Payout Policy and Real Investment Under Asymmetric Information

This paper develops a theoretical model explaining management’s choice of using corporate cash flow to pay dividends, repurchase shares, or invest in a real project. The model demonstrates the case in which managers have better information than investors about the quality of the firm (information asymmetry) and may invest excess cash in unprofitable projects rather than return it to shareholders (moral hazard). The results show that paying dividends is a dominated strategy for the high-quality firm. In an efficient market, there exists a separating equilibrium in which the high-quality firm invests in the new project while the low-quality firm pays dividends. However, if investors underreact to share repurchase announcements, there exists a separating equilibrium in which the high-quality firm repurchases shares while the low-quality firm pays dividends.


Introduction
Over recent decades, share repurchases has become a primary means of returning company's cash flows to shareholders. Grullon and Michaely (2002) documented that while share repurchase expenditures in the U.S. grew at an average annual rate of 26.1% over the period 1980 to 2000, dividends grew only at an average annual rate of 6.8%. In fact, in 1998, industrial firms spent more money on share repurchases ($181.8 billion) than on cash dividends ($174.1 billion). In general, the market has applauded the share repurchase programs. Prior research has documented an average abnormal return of approximately 3% on open market share repurchase announcements (e.g., Vermaelen (1981), Comment and Jarrell (1991), Ikenberry, Lakonishok, and Vermalen (1995), Stephens and Weisbach (1998), and Grullon and Michaely (2002)).
One of the most cited explanations for this positive announcement return is the signaling hypothesis, which suggests that the managers use payouts to convey favorable information about the firm's prospect to outside shareholders. Traditional dividend signaling models show that dividends convey favorable information about future profitability (e.g., Bhattachaya (1979), Miller and Rock (1985), John and Williams (1985), and Ambarish et al. (1987)). These models suggest that managers who foresee better performance can send positive signal to investors by paying out dividends today because they are confident that future capital requirements can be financed by future earnings. On the other hand, managers who do not expect any improvement in profitability are refrained from doing so because they might have to forego profitable investments or raise costly external funds in the future. According to Modigliani and Miller (1961), the value of the firm in a perfect market is independent of the payout policy, implying that dividends and share repurchases are perfect substitutes. Since the market is imperfect, however, the managers' choices between paying dividends and repurchasing shares affect firm value differently. At least with respect to the tax efficiency, firms should repurchase shares rather than pay dividends because share repurchases, generally treated by tax authorities as capital gains, are taxed at a lower rate than dividends. However, firms still pay a large portion of their earnings as cash dividends despite its tax disadvantage relative to share repurchases, and this is known as 'dividend puzzle' in finance literature (Black, 1976).
Several researchers attempt to explain this puzzle from theoretical perspective. For example, Ofer and Thakor (1987) develop a signaling model in which managers can signal their firm values by using either a dividend or a (tender offer) share repurchase or both. Their model shows that, when the difference between the true value of an undervalued firm and its market value is relatively low, the firm chooses to signal by dividends because of a relatively lower signaling cost than that of a share repurchase. However, when the true firm value is much higher than its market value, the firm chooses to signal by share repurchases because a relatively large dividend is needed for informationally consistent signaling. In an adverse selection model, Brennan and Thakor (1990) explain why share repurchases are disadvantageous compared to dividends. Their model demonstrates that when firms repurchase shares, some shareholders are better informed about the firm's prospects than others and able to take advantage of this information asymmetry but, when firms pay dividends, both informed and uninformed investors receive a pro rata amount. As a result, uninformed investors prefer dividends to share repurchases. Hausch and Seward (1993) develop a model in which the firm's choice of signaling with share repurchases or cash dividends depends on the level of internally-generated cash flows available for investment. Since the high-quality firm has less absolute risk aversion and more cash available for investment than the low-quality firm, the high-quality firm can more efficiently distinguish itself from the low-quality firm using a share repurchase. On the contrary, Chowdhry and Nanda (1994) argue that it is the fact that tender offer repurchases are associated with large stock price increases that makes them unattractive means of distributing cash. The occasions when share repurchases would not be costly to the firm, despite the large premium it must pay to acquire its own shares, are when the firm's stock is deeply undervalued by the market compared to its true value observed by managers. However, Persons (1997) argue that tender offer repurchases have advantages over other possible signals like dividends and firms overpay for tender offer repurchases because of heterogeneous shareholders' stock price valuation. A small increase in tender offer shares repurchased is more costly for a low-value firm to imitate than a small increase in dividends. Therefore, dividends are used to signal small differences in value while repurchases are used to signal large differences in stock price valuation.
Most of the previous models focus on the share repurchase tender offers, which are now relatively less common compared to open-market share repurchases, and consider only two choices of payouts (i.e., dividends or stock repurchases) while, in practice, the manager may use the firm's cash flow to invest in unprofitable projects in order to consume private benefits. Considering this alternative, Isagawa (2000) develops a signaling model in which the manager chooses between open-market share repurchases and a real investment in a new project from which the manager receives private benefits, and derives a separating equilibrium in which a manager with high private benefits chooses to invest in a new project while a manager with low private benefits chooses to repurchase shares. His model provides a key insight regarding the effect of private benefits on manager's repurchasing decision. Nevertheless, his model appears to be incomplete in that: (1) it does not include a cash dividend, which is a primary means of corporate payouts; (2) it considers only the case where the managerial compensation is tied only to the firm's long-term value; and (3) it does not consider an increase in managerial equity stake after shares are repurchased.
Hence, this paper contributes to Isagawa's (2000) analysis in the following ways. First, it develops a more complete signaling model in which the managers of a high-quality firm and a low-quality firm decide to use the firm's cash flow to invest in a new project, pay cash dividends, or repurchase shares via open market. Second, it considers the case where the managerial compensation is tied to both the short-term market value of the firm immediately after the manager announces his investment/payout policy, and the fundamental value of the firm after the return from investment is realized or the cash flow is returned to investors in the form of dividends or share repurchases. This provides additional insights into managerial myopia/farsightedness. Third, it considers an increase in managerial equity stake in the firm after shares are repurchased. Further, it considers the case where investors underreact to open market share repurchase announcements (Note 1). The rest of this paper is organized as follows. Section 2 outlines the signaling model of manager's payout/investment decisions. Section 3 analyzes the equilibrium outcomes. Section 4 concludes the paper.

The Model
Consider a market consisting of two all-equity firms whose type }, , where H represents a highquality type and L represents a low-quality type. A high-quality firm is characterized by better future prospects than a low quality firm (to be examined in more detail below). At date 0, each firm has shares outstanding, of which the manager has shares, and the outsiders have shares. Hence, In addition, each firm has assets in place of with , which will generate a date 1 cash flow . The market cannot observe firm type, so it assigns an equal probability to each firm being type H or L. At date 1, the management of each firm simultaneously decides between three possible uses of cash flow Firstly, each firm can invest the cashflow in a new project. This provides an income at date 2 of where and (i.e., type H firm has a positive NPV project available, while type firm has a negative NPV project available). Further, it takes as given that that is, the positive and negative NPV projects exactly balance each other, and, on average, the projects have zero NPV. (This assumption greatly simplifies the analysis without changing the intuition of the model). Secondly, each type can use the cashflow to invest at zero NPV in the financial market, using the proceeds to pay a dividend L ; 0 = + L H r r X at date 2. Thirdly, each firm can use the cash flow to repurchase some shares. The managers' date 1 policy decisions may provide information to the market regarding firm type. At date 2, types are revealed and payouts occur.
This model is a signaling game in which I solve for the Bayesian equilibria. Hence, the manager's objective function and the market's posterior beliefs upon observing the managers' date 1 decision must be specified. The manager has an equity stake in the firm that does not change under a policy of investing in the new project or paying dividends, but does change if the manager repurchases and destroys shares.
The manager's date 0 equity stake is represented as N N M = α . Under the dividend or investment policy, his equity stake remainsα throughout 2 dates. I also define a post-repurchase managerial equity stake as β . Since repurchasing increases the managerial equity stake, The managerial payoff function is defined as where α represents the managers' (exogenously given) equity stake in the firm, represents the date 1 market value of the firm (which is determined by the date 1 signal), and represents the date 2 fundamental value of the firm. Further, represents the weight that the manager assigns to the date 1 value of the firm, and represents the weight that the manager assigns to the date 2 value of the firm. If manager decides to use cash flow X to repurchase shares (with the repurchased shares being destroyed), he increases his equity stake to . β Next, the market's posterior beliefs are specified. Firstly, note that if both firms undertake identical policies, the market is unable to update its beliefs; it continues to assign an equal probability to each firm being high or low-quality. If the firms separate, the market's beliefs when it observes signals { }are specified as follows: if the market observes , it believes that the firms are respectively; if the market observes , it believes that the firms are respectively; and if the market observes , it believes that the firms are respectively. In Bayesian equilibrium, the firms' equilibrium strategies are consistent with these beliefs.
c) Separation inconsistent with market beliefs: If the firms separate with only firm L repurchasing shares, manager L's expected compensation are Proof: See Appendix.
Lemma 2 The effects of the firms' dividend policy on the manager's expected compensation are as follows: a) If both firms pay dividends, then b) If the high-quality firm repurchases shares, and the low-quality firm pays dividends, then, given the beliefs, the payoff for the low quality manager is c) If the low-quality firm repurchases shares, and the high-quality firm pays dividends, then, given the beliefs, the payoff for the high quality manager is Lemma 3 The effects of the firms' project-investment policy on the manager's expected compensation are as follows: a) If both firms invest in the new project, then If the high-quality firm repurchases, and the low-quality firm invests in the new project, then, given the beliefs, the payoff for the low quality manager is c) If the low-quality firm repurchases, and the high-quality firm invests in the new project, then, given the beliefs, the payoff for the high quality manager is If the high-quality firm invests in the new project, and the low-quality firm pays dividends, then, given the beliefs, the payoffs are e) If the low-quality firm invests in the new project, and the high-quality firm pays dividends, then, given the beliefs, the payoffs are Proof: See Appendix.

The case of efficient signaling
Using the payoffs given in lemma 1, 2, and 3, the equilibrium of the game can be derived. I first consider each firm's best responses when 2 / 1 2 1 = = w w .
and .
H Y X < b) If firm H chooses to repurchase shares, firm L's best response is also to repurchase shares if Note that I do not need to consider firm L's best response to firm H paying dividends, since paying dividends is a dominated strategy for firm H. To make analysis tractable, it is assumed that (Note 2) Proposition 1 From lemma 4, lemma 5, assumption (a1), and assumption (a2), the following equilibria are derived: , there is no equilibrium.
Corollary 1 If the manager is completely myopic ( )

The case of market underreaction to share repurchases
In this further analysis, firm H's manager attempts to signal that his firm is undervalued by announcing a share repurchase program. However, investors underreact to the share repurchase announcements. That is, they fail to recognize that managers repurchase shares in order to time the market (See, e.g., Ikenberry et al. (1995), Brockman andChung (2001), Zhang (2005), and Chan et al. (2007)). In particular, the investors do not update their belief when they observe the signal { } R D, or { } D R, , but continue to assign equal probability to both firm types. The amended managerial payoffs for such strategy combinations are Re-analyzing the managerial payoffs, I derive the following results.
Lemma 6 Paying dividends is a dominated strategy for firm H. Firm H's best responses are as follows: a) If firm L chooses to invest in the new project, firm H's best response is to invest in the new , firm H's best response is to repurchase shares.

b) If firm L chooses to pay dividends, firm H's best response is to invest in the new project if
c) If firm L chooses to repurchase shares, firm H's best response is also to repurchase shares.
Proof: See Appendix.
Lemma 7 Firm L's best responses are as follows:

a) If firm H chooses to invest in the new project, firm L's best response is to invest in the new
If firm H chooses to repurchase shares, firm L's best response is to pay dividends.
Proof: See Appendix.
To make analysis tractable, a further condition is introduced (Note 3) Proposition 2 From lemma 6, lemma 7, assumption (a1), and assumption (a2), I derive the following equilibria: , the unique equilibrium is regardless of whether (c1) holds.

Conclusion
I develop a signaling model that simultaneously considers the managers' payout/investment decisions. In the model, the manager's compensation is tied to both the short-term value of the firm so that the managerial myopia/farsightedness can be analyzed. The model shows that paying dividends is a dominated strategy for high-quality firm. If the managers place equal weights to short-term and long-term payoffs, there exists a separating equilibrium in which the high-quality firm invests in the new project while the low-quality firm pays dividends. If the managers are completely myopic, there is a pooling equilibrium in which both firms repurchase shares. In this case, the low-quality firm sends false signal to the market to maximize its short-term stock price at the expenses of long-term shareholders. On the other hand, if the managers are completely farsighted, there is a separating equilibrium in which the highquality firm invests in the new project while the low-quality firm pays dividends. In this case, paying dividends is a dominant strategy for the low-quality firm since the manager's objective is to create values for long-term shareholders.
In a further analysis of market underreaction to share repurchases, a separating equilibrium in which the high-quality firm repurchases shares while the low-quality firm pays dividends is obtained. This result supports the notion that a major reason for share repurchases is to signal undervaluation. Overall, this paper emphasizes the role of open-market share repurchases as signals for firm undervaluation. The future research could analyze the effects of private benefits on equilibrium outcomes or develop a more integrated model that also considers the role of dividends as a mitigation of agency cost of free cash flows.

Notes
1. If the market reacts immediately and fully to share repurchase announcements, it will be futile for firms to subsequently acquire shares since there is no capital gain from doing so. For example, Ikenberry et al. (1995) find that the average abnormal four-year buy-and-hold return measured after the initial announcements is 12.1%, suggesting that the market underreacts to open market share repurchase announcements.
2. Without assumptions (a1) and (a2), the number of permutations of conditions is significantly increased, making the analysis more complex.
3. This condition represents the case where firms have substantial free cash flows.
Thus, the number of shares repurchased (and destroyed) is The new total number of shares is . 2 The manager still holds Therefore, the manager's post-repurchase equity stake is  (8) are compared if firm L pays dividends. Since it is obvious that (11) < (2), (18) < (4), and (8) < (5), paying dividends is a dominated strategy for firm H.

Given
, firm L will choose to pay dividends rather than repurchase shares if 2 / 1 , firm L will choose to repurchase shares rather than pays dividends. Subtracting (10)

Given
, it follows that (14) < (10). Therefore, firm L will pay dividends if firm H repurchases shares. Then, (6), (13), and (17) are compared to find firm L's best response given that firm H invests in the new project. Subtracting (17) from (13) yields , firm L's best response is to invest in the new project. Firm L's best response is to . Subtracting (6) from (13) yields , firm L will choose to invest in the new project rather than repurchase , however, firm L will choose to repurchase shares rather than invest in the new project. Subtracting (17) from (6) yields Given , firm L will choose to pay dividends rather than repurchase shares if . If , firm L will choose to repurchase shares rather than pay dividends. ■ 2 / 1

Proof of Lemma 6
Given that firm invests in the new project, (12), (18), and (4) are compared to determine firm L H 's best response. Subtracting (18) from (4) yields Since (A9) is positive, firm H will not pay dividends. Subtracting (4) from (12)  Since (A13) is obviously positive, firm H will not pay dividends.

When
, firm L will choose to invest in the new project rather than repurchase shares , firm L will choose to repurchase shares.