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Corporate risk management and dividend signaling theory
Finance Research Letters 8 (2011) 188–195
Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Corporate risk management and dividend signaling theory Georges Dionne ⇑, Karima Ouederni HEC Montréal, 3000, Chemin Cote-Ste-Catherine, Room 4454, Montréal (QC), Canada H3T 2A7
a r t i c l e
i n f o
Article history: Received 27 September 2010 Accepted 20 May 2011 Available online 2 June 2011 JEL classification: G30 G32 G35 D82 Keywords: Signaling theory Dividend policy Risk management policy Corporate hedging Information asymmetry
a b s t r a c t This article investigates the effect of corporate risk management on dividend policy. We extend the signaling framework of Bhattacharya [1979. Bell Journal of Economics 10, 259–270] by including the possibility of hedging the future cash flow. We find that the higher the hedging level, the lower the incremental dividend. This result is intuitive. It is in line with studies suggesting that cash flows’ predictability decreases the marginal gain from costly signaling through dividends and the assertion that corporate hedging decreases cash flow volatility. It is also in line with the purported positive relation between information asymmetry and dividend policy (e.g., Miller and Rock [1985. The Journal of Finance 40, 1031–1051]) and the assertion that risk management alleviates the information asymmetry problem (e.g., DaDalt et al. [2002. The Journal of Future Markets 22, 261–267]). Our theoretical model has testable implications. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction Signaling theory states that changes in dividend policy convey information about changes in future cash flows (e.g., Bhattacharya, 1979; Miller and Rock, 1985). Dividend signaling suggests a positive relation between information asymmetry and dividend policy.1 The higher the asymmetric information level, the higher the sensitivity of the dividend to future prospects of the firm. Several empirical studies attempt to test the informational content of dividend changes, yet they disagree about the sign and the significance of the effect of information asymmetry on dividend policy (see Allen and Michaely (2003), for a survey). ⇑ Corresponding author. Fax: +1 514 340 5019. E-mail addresses: [email protected] (G. Dionne), [email protected] (K. Ouederni). Evidence that information asymmetry positively affects dividend policy has also been documented by the free cash flow theory (e.g., Lang and Litzenberger, 1989). 1
1544-6123/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.frl.2011.05.002
G. Dionne, K. Ouederni / Finance Research Letters 8 (2011) 188–195
189
Another strand of literature suggests that corporate risk management alleviates information asymmetry problems and hence positively affects firm value. Information asymmetry between managers and outside investors is one of the key market imperfections that make hedging potentially beneficial. Breeden and Viswanathan (1998) and DeMarzo and Duffie (1995) argue that hedging reduces noise around earnings streams and thus decreases the level of asymmetric information regarding firm value. DaDalt et al. (2002) provide empirical evidence supporting these theoretical studies. In this article we exploit the interaction between the level of information asymmetry and the dividend policy, along with its interaction with corporate risk management. We argue that risk management alleviates the asymmetric information problem, which is a main determinant of dividend policy. Though many studies that examine dividend policy determinants include several measures of information asymmetry, none, to our knowledge, consider hedging among these measures. Extending the signaling framework of Bhattacharya (1979), we provide theoretical support for the effect of corporate risk management on dividend payout policy. We find a negative relation between the hedge ratio and the incremental dividend payout. The remainder of the article is organized as follows. In Section 2 we present the theoretical model and its implications. Section 3 concludes the paper. 2. The model We assume that the firm operates in a dividend signaling world as modeled in Bhattacharya (1979). We assume that shareholders have a single-period planning horizon and the manager operates in the best interest of current shareholders. The model is developed in terms of marginal analysis for a new project taken on by an all-equity firm. We assume that the manager is better informed than outside investors about the firm’s future prospects. Thus the manager is the only agent informed about the distribution of the new project future cash flow. He attempts to signal his private information via the commitment of an incremental dividend (D). Dividends are taxed at the rate s while capital gains are not taxed. There is a penalty (b) incurred by shareholders in case of cash flow shortfall to cover the committed dividend. For example, the firm could either postpone reinvestments or resort to external funds to finance them. When the cash flow (x) exceeds the committed dividend, the amount of future external financing required for reinvestments is reduced by (x-D) and vice versa. We extend the model by assuming that it is possible for the manager to hedge a fraction (h) of the future cash flow using a linear hedging strategy, in the spirit of Froot et al. (1993). The reasoning behind this extension is simple. Outside investors often use estimates of earnings and cash flows as measures of firm value. Hedging reduces the noise around earnings and future cash flows by reducing the exposure of the firm to factors beyond the manager’s control. Consequently, hedging lessens the asymmetric information regarding firm value by reducing the noise in evaluation measures. We expect that the more willing the firm is to hedge its future cash flow, the less informative the dividend changes and the lower the manager’s incentives for costly signaling through dividend changes. We make the implicit assumption that corporate hedging activity is observable by outside investors. This assumption is realistic given the implementation of many disclosure requirement regulations by the Financial Accounting Standards Board (FASB) since the beginning of the 1990s (e.g., FAS105, FAS107, FAS119, FAS133, FAS138 and FAS161). The hedging strategy can be modeled by writing the future cash flow as:
~x1 ¼ hx0 þ ð1 hÞ~x
ð1Þ
where 0 6 h 6 1 is the hedge ratio, ~ x the random future cash flow and x0 the expected cash flow. The incremental part of the objective function of current shareholders is given by Eq. (2). The four terms in the equation are respectively: (i) the rise in the firm’s liquidation value; (ii) the aftertax promised dividend; (iii) the expected gain when the hedged cash flow is greater than the committed dividend; and (iv) the expected loss when the hedged cash flow is less than the committed dividend:
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G. Dionne, K. Ouederni / Finance Research Letters 8 (2011) 188–195
WðD; hÞ ¼
Z x 1 VðDÞ þ ð1 sÞD þ ðx0 h þ ð1 hÞx DÞf ðxÞdx þ ð1 þ bÞ 1þr xD # Z xD ðx0 h þ ð1 hÞx DÞf ðxÞdx
ð2Þ
x
where r is the after-tax interest rate; V(D) the response liquidation value of the firm resulting from the commitment and the payment of the dividend, and xD the minimum cash flow needed to pay the promised dividend without penalty. Its value is given by Eq. (3):
xD ¼
D hx0 ð1 hÞ
ð3Þ
2.1. Optimal dividend for a given hedge ratio Following Bhattacharya (1979) we assume that the future cash flow is uniformly distributed over [0, t]. Thus the maximization problem is reduced to:
" # 1 t 1 ð2D thÞ2 VðDÞ sD þ b max WðD; hÞ ¼ D 1þr 2 8 ð1 hÞt
ð4Þ
The first order condition solves:
V 0 ðD Þ ¼ s þ b
ð2D thÞ 2ð1 hÞt
ð5Þ
At the optimum, the marginal profit from the dividend increase (the increase of the firm value) equals its marginal cost (taxes and expected cost of external financing). The second order condition is given by Eq. (6):
@2 @D
2
WðD; hÞ ¼
1 b V 00 ðDÞ <0 1þr ð1 hÞt
ð6Þ
Because V(D) is increasing and concave, h lower than one is a sufficient condition for the second order condition to be satisfied.2 The hedge ratio h lies between 0 and 1 given that speculation and over-hedging are not considered in this model. 2.2. Signaling equilibrium The signaling equilibrium demands that V(D(t)) must be ‘‘equal to the true value of future cash flows for the project whose cash flows are signaled with dividend D’’ (Bhattacharya, 1979, p. 264). Under the assumption of a stationary dividend,3 the equilibrium function V(D(t)) is given by Eq. (7):
"
t 1 ð2D ðtÞ thÞ2 VðD ðtÞÞ ¼ K sD ðtÞ b 2 8 ð1 hÞt
#
ð7Þ
where K = 1/r. Differentiating Eq. (7) with respect to t and substituting for V0 (D) from Eq. (5), we obtain:
ðK þ 1Þ
2
lim
h!1
@2 @D2
sþ
" # 2 bD 1 h dD 1 1 bh bD2 b ¼K þ ð1 hÞt 2 ð1 hÞ dt 2 8 ð1 hÞ 2ð1 hÞt 2
ð8Þ
WðD; hÞ ¼ 1:
3 As in Bhattacharya (1979), the model has a perpetuity structure and succeeding generations of shareholders will have oneperiod horizons, which suggests a stationary dividend for any given t, owing to the intertemporally independently identically distributed nature of cash flows.
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G. Dionne, K. Ouederni / Finance Research Letters 8 (2011) 188–195
1
0.9
Payout Ratio A
0.8
0.7
0.6
0.5
0.4 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hedge Ratio h Fig. 1. The curve illustrates the relationship between A and h when s = 40%; b = 20% and r = 5%. The straight line illustrates A for h = 0 (Bhattacharya, 1979).
Assuming a linear solution for the first order differential Eq. (8), D(t) = A t, we obtain the following quadratic equation:
ðK þ 2Þ 2 2s K 1 K 2 A þ ð1 hÞ þ h ¼0 ð1 hÞ h A ðK þ 1Þ bðK þ 1Þ 4 ðK þ 1Þ b
ð9Þ
The positive root of the quadratic equation is equal to:
2sð1 hÞ bh ðK þ 1Þ ðK þ 1Þ þ b 2ðK þ 2Þ 2ðK þ 2Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 2sð1 hÞ bh KðK þ 2Þ 2 ðbh 4ð1 hÞÞ b bðK þ 1Þ2
A¼
ð10Þ
When h = 0 we obtain the corresponding values for (9) and (10) in Bhattacharya (1979). A is the incremental dividend payout. It also illustrates the sensitivity of dividend increases to earnings prospects. For reasonable values of tax rate (s 6 40%)4 and external financing cost (b 6 20%), A is decreasing in the hedge ratio.5 In Fig. 1, we show the function with some feasible parameters. We observe a negative effect of the hedge ratio on the incremental dividend payout. This result is intuitive. It is in line with studies suggesting that cash flows’ predictability decreases the marginal gain from costly signaling through dividends and the assertion that corporate hedging decreases cash flow volatility (Chang et al., 2006; Dichev and Tang, 2009). Earnings volatility affects earnings and cash flow predictability negatively. The marginal gain from signaling cash flows prospects through dividends therefore increases with market uncertainty about the future cash flows of the firm. Corporate hedging 4 Before JGTRRA (Jobs and Growth Tax Relief Reconciliation Act of 2003), the top marginal tax rate of dividends was 38.5%, while the top statutory rate of capital gains was 20%. JGTRRA equalized both tax rates at 15%. See Poterba (2004). 5 Notice that A is not strictly decreasing in the hedging level for all values of tax rates and external financing costs. For high but less feasible values of s > 40% and b > 20%, A first increases and then decreases in h.
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1 A* for a given h
0.9 0.8
Payout Ratio A
0.7
A=1-1/2 h*
0.6 0.5
O A=1/2 h*
0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hedge Ratio h Fig. 2. The curve illustrates A for a given value of h. The straight lines illustrate A = 1/2h and A = 1 1/2h (s = 40%; b = 20% and r = 5%). In Appendix A we show that h equals 1, which corresponds to the intersection of the three lines at O.
reduces the noise around the dividend streams. Thus, for a given 0 < h 6 1, a lower amount of dividend is needed to signal the same level of future performance and to obtain the same wealth effect. The result also corroborates corporate risk management studies supporting the existence of a negative relationship between the dividend policy and the hedge ratio (e.g., Dionne and Garand, 2003). 2.3. Optimal hedge ratio Another way to emphasize the interaction between the dividend policy and the corporate hedging policy is to maximize the incremental shareholders’ wealth in (4) with respect to the hedge ratio. The first and second order conditions along with the signaling equilibrium condition provide the following optimal hedge ratio (See Appendix A for details):
(
h ¼
2 Dt if 2 1 Dt if
D t D t
6 12 P 12
ð11Þ
To choose between the two solutions we substitute for the two expressions of h in Eq. (9) (the quadratic equation in A) and verify if the second order condition is satisfied by the values obtained. The only feasible or realistic solution is full hedging. This result confirms Froot et al.’s (1993) conclusion that the optimal hedge ratio for a concave payoff is equal to one when the firm has a single source of risk. Fig. 2 illustrates the possible cases and O identifies the optimal solution at h = 1 and A = 1/2. If we assume realistically that the promised dividend should be lower than or equal to the expected cash flow, then the optimal hedge ratio is equal to one.6 The most compelling argument for hedging lies in ensuring the firm’s ability to meet its cash flow commitment at the lowest cost. In this article we are interested in the dividend policy as a signaling device. The importance of meeting the dividend 6 It is technically possible for a solution for D to be higher than the expected cash flow and satisfy the maximization criteria, but it is difficult to justify the survival of an exogenous costly signaling equilibrium that requires a dividend higher than the expected cash flow (Bhattacharya, 1979, p. 263).
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commitment derives from information imperfections in the capital market (e.g. negative information released by dividend cuts). Thus, firms use funds available for reinvestment to make up cash flow shortfalls and then resort to costly external funds to finance their investment plans. The optimal solution corresponding to a promised dividend higher than the expected cash flow is consequently eliminated because it increases the probability of external financing penalty considerably. In the case of full hedging, the main signaling cost (i.e. external financing penalty) vanishes and the incremental firm value responds only to the tax rate.7 Thus, the equilibrium V(D(t)) = sD corresponds to a corner solution for the shareholder maximization problem: D = t/2 (the expected future cash flow). Intuitively, in the absence of uncertainty, the manager will promise to distribute the expected cash flow to maximize the existing shareholders’ wealth in a one-period model. 3. Conclusion The findings of this article reconcile dividend signaling theory with risk management theory. We contribute to the dividend signaling literature by emphasizing the interaction between corporate risk management policy and dividend policy. The interaction between these two corporate policies has received little attention in the literature despite their common link to information asymmetry. Using an extension of Bhattacharya’s signaling model, we find that the hedging of future cash flows reduces the sensitivity of dividends to future earnings. A straightforward implication of this result is that the informational content of dividend changes decreases with the hedge ratio. It leads to the empirical test of whether corporate risk management reduces the power of dividend changes to predict future changes in earnings. It thus proposes a new test of the dividend signaling theory. In this article we have restricted our attention to linear hedging strategies (i.e., forwards or futures sales or purchases), for two reasons. First, for these financial products, the firm’s hedging strategy can be expressed in closed form. Second, the widespread use of linear hedging instruments is reported by several survey studies.8 Alternative, nonlinear hedging strategies that involve instruments such as options could be considered in future works to make the results of this article more general. Appendix A The first order condition of the maximization of (4) with respect to h satisfies:
ð2D thÞð2tð1 hÞ þ ð2D thÞÞ ¼ 0
ðA:1Þ
The maximization problem has two complementary solutions:
(
h ¼
2 Dt 2 1 Dt
ðA:2Þ
The second order condition with respect to h is equal to:
8 > <
@2 @h2
WðD; hÞ ¼ 14
> : lim h!1
@2 @h2
2
1 b ð2DtÞ 1þr ð1hÞ3 t
< 0 for h < 1
WðD; hÞ ¼ 1
ðA:3Þ
It is satisfied for h 6 1. 7
The objective function of current shareholders for h = 1 is given by:
max WðDÞ ¼ D
1 t VðDÞ sD þ 1þr 2
And the first order condition solves: V0 (D) = s. 8 In a study of US nonfinancial firms, Gay et al. (2002) report that 69% of commodity risk exposures, 75% of currency exposures, and 70% of interest exposures are managed with linear derivatives. Huang et al. (2007) find that 73% of firms that use derivatives manage interest and currency risk exposures entirely in terms of linear hedging instruments. See also Frestad (2009).
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Thus the optimal hedge ratio is given by Eq. (A.4)
(
h ¼
if 2 Dt 2 1 Dt if
D t D t
6 12 P 12
ðA:4Þ
Because A = D/t we can rewrite these solutions as follow:
(
h ¼
if A 6 12
2A
2ð1 AÞ if A P 12
ðA:5Þ
To choose between the two solutions we substitute for h⁄ in the quadratic equation in A (Eq. (9)) and retain the solution that generates a dividend payout satisfying the second order condition. a. When we substitute for h = 2D/t in the quadratic Eq. (9) we get:
(1 Ajh¼2D ¼ t
K 2 ð1þKÞs 1 2
ðA:6Þ
A necessary condition for A to be bigger than or equal to 0.5 (i.e. D P t/2) is s 6 0.5. The feasible set of s (i.e. s 6 0.4) satisfies this condition. However, this solution generates a hedge ratio higher than 1, which does not satisfy the second order condition. Thus we retain A = 1/2. b. When we substitute for h = 2 (1 D/t) in the quadratic Eq. (9) we get:
( Ajh¼22D ¼ t
Kð1þbÞ 1 2 ð1þKÞðsþbÞ 1 2
ðA:7Þ
We can verify that for feasible values of b and s, A is greater than or equal to 0.5 (i.e. D P t/2). s + 0.5 b 6 0.5 is a necessary condition for A to be greater than 0.5. The feasible sets of s and b (i.e. s 6 0.4 and b 6 0.2) satisfy this condition. This solution satisfies the second order condition but it is dominated by A = 1/2 because it is unrealistic to suppose that the optimal solution is higher than the expected cash flow. Taken together the two maximization problems (with respect to D and h) lead to the following solution: h = 1 and A = 1/2. References Allen, F., Michaely, R., 2003. Payout policy. In: Constantinides, G.M., Harris, M., Stulz, R.M. (Eds.), Handbook of the Economics of Finance, vol. 1. Elsevier, Amsterdam, pp. 337–429 (Chapter 7). Bhattacharya, S., 1979. Imperfect information, dividend policy and ‘the bird in the hand’ fallacy. Bell Journal of Economics 10, 259–270. Breeden, D., Viswanathan, S., 1998. Why Do Firms Hedge? An Asymmetric Information Model. Working Paper. Fuqua School of Business, Duke University. Chang, C., Kumar, P., Sivaramakrishnan, K., 2006. Dividend changes, cash flow predictability, and signaling of future cash flows.. DaDalt, P., Gay, G., Nam, J., 2002. Asymmetric information and corporate use of derivatives. The Journal of Future Markets 22, 261–267. DeMarzo, P., Duffie, D., 1995. Corporate incentives for hedging and hedge accounting. Review of Financial Studies, Fall, 743– 771. Dichev, E., Tang, V., 2009. Earnings volatility and earnings predictability. Journal of Accounting and Economics 47, 160– 181. Dionne, G., Garand, M., 2003. Risk management determinants affecting firms’ values in the gold mining industry: new empirical evidence. Economics Letters 79, 43–52. Frestad, D., 2009. Why most firms choose linear hedging strategies? The Journal of Financial Research 32, 157–167. Froot, K., Scharfstein, D., Stein, J., 1993. Risk management: coordinating corporate investment and financing policies. The Journal of Finance 48, 1629–1658. Gay, G., Nam, J., Turac, M., 2002. How firms manage risk: the optimal mix of linear and non-linear derivatives. Journal of Applied Corporate Finance 14, 82–93. Huang, P., Ryan, H., Wiggins, R., 2007. The influence of firm- and CEO-specific characteristics on the use of nonlinear derivative instruments. Journal of Financial Research 30, 415–436.
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195
Lang, L., Litzenberger, R., 1989. Dividend announcements: cash flow signaling vs. free cash flow hypothesis? Journal of Financial Economics 24, 181–191. Miller, M., Rock, K., 1985. Dividend policy under asymmetric information. The Journal of Finance 40, 1031–1051. Poterba, J., 2004. Taxation and corporate payout policy. American Economic Review 94, 171–175.
Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Corporate risk management and dividend signaling theory Georges Dionne ⇑, Karima Ouederni HEC Montréal, 3000, Chemin Cote-Ste-Catherine, Room 4454, Montréal (QC), Canada H3T 2A7
a r t i c l e
i n f o
Article history: Received 27 September 2010 Accepted 20 May 2011 Available online 2 June 2011 JEL classification: G30 G32 G35 D82 Keywords: Signaling theory Dividend policy Risk management policy Corporate hedging Information asymmetry
a b s t r a c t This article investigates the effect of corporate risk management on dividend policy. We extend the signaling framework of Bhattacharya [1979. Bell Journal of Economics 10, 259–270] by including the possibility of hedging the future cash flow. We find that the higher the hedging level, the lower the incremental dividend. This result is intuitive. It is in line with studies suggesting that cash flows’ predictability decreases the marginal gain from costly signaling through dividends and the assertion that corporate hedging decreases cash flow volatility. It is also in line with the purported positive relation between information asymmetry and dividend policy (e.g., Miller and Rock [1985. The Journal of Finance 40, 1031–1051]) and the assertion that risk management alleviates the information asymmetry problem (e.g., DaDalt et al. [2002. The Journal of Future Markets 22, 261–267]). Our theoretical model has testable implications. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction Signaling theory states that changes in dividend policy convey information about changes in future cash flows (e.g., Bhattacharya, 1979; Miller and Rock, 1985). Dividend signaling suggests a positive relation between information asymmetry and dividend policy.1 The higher the asymmetric information level, the higher the sensitivity of the dividend to future prospects of the firm. Several empirical studies attempt to test the informational content of dividend changes, yet they disagree about the sign and the significance of the effect of information asymmetry on dividend policy (see Allen and Michaely (2003), for a survey). ⇑ Corresponding author. Fax: +1 514 340 5019. E-mail addresses: [email protected] (G. Dionne), [email protected] (K. Ouederni). Evidence that information asymmetry positively affects dividend policy has also been documented by the free cash flow theory (e.g., Lang and Litzenberger, 1989). 1
1544-6123/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.frl.2011.05.002
G. Dionne, K. Ouederni / Finance Research Letters 8 (2011) 188–195
189
Another strand of literature suggests that corporate risk management alleviates information asymmetry problems and hence positively affects firm value. Information asymmetry between managers and outside investors is one of the key market imperfections that make hedging potentially beneficial. Breeden and Viswanathan (1998) and DeMarzo and Duffie (1995) argue that hedging reduces noise around earnings streams and thus decreases the level of asymmetric information regarding firm value. DaDalt et al. (2002) provide empirical evidence supporting these theoretical studies. In this article we exploit the interaction between the level of information asymmetry and the dividend policy, along with its interaction with corporate risk management. We argue that risk management alleviates the asymmetric information problem, which is a main determinant of dividend policy. Though many studies that examine dividend policy determinants include several measures of information asymmetry, none, to our knowledge, consider hedging among these measures. Extending the signaling framework of Bhattacharya (1979), we provide theoretical support for the effect of corporate risk management on dividend payout policy. We find a negative relation between the hedge ratio and the incremental dividend payout. The remainder of the article is organized as follows. In Section 2 we present the theoretical model and its implications. Section 3 concludes the paper. 2. The model We assume that the firm operates in a dividend signaling world as modeled in Bhattacharya (1979). We assume that shareholders have a single-period planning horizon and the manager operates in the best interest of current shareholders. The model is developed in terms of marginal analysis for a new project taken on by an all-equity firm. We assume that the manager is better informed than outside investors about the firm’s future prospects. Thus the manager is the only agent informed about the distribution of the new project future cash flow. He attempts to signal his private information via the commitment of an incremental dividend (D). Dividends are taxed at the rate s while capital gains are not taxed. There is a penalty (b) incurred by shareholders in case of cash flow shortfall to cover the committed dividend. For example, the firm could either postpone reinvestments or resort to external funds to finance them. When the cash flow (x) exceeds the committed dividend, the amount of future external financing required for reinvestments is reduced by (x-D) and vice versa. We extend the model by assuming that it is possible for the manager to hedge a fraction (h) of the future cash flow using a linear hedging strategy, in the spirit of Froot et al. (1993). The reasoning behind this extension is simple. Outside investors often use estimates of earnings and cash flows as measures of firm value. Hedging reduces the noise around earnings and future cash flows by reducing the exposure of the firm to factors beyond the manager’s control. Consequently, hedging lessens the asymmetric information regarding firm value by reducing the noise in evaluation measures. We expect that the more willing the firm is to hedge its future cash flow, the less informative the dividend changes and the lower the manager’s incentives for costly signaling through dividend changes. We make the implicit assumption that corporate hedging activity is observable by outside investors. This assumption is realistic given the implementation of many disclosure requirement regulations by the Financial Accounting Standards Board (FASB) since the beginning of the 1990s (e.g., FAS105, FAS107, FAS119, FAS133, FAS138 and FAS161). The hedging strategy can be modeled by writing the future cash flow as:
~x1 ¼ hx0 þ ð1 hÞ~x
ð1Þ
where 0 6 h 6 1 is the hedge ratio, ~ x the random future cash flow and x0 the expected cash flow. The incremental part of the objective function of current shareholders is given by Eq. (2). The four terms in the equation are respectively: (i) the rise in the firm’s liquidation value; (ii) the aftertax promised dividend; (iii) the expected gain when the hedged cash flow is greater than the committed dividend; and (iv) the expected loss when the hedged cash flow is less than the committed dividend:
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WðD; hÞ ¼
Z x 1 VðDÞ þ ð1 sÞD þ ðx0 h þ ð1 hÞx DÞf ðxÞdx þ ð1 þ bÞ 1þr xD # Z xD ðx0 h þ ð1 hÞx DÞf ðxÞdx
ð2Þ
x
where r is the after-tax interest rate; V(D) the response liquidation value of the firm resulting from the commitment and the payment of the dividend, and xD the minimum cash flow needed to pay the promised dividend without penalty. Its value is given by Eq. (3):
xD ¼
D hx0 ð1 hÞ
ð3Þ
2.1. Optimal dividend for a given hedge ratio Following Bhattacharya (1979) we assume that the future cash flow is uniformly distributed over [0, t]. Thus the maximization problem is reduced to:
" # 1 t 1 ð2D thÞ2 VðDÞ sD þ b max WðD; hÞ ¼ D 1þr 2 8 ð1 hÞt
ð4Þ
The first order condition solves:
V 0 ðD Þ ¼ s þ b
ð2D thÞ 2ð1 hÞt
ð5Þ
At the optimum, the marginal profit from the dividend increase (the increase of the firm value) equals its marginal cost (taxes and expected cost of external financing). The second order condition is given by Eq. (6):
@2 @D
2
WðD; hÞ ¼
1 b V 00 ðDÞ <0 1þr ð1 hÞt
ð6Þ
Because V(D) is increasing and concave, h lower than one is a sufficient condition for the second order condition to be satisfied.2 The hedge ratio h lies between 0 and 1 given that speculation and over-hedging are not considered in this model. 2.2. Signaling equilibrium The signaling equilibrium demands that V(D(t)) must be ‘‘equal to the true value of future cash flows for the project whose cash flows are signaled with dividend D’’ (Bhattacharya, 1979, p. 264). Under the assumption of a stationary dividend,3 the equilibrium function V(D(t)) is given by Eq. (7):
"
t 1 ð2D ðtÞ thÞ2 VðD ðtÞÞ ¼ K sD ðtÞ b 2 8 ð1 hÞt
#
ð7Þ
where K = 1/r. Differentiating Eq. (7) with respect to t and substituting for V0 (D) from Eq. (5), we obtain:
ðK þ 1Þ
2
lim
h!1
@2 @D2
sþ
" # 2 bD 1 h dD 1 1 bh bD2 b ¼K þ ð1 hÞt 2 ð1 hÞ dt 2 8 ð1 hÞ 2ð1 hÞt 2
ð8Þ
WðD; hÞ ¼ 1:
3 As in Bhattacharya (1979), the model has a perpetuity structure and succeeding generations of shareholders will have oneperiod horizons, which suggests a stationary dividend for any given t, owing to the intertemporally independently identically distributed nature of cash flows.
191
G. Dionne, K. Ouederni / Finance Research Letters 8 (2011) 188–195
1
0.9
Payout Ratio A
0.8
0.7
0.6
0.5
0.4 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hedge Ratio h Fig. 1. The curve illustrates the relationship between A and h when s = 40%; b = 20% and r = 5%. The straight line illustrates A for h = 0 (Bhattacharya, 1979).
Assuming a linear solution for the first order differential Eq. (8), D(t) = A t, we obtain the following quadratic equation:
ðK þ 2Þ 2 2s K 1 K 2 A þ ð1 hÞ þ h ¼0 ð1 hÞ h A ðK þ 1Þ bðK þ 1Þ 4 ðK þ 1Þ b
ð9Þ
The positive root of the quadratic equation is equal to:
2sð1 hÞ bh ðK þ 1Þ ðK þ 1Þ þ b 2ðK þ 2Þ 2ðK þ 2Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 2sð1 hÞ bh KðK þ 2Þ 2 ðbh 4ð1 hÞÞ b bðK þ 1Þ2
A¼
ð10Þ
When h = 0 we obtain the corresponding values for (9) and (10) in Bhattacharya (1979). A is the incremental dividend payout. It also illustrates the sensitivity of dividend increases to earnings prospects. For reasonable values of tax rate (s 6 40%)4 and external financing cost (b 6 20%), A is decreasing in the hedge ratio.5 In Fig. 1, we show the function with some feasible parameters. We observe a negative effect of the hedge ratio on the incremental dividend payout. This result is intuitive. It is in line with studies suggesting that cash flows’ predictability decreases the marginal gain from costly signaling through dividends and the assertion that corporate hedging decreases cash flow volatility (Chang et al., 2006; Dichev and Tang, 2009). Earnings volatility affects earnings and cash flow predictability negatively. The marginal gain from signaling cash flows prospects through dividends therefore increases with market uncertainty about the future cash flows of the firm. Corporate hedging 4 Before JGTRRA (Jobs and Growth Tax Relief Reconciliation Act of 2003), the top marginal tax rate of dividends was 38.5%, while the top statutory rate of capital gains was 20%. JGTRRA equalized both tax rates at 15%. See Poterba (2004). 5 Notice that A is not strictly decreasing in the hedging level for all values of tax rates and external financing costs. For high but less feasible values of s > 40% and b > 20%, A first increases and then decreases in h.
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1 A* for a given h
0.9 0.8
Payout Ratio A
0.7
A=1-1/2 h*
0.6 0.5
O A=1/2 h*
0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hedge Ratio h Fig. 2. The curve illustrates A for a given value of h. The straight lines illustrate A = 1/2h and A = 1 1/2h (s = 40%; b = 20% and r = 5%). In Appendix A we show that h equals 1, which corresponds to the intersection of the three lines at O.
reduces the noise around the dividend streams. Thus, for a given 0 < h 6 1, a lower amount of dividend is needed to signal the same level of future performance and to obtain the same wealth effect. The result also corroborates corporate risk management studies supporting the existence of a negative relationship between the dividend policy and the hedge ratio (e.g., Dionne and Garand, 2003). 2.3. Optimal hedge ratio Another way to emphasize the interaction between the dividend policy and the corporate hedging policy is to maximize the incremental shareholders’ wealth in (4) with respect to the hedge ratio. The first and second order conditions along with the signaling equilibrium condition provide the following optimal hedge ratio (See Appendix A for details):
(
h ¼
2 Dt if 2 1 Dt if
D t D t
6 12 P 12
ð11Þ
To choose between the two solutions we substitute for the two expressions of h in Eq. (9) (the quadratic equation in A) and verify if the second order condition is satisfied by the values obtained. The only feasible or realistic solution is full hedging. This result confirms Froot et al.’s (1993) conclusion that the optimal hedge ratio for a concave payoff is equal to one when the firm has a single source of risk. Fig. 2 illustrates the possible cases and O identifies the optimal solution at h = 1 and A = 1/2. If we assume realistically that the promised dividend should be lower than or equal to the expected cash flow, then the optimal hedge ratio is equal to one.6 The most compelling argument for hedging lies in ensuring the firm’s ability to meet its cash flow commitment at the lowest cost. In this article we are interested in the dividend policy as a signaling device. The importance of meeting the dividend 6 It is technically possible for a solution for D to be higher than the expected cash flow and satisfy the maximization criteria, but it is difficult to justify the survival of an exogenous costly signaling equilibrium that requires a dividend higher than the expected cash flow (Bhattacharya, 1979, p. 263).
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commitment derives from information imperfections in the capital market (e.g. negative information released by dividend cuts). Thus, firms use funds available for reinvestment to make up cash flow shortfalls and then resort to costly external funds to finance their investment plans. The optimal solution corresponding to a promised dividend higher than the expected cash flow is consequently eliminated because it increases the probability of external financing penalty considerably. In the case of full hedging, the main signaling cost (i.e. external financing penalty) vanishes and the incremental firm value responds only to the tax rate.7 Thus, the equilibrium V(D(t)) = sD corresponds to a corner solution for the shareholder maximization problem: D = t/2 (the expected future cash flow). Intuitively, in the absence of uncertainty, the manager will promise to distribute the expected cash flow to maximize the existing shareholders’ wealth in a one-period model. 3. Conclusion The findings of this article reconcile dividend signaling theory with risk management theory. We contribute to the dividend signaling literature by emphasizing the interaction between corporate risk management policy and dividend policy. The interaction between these two corporate policies has received little attention in the literature despite their common link to information asymmetry. Using an extension of Bhattacharya’s signaling model, we find that the hedging of future cash flows reduces the sensitivity of dividends to future earnings. A straightforward implication of this result is that the informational content of dividend changes decreases with the hedge ratio. It leads to the empirical test of whether corporate risk management reduces the power of dividend changes to predict future changes in earnings. It thus proposes a new test of the dividend signaling theory. In this article we have restricted our attention to linear hedging strategies (i.e., forwards or futures sales or purchases), for two reasons. First, for these financial products, the firm’s hedging strategy can be expressed in closed form. Second, the widespread use of linear hedging instruments is reported by several survey studies.8 Alternative, nonlinear hedging strategies that involve instruments such as options could be considered in future works to make the results of this article more general. Appendix A The first order condition of the maximization of (4) with respect to h satisfies:
ð2D thÞð2tð1 hÞ þ ð2D thÞÞ ¼ 0
ðA:1Þ
The maximization problem has two complementary solutions:
(
h ¼
2 Dt 2 1 Dt
ðA:2Þ
The second order condition with respect to h is equal to:
8 > <
@2 @h2
WðD; hÞ ¼ 14
> : lim h!1
@2 @h2
2
1 b ð2DtÞ 1þr ð1hÞ3 t
< 0 for h < 1
WðD; hÞ ¼ 1
ðA:3Þ
It is satisfied for h 6 1. 7
The objective function of current shareholders for h = 1 is given by:
max WðDÞ ¼ D
1 t VðDÞ sD þ 1þr 2
And the first order condition solves: V0 (D) = s. 8 In a study of US nonfinancial firms, Gay et al. (2002) report that 69% of commodity risk exposures, 75% of currency exposures, and 70% of interest exposures are managed with linear derivatives. Huang et al. (2007) find that 73% of firms that use derivatives manage interest and currency risk exposures entirely in terms of linear hedging instruments. See also Frestad (2009).
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Thus the optimal hedge ratio is given by Eq. (A.4)
(
h ¼
if 2 Dt 2 1 Dt if
D t D t
6 12 P 12
ðA:4Þ
Because A = D/t we can rewrite these solutions as follow:
(
h ¼
if A 6 12
2A
2ð1 AÞ if A P 12
ðA:5Þ
To choose between the two solutions we substitute for h⁄ in the quadratic equation in A (Eq. (9)) and retain the solution that generates a dividend payout satisfying the second order condition. a. When we substitute for h = 2D/t in the quadratic Eq. (9) we get:
(1 Ajh¼2D ¼ t
K 2 ð1þKÞs 1 2
ðA:6Þ
A necessary condition for A to be bigger than or equal to 0.5 (i.e. D P t/2) is s 6 0.5. The feasible set of s (i.e. s 6 0.4) satisfies this condition. However, this solution generates a hedge ratio higher than 1, which does not satisfy the second order condition. Thus we retain A = 1/2. b. When we substitute for h = 2 (1 D/t) in the quadratic Eq. (9) we get:
( Ajh¼22D ¼ t
Kð1þbÞ 1 2 ð1þKÞðsþbÞ 1 2
ðA:7Þ
We can verify that for feasible values of b and s, A is greater than or equal to 0.5 (i.e. D P t/2). s + 0.5 b 6 0.5 is a necessary condition for A to be greater than 0.5. The feasible sets of s and b (i.e. s 6 0.4 and b 6 0.2) satisfy this condition. This solution satisfies the second order condition but it is dominated by A = 1/2 because it is unrealistic to suppose that the optimal solution is higher than the expected cash flow. Taken together the two maximization problems (with respect to D and h) lead to the following solution: h = 1 and A = 1/2. References Allen, F., Michaely, R., 2003. Payout policy. In: Constantinides, G.M., Harris, M., Stulz, R.M. (Eds.), Handbook of the Economics of Finance, vol. 1. Elsevier, Amsterdam, pp. 337–429 (Chapter 7). Bhattacharya, S., 1979. Imperfect information, dividend policy and ‘the bird in the hand’ fallacy. Bell Journal of Economics 10, 259–270. Breeden, D., Viswanathan, S., 1998. Why Do Firms Hedge? An Asymmetric Information Model. Working Paper. Fuqua School of Business, Duke University. Chang, C., Kumar, P., Sivaramakrishnan, K., 2006. Dividend changes, cash flow predictability, and signaling of future cash flows.
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Lang, L., Litzenberger, R., 1989. Dividend announcements: cash flow signaling vs. free cash flow hypothesis? Journal of Financial Economics 24, 181–191. Miller, M., Rock, K., 1985. Dividend policy under asymmetric information. The Journal of Finance 40, 1031–1051. Poterba, J., 2004. Taxation and corporate payout policy. American Economic Review 94, 171–175.