and σ. 17
Table 2: Sensitivity analysis of leverage with respect to g and σ This table presents the sensitivity analysis of leverage with respect to growth opportunities, g, and the coefficient of relative risk aversion, σ. The highlighted numbers show the calibrated values for g and σ as well as the implied leverage value in the steady state. σ 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 g 3 0.934 0.923 0.907 0.884 0.846 0.777 0.624 0.233 0.516 1.212 1.150 1.116 1.095 1.080 1.069 1.061 2.75 0.929 0.917 0.901 0.876 0.836 0.764 0.609 0.233 0.461 1.223 1.159 1.123 1.100 1.085 1.073 1.065 2.5 0.924 0.911 0.893 0.867 0.825 0.750 0.592 0.233 0.407 1.235 1.169 1.131 1.107 1.090 1.078 1.069 2.25 0.918 0.904 0.885 0.857 0.813 0.734 0.575 0.233 0.354 1.248 1.180 1.140 1.114 1.096 1.084 1.074 2 0.911 0.896 0.875 0.845 0.798 0.717 0.557 0.233 0.302 1.263 1.192 1.150 1.123 1.104 1.090 1.079 1.75 0.902 0.886 0.864 0.832 0.782 0.697 0.537 0.233 0.250 1.280 1.206 1.162 1.133 1.112 1.097 1.086 1.5 0.892 0.874 0.850 0.816 0.763 0.675 0.516 0.233 0.200 1.299 1.222 1.175 1.144 1.122 1.106 1.094 1.25 0.880 0.861 0.834 0.797 0.741 0.650 0.494 0.233 0.151 1.320 1.241 1.192 1.158 1.134 1.117 1.103 1 0.865 0.843 0.815 0.774 0.715 0.622 0.471 0.233 0.102 0.516 1.263 1.211 1.175 1.149 1.130 1.115 0.75 0.846 0.822 0.790 0.747 0.684 0.590 0.446 0.233 0.055 0.407 1.289 1.234 1.196 1.167 1.146 1.129 0.5 0.821 0.794 0.760 0.713 0.647 0.554 0.420 0.233 0.009 0.301 1.320 1.263 1.222 1.191 1.167 1.148 0.25 0.788 0.758 0.720 0.670 0.604 0.513 0.392 0.233 0.035 0.199 0.461 1.298 1.255 1.221 1.195 1.174 0 0.742 0.709 0.668 0.617 0.551 0.468 0.363 0.233 0.078 0.100 0.300 0.516 1.298 1.262 1.233 1.209 0.25 0.676 0.641 0.599 0.549 0.489 0.417 0.332 0.233 0.120 0.007 0.147 0.299 0.460 1.319 1.288 1.262 0.5 0.577 0.543 0.505 0.462 0.414 0.360 0.300 0.233 0.160 0.081 0.005 0.097 0.194 0.296 0.404 0.516 0.75 0.428 0.405 0.380 0.354 0.326 0.297 0.266 0.233 0.199 0.163 0.125 0.086 0.045 0.002 0.042 0.089 0.97 0.243 0.241 0.240 0.239 0.237 0.236 0.235 0.233 0.232 0.230 0.229 0.227 0.226 0.224 0.222 0.221 1 0.213 0.216 0.219 0.222 0.225 0.227 0.230 0.233 0.236 0.239 0.242 0.245 0.248 0.251 0.254 0.257 1.25 0.072 0.025 0.021 0.066 0.109 0.152 0.193 0.233 0.272 0.309 0.344 0.378 0.410 0.440 0.469 0.496 1.5 0.412 0.309 0.209 0.112 0.019 0.071 0.155 0.233 0.306 0.372 0.432 0.485 0.533 0.575 0.612 0.644 1.75 1.291 1.321 0.463 0.307 0.158 0.016 0.115 0.233 0.338 0.429 0.505 0.570 0.623 0.667 0.704 0.734 2 1.238 1.266 1.300 0.516 0.306 0.108 0.073 0.233 0.369 0.479 0.567 0.635 0.689 0.731 0.764 0.791 2.25 1.201 1.226 1.258 1.300 0.462 0.205 0.030 0.233 0.398 0.524 0.618 0.687 0.738 0.776 0.806 0.829 2.5 1.173 1.196 1.226 1.265 1.320 0.305 0.014 0.233 0.426 0.564 0.661 0.727 0.775 0.810 0.836 0.856 2.75 1.152 1.173 1.200 1.237 1.290 0.409 0.060 0.233 0.452 0.600 0.696 0.760 0.803 0.835 0.858 0.876 3 1.136 1.154 1.179 1.214 1.265 0.516 0.106 0.233 0.477 0.631 0.726 0.786 0.826 0.855 0.876 0.892 18
Assets = 100 d 6 Debt = Assets Equity Equity 60 r 0.1 = 100 60 = 40 Debt 40 Leverage 40% Assets 100 (a) No growth Assets = 100 d 1 6 Equity 75 r g 0.1 0.02 Debt = 100 75 = 25 (b) Positive growth Debt 25 Leverage 25% Assets 100 Figure 1: The impact of growth on leverage. We assume that firm assets are equal to 100, dividends per share (d and d +1 ) are six, interest rate, r, is 0.1, and growth rate, g, is 0.02. Gupta (1969) reports the positive relation between sales growth rate and leverage for US firms in 1961-1962 financial year. The author suggests that this might be due to their (i.e., high-growth firms) greater desire for financial structure flexibility. However, the later empirical tests generally suggest that leverage is lower for firms with higher growth opportunities. Smith Jr. and Watts (1992), Rajan and Zingales (1995), Barclay et al. (2003), and Billett et al. (2007) find that firms with greater market-to-book ratio are less levered. Gaver and Gaver (1993) report that those firms with higher growth opportunities measured by an index that is comprised of six factors, including R&D expenditure and market-to-book ratio, are less levered. Goyal et al. (2002) show that defense firms increased their leverage in response to an exogenous decrease in growth opportunities (US defense spending cut in 1989-1995). Lang et al. (1996) assume that firm growth is endogenous and leverage is exogenous. They find that negative relation between leverage and future growth of employees and capital expenditure. Thus, our next hypotheses are: Hypothesis 2a: Debt-to-assets ratio decreases with growth opportunities (suggesting that σ < β). Hypothesis 2b: Debt-to-assets ratio increases with growth opportunities (suggesting 19
that σ > β). 3.2 Empirical results In this subsection, we present our empirical results. First of all, we describe our sample. Then we test our hypotheses by estimating the least-squares dummy variable models (the fixed effects models). We include firm and year fixed effects in the models to control for unobserved firm-level heterogeneity, time period-related factors, and the fact that financing policy is highly firm specific. The standard errors are corrected for clustering at the firm level to accommodate heteroscekedasticity and within-firm autocorrelation. 3.2.1 Data Our initial sample is drawn from Compustat. It covers the period 1985 to 2012. We eliminate financial firms (with Standard Industrial Classification (SIC) codes 6000-6999) since they have different capital structure and might be subject to the regulatory authority. We also exclude public utility firms (with SIC codes 4900-4999) because they operate in regulated industries and their financing and capital structure decisions might be impacted by the changes in the regulatory environment. To be included in our sample, firms must have positive values in book value of assets (Compustat item AT) and sales (Compustat item SALE) and non-missing SIC code (either Compustat item SIC or SICH). Further, all the firms must be incorporated in the United States. The final data set is comprised of more than 100 thousand firm-year observations. We measure the firms growth opportunities using industry (defined by the two-digit SIC code) 3-year sales growth, adjusted for inflation using the GDP deflator ( ISAL). 22 Industry-based growth proxy is superior to those based on firm level data, as it does not include idiosyncratic disturbances and thus better reflects the firms growth opportunities. Table 3 provides descriptive statistics for the sample. 3-year industry sales growth is 22 See Table B.2 in Appendix B for variable definitions. 20
Table 3: Descriptive statistics This table presents the descriptive statistics. ISAL is industry (defined by the two-digit SIC code) 3-year sales growth, adjusted for inflation using the GDP deflator. AGE is the number of year the company has data on COMPUSTAT. DEBT is the sum of long-term debt (Compustat item DLTT) and debt in current liabilities (Compustat item DLC) over book value of assets (Compustat item AT). ASSETS is the natural logarithm of book value of assets (in millions of U.S. dollars (converted into 2009 constant dollars using the GDP deflator)). Q is market value of assets divided by book value of assets. ROA is operating income before depreciation (Compustat item OIBDP) divided by book value of assets. CASH is cash and short-term investments (Compustat item CHE) over book value of assets. PPE is net property, plant, and equipment (Compustat item PPENT) divided by book value of assets. CAPEX is capital expenditures (Compustat item CAPX) to book value of assets ratio. RD is research and development expense (Compustat item XRD) divided by book value of assets. RDD is equal to one when research and development expense is reported in Compustat and zero otherwise. *** and ** indicates significance at 1% and 5% levels, respectively. Correlation with Variable Obs. Mean 25 th perc. Median 75 th perc. St. dev. ISAL ISAL 137073 0.291 0.119 0.241 0.407 0.263 Q 132375 2.629 1.095 1.504 2.454 3.963 0.011*** DEBT 153239 0.309 0.040 0.216 0.417 0.411 0.006** AGE 152139 12.243 5 9 18 9.891 0.173*** ASSETS 153831 4.730 3.042 4.638 6.284 2.278 0.062*** ROA 153377-0.046-0.026 0.096 0.164 0.542 0.011*** CASH 153720 0.179 0.022 0.084 0.256 0.220 0.007*** PPE 153574 0.279 0.090 0.208 0.407 0.237 0.009*** CAPEX 153831 0.065 0.017 0.039 0.079 0.081 0.096*** RD 153831 0.067 0 0 0.059 0.173 0.040*** RDD 153831 0.579 0 1 1 0.494 0.076*** 0.291 on average, implying that annual sales of the whole industry increase by approximately 10% per year. Market value of equity per share ( P m ) is proxied by market-to-book ratio (Q). The mean (median) value of Q is 2.629 (1.504). The mean (median) value of financial leverage (DEBT) is 0.309 (0.216). The last column in Table 3 shows coefficients of Pearson correlation. There is a positive correlation between market-to-book ratio (Q) and ISAL, supporting our Hypothesis 1a. We find that our growth proxy is positively correlated with capital expenditure scaled by assets (CAPEX) that was used by the previous studies as the measure for growth opportunities. However, ISAL is negatively correlated with another growth measure R&D expense over assets (RD). 23 Thus, the growth 23 Market-to-book ratio is also frequently used as a proxy for growth opportunities by the previous 21
measure used in this paper, ISAL, is likely to provide new insights on how external growth opportunities impact a firm s financing policy. DEBT is positively correlated with ISAL, supporting Hypothesis 2a. Consistent with Autio et al. (2000), external growth opportunities are negatively correlated to the firm s age. 3.2.2 The impact of a firm s growth opportunities on share price To test our Hypotheses 1a and 1b, that share price increases or decreases with firm s growth opportunities, we regress market-to-book ratio on the firm s growth opportunities controlling for certain firm characteristics and lagged values of market-to-book ratio. In order to control for firm and time period-specific factors, we include in the models firm and year fixed effects. Specifically, we estimate the following model: Q it =β 0 + β 1 Q it 1 + β 2 ISAL it + β 3 ASSETS it + β 4 ROA it + β 5 PPE it + β 6 CAPEX it +β 7 RD it + β 8 RDD it + λ t + µ i + ɛ it ; (31) where the indices i and t correspond to firm and year, respectively, ASSETS is the natural logarithm of market value of assets (in millions of U.S. dollars (converted into 2009 constant dollars using the GDP deflator)), ROA is returns on assets, PPE is net property, plant, and equipment (NPPE) divided by book value of assets. RDD is equal to one when R&D expense is unreported in Compustat and zero otherwise, λ and µ are year and firm fixed effects, respectively. The standard errors are corrected for clustering at the firm level to accommodate heteroscekedasticity and within-firm autocorrelation. 24 Model 1 in Table 4 shows the positive relation between Q and ISAL, supporting our Hypothesis 1a. This is consistent with Habib and Ljungqvist (2005) who find that Q increases with forecasts of industry growth. Average Q and ISAL are 2.629 and 0.291, respectively. This suggests that the average impact of ISAL on Q is 4% ( 0.291 0.351 2.629 0.039 ), after controlling for firm characteristics, firm and year fixed effects. studies. 24 This applies to all regressions estimated in this paper. 22
Table 4: Determinants of market-to-book ratio (Q) This table presents the results of least squares regressions where the dependent variable is market-to-book ratio (Q). Q is market value of assets divided by book value of assets. ISAL is industry (defined by the two-digit SIC code) 3-year sales growth, adjusted for inflation using the GDP deflator. AGE is the number of year the company has data on COMPUSTAT. DEBT is the sum of long-term debt (Compustat item DLTT) and debt in current liabilities (Compustat item DLC) over book value of assets (Compustat item AT). ASSETS is the natural logarithm of book value of assets (in millions of U.S. dollars (converted into 2009 constant dollars using the GDP deflator)). ROA is operating income before depreciation (Compustat item OIBDP) divided by book value of assets. CASH is cash and short-term investments (Compustat item CHE) over book value of assets. PPE is net property, plant, and equipment (Compustat item PPENT) divided by book value of assets. CAPEX is capital expenditures (Compustat item CAPX) to book value of assets ratio. RD is research and development expense (Compustat item XRD) divided by book value of assets. RDD is equal to one when research and development expense is reported in Compustat and zero otherwise. IGROWTH E is industry (defined by the two-digit SIC code) expected 1-year sales growth generated using analyst forecasts from I/B/E/S. GROWTH E is the firm s expected 1-year sales growth generated using analyst forecasts from I/B/E/S. *** and ** indicates significance at 1% and 5% levels, respectively. Model 1 Model 2 Model 3 Model 4 Model 5 Q t Q t Q t Q t Q t Q t 1 0.331*** 0.332*** 0.343*** 0.290*** 0.213*** [31.326] [29.618] [29.152] [25.097] [12.506] ISAL t 0.207*** [4.594] ISAL t+1 0.317*** [7.569] ISAL t+2 0.104*** [2.602] IGROWTH E t 0.280** [2.317] GROWTH E t 0.228*** [5.305] ASSETS t 0.537*** 0.519*** 0.505*** 0.753*** 0.635*** [22.085] [20.939] [19.775] [20.648] [13.998] ROA t 2.487*** 2.250*** 2.090*** 2.627*** 1.163*** [22.616] [18.265] [15.492] [21.459] [4.033] PPE t 0.928*** 0.893*** 0.899*** 1.164*** 1.307*** [5.769] [5.748] [5.703] [4.385] [6.988] CAPEX t 1.695*** 1.630*** 1.599*** 1.519*** 1.265*** [6.391] [7.127] [6.875] [3.790] [3.948] RD t 0.781*** 1.194*** 1.509*** 0.347 3.091*** [2.688] [3.753] [4.399] [1.056] [7.383] RDD t 0.185*** 0.165*** 0.177*** 0.239** 0.072 [3.289] [3.103] [3.296] [2.393] [0.840] Year fixed effects Yes Yes Yes Yes Yes Firm fixed effects Yes Yes Yes Yes Yes Observations 107,771 98,861 91,088 71,711 33,180 Adj. R-squared 0.695 0.688 0.682 0.711 0.542 F-test 115.7*** 103.0*** 95.7*** 111.3*** 81.6*** 23
Consistent with previous results, we find that firms subject to higher growth opportunities are more valuable. Thus, we conclude that the empirical results support our Hypothesis 1a. To take into account that the contemporaneous ISAL value reflects the historical industry growth, we regress Q t on either ISAL t+1 or ISAL t+2. Each of the two variables shows the 3-year industry growth and surrounds the time period t in which Q t is computed. Models 2 and 3 in Table 4 show that the relation between growth opportunities and Q is significantly positive, implying that firms operating in industries with higher future growth rates are more valuable. Further, we find that Q increases not only with ISAL but also with CAPEX and RD that were used by the previous studies as the measures of growth opportunities. CAPEX and RD can be seen as proxies for internal growth opportunities but ISAL measures external growth opportunities. Thus, Q is positively impacted by all three proxies of growth opportunities. 25 Overall, our results support Hypothesis 1a but not Hypothesis 1b. 3.2.3 The impact of a firm s growth opportunities on financing policy To test our Hypotheses 2a and 2b, that firm s leverage decreases/increases with growth opportunities, we regress debt ratio (DEBT) on the firm s growth opportunities ( ISAL) controlling for some common factors, such as firm size (ASSETS), profitability (ROA), and tangibility (PPE), firm and year fixed effects. We also include lagged values of DEBT in the model. Further, we control for firm age as younger firms tend to have less debt, and agency problems associated with excess cash flow by including firm age and cash holdings 25 The coefficient estimate for RD is significantly positive whereas the coefficient estimate for RDD dummy is significantly negative. This suggests that only large R&D expenditures are associated with higher market-to-book ratios. 24