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ISSN 2229- 2229-6891 INTERNATIONAL RESEARCH JOURNAL OF APPLIED FINANCE Volume. IV Issue. 2 February 2013 Contents Effect of Equity Financing on Product Market Behavior Jaideep Chowdhury 164 - 173 Forecasting the Yield on 10-Year State Bonds as Part of the WACC For Regulated Industries Mark Hartog Va...

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Contents Effect of Equity Financing on Product Market Behavior Jaideep Chowdhury

164 - 173

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Effect of Equity Financing on Product Market Behavior

Jaideep Chowdhury Department of Finance and Business Law College of Business James Madison University Harrisonburg Virginia USA 22801 [email protected]

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! " #$! Abstract The literature on how financing decisions affect product market decisions have largely ignored equity financing. Given the importance of equity as a significant source of external financing, we introduce equity financing in a model of product market financial market interaction. We develop the model where debt and equity are endogenous and a firm’s output is financed by both debt and equity. We show that a financially constrained firm always produces less than what the firm would have produced if it was not financially constrained. Keywords: Product Markets,Equity Financing, Captial Markets, Limited Liability Effect JEL Classification: L13, G32 Introduction Equity market is an important source of external financing for firms. The literature on the interaction of financing decisions with product market behavior has debated how debt financing may lead to more aggressive or less aggressive behavior in the product market. But little is known about how equity financing may affect a firm’s product market behavior. We present a model to draw key insights into how a financially constrained firm behaves in the product market if it issues both debt and equity to finance its output. The corporate finance literature has developed models of debt contracts where the threat of liquidation leads to underinvestment and less aggressive behavior in the product market. In contrast, the industrial organization literature has shown that debt financing can lead to more aggressive behavior in the product market. The corporate finance literature deals with ex-ante behavior of a firm in the sense that debt causes a firm to decrease its cost of production and probability of bankruptcy by acting less aggressively in the output market, i.e., undertaking less risky strategies in the product market. The industrial organization literature, starting with the seminal paper of Brander and Lewis (1986) assumes that a firm caters to the equity holders and undertakes risky projects by issuing debt. The equity holders reap the benefit of upside risk while being protected from the downside risk by limited liability. This ‘risk shifting’ from equity holders to debt holders results in a firm acting more aggressively in the product market. All the subsequent papers debated if a firm acts more aggressively or less aggressively in the product market following debt financing. None of the papers in the literature look into how equity financing can affect firm output. One reason why equity is ignored is that equity form a small fraction of the total external financing by a firm as pointed out by Campello(2005). But Fama and French (2005) have shown that equity constitute a significant portion of a firm’s external financing. Previous authors had considered only IPO and SEO as the form of equity financing. But Fama and French argue that there are seven different ways by which the firm can raise equity. Given the importance of equity in external financing, we introduce both debt and equity as two source of external financing and investigate the effect of debt and equity financing on a firm’s output. We use the framework of Povel and Raith (2004), who introduces variable production cost in the standard Brander and Lewis framework with endogenous debt. In their framework, a firm issues debt and cash in hand to finance its output. In our framework, a firm issues both debt and equity to finance its output. We show that if a financially constrained firm issues both debt and equity to finance its output, the output produced is always lower than the output that would have been produced if the firm 165

! " #$! was not financially constrained. In our model, we assume a three-stage game and a Cournot duopoly setup. In the first stage, the firms decide on the amount of debt and equity. In the second stage, the firms choose the outputs to be produced. In the third stage, the state of the nature is realized and the equity holders and debt holders are paid off. We assume that the firms cater to the interests of the equity holders. As the equity holders are protected by limited liablity, the firms engage in risky product market strategies and increase output. This increase in output may generate higher profits for the equity holders. This is the benefit of acting aggressively in the product market. But aggressive risk taking behavior increases the probability of default. We assume that if a firm goes bankrupt, the firm is liquidated and the firm’s assets are sold off. A portion of these assets are used to pay off the debt holders and the equity holders do not recieve anything. So in case the firm is liquidated, the equity holders not only loose their current investment but also loose all the future profit the firm could have generated. Acting aggressively in the product market is costly to the equity holders. The managers of a financially constrained firm weigh the costs and benefits of acting aggressively. We show that the costs outweigh the benefits and the firm acts less aggressively in the product market. The Existing Literature Traditionally the industrial organization literature focused on a firm’s strategies where the firm’s objective is to maximize profits. The corporate finance literature consider financial decisions of firms in terms of maximization of equity values. But in truth, the financial market decisions and product market decisions are interlinked. Brander and Lewis ( 1986), in their seminal paper, studied the linkage between financial markets and product markets. They show that limited liability may lead to a leveraged firm taking a more aggressive stand. Their 1988 follow-up paper included the bankruptcy costs and arrived at the same conclusion. These two papers were followed by a series of other papers. Maksimovic (1988), Hendel (1996) and Chowdhury and Haller (2012) showed that the leveraged firms become more aggressive while Glazer (1994) and Chevalier and Scharfstein (1996) demonstrated that the leveraged firms become less aggressive. Either effect can happen in Showalter (1995). Poitevein (1989) and Fudenburg and Tirole (1986) have investigated the predatory action taken by competitors in the context of capital market imperfection and entry. Bolton and Scharfstein (1990) discuss a two period model involving a financially constrained firm and a bank. Maurer (1999) and Faure-Grimaud (2000) derives debt as an optimal contract. Povel and Raith (2004) build a model with two firms. One of them is financially constrained. They introduce variable production cost and show that costly production creates a feedback from the product market to the financial market. Our paper contributes to the literature on financing decision and product market interaction. We complement this literature by introducing equity financing in a model set-up similar to Povel and Raith (2004). In our model, firm output is financed by both endogenous debt and equity. This paper is the first paper to our knowledge which introduces equity as a source of financing in the literature on how financing decisions affect product market decisions. The Model Let us consider a duopoly market where one firm is financially constrained and the other firm is not. Without loss of generality, we assume that firm i is financially constrained and depends on external financing to finance its production cost. Firm j is financially unconstrained and does not need external financing to finance its production. In the first stage, firm i chooses a mix of debt and equity. In the second stage, the firms i and j choose their outputs and engage in a Cournot 166

! " #$! duopoly game. There is no fixed cost of production. For firm i, the variable cost of production is given by cqi and financed by debt and equity. Further, we assume that there is no agency problem between the managers and the equity holders. The managers truthfully maximize the equity value of a firm. The outputs are chosen in the second stage before the actual demands are generated. This often happens in practice: the firms choose output levels based on estimated demand. The actual market demand depends on the state of the nature. There can be good and bad states of the nature. The state of the nature is random and unknown ex ante to the firms. In the third stage, after the firms have produced their outputs, the state of the nature is realized and the actual demand is generated. If the state of the nature and hence the demand is good (bad), the firms generate a profit (loss). A portion of the financially constrained firm i’s revenue is used to pay back its debt. If the state of the nature is bad and the revenue is not enough to repay the debt, the firm i declares bankruptcy and is liquidated and its assets are sold off to pay the debt holders. We assume that the equity holders are not paid anything in case of liquidation. The Model Set-up Both the firms are risk neutral firms. In stage 1, firm i issues a mix of debt and equity. In stage 2, the firms i and j compete in the product market as Cournot duopolists. The revenue of firm i is denoted by R i (q1 , q2 , z ) . The state of the the nature is represented by the random variable z , which is distributed with density f (z ) > 0 over a range [ z , z ] . The revenue of firm i has the standard properties:

R i and R j are twice differentiable in all arguments. Further, Rii > 0 Riii < 0 ; R ij < 0 Riji < 0 ;

R i is strictly concave and has a unique maximum in qi for given q j and z; Rzi > 0 Rizi > 0 ; Riii R jjj > Riji Rijj ; R i (q, z ) = 0. These assumptions are standard in the literature, like in Brander and Lewis (1986) and Povel and Raith (2004). Firm i issues debt of size Dim in stage 1 where Dim is the market value of the debt. Firm i finances its output qi using debt and equity. After the state of the the nature is realized, the firm pays back the debt holder the amount Di , the face value of debt, if the revenue generated is at least equal to Di . zˆ , the switching state of the nature, is that state of the nature at which firm i has earned just enough revenue to pay off its debt obligations.

Di = R ( qi , q j , zˆ )

(1)

Di , the face value of debt, equity issued and zˆ are endogenous and determined within the model. The firm uses both debt and equity to finance its variable cost of production. Dim + E = cqi

(2)

where c is the constant marginal cost of production and E is the amount of equity issued by the 167

! " #$! firm. We call this the cost of production constraint. Firm i maximizes Ri − Di , where Ri is the expected revenue, over all the states of the nature. When the state of the nature is bad, i.e, z < zˆ , the firm does not earn enough revenue to pay back the face value of debt Di . The debt holders recieve the the entire revenue R ( q, z ) , where z < zˆ . Firm i’s equity holders are said to be protected by limited liability as the entire debt need not be paid back by the equity holders when the state of the nature is bad. The managers of firm i maximize the residual value of the firm after paying the debt holders. The residual value of the firm is given by z

Ve = ∫ ( Ri (qi , q j , z) − Di ) f ( z )dz zˆ

(3)

This residual value is also the value of the firm to the equity holders. The equity holders invest E and the return to the equity holders is given by re . In the short run, the firm promises to pay at least rate of return of re to the equity holders, that is Ve ≥ (1 + re ) E

(4)

But in the long run, the equity holders recieve a return of re , which is the same as equity holders of other firms in the same or related industry. The equity holders participation constraint is given by Ve = (1 + re ) E

(4a)

Firm i issues debt with market value Dim at a rate of return of rd and pays back the face value of debt Di . rd is the prevailing rate of return in the bond market. The debt holders get back the face value of debt Di when the state of the nature is good, z > zˆ . When the state of the nature is bad, z < zˆ , the debt holders get the entire revenue of the firm, R i (q, z ) . Following Brander and Lewis (1988), we introduce bankruptcy cost in the model. The expected bankruptcy cost is given as zˆ

γD i (q, zˆ) ∫ f ( z )dz z

where γ ∈ (0,1) . When a firm declares bankruptcy, the firm has to pay a fraction γ of the face value of debt D i (q, zˆ) as bankruptcy cost. Whenever the firm declares bankruptcy, effectively the debt holders have to bear this cost as the revenue payment to the debt holders will be reduced by the amount of the cost of bankruptcy. We also assume when a firm declares bankruptcy, the firm is liquidated. We make this assumption to exempt us from the derivation of an optimal debt contract which is not the goal of this paper. Due to liquidation, the firm’s assets are evaluated and sold off to a third party. We also assume that the total liquidation value of the firm is L and this liquidation value is at least as large as the γ fraction of the revenue generated by the firm in zˆ

the bad state of the nature, i.e. we assume L > γ ∫ R i (q, z ) f ( z )dz . A fraction of the liquidation z

168

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value L, γ ∫ R i (q, z ) f ( z)dz is paid to the debt holders as liquidation payment, which is common z

zˆ

in real life. The rest L − γ ∫ R i (q, z ) f ( z )dz is a deadweight loss. The equity holders are not paid z

anything in case of bankruptcy and subsequent liquidation. The debt holders invest the market value of debt Dim in firm i. The debt holders are assumed to be risk neutral. As a result, the expected amount to be paid back to the debt holders is (1 + rd ) Dim . The expected amount to be paid pack to the debt holders is given by zˆ

z

zˆ

zˆ

z

zˆ

z

z

Vd = ∫ R i (q, z ) f ( z )dz + D i (q, zˆ) ∫ f ( z )dz − γD i (q, zˆ )∫ f ( z )dz + γ ∫ R i (q, z ) f ( z )dz.

The first term is the amount of revenue the debt holders get when the state of the nature is bad, i.e. z < zˆ . The second term is the face value of debt that the debt holders get back when the state of the the nature is good, z > zˆ . The third term is the bankruptcy cost which reduces the amount the debt holders get back in case of bankruptcy. The fourth term is the liquidation amount the debt holders recieves when the firm is liquidated. All these four terms add up as the expected value of debt to the debt holders. Debt holders expect a return of (1+ rd ) Dim where rd is the rate prevailing in the bond market. The debt holders participation constraint is given by zˆ

z

z

zˆ

Vd = ∫ R i (q, z ) f ( z )dz + D i (q, zˆ) ∫ f ( z )dz zˆ

zˆ

z

z

−γ Di (q, zˆ) ∫ f ( z )dz + γ ∫ R i (q, z ) f ( z )dz

(4b)

= (1 + rd ) Dim .

The managers of firm i maximize the residual value of the firm, given by equation 3, subject to the equity holders’ participation constraint (equation 4a), the debt holders’ participation constraint (equation 4b), the cost of production constraint (equation 2) and given the definition of the switching state of the nature (equation 1) . The maximization problem for the managers of firm i is given by

z

i i i max Ve = ∫z ( R (qi , q j , z ) − D ) f ( z )dz qi , zˆ

Vei = (1 + re ) E ,  i m Vd = (1 + rd ) Di , s.t. m  Di...