Bank Loans, Trade Credits, and Borrower Characteristics: Theory and Empirical Analysis. Byung-Uk Chong*, Ha-Chin Yi** March, 2010 ABSTRACT

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1 Bank Loans, Trade Credits, and Borrower Characteristics: Theory and Empirical Analysis Byung-Uk Chong*, Ha-Chin Yi** March, 2010 ABSTRACT Trade credit is a non-bank financing offered by a supplier to finance the purchase of its product. Trade credit is one of the important sources of debt financing which can substitute bank loan. Trade credit is prevailing among riskier borrowers, competing with bank loan in corporate loan market. The prevalence of trade credit implies that there exist mutual economic benefits for both suppliers and buyers from transacting trade credits even though the default rate of trade credits is much higher than that of bank loans. This paper models the economic incentive for product suppliers to offer trade credits to riskier borrowing firms which might not be able to obtain financing from conventional and specialized financial institutions such as banks. When the product market is imperfect, a product supplier can obtain additional mark-up by increasing the sale of products. That is, there is a gain to offering trade credits to facilitate the purchase of inputs to riskier borrowing firms who cannot obtain bank financing. Therefore, trade credits service riskier borrowing firms than bank loans in the corporate loan market. The empirical analyses using Compustat and LPC DealScan data supports the theoretical prediction that a riskier borrower seek for more trade credit financing, independent of bank loan access. JEL Classification: D82, G21 Key Words: Asymmetric Information, Bank Loan, Trade Credit, Corporate Loan Market, Debt Financing Choices * Corresponding author, Associate Professor of Finance, College of Business Administration, Ewha Womans University, Seoul, Korea, Tel: , chongb@ewha.ac.kr ** Associate Professor of Finance, Department of Finance and Economics, McCoy College of Business Administration, Texas State University-San Marcos, Tel: , hy11@txstate.edu

2 1. Introduction Trade credits are financing instruments offered by product suppliers to their customers. Firms obtain financing from specialized financial intermediaries, mainly banks, as well as from product suppliers, generally by delaying the payment. Suppliers not only sell products, but also offer trade credits to facilitate the sale of their products. Like bank loans, trade credits are one of the most important sources of short-term external financing for firms. There is a general notion that trade credits are considerably more expensive than bank loans as trade credits are widespread among firms facing obstacles to obtain financing from banks. The reliance on trade credits increases with the degree of credit rationing on financially constrained firms. This paper provides a unique theoretical model for trade credit in the corporate loan market where firms obtain financing to purchase inputs for business projects. In the presence of bank financing for short-term commercial lending such as line of credit, it is not obvious why the sale of a product is bundled with a trade credit by the suppliers. This paper provides a theoretical model explaining why trade credits are offered by a majority of non-financial firms. In doing so, this paper models the prevailing wisdom that trade credits service riskier pool of borrowers than bank loans in the short-term corporate loan market. Trade credit is an important source of financing which is crucial for firms running out of bank credits. Accordingly, most theories of trade credit assume that 1

3 suppliers have some advantage over banks. A widespread notion in the trade credit literature is that trade credit substitutes for bank loan because suppliers have access to privileged information about their customers riskiness. Smith (1987) and Mian and Smith (1992) argue that the sales effort of suppliers gives them informational advantage in assessing their customers credit risk. Biais and Gollier (1997) explain why suppliers are willing to lend to firms that have exhausted their debt capacity with banks. They show that suppliers can more effectively identify firms whose credit risk is overestimated by banks. Knowing that a firm s credit line is unduly low based on their business relationship with the firm, the suppliers are willing to extend a trade credit. In Biais and Gollier (1997), it is optimal for suppliers to vary interest rates with borrower s credit risk. Petersen and Rajan (1997) show that, vis-à-vis banks, suppliers extend more credit to firms with current losses but positive growth of sales. They interpret this finding as evidence that suppliers have comparative advantage in identifying firms with growth potential. Petersen and Rajan (1997) also argue that suppliers may have lower monitoring costs and are thus able to provide trade credits to firms constrained in their bank financing. In another stream of trade credit literature, the structure of product market has been a main cause of the prominence of trade credit in the corporate loan market. Brennan et al. (1988) provide a model where a monopolist finances the sale of its products, setting the price of good and the interest rate in vendor financing to maximize combined expected profits from the sale of products and offering of trade 2

4 credits. They argue that the monopolist will use the interest rates to discriminate the demand for the product if the regulators force the monopolist to set the same product price to all customers. In this setting, they show that an elastic demand induces the monopolist to offer vendor financing at subsidized interest rates while the optimal interest rate varies with customers characteristics. In Brennan et al. (1988), the product supplier internalizes the impact of price elasticity of demand in the debt costs by offering subsidized interest rates to their customers. The product differentiation hypothesis for trade credits argues that business managers use trade credits to differentiate their products like advertising. Nadiri (1969) extends the Dorfman-Steiner (1954) model, originally developed to describe optimal advertising expenditures, to explain trade credit decision. Trade credit is a non-price factor that influences product demand. Therefore, the application of this method to optimal credit decisions is known as the product differentiation hypothesis for trade credit. In Nadiri (1969) s model, managers maximize firm value by choosing product price and trade credit. The end product of this maximization is that the optimal ratio of trade credit to revenues is directly proportional to the elasticity of demand with respect to trade credit and inversely proportional to elasticity of demand with respect to product price. The optimal receivables-to-sales ratio is positively related to profit margin while the optimal profit margin is negatively related to price elasticity of demand. This result suggests the intuitive notion that firms offer more generous credit terms when they can make greater profit margin from additional 3

5 sales. In Nadiri (1969) s application of the Dorfman-Steiner model, trade credit is an investment that firms use to help maintain their long-term relations with customers. Trade credit generates returns over time as the returns to investment do not come immediately. Petersen and Rajan (1997) test the product differentiation hypothesis along with other theories of trade credit. They find a positive cross-sectional relation between account receivables and profit margin, as predicted by Nadiri (1969) s model of the product differentiation. Modeling trade credit based on credit rationing or adverse selection problems in the corporate loan market is another stream in the literature. As in Stiglitz and Weiss (1981), under asymmetric information about borrowing firm s risk type credit rationing arises either when a lender cannot set appropriate interest rate suiting borrowing firm s risk type or when the lender is not willing to offer a loan at any interest rate. Schwartz and Whitcomb (1979) focus on the credit rationing issue to explain why firms obtain trade credits. They find that the firms under credit constraint in bank financing tend to use trade credits. Smith (1987) shows that banks face adverse selection problem under private information on borrowing firm s risk type. Banks offer financing as much as a low-risk borrowing firm desires at lower rates and ration credit to high-risk borrowing firms while product suppliers offer trade credits at high interest rates to high-risk borrowing firms. Therefore, the corporate loan market is separated into low- and high-risk firms in their selection of financing sources. That is, low-risk borrowing firms select bank loans at low interest rate while 4

6 high-risk firms select trade credits at high interest rates, resulting in separating equilibrium in the corporate loan market. Further, this paper also models possible subsidization between the sale of products and extension of credits. The subsidization within a firm can rely on the imperfect market structure. In particular, Gilligan and Smirlock (1983) show that, in order to maximize the value of the firm, a multi-product firm can obtain revenues in excess of production costs on goods sold in monopolized market and uses these rents to subsidize the production of goods sold in competitive markets. In line with this idea, Chong (2007) and Barron et al. (2007) provide a model for the tie-in between financing and sale of products. Chong (2007) and Barron et al. (2007) examine the behavior of captive finance companies which are affiliated to parental manufacturing firms. The credits offered by the captive finance companies are similar to the trade credits extended by the product suppliers in that both of them are offered to facilitate the financing for purchase of products of the suppliers. In terms of modeling, Chong (2007) adopts the adverse selection and credit rationing modeling in the sense of Stiglitz and Weiss (1981). Barron et al. (2007) assume symmetry in information between lenders and borrowers. Both Chong (2007) and Barron et al. (2007) show that the loan approval rate of captive finance companies is higher than that of banks or independent lending institutions since the captive financing generates the increase in the sale of products and the resulting increase in profits when the structure of 5

7 product market is imperfect. This paper extends both Chong (2007) and Barron et al. (2007) by adopting signaling and information asymmetry respectively in the model. Trade credit model is mainly based on the imperfect structure of product market in that suppliers would otherwise have no incentive to sell its product on trade credit. Borrowing firms would be indifferent between different financing sources if there exist perfect substitutes in the corporate loan market. In such an economy, the suppliers achieve no benefits by offering trade credits while firms can borrow at competitive interest rates from conventional financial institutions (banks) in the corporate loan market. Thus, the economic investigation of trade credits needs to be based on the imperfectness either in the financial market or in the product market or both. Incorporating the analytical and empirical outcomes of the previous studies, this paper provides a unique theoretical model where trade credits service riskier borrowers than bank loans in the corporate loan market. This paper models the equilibrium in the monopolistically competitive market where firms need to buy inputs to conduct business projects. Then, the model in this paper links the monopolistically competitive input market and the perfectly competitive loan market to characterize the prominence and features of trade credit when a firm s purchase of input requires financing. The remainder of this paper is organized as follows. Section 2 introduces a simple model of a supplier s expected demand for its product (input) in monopolistically competitive market, assuming that firms do not need financing for 6

8 the purchase of inputs. Section 3 extends the equilibrium characterized in section 2 by assuming that all firms require financing to purchase the inputs for business projects. Section 3 assumes that only bank financing is available in the corporate loan market. The interaction between input and corporate loan markets is modeled given that the firm s purchase of inputs is constrained by the availability of financing. Section 4 provides a model explaining how an input supplier obtains gains from the additional sale of its products by offering trade credits. This section shows that the positive mark-up on the sale of a product provides the supplier with an incentive to offer trade credits to borrowing firms which would not be provided such loans by banks due to their high credit risk. In other words, the existence of positive mark-up induces the input supplier to set an optimal credit standard for trade credit lower than that of a bank loan in equilibrium. Based on the theoretical model, section 4 also provides the numerical simulations that characterize the equilibrium in monopolistically competitive input market with both bank loans and trade credits available in the corporate loan market in comparison with the one with only bank loans available. Section 5 discusses the empirical testing strategies and describes the sample firms from Compustat and Loan Pricing Corporation (LPC) DealScan databases. Section 6 shows the results of empirical model, and Section 7 provides robustness checks. Section 8 summarizes and concludes. 7

9 2. Equilibrium in Monopolistically Competitive Input Market without Financing Requirement This paper adopts and applies Perloff and Salop (1985) s search model to the monopolistically competitive market where each firm buys an input to conduct a business project. The imperfect structure of the input market generates positive markup with which the input price is above the marginal costs. Before further development of the model with financing requirement in later sections, this section provides a model for the equilibrium in monopolistically competitive input market where each firm does not require financing for the purchase of input. There are N suppliers selling differentiated inputs in monopolistically competitive market, and these suppliers incur identical marginal costs κ and fixed costs K of production. There are M firms, each of which planning to purchase one unit of input for business project. M is assumed to be fixed number in the entire development of the model in this paper. In this section, these M firms do not need financing since they have enough funds to purchase the inputs to conduct business projects. Each firm invests in a single project. By searching and choosing one among these i= 1,2,..., N differentiated inputs to conduct business project, each firm j, j = 1,2,..., M generates different future cash flows and the resulting stochastic present values vj = ( v1 j,..., vij,..., Nj) v of the business project. Note that the stochastic present value of future cash flows of a firm s project 8

10 depends on which input the firm searches and chooses. The stochastic present value of each firm s project, v j, j = 1,2,..., M is independently drawn from the identical distribution function F( v j ) with the associated density function f ( v j ). Given prices p ( p,..., p,..., p ) = for the N available differentiated inputs, 1 i N each firm will choose the input for which his net present value (NPV), b, is maximized. A particular firm j s net present value of the project when purchasing the input from supplier i is given by: bij = vij pi (1) where b is firm j s net present value when using supplier i s input, is firm j's ij v ij present value when using supplier i s input, and p i is the price of supplier i s input, which is also the initial investment for firm j s project. If bij b kj for a given supplier, then v p p +, and the firm will choose to purchase the input from kj k i vij supplier i over supplier k. The probability that b ij b kj is Pr( bij b kj ) = F ( pk pi + vij ). Since each firm s present value is identically and independently distributed across firms, the proportion of firms which purchase the input from supplier i is given by: Pr ( bi max bk) ( k i ) = Π F p p + v f ( v )dv (2) k i k i 9

11 It follows that the expected demand for the input sold by supplier i, Di( p 1,..., pi,..., p N), equals the proportion of firms which buy that input given by equation (2) times the number of firms M as following: ( ) ( ) ( ) D p,,..., p,..., p = M Pr b max b = M Π F p p + v f( v) dv (3) i 1 i N i k k i k i k i Under the assumption that each supplier has the identical and constant marginal cost κ and fixed costs K, the expected profits of input supplier i are given by: ( p,..., p,..., p ) ( p κ ) D ( p,..., p,..., p ) Π = K (4) i 1 i N i i 1 i N Perloff and Salop (1985) show that, given the identical marginal and fixed costs of production across suppliers, the market reaches a unique zero-profit singleprice equilibrium. Following Perloff and Salop (1985), this paper considers the case where a unique symmetric zero-profit equilibrium price exists such that p i i= 1,2,..., N. This implies an expected demand of supplier i given by: (,...,,..., ) ( ) N 1 ( ) = p, Di p pi p = M F p pi + v f v dv (5) Under the Bertrand-Nash assumption that each supplier chooses the input price to maximize its expected profits, taking other suppliers prices as given, supplier i s first-order condition with respect to p i is given by: p i = κ ( 1,...,,..., ) (,...,,..., ) D p p p Di p1 pi p pi i i N N (6) 10

12 Given the form of expected demand (5), the characterization of the optimal price of the supplier i s input is given by: N 1 ( ) ( ) M F v f v dv 1 p = κ + = κ + N 2 2 N 2 2 ( N 1) M F( v) f ( v) dv N( N 1) F( v) f ( v) dv (7) In the monopolistically competitive input market, a zero-profit equilibrium is characterized by the usual Chamberlinian tangency of demand curve with average cost curve. Since all suppliers are assumed to be identical, the expected demand of each input supplier is characterized by the equal share of firms purchasing inputs, M / N. Then, the zero-profit condition is given by: M p K N ( κ ) = 0 (8) Equations (7) and (8) characterizes the optimal input price p strictly larger than the marginal cost of production κ and the number of firms N in the symmetric zeroprofit equilibrium of the monopolistically competitive input market. 3. Bank Credit Decision and Equilibrium in Input Market with Financing Requirement Different from section 2, section 3 assumes that all M firms require financing to purchase one unit of input to conduct a business project. In section 3, financing is available only from banks in the corporate loan market. First, this section provides a model of bank credit decision under information asymmetry with regard to borrowing 11

13 firm s risk type. Then, this section models the equilibrium in the input market when each firm requires financing for the purchase of input, leading to a model economy where the interaction between the input and the loan markets characterizes the equilibrium. For simplicity, the model considers a two-period model. In the first period, a firm applies for a loan at a lender of a particular type k to finance the purchase of input for project. If approved, the firm obtains a loan with interest rate r from a bank. In the second period, the firm pays off the loan or defaults. This paper considers two different types of credit instruments in the corporate loan market bank loan (denoted by the subscript B ) and trade credit offered by input suppliers (denoted by the subscript T ). The bank loan in this paper can be regarded as a line of credit or loan commitment for short-term financing. Thus, a borrowing firm can choose a financing source between the two close substitutes - bank loan and trade credit - without transaction and search costs. There are two types of borrowing firms: firms who will pay off the loan the safe firms (denoted by subscript S ) and firms who will default the risky firms (denoted by subscript R ). The risk type of an individual borrowing firm is private information. A lender does not know whether an individual firm is safe or risky, but does have the prior beliefs on the given distribution of safe and risky firms, η and (1 η ), respectively. 12

14 To make a credit decision, each lender uses an imperfect but informative signal on the credit risk of a firm, θ. This signal summarizes the observable characteristics of a potential borrowing firm and indicates its credit risk. If a firm is safe, the signal θ is drawn from the normal distribution, GS ( θ ) with mean μ S and variance 2 σ. If a firm is risky, the signal θ is drawn from the normal distribution, G ( ) R θ with mean μ R and variance 2 σ. Note that the variance, 2 σ, is assumed to be fixed and identical in both distributions. It is assumed that GS ( θ ) first-order stochastically dominates G ( θ ), implying that safe firms on average tend to generate higher signals than risky firms, i.e., μs > μr. R The decision of a lender of type k to approve or reject a borrowing firm depends on its cutoff signal, ˆk θ. If the signal obtained for the firm is higher than ˆk θ, the lender offers the loan. If the signal is lower than ˆk θ, the lender rejects the firm and does not offer the loan. The optimal cutoff signal ˆk θ indicates the credit policy of a lender of type k. This cutoff signal is publicly observable in the corporate loan market. 1 1 Barron et al. (2007) assume that the differential credit standards of a bank and a captive finance company are not publicly observable, resulting in a borrower s random selection of lender type given a unique competitive loan interest rate. Extending Barron et al. (2007), this paper models the selection mechanism by incorporating differential loan rate and credit standards both of which are publicly observable in the corporate loan market under information asymmetry. 13

15 If a firm is not approved for a loan, the firm cannot obtain a loan from other lender(s), and thus it cannot purchase the input and cannot conduct the business project. This assumption is strong, and is adopted to simplify the analysis. We could instead assume that a firm who is denied for a loan at a lender of a particular type can apply, at some cost, for a loan at other lending institutions. In this case, Shaffer (1998) shows that the result would be a type of "winner s curse" in lending. In particular, if credit evaluation is imperfectly correlated across lenders and each lender is unaware of whether a borrower has been rejected by other lender(s), then the pool of borrowers will worsen. If the lenders do know whether a borrower has been rejected at other lender(s), lenders may not be willing to offer loans to borrowers who have been previously rejected, and the result would be similar to the assumption of this paper that a firm not approved for a loan cannot obtain financing from other lender(s). The corporate loan market is perfectly competitive. The interest rate of a bank loan offered to a firm depends on the firm s credit risk estimated on the firm s signal θ. The borrowing firms with an identical signal θ are offered a loan with an identical loan rate r ( θ ) from all banks. In the perfectly competitive corporate loan market, the equilibrium interest rates r ( θ ) θ generate zero marginal profits per borrower. This zero-profit condition reflects that antitrust regulation and free entry in banking industry are effective in eliminating excess profits. 14

16 This paper assumes that the net present value of a firm s business project generated through the input purchased on financing is so high that the firm s decision to accept financing offer does not depend on the interest rate charged. Banks incur a common cost of funds ρ. ρ can be regarded as the deposit rate on bank savings account by which banks raise funds for offering loans and on which firms invest their funds. If a borrower defaults, the bank takes a collection activity. The rate of return from the collection of salvage value of collateral net of costs is c. No down payment is assumed in the model although inclusion of an identical down payment would not change the conclusions of the model. For a borrowing firm with signal θ, a bank earns net return r ( θ ) ρ per dollar of loan if the borrower is safe and it incur s losses ( ρ c) per dollar of loan if the borrower is risky. A bank's expected profits per dollar of loan offered to a firm with signal θ are given by: ( ) = Pr ( S ) r( ) 1 Pr ( S ) ( c) π θ θ θ ρ θ ρ (9) where Pr ( S θ ) denotes the probability that a firm is safe conditional on the signal θ. In this paper, it is assumed that the total loan amount equals the input price p for which a firm obtains financing. Thus, the total expected profits per borrower or per loan are p π ( θ ) = p Pr ( S θ) r( θ) ρ 1 Pr ( S θ) ( ρ c). The zero-profit ( π( θ ) = 0 with signal θ is characterized by: ) loan rate charged to a potential borrowing firm 15

17 ( θ ) r ( S θ ) ( S θ ) ρ c 1 Pr = (10) Pr Equation (10) implies that the interest rates varying across borrowing firms are determined by the borrowers credit risk signaled by θ. Sinc e a higher signal increases the probability that the individual is a safe borrower conditional on θ or Pr ( S θ) / θ > 0, the increase in signal θ lowers the interest rate r ( θ ) as following: ( ) ( ) θ Pr ( S θ ) ( ) r θ ρ c Pr S θ = < 0 2 θ (11) That is, a potential borrowing firm with a higher (lower) signal will pay a lower (higher) interest rate in the zero-profit equilibrium of the corporate loan market. Since the credit risk signaled by θ varies across firms, not all the firms are approved for a loan even at very high interest rate. In the sense of Stiglitz and Weiss (1981), the high interest rate can result in the adverse selection and thus an upper limit on the interest rate of a bank loan arises in the corporate loan market. Let this upper limit of the loan rate be denoted by r. At this upper limit of interest rate r, a cutoff signal is defined, below which a borrower will be denied a loan because the expected profits from lending will be negative. That is, the signal producing zero expected profit at r characterizes the optimal cutoff signal for approval of a bank loan. From equation (9), the optimal cutoff signal for a bank loan, by: ˆB θ, is characterized 16

18 ( S ˆ ) ( ρ c) ( ) Pr θ B = r c (12) The loan approval decision of a bank is based on its cutoff signal ˆB θ. If the signal from a borrowing firm is higher than ˆB θ, the bank offers the loan. If the signal from a borrowing firm is lower than ˆB θ, the bank rejects the firm. Given the optimal cutoff signal ˆB θ, the average approval rate of a bank loan Ω ( θˆb ) is defined by: ( ˆ θ ) ( ˆ B η 1 GS θ ) B ( 1 η) 1 GR( θˆb) Ω = + (13) Note that an increase in ˆB θ lowers the number of firms approved for bank loans, i.e., ( B) Ω ˆ θ / ˆ θ < 0. When only bank loans are available in the corporate loan market, B the total effective of number of firms which can finance the purchase of an input on bank financing is given by: M B ( ˆ θb) =Ω M (14) Among the M total potential borrowing firms, only M B firms with the signal θ ˆ θ B, ) are app roved for loans. Each firm j, j = 1,2,..., MB will choose the input for which his net present value is maximized. When only bank credit is available to finance firms purchase of inputs in the corporate loan market, let p and N denote the equilibrium input price and the 17

19 number of input suppliers, respectively. Following (7), the optimal price of the supplier i s input is given by: N 1 ( ) ( ) MB F v f v dv 1 κ N N ( 1) B ( ) ( ) ( 1) ( ) ( ) p = κ + = N M F v f v dv N N F v f v dv (15) With the effective number of input buyers M B, equation (15) characterizes the symmetric optimal input price p strictly greater than the marginal cost of production κ. That is, there exists positive mark-up ( p κ ) 0 > on the sale of each additional input. In this paper, this positive mark-up provides the key incentive for an input supplier to offer trade credits to riskier borrowers. Since all suppliers are assumed to be identical, the expected demand of each input supplier is characterized by the equal share of firms purchasing inputs, Ω ( θˆb )( M / N ). The zero-profit condition is given by: M ( θ ) ( κ) Ω ˆ B p K = 0 N (16) While both (8) and (16) describe the usual Chamberlinian tangency of demand curve with average cost curve in monopolistically competitive market, the zero-profit condition (16) with financing requirement modifies the zero-profit condition (8) without financing requirement. In (16), each input supplier s demand is equal share of input buyers who are only approved for bank loans. 18

20 The equilibrium in the perfectly competitive corporate loan market is characterized by the optimal cutoff signal for a bank loan, θ ˆB, and the symmetric zero-profit equilibrium in monopolistically competitive input market is characterized by the input price p and the number of firms N. p and N can be solved for by the two equations (15) and (16). The simulation in the appendix provides a numerical characterization of the equilibrium. The credit standard for a bank loan (optimal cutoff signal) ˆB θ determines the expected performance of a bank loan. That is, the optimal cutoff signal ˆB θ specifies the expected probability of default, Δ ( θˆb ), of a firm approved for a bank loan as following: ( θˆb ) Note that an increase in ˆB ( 1 η) 1 G ( ˆ R θ ) B ( ˆ ) ( ) G ( ˆ ) Δ = (17) η 1 GS θ B + 1 η 1 R θ B borrowers who are given a loan or ( ˆ θb) θ lowers the probability of default, Δ ( θˆb ), of those Δ / ˆ θ < 0. Note also that, given the optimal cutoff signal, ˆB θ, the in crease in the given proportion of safe firms will reduce the probability of default or ( θb ) Δ ˆ / η < 0. B 19

21 4. Co-Existen ce of Bank Loans and Trade Credits in Corporate Loan Market This section provides a model explaining why an input supplier offers trade credits to riskier firms which might not be able to obtain financing from banks. As in section 3, each of M firms requires financing to purchase an input for its business project. While bank loans are already available in the corporate loan market, one incentive for an input supplier to offer trade credits is that the supplier can increase expected combined profits from selling products and offering trade credits to firms which would have been denied financing from banks. Consequently, the likelihood of repayment of a trade credit is lower than that of a bank loan. This section provides a model for this prevailing wisdom in the short-term corporate loan market. As shown in the previous section, when the input market is imperfect, i.e., monopolistically competitive, the mark-up obtained from each additional sale of input is p ositive or ( p κ ) > 0. This positive mark-up, ( p κ ) 0 >, provides an incentive for an input supplier to offer trade credits which are tied to the sale of its products. In addition, the positive mark-up, ( p κ ) 0 >, can make the input supplier set more lenient credit standard than that of a bank. Given the positive mark-up, ( p κ ) 0 >, suppose that a deviant input supplier offers trade credits at the same interest rate r as each bank charges. There are no additional fixed costs for an input supplier to offer trade credits. To purchase the input from this deviant input supplier, each firm can apply for a bank loan or ask for a trade credit to the supplier. 20

22 Given the upper limit of interest rate r on which the optimal cutoff signal of a bank loan is set in the perfectly competitive loan market, the symmetric zero-profit equilibrium price of input, p, and the equilibrium number of firms, N, the initial deviant input supplier maximizes its expected combined profits from selling its products and offering trade credits by choosing an optimal cutoff signal for credit decision. The input supplier would set the optimal cutoff signal for trade credit at the level lower than that for bank loan or ˆ θ additional profits. D < ˆ θ to increase the sale of products for Since each bank sets the cutoff signal ˆB θ while making zero expected profit at the upper limit of interest rate r, the input supplier will incur expected losses from offering a trade credit at the optimal cutoff signal ˆD θ given r. This is because the input supplier offers trade credits to riskier pool of firms with the signal θ ˆ, ˆ θd θb) B at the upper limit of market interest rate r. Thus, the input supplier will charge risk pr emium α ( 0,1) per dollar of loan to the firms asking for trade credits in addition to r. For simplicity, this paper assumes that the risk α premium charged on a trade credit ( 0,1) is exogenously given and identical across borrowing firms. It is obvious that α is strictly positive since the riskier borrowers turned down by banks apply for trade credits. One can doubt that, in equilibrium, the characterization of α has to be such a risk premium that generates zero expected profit from offering a trade credit. 21

23 However, since the sale of input and the offering of trade credit are tie-in sale by an input supplier, there exits much flexibility in the combination of input price and risk premium. That is, the supplier sets α in relation to the magnitude of the mark-up ( p κ ) 0 > when it bundles the sale of an input and extension of a trade credit. Then, an input supplier could decrease α and increase the input price or vice versa while maintaining the same level of combined profits. Hence, it is very difficult to characterize α endogenously simply based on the zero-profit condition of offering a trade credit. In this paper, the characterization of α and its effect on the equilibrium are thus examined as a matter of comparative statics. The optimal cutoff signals ˆB θ for a bank loan and ˆD θ for a trade credit respectively are publicly observable. Thus, each borrowing firm would select the type of financing source at which it can be approved for a credit. Since the borrowers observe the market interest rate r and the risk premiums α on trade credits, the borrowers with the signal θ ˆ θb, ) will self-select bank loans while the borrowers with the signal θ ˆ θ, ˆ D θ B ) will self-select trade cred its. Therefore, trade credits service riskier pool of borrowers than bank loans do. Then, the expected probability of default of a trade credit offered to a firm which would have been turned down by a bank is given by: Δ ( ˆ θ, ˆ D θb) ( 1 η) G ( ˆ ) ( ˆ R θb GR θ ) D ( ˆ ) ( ˆ ) + ( 1 ) ( ˆ ) ( ˆ ) = η G θ G θ η G θ G θ S B S D R B R D (18) 22

24 ψ ( θˆd ) The average profit per dollar of a trade credit granted to such a riskier firm,, is given by: ( ) ( D ) ( r ) ( ˆ θ )( c) ψ ˆ θ 1 ˆ, ˆ, ˆ D = Δ θ θ B ρ Δ D θb ρ + α (19) where ( ) ψ θ denotes the expected profits from offering a dollar of trade credit with the inclusion of risk premium α. Given p and N, the deviant input supplier s total expected combined profits from selling the products and offering the trade credits are given by: ( ˆ θ ) ( ˆ θ M ) ( κ ) ( ˆ θ ) ( ˆ θ M ) ( κ ) ψ ( ˆ θ ) D B D B D Π =Ω p + Ω Ω p + p K N N (20) The deviant input supplier offers trade credits if and only if its total expected combined profits as defined by (20) are larger than the expected profits from selling the inputs when all firms obtain loans only from banks as defined by (16). Given zero profits for their original set of customers approved for bank loans, this holds for the deviant input supplier if and only if positive profits are generated from the additional customers with the signal θ ˆ, ˆ θd θb) as following: ( ˆ ) ( ˆ M θd θb) ( p κ) pψ ( D) Ω Ω + N ˆ θ > 0 (21) (21) is the necessary and sufficient condition for an input supplier to offer trade credits. (21) implies two necessary conditi ons. First, Ω( ) ( ˆ θ ) θˆd Ω 0 B > indicates the input supplier lowers the optimal cutoff signal for a trade credit below the optimal 23

25 cutoff signal for a bank loan. Second, ( p κ) pψ ( ˆD ) + θ > 0 indicates that the combined expected marginal profits from selling an input and offering a trade credit Ω Ω ˆ > 0 needs to be positive. When both ( θˆd ) ( θ B ) a nd ( p κ) + pψ ( ˆ θd ) > 0 are met, the necessary and sufficient condition (21) holds. A lower cutoff signal will increase the sale of product due to ( ˆ θd) Ω / ˆ θ < 0, and each additional sale generates positive profits given the positive mark-up ( p κ ) > 0. Since the gains to the additional sales are overwhelmed by loan losses beyond some level of θ, a further reduction in the cutoff signal ˆD θ is limited. The above discussion explains the input supplier s incentive to offer trade D credits. When both bank loans and trade credits are available in the perfectly competitive corporate loan m arket, the equilibrium in the monopolistically competitive input market is characterized financing available. differently from the one with only bank The equilibrium in the monopolistically competitive input market is characterized when all symmetric input suppliers offer trade credits. For the equilibrium with both bank loans and trade credits available, let ˆp and ˆN denote the symmetric zero-profit equilibrium input price and the number of input suppliers, respectively. The optimal cutoff signal for a trade cred it is denoted by ˆT θ. In the new 24

26 equilibr ium of monopolistically competitive input market, the zero-profit condition is characterized by: ( ) ( ) ˆ ˆ M ˆ ˆ ˆ Π θ =Ω θ p κ θ θ pˆ κ pˆψ ˆ θ K 0 T B Nˆ + Ω Ω + = T B Nˆ B M ( ) ( ) ( ) ( ) ( ) (22) where ψ ( θ ) ( θ θ ) ( r ) ( )( c) ˆ 1 ˆ, ˆ ˆ, ˆ T = Δ T B ρ Δ θt θb ρ + α. Note that the zero-profit condition (22) is no longer the Chamberlinian tangency condition since the expected profits of an input supplier are now composed of both the sale of products and the offering of trade credits. Each input supplier sets the cutoff signal to maximize the expected combined profits from selling products and offering trade credits to firms. The optimal cutoff signal for a trade credit, ˆT θ, is set at the level where the marginal combined profits from selling a product and offering a trade credit is zero. This optimal cutoff signal of a trade credit is characterized by: ˆ κ + ˆ Pr θt ρ 1 Pr θt ρ α + = 0 ( p ) p ( S ˆ )( r ) ( S ˆ ) ( c) (23) In comparison with ˆB θ, the optimal cutoff signal of a trade credit ˆT θ is characterized by solving (23) for Pr ( ˆ T ) S θ as following: pˆ κ ( ρ c) α Pr ( S ˆ θt ) = < Pr = r c r c pˆ ( S ˆ θb) ( ) ( ρ c) ( ) (24) 25

27 With the positive mark-up on the sale of an input ( p κ ) ˆ > 0 and the positive risk premium on a trad e credit α ( 0,1), the optimal cutoff signal for a trade credit is lower than that of a bank loan, i.e., ˆ θ < ˆ θ, in equilibrium. Proposition 1 summarizes the differential performances of a bank loan and a trade credit as follows: T B Proposition 1: The credit standard of a trade credit is lower than that of a bank loan, i.e., ˆ θ ˆ T < θb. As a consequence, the expected default rate of a trade credit is higher than that of a bank loan, i.e., Δ ˆ θ ˆ θ >Δ θ. ( T, B ) ( ˆB ) More lenient credit standard of the trade credit induces riskier borrowing firms to self-select the trade credit, leading to the separation of the corporate loan market. Trade credits service riskier pool of borrowers with θ ˆ, ˆ θt θb) while bank loans service the safer ones with θ ˆ θ B, ). Consequently, the likelihood of loan repayment of a trade credit is ( ˆ θ, ˆ ) ( ˆ T θb θb) lower than that of a bank loan. That is, Δ >Δ given the inherent relationship between the optimal cutoff signal and the likelihood of default. Given the zero-profit cutoff signal of a bank loan ˆB θ at r, the optimal cutoff signal ˆT θ for a trade credit, and other market parameters, the magnitude of expected profits from offering a trade credit ψ ( ˆT θ ) is determined by the level of risk premium 26

28 α. Noting that at r π ( ˆ θ ) 0 ( ˆ B = > π θt ), ( ˆT ) ψ θ can be (i) negative if α is too low to offset the loan losses, (ii) zero if α offsets the loan losses, and (iii) positive if α is high enough to offset the loan losses. In all three cases, the input supplier has an incentive to offer trade credits if ( pˆ κ) pˆψ ( ˆ θt ) + > 0 holds. Especially, in case of (i), the positive additional marginal profits ( p κ ) ˆ > 0 from selling a product subsidizes the lo sses from offering a trade credit ( ˆ T ) ˆ pψ θ < 0 per borrower if the necessary condition ( p κ) pψ ( ˆ θt ) ˆ + ˆ > 0 holds. With this necessary condition met, an input supplier has the incentive to subsidize the losses on offering a trade credit when it can obtain additional profits from the sale of products. Given the imperfect structure of the input market, the subsidization can be obtained through the positive mark-up ( pˆ κ ) > 0 from an additional sale of inputs since the supplier can increase the number of input buyers by offering trade credits to riskier pool of firms which cannot obtain financing from banks. In the numerical simulations, the results of comparative static s will be provided across different levels of risk premium α on the trade credit. Recall that the aggregate num ber of purchasers of inputs is M ( ˆ B =Ω θb) M when borrow ers obtain financing only from banks. When both bank loans and trade credits are now available in the corporate loan market and the input suppliers offer 27

29 trade credits to borrowing firms denied by banks, the aggregate effective number of input buyers is given by: ( ˆ θ ) ( ˆ θ ) ( ˆ θ ) ( ˆ θ ) MT = Ω T + Ω T Ω B M =Ω T M (25) Since ˆ θ T < ˆ θb, it is obvious that M ( ˆ ) ( ˆ T =Ω θt M > MB =Ω θb) M. Thus, when the trade credits are offered by the input suppliers, more firms are approved for financing than when only bank financing is available in the corporate loan market, and the total number of firms purchasing the inputs increases. With the larger aggregate number of firms purchasing the inputs, the characterization of the optimal input price is given by ( ˆ T ) MT M B ψ θ 1 MT pˆ = κ + + Nˆ 2 2 Nˆ 2 2 Nˆ ( Nˆ 1) F( v) f ( v) ˆ dv N( Nˆ 1) F( v) f ( v) dv (26) Equations (22), (23), and (26) simultaneously characterize the symmetric zero-profit equilibrium price of differentiated inputs ˆp, the symmetric zero-profit equilibrium number of input suppliers ˆN, and the optimal cutoff signal for a trade credit ˆT θ when both bank loans and trade credits are available in the corporate loan market. Note that (26) modifies (15) in that the additional term takes into account the effect of profits or losses from offering trade credits on the optimal input price. Given that the characterization of equilibrium cannot be derived in closed form solutions, this paper conducts numerical simulations to characterize the symmetric zero-profit equilibrium input price, the number of input suppliers, and the 28

30 optimal cutoff signals for a bank loans and a trade credit. Further, the numerical simulations examine the effects of various levels of risk premium α on the characterization of equilibrium in a comparative static manner. The outcomes of simulations are dependent upon the appropriate specifications of parameters in the theoretical model. Table 1 describes the parametric specifications for numerical simulations of the variables in the analytical model. Given the parametric specifications for numerical simulations in Table 1, Table 2 Panel A provides the equilibrium outcome when only bank loans are available in the corporate loan market. As shown in Table 2 Panel A, the equilibrium in the corporate loan market is characterized by the cutoff signal and the approval rate for a bank loan. The equilibrium in the monopolistically competitive input market is characterized by the zero-profit symmetric input price and the number of input suppliers. The cutoff signal and resulting loan approval rate specifies the effective number of input buyers. Table 2 Panel B reports the various levels of risk premium on trade credit α. In the numerical simulations, the equilibrium outcomes are characterized across various levels of α from 50 basis points to 150 basis points. Table 2 Panel C provides the equilibrium characterizations of a trade credit in the corporate loan market and monopolistically competitive input market when both bank loans and trade credits are available. First, when comparing the numerical simulations reported in Panel A and Panel C in Table 2, the results indicate that, as described in Proposition 1, the optimal credit standards of a trade credit (cutoff signal) for all 29

31 levels of the risk premium α are lower than that of a bank loan. The loan approval rates and the resulting expected default probabilities of a trade credit for all levels of the risk premium α are higher than those of a bank loan. The characterizations of equilibrium are summarized in Proposition 2 below: Proposition 2: As the risk premium on trade credit α increases, the cutoff signal for trade credit θˆt decreases, the number of input suppliers ˆN increases, and the input price ˆp decreases. Proposition 2 shows that the increase in α and the resulting decrease in θ raises the ˆT effective number of borrowing firms (input buyers) approved for credits, leading to the entry of more input suppliers to the industry and lowering of equilibrium input price. In the m eanwhile, the aggregate effective number of firms purchasing inputs increases. Note that the necessary and sufficient condition for offering a trade credit ( ) ( ) M ( pˆ ) pˆ ( ) 0 requires ( θ ) ( θ ) Ω ˆ θ Ω ˆ θ κ + ψ ˆ θ > T B ˆN T ( pˆ κ) pˆψ ( ˆ θt ) Ω ˆ Ω ˆ > 0 T B + > 0. In the numerical simulations, the necessary condition for offering a trade credit ( p κ) pψ ( ˆ θt ) ˆ + ˆ > 0 is met for all specifications of α. The expected profits on a trade credit vary from negative to positive amounts as α increases. Especially, if ( pˆ κ) + pˆψ ( ˆ θt ) > 0 and ( ˆ T ) ˆ pψ θ < 0, the positive mark-up 30

32 on the sale of a product subsidizes the losses on offering a trade credit while combined profits are still positive. Further, the analytical results of the model provide a lot of implication for empirical tests. Among many empirical analyses possible, we first can test whether suppliers offer trade credits to facilitate the sale of their products to riskier borrowers who have difficulty in obtaining credits from banks. Second, the difference in debt costs between bank loans and trade credits can be empirically examined. The significant difference in debt costs can shed light on the differential risk-taking behavior of banks and product suppliers and the resulting mechanism for borrowers self-selection of debt financing sources under information asymmetry in the corporate loan market. 5. Empirical Testing Strategies We propose in the theoretical section of this study that credit standard for trade credits are lower than that of bank loan credits. We test whether our data supports this by analyzing two samples from Compustat and Loan Pricing Corporation (LPC) DealScan. First we run regression with Compustat data only and later we add LPC DealScan data to create a dummy variable for bank loan access as a test of robustness. In both samples, our main test variable is equity volatility, a proxy for total risk, where equity volatility is annual standard deviations of daily returns from the Center for Research in Security Prices (CRSP). With matched sample 31

33 between Compustat and LPC DealScan, we conduct robustness checks by replacing equity volatility with the alternative risk variable, loan credit spread from loan contracts. If two variables yield positive signs consistently with different specifications in regression analyses, we can conclude that risky borrowers demand more trade credits. Our empirical model is as follows: Accounts Payable / Assets = α + β 1 (Firm risk: Equity volatility) + β 2-4 (Firm characteristics: Age, Size, Leverage) + β 5 (Need for External Financing: Capital expenditures) + β 6 (Cash availability/profitability: Net income) + β 7 (Maturity Matching: Current assets) + β 8 (Liquidity: Raw materials) + β 9-n (Control Variables: Year dummies, Industry dummies) + ε i, The dependent variable is accounts payables scaled by assets. Accounts receivables of the supplier are a proxy for how much it lends its customers, while accounts payables of the borrower/customer are the firm s borrowing from its supplier. Table 3 enumerates both dependent and explanatory variables in more details; it shows measurements and predictions. The firm s ability to generate cash internally decreases its demand for trade credit, if trade credit financing takes a lower position in the firm s pecking order structure than internally generated cash. The firms with a large financing need for growth firm first rely on internally generated cash; if international generated cash is short, then the firm relies on trade credit financing and other financing choices such as bank loans. We measure external financing need with capital expenditure from 32

34 statement of cash flows (CAPX) and expect a positive sign. Alternatively, we measures of the firm s investment opportunities with a change in sales scaled by assets [Petersen and Rajan, 1997]. We include the firm s ability to generate internal cash by taking net income divided by total assets (NI_AT). The firm s ability to generate internal cash decreases its demand for trade credit financing, and therefore, we expect a negative sign on NI_AT. A firm generally attempt match their asset maturity with liability maturity and we include a variable that measures a portion of current asset relative to total asset excluding cash (CA). We expect a positive sign, if maturity matching story is valid. Fabbri and Menichini (2010) argue that trade credit is not necessarily more expensive than bank credits because of the liquidity advantage of the supplier. If the borrowing firm s inputs are more valuable to suppliers than to banks, the liquidity advantage of the supplier can outweigh a bank s low cost of funds in lending contracts. Here, liquidity is defined as liquidity advantage from the supplier s perspectives. If the buyer s assets still preserve liquid status in re-sale market in the form of unprocessed input, they are more valuable to suppliers, if default risk of the buyers increases. Knowing this, the buyer demands more trade credit financing if a larger portion of assets constitutes liquid ones. We expect a positive sign on liquidity measure (Raw_Mat). Following the sample formation process of Petersen and Rajan (1997), we downloaded all the firms existed in Compustat database, excluding SIC code of