Impact of Different Dividend Treatment of Restricted Stock. and Option Grants on Equity Value

Transcription

1 Impact of Different Dividend Treatment of Restricted Stock and Option Grants on Equity Value Sigitas Karpavičius a and Fan Yu b a Flinders Business School, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia. sigitas.karpavicius@flinders.edu.au. Phone: b School of Management, Fudan University, 670 Guoshun Road, Shanghai , China. yu_fan@fudan.edu.cn. April 2, 2015 Abstract Stock options and restricted stock are the two main vehicles of equity-based compensation. In this paper, we analyze how different dividend treatment of stock options and restricted stock grants impacts stock price and the riskiness of the firm. We find that if a firm s manager s utility function includes contemporaneous dividends (as in the case of restricted stock grants), the manager increases the risk level of equity in order to maintain the preferred risk level of her utility function. Increased risk level negatively impacts stock price. The calibrated model reveals that the impact on stock price is 1.5% and that such firms are riskier. Key words: Stock options, Restricted stock grants, Dividends, Firm value. JEL classifications: G32, H32, M12. Corresponding author.

2 1 Introduction Equity-based compensation is used to align the interests between managers and shareholders. In recent years, the equity component (i.e., the mix of restricted stock and options) of the median chief executive officer (CEO) of all the ExecuComp firms is equal to around half of the total CEO pay (Murphy, 2013). In 2011, options accounted for 21% of S&P 500 CEOs pay and the proportion of restricted stock increased to 36% (Murphy, 2013). Stock and options differ in several ways: costs to a firm, incentive structures, accounting treatment and tax implications, and dividend treatment. Previous studies have extensively analyzed the above-mentioned differences except for the last one. 1 This study fills the gap. In this paper, we isolate the different dividend treatment of stock options and restricted stock grants from other differences between stock options and restricted stock and analyze how it impacts the stock price and the riskiness of the firm. There is an extensive literature on how firm value and risk impact and are impacted by stock options and restricted stock grants. Agrawal and Mandelker (1987) report the positive relation between common stock and option holdings of managers and the riskiness of the firm measured by leverage and return variance. Mehran (1995) finds that Tobin s q and return on assets both increase with the percentage of equity held by managers and with the percentage of their compensation that is equity-based. A more recent study by Habib and Ljungqvist (2005) finds that Tobin s q is positively impacted by CEO stockholdings but negatively impacted by option holdings for the sample of US industrial firms during 1992 to 1997 period. They argue that CEOs were granted too few shares and too many stock options. Tian (2004) finds that granting more stock options creates greater incentives to increase stock price only if option wealth does not exceed a certain fraction of the total wealth. Additional options reduce incentives and become counterproductive. Further, Tian (2004) finds that stock options lead to lower (higher) idiosyncratic (systematic) risk. Similarly, Armstrong and Vashishtha (2012) find that stock options help increase a firm s 1 We discuss the differences in more details and associated empirical tests in Section 2. 1

3 total and systematic risks but have no impact on the firm specific risk. The authors argue that this might adversely affect firm values due to excessive systematic risk in equity markets. Lewellen (2006) reports that leverage is positively impacted by option ownership and negatively impacted by share ownership. Several recent studies analyze the determinants of the optimal mix of restricted stocks and option grants. Core and Guay (1999) report that the optimal mix of incentives from stock and options defined as the logarithm of the sensitivity of the total value of stock and options held by the CEO to a 1% change in stock price depends on firm size, growth opportunities, and monitoring costs. Core and Guay (1999) find that firms use annual grants of options and restricted stock to CEOs to manage the optimal level of equity incentives; that is, firms use new grants of stock options and restricted stock to correct deviations from the optimal incentive levels. 2 A dynamic model in Parrino et al. (2005) implies that the combination of stock options and restricted stock held by managers impacts their risk-taking incentives. Ortiz-Molina (2007) finds that stock option grants and the probability of receiving new option grants decrease in leverage, but they increase in the amount of convertible debt. Kadan and Swinkels (2008) analyze the choice between stocks and options to provide effort incentives to a risk-averse manager. Their theoretical model and empirical tests imply that the proportion of restricted stock in the compensation mix increases with bankruptcy risk (measured in the empirical analysis using Z-score, KMV- Merton default probability, and credit rating). To analyze how different dividend treatment of stock options and restricted stock grants impacts stock price and the riskiness of the firm, we expand the dynamic partial equilibrium model developed in Karpavičius (2014) to include dividends in the manager s utility function. That is, we assume that the firm s manager maximizes either a) the market 2 Most of the literature on optimal CEO compensation has focused on the CEO incentives measured by CEO portfolio delta (the change in the CEO s wealth for an incremental change in the stock price or pay-performance sensitivity) and vega (the dollar change in the CEO s wealth for a 0.01 change in standard deviation of stock returns) rather than on optimal ratio of restricted stock to stock options. See Murphy (2013) for recent survey on executive compensation. 2

4 value of equity or b) the sum of the market value of equity and total contemporaneous dividends. The model replicates the life and simplified behavior of a representative firm in a dynamic world with a changing environment and is based on the following assumptions: a firm s manager maximizes a certain objective function that positively depends on shareholder value in each period, to respond to the changes in the environment (i.e., exogenous shocks), the firm s manager makes 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 capital stock a firm uses a mix of equity and debt to finance its activities a firm uses Cobb-Douglass technology to produce 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. In the case of restricted stocks, a firm s manager maximizes the sum of the market value of equity and contemporaneous dividends. We find that if a firm manager s utility function includes contemporaneous dividends (as in the case of restricted stock grants), the manager increases the risk level of equity in order to maintain her preferred risk level of utility function. Increased risk level negatively impacts stock price. The calibrated model reveals that the impact is 1.5%. Given the constant dividend stream, lower stock price leads to higher return on shareholder capital. We show that firms run by managers who maximize the sum of the market value of equity and contemporaneous dividends are riskier; that is, they have a greater financial leverage (by 4.0%) and slightly greater probability of default. The rest of the paper is structured as follows. Section 2 discusses the key differences 3

5 between restricted stock and stock options grants. Section 3 develops a dynamic stochastic partial equilibrium model. Obtained results are detailed in Section 4. Finally, Section 5 concludes. 2 Restricted stock vs. option grants Dittmann and Maug (2007) calibrate the standard principal-agent model with constant relative risk aversion and show that the optimal contract should include stock and lower base salaries but not options. However, the model with loss-averse CEOs in Dittmann et al. (2010) can explain observed option holdings and high base salaries. Thus, theoretical models can explain why firms use both restricted stock and option grants to motivate and remunerate their managers. Stock and options differ in several ways: costs to a firm, incentive structures, accounting treatment and tax implications, and dividend treatment. 3 Below, we discuss the differences between restricted stock and option grants in more details. 2.1 Riskiness CEO vega rather than pay-performance sensitivity (which is equivalent to CEO delta) reflects managerial risk preferences and helps encourage risk-taking (Coles et al., 2006; Low, 2009). Managers with higher vega are expected to be less risk averse. Guay (1999) finds that the average vega of option is 33 times greater than the average vega of stock (0.167 vs ). Thus, CEO s portfolio vega and risk-taking are mainly impacted by stock option grants. This suggests that a manager who has been rewarded with stock options and who would like to improve their value, is more likely to adopt riskier corporate policies that would lead to a more volatile stock price. In contrast, riskier corporate policies would have a marginal impact on the value of stock holdings. 3 In addition, restricted stockholders have voting rights whereas option holders have no voting rights. 4

6 Options are riskier: $1 of options is worth less to a risk-averse CEO than $1 of stock, rendering them more expensive to the firm (Oyer and Schaefer, 2005). In other words, a firm can lower the cost, by replacing options with restricted stock if the participation constraint is the binding constraint. On the other hand, $1 of options provides greater incentive than $1 of stock when options are in the money (Hall and Murphy, 2000). This makes options a cheaper way to compensate a CEO if the incentive compatibility constraint is the binding constraint. Carpenter (2000) develops a theoretical model which implies that the impact on stock options on risk-taking is ambiguous. Under certain circumstances, additional stock options lead to lower volatility. Bryan et al. (2000) find that restricted stock is relatively inefficient in inducing risk-averse CEOs to accept risky but value-increasing investment projects. 2.2 Incentives The incentives provided by restricted stock and options are different along two dimensions. First, restricted stock provides a symmetric marginal incentive along the stock price at a given CEO wealth level. Restricted stock always has a delta equal to one at any price level. However, options provide an asymmetric marginal incentive. On the down side of the stock prices, the delta of the options approaches zero when they are deep out of the money. The options then provide negligible incentives to the CEO because a non-dramatic increase in the stock price will not change the option value. Contrary to this, the value of restricted stock will respond to any stock price change. On the upper side of the stock prices, $1 of options provides a higher delta than $1 of stock. Managers have stronger, if not distorted, incentives to boost the stock price when the options are deep in the money. Kadan and Yang (2005) report that deeply in-the-money executive stock options lead to more earnings management and insider trading at the vesting years of the options. The extent of this increases as the managers are granted more options. Ryan Jr. and Wiggins III (2002) find that executive stock options positively impact research and development expenditure 5

7 (R&D), whereas the R&D decreases with restricted stock. Second, options encourage executive risk taking, which can mitigate problems with executive risk aversion. 4 A CEO tends to be more risk averse than shareholders would otherwise prefer because her portfolio is not well diversified and is overinvested in the firm s assets. Holding options provides the CEO with incentives to take riskier projects because the value of an option increases in the riskiness of the underlying assets. Options can be used to align interests in risk taking and therefore increase shareholder wealth. Guay (1999) finds that options, not restricted stock, can induce risk-averse managers to invest in valuable risk-increasing projects which they may otherwise forgo. 2.3 Accounting treatment and tax implications Prior to 2005, the accounting treatment discriminated between restricted stock and options. Before FAS 123 became effective, stock options did not need to be recognized as an expense when granted at, or out of, the money; however, there is a real economic cost associated with the option grant. This accounting treatment helped overstate income. Nevertheless, the cost of granting restricted stock was recognized as an expense. Murphy (2002) argues that the favorable accounting treatment toward options leads firms to erroneously view stock options as a low-cost way of compensating executives. The SEC adopted FAS 123 effective June The new rule requires public firms to expense option grants at fair value. Therefore, the driving force of earning management for the compensation choice between restricted stock and options was removed after Accounting rules for expensing restricted stock and stock options, set by the Financial Accounting Standards Board (FASB), are separate from taxation rules, set by the Internal Revenue Service (IRS). FAS 123 does not have any impact on the tax implications of restricted stock or options. 4 A CEO can hedge her portfolio at cost but she is not able to hedge it continuously and she is not allowed to hold a short position of the firm s stock. All these constraints limit her ability to hedge. Therefore, it is reasonable to assume that CEOs are risk averse. 6

8 A CEO is typically granted at-the-money options. There is no immediate tax implication upon receipt of these, for either the CEO or the firm. However, the firm expenses the options at the grant date, as per the new accounting rules. When options are exercised, the CEO pays tax on the difference between the stock price and the exercise price at the ordinary income tax rate. The firm deducts the same amount as a compensation expense for tax purposes. When the CEO sells the shares, she pays tax on the difference between the sale price and the market price at exercise of the option at the capital gains tax rate. No immediate tax implication occurs upon receiving restricted stock. On the vesting date, the CEO has to pay tax on the market value of her stock at the ordinary income tax rate. The firm then gets a tax deduction equal to the fair value. When the CEO sells the shares, she will be taxed on the appreciation of the shares at the capital gains tax rate. The appreciation is not recognized as an expense for the firm. From the perspective of the CEO, options enjoy favorable tax treatment because no tax liability occurs when the options are vested, whereas restricted stock imposes tax liability when the stock is vested. 2.4 Dividends Unlike stock options, restricted stock entitles a CEO to receive dividends when they are paid to shareholders. Lambert et al. (1989) find that dividends are reduced relative to expected dividends after the initial adoption of stock options for senior-level executives. Stock options encourage stock repurchases rather than dividends because the value of an option declines when a stock goes ex-dividend but not when a company repurchases shares (Jagannathan et al., 2000). This gives strong material incentives for managers that hold stock options not to pay dividends. Fenn and Liang (2001) find a strong negative (positive) relation between dividends (share repurchases) and CEO stock options. They also report that CEO stockholdings do not impact the firms payout method choice. However, Fenn and Liang (2001) consider total CEO stockholdings rather than restricted stock grants per fiscal/calendar year. 7

9 In this paper, we isolate the different dividend treatment of stock options and restricted stock grants from other differences between stock options and restricted stock and analyze how it impacts stock price and the riskiness of the firm. To achieve this, we construct the model which takes into account different dividend treatment and ignores other differences between stock options and restricted stock. That is, we assume that the firm s manager maximizes either a) the market value of equity or b) the sum of the market value of equity and contemporaneous dividends. To properly isolate the different dividend treatment, we assume that dividends are exogenous from the perspective of the firm s manager. This helps reveal the impact of simultaneous operating, financing, and investment decisions made by the firm s manager on firm value in isolation of the manager s preference for dividends. If a firm s manager maximizes the sum of the market value of equity and contemporaneous dividends then one might argue that managerial and shareholder interests are perfectly aligned. On the other hand, in this case, the manager has less incentives to maximize equity value, ceteris paribus, as the decrease in utility due to lower shareholder value is offset by dividends. Further, the manager s risk incentives might be distorted as dividends are less risky than equity. The analysis in the following sections will reveal which effect dominates. 3 The model We use the dynamic stochastic partial equilibrium (DSPE) model developed in Karpavičius (2014). 5 The model replicates the life and behavior of a representative firm in a dynamic world. We consider a firm with an infinite life span in discrete time. It is assumed that a firm s manager has rational expectations about the future and acts completely in the best interests of shareholders. In each time period, the firm s manager has 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). We assume that the 5 In this section, the description of the model is broadly similar to one in Karpavičius (2014). 8

10 model is stationary and there is no growth. A firm produces a single tradable final good that is sold in a competitive market. 3.1 A firm A standard utility function assumes that the agent is maximizing her consumption. As CEOs consumption data is not available, their consumption expenditure can be instrumented using managers pay levels. In recent years, the equity component (i.e., the sum of restricted stock and option grants) of the median CEO of all the ExecuComp firms is equal to around half of the total CEO pay (Murphy, 2013). Thus, a CEO who wants to maximize her utility function that is only determined by her consumption should increase her consumption expenditure and thus her income. Since her income increases with shareholder value (because of the equity component), the manager s ultimate goal is to maximize shareholder value. This would lead to the maximum consumption level for the firm s manager. Thus, without loss of generality, 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. 6 We assume that 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. The instantaneous objective function, U t, is given by: U t = (P m t N t + µ d t N t 1 ) 1 σ, (2) 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 elastic- 6 For more details, see the discussion on page 292 of Karpavičius (2014). 9

11 ity of substitution). d t is dividends per share at time t. We assume that dividends per share are exogenous from the perspective of the firm s manager. 7 0 µ 1 reflects the firm s manager s attitude/preferences towards dividends. This would represent a case if a manager is compensated with restricted stock and without stock options. µ = 1 implies that the manager is maximizing the sum of market value of equity and total contemporaneous dividends. This would represent a case if a manager is compensated with restricted stock and without stock options. We assume that share price and dividends impact the firm s manager s utility uniformly. This is not consistent with the empirical findings that households treat capital gains and dividends differently. Baker et al. (2007) report that consumption is impacted by dividends stronger than by capital gains. We ignore this finding in order to simplify the model. This should not significantly impact our results; however, it enables us to analytically solve the model in the steady state. If µ = 0, the firm s manager s utility function is the same as in Karpavičius (2014). In this scenario, the manager obtains no utility from dividends. In contrast, the manager is worse off because the dividends decrease stock price (because of the model s construction (see Equation (3) below)). This scenario isolates the different dividend treatment of stock options and restricted stock grants from other differences between stock options and restricted stock (i.e., costs to a firm, incentive structures, accounting treatment and tax implications). The firm s manager maximizes the objective function subject to the balance sheet 7 Tilde ( ) denotes that the variable is exogenous from the perspective of the firm s manager. 10

12 equation and asset composition of the firm: Pt b N t = Pt 1N b t 1 + Pt 1N m t Pt 1N m (N t N t 1 ) 2 t 1 Φ N }{{} N t 1 New share issue + π t d t N t 1 }{{} Retained earnings Φ D (D t D t 1 ) 2 D t 1 Φ K (K t K t 1 ) 2 K t 1, (3) K t = κ(d t + P b t N t ). (4) P b t is book value of equity per share at time t. The left hand side of Equation (3) 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. 8 The relation between market value and book value of equity is given by: P m t = P b t e qt, (5) 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, (6) where η q t N(0, σ2 q), 0 ρ q < 1, and σq 2 > 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. Dividends at time t, d t, 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. The quadratic number of shares outstanding, debt, and capital 8 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. 11

13 (N adjustment costs, Φ t N t 1 ) 2 (D N N t 1, Φ t D t 1 ) 2 (K D D t 1, and Φ t K t 1 ) 2 K, are assumed in order to reduce volatility of the number of shares outstanding, N t, debt, D t, and capital stock, K t. 9 Φ N 0, Φ D 0, and Φ K 0 are the number of shares outstanding, debt, and capital adjustment cost parameters. Due to quadratic debt adjustment costs, short-term debt becomes equivalent to long-term debt with variable interest rates. Equation (3) implies that it is costly for a firm to increase or decrease its capital stock, the number of shares outstanding, and debt. Equation (4) 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 for the population of Compustat firms during The rest of the financial capital, (1 κ) (D t + P b t 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 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 9 For robustness, we assume that there are no adjustment costs and find qualitatively similar results to those reported in this paper. 12

14 can borrow funds evolves according to the following equation: ( ) r t = r D t 1 + Φ r D t + Pt bn, (9) t 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 Ȳ p t = p, (11) Y t where Ȳ and p are respectively the demand for a firm s products and market price in the steady state. 10 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 + ηt a, where ηt a N(0, σa). 2 (13) 10 The term steady state refers to the deterministic steady state. Throughout this paper, variables with bars denote steady-state values. 13

15 α is capital share. Equation (12) implies that production output is the increasing function of capital stock and other production inputs. We assume that dividends are exogenous from the perspective of the firm s manager. Dividends per share, d t, consist of constant and variable parts. The constant part is equal to the steady-state dividends per share, d, multiplied by ψ. It is equivalent to a certain amount of cash per share distributed to shareholders at the end of each period. The variable part of dividends per share is net income per share multiplied by its weight, (1 ψ): d t = ψ d + (1 ψ) π t N t 1, (14) where ψ is the weighting parameter. In the steady state, total dividends are equal to net income, implying 100% payout policy as in Modigliani and Miller (1958, 1963). The value of the weight of the constant part of dividends, ψ, does not impact steady-state dividends per share The equilibrium In each period, the firm s manager chooses strategy {C t, K t, N t, D t } t= t=0 to maximize her expected lifetime utility subject to constraints (Equations (3) and (4)), 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) Maximization of objective function (Equation (1)) subject to the evolution of shareholder value and asset composition of a firm (Equations (3) and (4)) yields the following 11 However, ψ impacts dividends per share in a stochastic environment (see Karpavičius, 2014). 14

16 first-order conditions: C t : C t = (1 α)(1 η)s t, (16) ( : eqt e q t ) K σ t e qt D t + µ K t κ κ d t N t 1 + λ t [ 1 ( )] κ 2Φ Kt K 1 K t 1 { [ ( ) ( ) βe t λ t+1 κ + eqt Nt+1 Kt Φ K Φ K κ N t K t [ +ψ (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 Nt t 1 2Φ N 1 N t 1 ) σ e q t+1 D t+1 + µ d t+1 N t ( + µβ d e q t+1 K t+1 t+1 κ { [ = βe t λ t+1 e qt N t+1 (N t ) 2 ( ) ( ) d]} 2 Kt κ D Nt+1 t Φ N + Φ N + ψ, (18) N t ( e q t ) K σ [ ( : e qt t e qt D t + µ D t κ d Dt t N t 1 + λ t 1 2Φ D { [ [ (Dt+1 ) 2 = βe t λ t+1 Φ D 1] ( ) Nt e qt 1 N t + ψ (1 τ) r ( 1 + 2Φ r κ D t K t D t )] 1 D t 1 )]}, (19) where λ t is a Lagrange multiplier. Equation (16) defines the optimal level of production input, C t, and Equations (17)-(19) are Euler conditions. The equilibrium of the model is defined by the evolution of shareholder value, asset composition constraint, first-order conditions, and several variable definitions (in total 14 equations). 12 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 12 Specifically, the equilibrium of the model is defined by Equations (3)-(14), (16)-(19). 15

17 model s variables and parameters, we analyze the properties of the model in the steady state by using the following procedure: the time subscripts are dropped and the steadystate values of each endogenous variable are expressed in terms of parameters. When the time subscripts are dropped, the model reduces to 12 equations: Equation (11) cancels out and the steady-state expressions of Equations (3) and (14) are identical. 13 To express the steady-state values of each endogenous variable in terms of parameters and constants, the number of endogenous variables must 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. 3.3 Calibration The model is calibrated as in Karpavičius (2014). Initially, we assume that µ = 0, later we will relax this assumption. The model is calibrated assuming that the variables are measured quarterly. The calibration of the model is summarized in Table 1. We assume that steady-state values for the number of shares outstanding, N, and dividends, d, are equal to one. Quarterly discount factor, β, is set to It corresponds to a 8% annual discount rate. The coefficient of manager s risk aversion, σ, is 1.8. We assume that ψ is 0.8. It implies that the weight of constant dividend is 0.8. Following macroeconomic literature, quarterly capital depreciation rate, δ, is set to and capital share in the production function, α, is set to 0.3. The total factor of productivity, A, is one. Further, we assume that a firm can invest only 28.5% of its financial resources in the productive capital (κ = 0.285). The steady-state quarterly interest rate on corporate bonds, r, is set to It implies that the hypothetical annual interest rate for firms without debt is 4%. Thus, debt financing is cheaper than equity financing. The corporate income tax rate, τ, is 13 In the steady state, d t = d t = d. See Appendix A for the model in the steady state. 16

18 Table 1: Calibration of the parameters This table presents the calibrated parameter values. Coefficient Description Value µ Dividends weight in the utility function 0 N Shares outstanding in the steady state 1 d Dividends in the steady state 1 A Total factor of productivity 1 κ Fixed assets-to-capital ratio τ Corporate income tax rate 0.3 r Interest rate for unlevered firm 0.01 α Capital share 0.3 η Price elasticity of demand 0.2 β Subjective discount factor 0.98 ψ Weight of the constant part of dividends 0.8 Φ D Debt adjustment cost parameter 0.25 Φ K Capital adjustment cost parameter 0.25 Φ N Number of shares outstanding cost parameter 8 Φ r Parameter of risk premium 1 δ Capital depreciation rate σ Coefficient of constant relative risk aversion 1.8 ρ q Autocorrelation coefficient of stock price shock 0.5 σ q Standard deviation of stock price shock 0.05 ρ a Autocorrelation coefficient of productivity shock 0.5 σ a Standard deviation of productivity shock I assume that price elasticity of demand, η, is 0.2. It implies that if the production supply increases by 10%, the sale price decreases by 2%, and vice versa. The parameter of risk premium, Φ r, is set to one. It implies that if a firm s leverage increases by ten percentage point, the quarterly interest rate will increase by ten basis points if r is To introduce some persistence in the artificially generated time series, we calibrate debt and capital adjustment cost parameters, Φ D and Φ K, to In unreported simulations, we found that the number of shares outstanding tend to be quite volatile in contrast to empirical data. Thus, Φ N is set to eight. The calibrated parameter values imply quite reasonable firm characteristics in the steady state. Book (and market) leverage is Quarterly dividend yield is implying that shareholders earn 10.6% per year on their investment. 14 Net margin (net 14 The model is stationary; therefore, capital gains are zero. 17

19 income, π, over sales, S) is equal to Gross margin (difference between sales and costs, ( S C), over sales) is equal to The steady-state value of tangibility (fixed assets, K, over total assets, ( D + P b N)) is Real quarterly return on CRSP value weighted index is for the period The calibration implies slightly higher ( ) return d P = The effective annualized borrowing rate ( r) is Thus, from the firm s perspective, equity financing is more expensive than debt financing. 4 Results In this section, we present the results. First of all, we analyze the impact of dividends weight in the utility function, µ, on share price. Then, we investigate how µ affects the riskiness of the firm. Further, we investigate the convergence path of variables towards the new steady state after dividends have been included in the utility function. 4.1 The impact on share price To analyze the impact of dividends weight in the utility function, µ, on share price, we derive the following relation in the steady state using Equations (4), (5) and, (18): 16 P m = P b = ( βψ d µβ d P b σ 1 β 1 β N + µ d N). (20) λ To express the steady-state share price in terms of constants and parameters (i.e., to bring P b to the left-hand side of Equation (20) and express λ in terms of constants and parameters), one would need to use the majority of equations in Appendix A and solve a polynomial of degree three. The obtained equation features high complexity and does not provide any additional insight on the relation between share price and µ. Thus, we do not 15 Table B.1 in Appendix B presents the steady-state values of all variables. 16 See Equations (A.2), (A.3) and, (A.11) in Appendix A. 18

20 μ Figure 1: The impact of dividends weight in the utility function, µ, on share price in the steady state, P m. report the steady-state share price in terms of constants and parameters. 17 If µ = 0 then P m = P b = βψ d 1 β, consistent with Karpavičius (2014). A Lagrange multiplier, λ t, is referred to the shadow price for capital and debt. 18 It reflects the impact on the firm s manager s utility of an additional unit of capital or debt. λ > 0; thus, the last term in Equation (20) is a positive number. According to Equations (17) and (19): 19 ( P b N + µ d N) σ λ = 1 β { 1 + κψ(1 τ) [ α(1 η) S K + r φ r κ [ ( = 1 β 1 + ψr (1 τ) 1 + 2φ r κ D K ( ) 2 D δ]}, (21) K )]. (22) Thus, greater µ leads to the lower equilibrium share price. Figure 1 shows the negative relation between share price and µ. If µ changes from zero to one, share price decreases from to 38.61, that is, it decreases by 1.5%. Dividends per share in the steady state are constant and equal to one. Thus, the return on shareholder capital (which is equivalent to dividend yield as capital gains are zero in 17 It is available upon request. 18 In equilibrium, the shadow price for debt is equal to the shadow price for capital. 19 See Equations (A.10) and (A.12) in Appendix A. 19

21 μ Figure 2: The impact of dividends weight in the utility function, µ, on leverage in the P steady state, m N P m. N+ D the steady state) increases from to Finance theory suggests that expected return increases with risk. In the next subsection, we test whether there is a positive relation between firm risk and µ. 4.2 The impact on riskiness Leverage increases from to in the steady state, that is, by 4.0%, if µ changes from zero to one (see Figure 2). Further, we analyze the impact of µ on default rates. Given that leverage increases with µ, we expect that greater leverage would lead to the higher probability of default. We will show this numerically by using simulations. In order to analyze this issue numerically, we solve the model using the same procedure as in Karpavičius (2014). We assume that the AR(1) coefficients for both shocks are equal to 0.5 (see Table 1). It implies that the magnitude of shocks diminishes over time, and two years (eight quarters) later it is less than 1% of its initial value. Thus, the shock has almost no impact after two years. The assumption reflects the competitive and dynamic environment in which a firm 20

22 Table 2: Firm defaults This table presents the number of firm defaults across different values of µ. The sample includes 1,000 simulated firms for 1,000 time periods. We run 1,000 simulations using the same shock patterns for different values of µ. Time period , µ operates. Further, the standard deviations of the shocks are set to 0.05 (see Table 1). 20 We use simulated data and count the number of cases when firms default. We assume that a firm defaults if its share price, or the number of shares outstanding, becomes nonpositive. To generate an artificial dataset with heterogeneous firms, we use the following procedure. We first simulate 1,000 firms for 1,100 time periods and then drop the first 100 time periods. In each simulation, shocks are random. Thus, these 1,000 time series should be unique. Then we compute in how many cases firms go bankrupt. Using the same shock patterns, we run 1,000 simulations for the following values of µ: 0, 0.25, 0.5, 0.75, and 1. Table 2 presents the results. We find that firm default rates increase with µ; however, the impact of µ is negligible. Till period 1,000, the number of defaults are lower by 1-4 instances if µ = 0 compared to the case when µ = 1. Thus, there is some evidence that lower µ values are associated with lower risk. The firm manager s risk-return preferences are determined by her subjective discount factor, β, and coefficient of constant relative risk aversion, σ. In this paper, we assume 20 It means that there is a probability of approximately 68% that the unexpected change in the productivity or market value of equity per share in any given period will be between 0.05 and

23 that the manager s instantaneous objective function depends on either market value of equity of the firm or the sum of market value of equity of the firm and total dividends (see Equation (2)). The equity value is uncertain as it depends on the number of factors whereas dividends are less uncertain because of their smoothness parameter, ψ. The higher value of ψ, the greater certainty of dividends. Suppose, initially, the manager s instantaneous objective function depends only on market value of equity. The values of β and σ determine the riskiness and value of the firm. Let s assume that the riskiness level of the manager s instantaneous utility objective is then equal to Ω; that is, the given values of β and σ are the determinants of Ω. If total dividends are added to the manager s instantaneous objective function (as in the case where the manager is compensated with restricted stock only), the weighted average of the riskiness levels of the equity and total dividends drops below the level of Ω because dividends are less risky than equity. Thus, the value of the manager s instantaneous objective function becomes less risky than Ω which is the optimal risk level from the manager s perspective. As a result, the manager increases the riskiness of equity and the weighted average of the riskiness levels of the equity and total dividends reaches the level of Ω again. As dividends per share in the steady state are constant, the higher risk level of the equity implies higher effective discount rate and, thus, a lower share price. The results presented in this section suggest that greater µ leads to a lower stock price, higher expected return on shareholder capital, and slightly increased risk. Thus, the noninclusion of dividends in the payoff of stock options reduces managerial risk incentives associated with non-linearity of the option s payoff. 4.3 Convergence towards a new equilibrium In this section, we analyze the convergence path of variables towards the new steady state after dividends have been included in the utility function. We model this situation as deterministic shock. We assume that at time t = 1, µ changes from zero to one, and 22

24 p N π d K D Pᵇ, Pᵐ (right axis) (a) (b) I Leverage r (right axis) (c) S Y C (right axis) (d) Figure 3: The impact of the increase of µ from 0 to 1. The responses are expressed in levels. then we compute the impulse responses of variables. Figure 3 presents the results. The responses are expressed in levels. As the model contains several adjustment costs, the convergence is quite slow. Once dividends have been included in the utility function, the firm s manager realizes that stock is overpriced (as the manager now discounts dividends using a higher discount rate). Thus, a firm issues new shares in the short term (see Figure 3a). The newly-raised capital is used to repay some debt and acquire productive capital stock (see Figure 3b). Thus, investment increases (see Figure 3c). As a firm uses Cobb-Douglas technology, it is optimal to increase the amount of production input, C t (see Figure 3d). Since both production factors increase, 23

25 the production volume also increases, which leads to a lower price per output unit (see Figure 3a). However, the impact of higher production volume offsets a lower price, and the sales revenues slightly increase. Greater sales revenues positively impact net income, π t. Due to the greater number of shares outstanding, total dividends paid increase but the dividend per share decreases, leading to the lower stock price. In the medium term, investment decreases and reaches the initial level. Then a firm starts repurchasing shares. This activity is financed by increased debt. Lower number of shares outstanding leads to greater dividends per share and it converges to its initial steady state. As the firm s manager achieves the same utility level with lower market capitalization when dividends are included in his utility function, market capitalization is lower in the new steady state. This leads to the lower capital stock and optimal production level. Thus, net income decreases too. The latter and the number of shares outstanding are lower by 1% in the new steady state. Optimal capital stock decreases less than equity; thus, a firm raises additional debt. As a result, leverage and effective interest rate increase slightly. The values of variables in the new steady state are slightly different from those when the model is calibrated as in Table1, and assuming that µ = 1 (see last column in Table B.1 in Appendix B). The reason is that the model uses the steady state values for production volume and price per unit, Ȳ and p, respectively (see Equation (11)); however, they depend on µ (see Table B.1 in Appendix B). Thus, when we analyze the convergence path of variables towards the new steady state after dividends have been included in the utility function, we assume that µ = 0 and then its value changes to one; however, steady state values for production volume and price per unit remain unchanged in the model in order to ensure continuity. 24

26 5 Conclusion Stock options and restricted stock are the two main vehicles of equity-based compensation. They differ in several ways: costs to a firm, incentive structures, accounting treatment and tax implications, and dividend treatment. In this paper, we isolate the different dividend treatment of stock options and restricted stock grants from other differences between stock options and restricted stock and analyze how it impacts stock price and the riskiness of the firm. If a manager is granted with restricted stock, she is qualified to receive dividends. If she is granted with stock options, she will not receive dividends. We find that if a firm s manager s utility function includes contemporaneous dividends (as in case of restricted stock grants), the manager increases the risk level of equity in order to maintain her preferred risk level of utility function. Increased risk level leads to a greater effective dividend discount rate and, thus, negatively impacts the stock price. The calibrated model reveals that the impact is 1.5%. Given the constant dividend stream, the lower stock price leads to higher return on shareholder capital. We show that firms are slightly riskier when run by managers who maximize the sum of the market value of equity and contemporaneous dividends; that is, they have a greater financial leverage (by 4.0%) and slightly greater probability of default. This paper contributes to the existing literature in three significant ways. Firstly, the study improves our understanding of how stock options and restricted stock impact firm value, and shows that the way a firm pays its CEO impacts the firm value. The results suggest that equity-based compensation that does not include contemporaneous dividends provides less risky incentives to the firm s manager, ceteris paribus. Thus, in terms of stock price, stock options are superior to restricted stock grants. We do not argue that our results imply that firms should stop issuing restricted stock grants to their managers as then stock price would increase by 1.5%. We rather suggest that different treatment of stock options and restricted stock grants is also an important factor (besides costs to a 25

27 firm, incentive structures, accounting treatment and tax implications) to determine the optimal composition of equity-based compensation. Secondly, we show that the non-inclusion of dividends in the payoff of stock options reduces managerial risk incentives associated with non-linearity of the option s payoff. In addition, the same restricted stock grants of dividend-paying firms provide riskier incentives than those of non-dividend-paying firms. These issues should be taken into account by compensation consultants and remuneration committees of boards of directors of dividend-paying firms while setting optimal level and composition of CEO pay. Lastly, the paper contributes to the area of dynamic modeling. We expand the dynamic partial equilibrium model developed in Karpavičius (2014) to include dividends in the utility function with the aim of analyzing the impact of different dividend treatment of stock options and restricted stock grants. The model can be further used to analyze the optimal CEO compensation. We leave this important issue for future research. 26

28 A The model in the steady state The equations of the model in the steady state are as follows: π = d N, (A.1) K = κ( P b N + D), P m = P b, Ī = δ K, (A.2) (A.3) (A.4) π = [ ] S C D r Kδ (1 τ), (A.5) ( ) D r = r 1 + φ r P b N + D, (A.6) S = pȳ, Ȳ = A K α C1 α, (A.7) (A.8) C = (1 α)(1 η) S, (A.9) ( ) σ { [ K 0 = κ D + µ d N λ + β λ 1 + κψ(1 τ) α(1 η) S K ( ) 2 D +r φ r κ δ]}, (A.10) K ( K 0 = λ κ 0 = N D N ( K κ D + µ d N ) ( K + βµ d ) σ ( K d N β λ κ κ D + µ ) σ [ + λ β λ 1 + ψr (1 τ) N D N ( 1 + 2φ r κ D K ) + ψ d, (A.11) )]. (A.12) 27

29 B Additional table Table B.1: Steady-state values This table presents the values of the variables in the steady state. The model is calibrated as in Table 1. Variable Description µ = 0 µ = 1 C Amount of production input D Debt Ī Investment K Capital stock P b Book value of equity per share P m Market value of equity per share S Sales revenue Ȳ Output volume p Price per output unit r Interest rate λ Lagrange multiplier π Net income

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