Inventory, Risk Shifting, and Trade Credit

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1 Inventory, Risk Shifting, and Trade Credit Jiri Chod Boston College Abstract This paper provides a new motivation for the use of trade credit based on the agency theory. Debt financing results in the well-known agency conflict between the creditor and the firm s shareholders who have the incentive to maximize the value of equity rather than total firm value. Due to limited liability, maximizing the value of equity leads to risk seeking behavior known as the asset substitution problem. Trade credit mitigates this problem because its terms are tied to the actual procurement decision and thereby prevent excessive risk taking. Whereas it is difficult for a firm to commit to value maximizing procurement decision when borrowing cash, buying on credit is in itself a commitment. We illustrate this benefit of trade credit in the context of a financially constrained retailer procuring inventory of two products under uncertain demand. When using bank financing, the retailer overinvests (underinvests) in the riskier (less risky) product where riskiness is a function of salvage value, profit margin, mean demand, and demand volatility. In contrast, a retailer relying on trade credit chooses the first-best inventory levels, for which it is rewarded by a lower cost of borrowing. Keywords: Trade credit, debt, agency, asset substitution, newsvendor model, inventory 1 Introduction Estimates suggest that about 80% of US firms offer their products on trade credit (Tirole 2006). According to Financial Times, trade credit financed about 90% of global merchandise trade in 2007, valued at about $25 trillion (Williams 2008). The question why most firms provide credit to their customers while simultaneously receiving credit from their suppliers in the presence of specialized financial intermediaries, has been puzzling financial economists for at least half a century. 1 At the same time, operations researchers have been studying the effect of trade credit financing on optimal inventory control and supply chain efficiency. 2 This paper aims to contribute to both of 1 See e.g., Petersen and Rajan (1997) and references therein. 2 See e.g., Seifert, Seifert, and Protopappa-Sieke (2013) and references therein. 1

2 these literatures. First, we provide a new motivation for the use of trade credit based on the agency theory. Second, we use a multi-item newsvendor framework to examine how the benefit oftrade credit depends on product characteristics such as profit margin, salvage value, mean demand, and demand volatility. Debt financing creates an agency conflict between the creditor (bank) and the borrower (firm) generally known as the asset substitution problem (Jensen and Meckling 1976). Due to limited liability, a firm maximizing the value of equity has an incentive to increase risk after issuing debt. Because the bank anticipates the firm s risk-seeking behavior and prices the debt accordingly, it is the shareholders who ultimately bear the agency cost of debt through a higher cost of borrowing. Consider a retailer who uses a bank loan to finance inventory of multiple different products. After obtaining the loan, the retailer has an incentive to order more of the riskier items and fewer of the safer items than what would maximize total value of equity and debt. The bank cannot prevent such behavior, but it can anticipate it and penalize it by charging a higher interest rate. The asset substitution problem cannot arise when credit is provided by the asset supplier who can determine the credit terms in response to the actual inventory decision. Consider a retailer who buys multiple items from the same supplier using trade credit. In this case, the retailer has no incentives to favor the risky products because he would be immediately punished by stricter credit terms. Instead, the retailer has incentives to order inventory that maximizes total value of equity and debt, for which he gets rewarded by a lower interest rate. Our theory is most closely related to Burkart and Ellingsen (2004) who argue that lending goods as opposed to lending cash limits the firm s ability to divert cash for private benefits such as empire building or outright company looting. In contrast to Burkart and Ellingsen, we do not assume such opportunistic behavior on the part of the firm. Instead, we show that lending goods as opposed to lending cash mitigates the agency cost of debt as soon as the firm (i) maximizes shareholder value, (ii) faces demand uncertainty, and (iii) procures multiple items from the same supplier. To demonstrate our argument in a rigorous model, we consider a retailer who orders inventory of two products from the same supplier while facing uncertain demand. Once demand is realized, the retailer sells as much inventory as possible at predetermined prices, and salvages the unsold units at given salvage values. We assume that the retailer has a limited wealth and, thus, has to use external financing. We consider two alternative sources of this financing: a fairly priced bank loan and a fairly priced trade credit provided by the supplier. The fundamental difference between bank financing and trade credit is that the bank determines the interest before the retailer makes the inventory decision whereas the trade credit terms are based on the order quantities. This 2

3 difference reflects the monitoring advantage of the supplier over the bank regarding the retailer s inventory decision. Whereas it would be difficult for a bank to implement and enforce debt covenants specifying the borrower s order quantities, 3 the supplier observes the order quantities automatically. We use a numerical study to examine how the inventory decision, cost of borrowing, and benefit of trade credit depend on product characteristics. We observe that with bank financing, the firm tends to overinvest (underinvest) in inventory of the product with the lower (higher) salvage value, higher (lower) profit margin, higher (lower) mean demand, and most interesting, lower (higher) demand volatility. In each of these instances, the firm overinvests (underinvests) in the riskier (less risky) product. The product with a lower salvage value is riskier because salvage revenue mitigates the loss in bankruptcy states. In our numerical study, the product with a higher margin, higher mean demand, or lower volatility represents a bigger inventory investment, and thus, is riskier in the sense that it is more likely to cause bankruptcy. The use of trade credit eliminates all of these distortions of the inventory decision, reduces the cost of borrowing, and increases firm value. The asset substitution problem can exist only when the assets, i.e., the inventory items, are somehow differentiated. Therefore, the greater the product variety, the greater the agency cost of bank financing, and the greater the benefit of trade credit. Relation to the Literature The existing theories explaining why firms use trade credit fall into several categories. The first category argues with a monitoring advantage of the supplier over a financial institution. There are several potential sources of this advantage. (i) The supplier may gain superior information about the credit worthiness of the buyer in the course of their business relationship (Smith 1987, Brennan, Maksimovic, and Zechner 1988, Biais and Gollier 1997, Jain 2001). (ii) The supplier of a unique input may have an advantage over a bank in controlling the buyer s behavior using the threat of cutting off future supplies (Cunat 2007). (iii) The supplier may have an advantage over a bank in salvaging the repossessed merchandise in case of the buyer s default (Frank and Maksimovic 2004, Mian and Smith 1992). Another set of explanations view trade credit as a way to price discriminate (Smith 1987, Brennan, Maksimovic, and Zechner 1988, Mian and Smith 1992). Because credit terms are often invariant to the credit quality of the buyer, trade credit reduces effective price for the low-quality borrowers who tend to be more financially constrained, and hence, more price elastic. Transaction 3 For example, Smith and Warner (1979) find that debt covenants restricting production or investment policy would be expensive to employ and are not observed. 3

4 cost based explanations recognize that trade credit enables separating flows of money from the flows of goods, which can be highly volatile or seasonal. This separation allows firms to reduce precautionary money holdings (Ferris 1981). Emery (1984) argues that trade credit financing enables firms to circumvent noncompetitive rents of financial institutions. According to Emery (1987), a supplier can use trade credit to smooth out demand variability and thereby reduce inventory cost. One stream of literature considers trade credit to be a guarantee, or a signal, of product quality provided by the supplier to the buyer (Smith 1987, Lee and Stowe 1993, Long, Malitz, and Ravid 1993, and Babich and Tang 2012). Wilner (2000) recognizes the importance of long-term business relationships, which force dependent sellers-creditors to grant more concessions in debt renegotiation than a bank. This induces buyers to use trade credit even if it comes at a higher cost relative to bank financing. Kim and Shin (2012) argue that trade credit binds the interests of individual firms with those of the supply chain as a whole and thereby mitigates moral hazard problems. Petersen and Rajan (1997) test the various motivations using small business survey data, and conclude that trade credit is likely to serve multiple purposes. To the best of our knowledge, the only article that develops an agency-based theory of trade credit is Burkart and Ellingsen (2004). As they point out, the aforementioned theories are not without shortcomings: [Monitoring advantage theories] do not explain why suppliers regularly lend inputs, but only very rarely lend cash.... Price discrimination theories cannot account for trade credit in competitive markets; the collateral liquidation theory cannot account for trade credit in service industries; product quality theories cannot account for trade credit in homogeneous goods industries, and the long-term relationship theory cannot account for trade credit in single business transactions. Burkart and Ellingsen propose a theory that can explain the use of trade credit in all those instances by identifying a monitoring advantage of the supplier that applies exclusively to input transactions. The advantage of loaning inputs (trade credit) rather then cash (bank financing) is that inputs are less liquid and therefore less easily diverted for private benefits of the entrepreneur or manager than cash is. Similar to Burkart and Ellingsen, we recognize that trade credit alleviates a possible agency conflict between the borrower and the lender. However, rather than assuming an opportunistic entrepreneur/manager who is able to divert cash for private benefits, we consider sourcing of multiple items under demand uncertainty, which is enough to create an agency problem that trade credit can eliminate. This problem, known as asset substitution, was first described by Jensen and Meckling (1976) and has received a considerable attention in the literature since (see e.g., Leland 1998 and the references therein). Nevertheless, we believe our paper to be the first to recognize mitigation of 4

5 the asset substitution problem as a potential benefit of trade credit financing. In the empirical literature, Huyghebaert and Van de Gucht (2007) find evidence that risk shifting incentives have a negative impact on bank debt and a positive impact on leasing and trade credit as proportions of total debt. They measure risk shifting incentives by industry-wide asset liquidity multiplied by historical bankruptcy rate, and explain its impact on the use of trade credit by pointing out that trade credit generally is very short-term debt, and therefore less subject to information and incentive problems. In a recent empirical study of the relation between trade credit terms and buyer and supplier characteristics, Klapper, Laeven, and Rajan (2012) demonstrate that discounts for early payment tend to be offered to riskier buyers, indicating that the trade credit interest reflects the buyer s credit risk. Trade credit has also received a considerable attention in the operations management literature, which has mainly addressed its effect on optimal inventory control (Haley and Higgins 1973, Jaggi, Goyal, and Goel 2008, Gupta and Wang 2009, Luo and Shang 2013) and supply chain performance (Chaharsooghi and Heydari 2010, Lee and Rhee 2010). The supply chain literature that compares tradecreditwithbankfinancing includes Kouvelis and Zhao (2012) who model the strategic interaction between a newsvendor-like retailer and its supplier, both of which are financially constrained and face bankruptcy risk. They characterize the optimal trade credit contract from the supplier s perspective, and show that the retailer always prefers this contract to bank financing, and that trade credit improves supply chain efficiency. Yang and Birge (2011a) consider the interaction between a supplier and a newsvendor-like retailer who finances inventory using the optimal mix of cash, trade credit, and short-term debt. They demonstrate, among others, that trade credit enhances supply chain efficiency by serving as a risk-sharing mechanism. In particular, trade credit shifts some of the inventory risk from the retailer to the supplier, which induces the retailer to increase the order quantity. Dong, Guo, and Turcic (2013) consider alternative supply chain contracts between a manufacturer and his retailer(s) while considering product market competition. They show that a manufacturer may extend trade credit to a retailer even in the absence of both budget constraint and market frictions in order to increase retailer s aggressiveness. Seifert et al. (2013) provide a comprehensive survey of the trade credit literature spanning all disciplines. As they point out, most existing trade credit models focus on a single product setting. We show that considering multiple products makes a qualitative difference because of the additional benefit of trade credit in alleviating the asset substitution problem. The literature that recognizes operational implications of the asset substitution problem includes Chod and Zhou (2014) who 5

6 examine substitution between product-flexible and product-dedicated capacity. Finally, our work is related to Van Mieghem (2007) and Chod, Rudi, and Van Mieghem (2010) who examine the role of risk in multi-item newsvendor networks. Whereas this literature assumes a risk-averse decision maker, we endogenize risk attitude by taking into account external financing and bankruptcy risk. 2 Model In the following, E denotes expectation, bold font denotes vectors, and prime denotes transpose. We assume that all agents are risk-neutral, and banks as well as suppliers can access capital at the risk-free rate, which we normalize to zero. Consider a retail firm that is a price-taker in both input and output markets, and has to order inventory of two products while customer demand is uncertain. We denote the order quantities, unit costs, and product demands as Q =( 1 2 ) 0 c =( 1 2 ) 0 and D =( 1 2 ) 0 respectively. Demand is allowed to follow an arbitrary continuous distribution over R 2 +, and we denote its mean vector and covariance matrix as μ =( 1 2 ) 0 and µ 2 Σ = respectively. Once demand is realized, the firm sells quantities min( ), 2 = 1 2 at regular prices p = ( 1 2 ) 0 and salvages the unsold inventory min ( ), = 1 2 at salvage values s = ( 1 2 ) 0 The firm s sales revenue is thus equal to (D Q) = P 2 =1 ( min( )+ ( min ( ))) To avoid trivial scenarios, we assume =1 2 If we partition the state space of the demand vector, R 2 + into the following four events and Ω 0 (Q) ={D 0 : =1 2} Ω 1 (Q) ={D 0 : } Ω 2 (Q) ={D 0 : } Ω 3 (Q) ={D 0 : =1 2} (1) we can also write the sales revenue as (D Q) =s 0 Q+ (p s) 0 D if D Ω 0 (Q) (p s) 0 ( 1 2 ) if D Ω 1 (Q) (p s) 0 ( 1 2 ) if D Ω 2 (Q) (p s) 0 Q if D Ω 3 (Q) (2) These events are illustrated in Figure 1a. If D Ω 0 both demands are relatively low and, therefore, some inventory of each product has to be salvaged. If D Ω 1 (Ω 2 ), demand for product 2 (1) is relatively low so that some inventory of this product has to be salvaged, whereas demand for 6

7 (a) (b) D 2 D b 2a 3a Q 2 Q 2 0a 0 1 1a L r p1q 1 s2q p s b 1b Q 1 D 1 L r s1q 1 p2q p s Q 1 D 1 Figure 1: (a) Partitioning of the demand state space as defined in (1). (b) Partitioning of the demand state space as defined in (16). The shaded area corresponds to the bakruptcy event Ω product 1 (2) is so high that its entire inventory can be sold at the regular price. Finally, if D Ω 3 demand for each product exceeds the existing inventory,all ofwhichcanbethereforesoldatthe regular price. It is also useful to define Ω 12 Ω 1 Ω 2 Ω 123 Ω 1 Ω 2 Ω 3 etc.. Let be the firm s remaining wealth after all non-inventory costs have been incurred. Assuming that this wealth does not suffice to finance the entire inventory investment, i.e., c 0 Q we consider two forms of external financing: bank loan and trade credit. 2.1 Bank Financing Suppose that before buying the inventory, the firm borrows dollars from a bank, promising to repay + dollars once the selling season is over. We assume that the firm is not allowed to pay dividends before repaying the debt. 4 This means that the firm has no incentives to borrow more than what it needs to finance inventory, i.e., + = c 0 Q (3) 4 In practice, this is typically ensured through debt covenants requiring that dividends be paid only from earnings generated subsequent to borrowing or earnings above a given amount (see, e.g., Smith and Warner 1979). 7

8 It is unusual for debt covenants to prescribe a specific operationalpolicy,soweassumethatitis within the firm s discretion how to allocate the available capital + betweentheinventoryof the two products. Depending on the realized demand, the firmmayormaynotbeabletorepaythedebtinfull. Thus, we distinguish two events: (a) If (D Q) +, the sales revenue is sufficient to repay the debt in full. The value of debt is + whereas the value of equity is (D Q) (b) If (D Q) +, thefirm is unable to repay the debt in full, declares bankruptcy, and is taken over by the lender. Assuming a fixed bankruptcy cost denoted as, thepayoff to the lender is (D Q) 5 The equity becomes worthless. We denote the domains of the demand state space corresponding to these two events as Ω and Ω respectively, so that subscript is mnemonic for bankruptcy. Superimposing these two events on the four events Ω 0 Ω 3 so that e.g., Ω 0 Ω 0 Ω we can distinguish seven events, which are formally defined in the Appendix and illustrated in Figure 1b. In this figure, the shaded area indicates the demand realizations leading to bankruptcy. Following the literature (e.g., Biais and Gollier 1997, Wilner 2000, Burkart and Ellingsen 2004), we assume a competitive credit market, which ensures that debt is fairly priced, i.e., the bank expects to make zero profit. The bank is repaid principal plus interest, + if D Ω and it receives the firm s sales revenue minus the bankruptcy cost, if D Ω. Therefore, fair pricing requires that =Pr(Ω )( + )+Pr(Ω ) E ( Ω ) (4) We also assume that the firm is fully controlled by shareholders who maximize the expected terminal value of equity, which we denote by. Because the value of equity is if D Ω and it is zero if D Ω,wehave =Pr(Ω ) E ( Ω ) (5) The firm s choice of optimal debt and inventory is a two-stage decision problem. In the second stage, the loan terms ( ) are given, and the firm chooses the optimal inventory levels. Using 5 Whether the bankrupcty involves reorganization (Chapter 11) or liquidation (Chapter 7), it involves considerable legal and accounting fees as well as fees to government agencies (e.g., Ang et al. 1982). 8

9 the superscript to denote the optimal solution in the bank financing scenario, the second-stage problem can be written as Q ( ) = arg max (Q ) subject to (3). (6) Q 0 In the first stage, the firm chooses the optimal loan amount, taking into account the interest determined by the bank according to (4). In this stage, both the firm and the bank anticipate the firm s second-stage inventory choice (6). Formally, we have =argmax 0 ( ( ) Q ( ) ) (7) where ( ) and Q ( ( )) satisfy (4) together with (6). The next proposition characterizes the optimal loan and inventory levels assuming that they are all positive. Proposition 1 For any given loan amount the optimal inventory Q ( ) and interest ( ) must satisfy Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 = Pr (Ω 23 ) 2 +Pr(Ω 01 ) 2 (8) 1 2 together with (3) and (4). The optimal loan amount satisfies µ Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 =Pr(Ω ) 1+ ( ) (9) 1 The optimality condition (8) provides the rule according to which the firm allocates the available capital between the inventory of the two products. It ensures that the expected payoff of the last dollar invested in the inventory of each product is the same. This payoff depends on the regular product price, the probability that the last unit will be sold at the regular price, the salvage value, the probability that the last unit will be salvaged, and the unit cost. Most important, when the firm calculates these expected payoffs, it takes into account only non-bankruptcy states, Ω. This is because the revenue realized in bankruptcy states accrues to the bank and not to the shareholders. Although the revenue that the bank expects to earn in bankruptcy states affects the interest and thereby the value of equity, it is irrelevant for the inventorydecision. Thereasonisthatbythetimethefirm chooses inventory, the interest has been already determined. The optimality condition (9) equates the expected benefit and cost of the last dollar borrowed. The left-hand side of (9) is the expected revenue that will accrue to the shareholders as a result of increasing the loan by one dollar. The right-hand side of (9) is the corresponding increase in the loan principal and interest that the shareholders expect to repay. In the next section, we consider an alternative scenario in which the loan is provided by the inventory supplier. 9

10 2.2 Trade Credit Suppose, once again, that the firm orders inventory Q at the unit costs c while its wealth is less than the total inventory cost Q0c. Suppose further that both items are ordered from the same supplier. In this section, we assume that the loan = Q0c is provided by the supplier in the form of trade credit. The interest is again denoted as so the firm pays the supplier upfront and + at the end of the selling season. 6 As is common in the finance and economics literatures (e.g., Biais and Gollier 1997, Burkart and Ellingsen 2004), we assume that the supplier is competitive and, similar to the bank, makes zero expected profit from providing credit. This means that the trade credit interest has to satisfy the fair pricing constraint (4). The fundamental difference between bank financing and trade credit is that the supplier can make the credit terms contingent on the order quantities. The firm orders inventory Q and simultaneously requests trade credit in the amount of = Q0c The supplier responds by setting a fair interest according to (4). Using superscript TC for the optimal solution in the trade credit scenario, the firm s decision problem can be written as Q =arg max Q (Q) (Q) (10) Q 0 where the value of equity is given by (5), and the credit terms, (Q) and (Q), aregiven by (3)-(4). The next proposition characterizes the solution to (10) when the optimal inventory levels as well as trade credit are positive. Proposition 2 For any given inventory vector Q, trade credit (Q) and interest (Q) are given by (3)-(4). The optimal inventory vector Q satisfies µ Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 = Pr(Ω ) 1 + (Q) (11) 1 µ and Pr (Ω 23 ) 2 +Pr(Ω 01 ) 2 = Pr(Ω ) 2 + (Q) 2 (12) The optimality conditions (11)-(12) equate the revenue from the last unit of inventory of each product that the firm expects to receive, and the corresponding increase in the principal and interest that the firm expects to repay. Before comparing the trade credit and bank financing scenarios, 6 This contract corresponds to a common form of trade credit terms known as two-part terms, which specifies the early payment discounted price, the discount period, the payment due date, and the effective interest rate (Klapper, Laeven, Rajan 2012). In our model, c is the vector of the discounted prices for upfront payment, is the interest rate, and the due date is the end of the selling season. 10

11 we need to define some notation. Namely, we let Q and (Q ) be the optimal loan principal and the corresponding fair interest under trade credit financing, and we let Q Q ( ) and ( ) be the optimal inventory and the corresponding fair interest under bank financing. The next proposition formalizes the advantage of using trade credit. Proposition 3 Compared to bank financing, the use of trade credit leads to a higher expected value of equity. Q Q The benefit of trade credit stems from eliminating the agency cost involved in bank financing. Once the firm obtains a bank loan, it chooses inventory that maximizes the value of equity while ignoring the value of debt. Because the bank can anticipate this, it prices the loan accordingly. The resulting loss of total firm value, known as the agency cost of debt, is thus ultimately born by the firm through a higher cost of borrowing. There is no agency cost associated with trade credit because the trade credit interest is contingent on the inventory decision. The firm knows that taking too much risk when making the inventory decision would automatically result in less favorable credit terms. The order quantities that maximize the value of equity are those that maximize total firm value. The difference between the two financing methods becomes most transparent in the absence of bankruptcy cost. We consider this special case because the simplified optimality conditions provide us with useful intuition regarding how exactly the agency conflict distorts the inventory decision. Corollary 4 In the absence of bankruptcy cost, a firm relying on trade credit financing chooses the same inventory levels as an all-equity firm. Namely, the optimal inventory Q is given by Pr ( )= =1 2 (13) When bankruptcy is costless, a firm relying on trade credit chooses the inventory of each product according to the standard newsvendor formula. The optimality conditions (13) can be combined into Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 = Pr (Ω 23) 2 +Pr(Ω 01 ) 2 (14) 1 2 Equation (14) provides the rule according to which the firm allocates the total inventory investment, + between the inventory of the two products. At optimality, the expected revenue from the last dollar invested in the inventory of each product has to be the same. Recall the analogous rule that we established in Proposition 1 for the bank financing scenario: Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 = Pr (Ω 23 ) 2 +Pr(Ω 01 ) 2 (15)

12 The difference between the two allocation rules, (14) and (15), is that a bank-financed firm takes into account only the revenue that accrues to shareholders, i.e., the revenue generated in non-bankruptcy states Ω. By taking a closer look at these rules, we can obtain some intuition about how exactly bank financing distorts the inventory decision. First of all, a bank-financed firm ignores the salvage revenue generated in bankruptcy states Ω, and therefore, it underestimates the total benefit of salvage value. As a result, we would expect that bank financing distorts the inventory mix in favor of the product with a lower salvage value, ceteris paribus. When evaluating the regular sales revenue, a bank-financed firm ignores the revenue generated in bankruptcy states Ω 1 and Ω 1 Suppose that in the trade credit scenario, product 1 is riskier in the sense that Pr(Ω 2 ) Pr(Ω 1 ), i.e., Pr(low sales of product 1 lead to bankruptcy while product 2 is sold out) Pr(low sales of product 2 lead to bankruptcy while product 1 is sold out). Even though the firm undervalues revenue from both products, it especially undervalues the revenue from product 2, i.e., the less risky of the two products. We would therefore expect a bank-financed firm to adjust the inventory mix in favor of the riskier product, i.e., the one that is in itself more likely to cause bankruptcy. Intuitively, a product that is more profitable or more demanded and, therefore, represents a bigger inventory investment, is the one that has a higher potential to bring about bankruptcy. In the next section, we verify our intuition and compare inventory levels, credit terms, and firm values in the bank financing and trade credit scenarios using a numerical simulation. 3 Numerical Analysis When the two products have all parameters identical ( 1 = 2 1 = 2 1 = 2 etc. ), they are equally risky and the asset substitution problem, or favoring the riskier product, is not an issue. The firm orders the same quantity of each product regardless of the financing method, so there is no benefit of using trade credit. This benefit exists only when the products are not alike. We examine how exactly the asymmetry in various product characteristics affects the inventory decision, cost of borrowing, and the benefit of using trade credit in a series of numerical experiments. In each of these experiments, we start with a base case, in which all parameters are the same for both products, and thus, 1 = 2 = 1 = 2. We then examine the impact of changing various parameters of product 2 such as (i) salvage value, (ii) profit margin, (iii) mean demand, and (iv) demand variability, always one at a time. We assume that demand follows a bivariate lognormal distribution and we use the following 12

13 base-case parameter values: =1 =1 2 =0 = 100 and =75for =1 2; =0 = 5, and { } Thereasonwhyweusearelativelylowprofit margin and a relatively high coefficient of variation of demand is that we want to capture situations, in which the bankruptcy risk, and therefore, the agency cost of debt are considerable. In our model, this isthecasewhenprofit margins are relatively low and demand variability is relatively high. With our base-case parameter values, the probability of bankruptcy ranges between 8-11%, depending on demand correlation. As we show below, at this level of bankruptcy risk, the benefit ofusing trade credit is indeed considerable. Recall that is the firm s wealth available to finance inventory. Thus, setting =0means that the firm s own capital covers all non-inventory costs, whereas the inventory is financed entirely by debt (trade credit or bank loan). When 0 i.e., the inventory is partially financed by the firm s own capital, our results are qualitatively the same, but of a smaller magnitude. Our choice of bankruptcy cost, =5 means that at the base-case parameter values, the bankruptcy cost represents, depending on demand correlation, % of the expected firmvalueatdefault, E ( Ω ) This is in line with empirical data. For example, Bris, Welch and Zhu (2006) estimate the default cost to vary between 0 20% of the firm value at default. Although we ran all of our numerical experiments for three different values of demand correlation, we only show results for the correlation at which the agency cost is most significant, and which we indicate in the figure captions. Finally, the numerical study is based on simulating 100,000 bivariate demand scenarios, and the optimization is done directly using Global Search algorithm in Matlab. Next, we present our numerical results starting with the effect of salvage value. 3.1 Salvage Value The effect of salvage value is illustrated in Figure 2. When 2 = 1 =0 the products are identical and the firm orders the same quantity of each. As 2 increases, product 2 becomes more attractive and its optimal inventory level increases (Figure 2a). The higher salvage value of product 2 reduces the bankruptcy risk, and hence, the interest rate, (Figure 2b). The lower cost of capital together with the higher salvage value of one of the products, result in a larger total inventory investment and the corresponding loan, = c 0 Q (Figure 2c). The lower cost of capital means that the firm increases the order quantities of both products, but the increase is more significant for product 2 whose salvage value has increased (Figure 2a). Although all of these effects are similar in both financing scenarios, they have a different magnitude. When a firm chooses inventory after securing a bank loan, it disregards the revenue generated 13

14 120 (a) Inventory Levels 3% (b) Interest Rate % (%) % (%) s 2 s 2 0% (c) Total Inventory Investment (Borrowing) 6% (d) Relative Benefit of Trade Credit 140 5% % % 2% 1% (%) 0 s 0% 2 s Figure 2: The effect of increasing salvage value, 2, on (a) optimal inventory levels, Q, (b) interest rate, (c) total inventory investment c0q =, and (d) the relative benefit of using trade credit, ( ) for =

15 60 (a) Inventory Levels 8% (b) Relative Benefit of Trade Credit 6% (%) 40 4% 20 2% p 2 p 2 0% Figure 3: The effect of price, 2, on (a) optimal inventory levels, Q, and (b) the relative benefit of using trade credit, ( ) for = 0 5 in bankruptcy states. A bank-financed firm thus undervalues the salvage revenue and, as a result, underinvests in the product with a higher salvage value, 2 2, and overinvests in the product with a lower salvage value, 1 1 (Figure 2a). Because the bank anticipates this distortion of the firm s inventory decision, it charges a higher interest rate compared to the trade credit rate (Figure 2b), to which the firm responds by borrowing and investing less (Figure 2c). Finally, Figure 2d shows the percentage increase in firm value resulting from the use of trade credit as opposed to bank financing, 100%. As the salvage value of product 2 increases, so does the difference in the riskiness of the two products. As a result, the asset substitution problem becomes more significant, and the benefit of using trade credit increases. 3.2 Profit Margin To study the effect of asymmetry in profit margins,westartwiththebasecaseandvarythe regular price of product 2, 2, as shown in Figure 3. When 2 = 1 =1 2 the order quantities of the two products are equal in both financing scenarios, and there is no benefit of using trade credit. When 2 6= 1, a bank-financed firm overinvests in the high-margin, high-inventory product and underinvests in the low-margin, low-inventory product, as shown in Figure 3a. The product that is less profitable, and thus, represents a smaller portion of the inventory investment is unlikely to cause bankruptcy no matter how poorly it sells, as long as the high-margin, high-inventory product sells 15

16 70 (a) Inventory Levels 8% (b) Relative Benefit of Trade Credit % 40 4% % (%) % Figure 4: The effect of mean demand, 2, on (a) optimal inventory levels, Q, and (b) the relative benefit of using trade credit, ( ) for = 0 5. out. In this sense, the low-margin, low-inventory product is less risky. Because a bank-financed firm seeks risk, it adjusts the inventory mix in favor of the high-margin, high-inventory product. The larger the asymmetry in profit margins, the larger the distortion of the inventory decision under bank financing (Figure 3a), and the larger the benefit of trade credit (Figure 3b). Our numerical experiments also indicate that whenever 1 6= 2 the use of trade credit reduces the cost of borrowing,, and increases the total inventory investment, c 0 Q. 3.3 Mean Demand The effectofasymmetryinmeandemandisshowninfigure4. At 2 = 1 = 100 there is no difference between the two products or between the two financing scenarios. The effect of asymmetry in mean demand is very similar to that of asymmetry in profit margins. The product with a lower mean demand, and thus, a lower inventory level is less risky, in the sense that its low sales are unlikely to cause bankruptcy when the more important product sells out. Therefore, abank-financed firm, which seeks risk, overinvests in the high-demand, high-inventory product, and underinvests in the low-demand, low-inventory product, as shown in Figure 4a. Figure 4b illustrates how this distortion of the inventory decision impacts firm value. 16

17 60 (a) Inventory Levels 1.2% (b) Relative Benefit of Trade Credit (%) 0.9% % % % Figure 5: The effect of demand volatility, 2, on (a) optimal inventory levels, Q, and (b) the relative benefit of using trade credit, ( ) for = Demand Volatility Figure 5 illustrates the effectofasymmetryindemandvolatilities. At 2 = 1 =75 there is no difference between bank financing and trade credit financing. When 1 6= 2 the product with more uncertain demand represents a smaller portion of the total inventory (Figure 5a). Contrary to intuition, this product is less risky because no matter how poorly it sells, it is unlikely to cause bankruptcy as long as the other product, which represent a larger inventory investment, sells out. A bank-financed, risk-seeking firm therefore overinvests in the low-volatility product and underinvests in the high-volatility product as shown in Figure 5a. Theresultthataleveredfirm overinvests in the low-volatility product and underinvests the high-volatility product is not what we would have expected. It is one of the tenets of the corporate finance theory that debt leads to risk seeking (Jensen and Meckling, 1976). In our setting, this is still the case. However, we observe that the product with more volatile demand can be less risky when it represents a smaller portion of the inventory investment, and therefore, its low sales are unlikely to cause bankruptcy. We expected to observe the opposite effect for high-margin products whose optimal inventory increases in demand volatility (in which case the riskier product would be the one with higher demand volatility). However, in our numerical experiments based on lognormal demand distribution, optimal inventory does not increase in demand volatility unless the critical ratio ( ) & 0 8, 17

18 i.e., & 5 With such high profit margins, the firm cannot go bankrupt with one of the products being sold out (Pr (Ω 12 )=0), in which case asymmetry in demand volatility alone does not result in asset substitution. In other words, we did not find any parameter combination for which we wouldobserveresultscontrarytothoseshowninfigure5. 4 Concluding Remarks The contribution of this paper is twofold. First, it shows how debt financing distorts the inventory decision of a multi-item newsvendor when products differ in financial or demand parameters. Second, it demonstrates that this distortion disappears when the inventory is financed by trade credit as opposed to a conventional bank loan. By borrowing goods rather than borrowing cash, the firm is able to commit to the first-best inventory decision. This commitment reduces the creditor s risk, cost of borrowing, and increases firm value. In contrast to most existing trade credit theories based on a monitoring advantage of the supplier, our theory can explain why suppliers usually lend goods, but rarely lend cash. This benefit of trade credit does not apply only to newsvendor-type inventory problems. It exists whenever a firm chooses among multiple inputs provided by the same supplier, and needs to rely on external financing. Consider a manufacturer choosing between two production technologies offered by the same engineering company. Suppose further that the value maximizing technology is less risky, whereas the alternative has a higher upside potential. A bank-financed firm may choose the riskier technology, betting the bank s money on the upside potential. When using trade credit financing, the firm has the incentive to choose the value maximizing technology, for which it will be rewarded by more favorable credit terms. The aforementioned benefit of trade credit is obviously only one of many factors determining a firm s choice of financing. In reality, other factors are likely to come into play. For example, a bank may enjoy a lower cost of capital than the supplier, the supplier may have an informational advantage over the bank, the supplier may be able to recover a higher salvage value from unsold inventory in case of default, etc. We did not try to capture all of the potential differences between trade credit and bank financing, most of which have been examined in the literature. Our goal was to formulate the simplest model possible that would demonstrate the role of trade credit in mitigating the asset substitution problem. Nevertheless, our model relies on several assumptionsthatlimititsscope. First,weassumethat trade credit fairly priced. This assumption is critical because it ensures that the firm is rewarded 18

19 for mitigating risk. It also means that our model applies to markets where competition forces the suppliers to provide credit at their marginal cost of capital. Second, we take the wholesale price as given, which implicitly assumes that the buyer is not large enough to affect this price. In other words, our model assumes a competitive input market in which neither the buyer nor the supplier can affect the price or the credit terms. This is in contrast to Kouvelis and Zhao (2012) and Yang and Birge (2011a) who model the strategic interaction between a buyer and a supplier-creditor that has a monopoly power. Finally, we assume that both products are sourced from the same supplier. This is critical for the firm s ability to commit to the first-best inventory mix when the credit terms are being determined. Our intuition is that sourcing from multiple suppliers will still mitigate, but not entirely eliminate asset substitution. The issue is not trivial because it depends, among others, on the repayment priority rules applied in the case of default (see Yang and Birge 2011b, and the references therein), and we leave it for future research. Appendix The seven domains of the demand state space: Ω = = are defined as follows: Ω 0 = D 0 : D Q (p s) 0 D + s 0 Q + ª Ω 0 = D 0 : D Q (p s) 0 D + s 0 Q + ª ½ ¾ Ω 1 = D 0 : ½ Ω 1 = D 0 : ¾ ½ ¾ Ω 2 = D 0 : ½ Ω 2 = D 0 : ¾ Ω 3 = {D 0 : D Q} (16) ProofofProposition1: The second-stage problem (6) can be written as 1 ( ) = arg max ( 1 2 ( 1 ) ) s.t where 2 ( 1 )= Assuming Q ( ) 0 the first-order condition for 1 ( ) is 1 19

20 1 =0. The objective function defined in (5) can be expanded using (2) and (16) as µ µ = Pr(Ω 0 ) E ( 1 1 ) Ω0 µ µ Pr(Ω 1 ) E Ω1 µ Pr(Ω 2 ) E ( 1 1 )+ 2 2 Ω2 µ Pr(Ω 3 ) E Ω3 (17) Differentiating (17) with respect to 1 we obtain µ µ µ µ =Pr(Ω 0 ) 1 2 +Pr (Ω 1 ) 1 2 +Pr (Ω 2 ) 1 2 +Pr (Ω 3 ) Thus, the first-order condition for 1 ( ), 1 =0 can be written as in (8). In addition, Q ( ) has to satisfy the financing constraint (3) and ( ) has to satisfy the fair pricing constraint (4). The first-stage problem (7) can be written as =argmax 0 ( ( ) Q ( )), where Q ( ) and ( ) are given jointly by (8) together with (3) and (4). The optimal 0 must satisfy the first-order condition =0 (ThisisbecauseQ is an interior solution, and thus, Q ( ) as well as ( ( ) Q ( )) are differentiable in at ). We have = = Pr (Ω ) Pr (Ω ) + 1 (Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 )+ 2 (Pr (Ω 23 ) 2 +Pr(Ω 01 ) 2 ) Using (8), this can be rewritten as = Pr (Ω ) Pr (Ω ) Using (3), this further simplifies into + (c0 Q) Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 1 = Pr (Ω ) Pr (Ω ) + Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 and the optimality condition =0can be written as in (9). Proof of Proposition 2: The optimal Q 0 has to satisfy the first-order conditions =0, =1 2 where is given by (5), and where (Q) and (Q) embedded in are given 1 20

21 by (3)-(4). Differentiating with respect to 1 we obtain = = Pr(Ω 13 ) 1 +Pr(Ω 02 ) 1 1 Pr (Ω ) Pr (Ω ) 1 Therefore, the first-order condition 1 =0can be written as (11). Similarly, we can rewrite 2 =0as (12). ProofofProposition3: In the trade credit scenario, the optimal inventory and the corresponding loan and interest maximize the value of equity subject to the financing and fair pricing constraints, i.e., Q =arg max (Q ) s.t. (3) and (4). Q 0 In the bank financing scenario, the optimal inventory and loan, and the corresponding interest maximize the value of equity subject to the financing, fair pricing, and second-stage incentivecompatibility constraints, i.e., Q =arg max Q 0 (Q ) s.t. (3), (4), and (6). Because the bank financing scenario involves an additional constraint, it generally leads to a lower value of the objective function. ProofofCorollary4: Suppose =0 From Proposition 2, we know that Q satisfies µ Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 = Pr(Ω ) 1 + (Q) (18) 1 where (Q) satisfies µ and Pr (Ω 23 ) 2 +Pr(Ω 01 ) 2 = Pr(Ω ) 2 + (Q) 2 The implicit differentiation of (20) yields (19) 0=Pr(Ω ) +Pr(Ω ) E c 0 Q + Ω (20) (Q) = Pr (Ω 1 ) 1 +Pr(Ω 02 ) 1 Pr (Ω ) 1 1 Pr (Ω ) and (Q) = Pr (Ω 2 ) 2 +Pr(Ω 01 ) 2 Pr (Ω ) 2 2 Pr (Ω ) Hence, the optimality conditions for Q (18)-(19) simplify into Pr (Ω 13 ) 1 +Pr(Ω 02 ) 1 = 1 and Pr (Ω 23 ) 2 +Pr(Ω 01 ) 2 = 2 21

22 This can be further rewritten as (13), which are the optimality conditions of a standard profitmaximizing newsvendor. References Ang J.S., Chua J.H., McConnell J.J The administrative costs of corporate bankruptcy: A note. Journal of Finance 37(1) Babich, V., C.S. Tang Managing opportunistic supplier product adulteration: Deferred payments, inspection, and combined mechanisms. Manufacturing & Service Operations Management 14(2) Biais, B., C. Gollier Trade credit and credit rationing. Review of Financial Studies 10(4) Bougheas, S., S. Mateut, P. Mizen Corporate trade credit and inventories: New evidence of a trade-off from accounts payable and receivable. Journal of Banking & Finance 33(2) Brennan, M.J., V. Maksimovic, J. Zechner Vendor financing. Journal of Finance 43(5) Bris, A., I. Welch, N. Zhu The costs of bankruptcy. Journal of Finance 61(3) Burkart, M., T. Ellingsen In-kind finance: A theory of trade credit. American Economic Review 94(3) Chaharsooghi, S.K., J. Heydari Supply chain coordination for the joint determination of order quantity and reorder point using credit option. European Journal of Operational Research 204(1) Chod, J., N. Rudi, J.A. Van Mieghem Operational Flexibility and Financial Hedging: Substitutes or Complements? Management Science 56(6) Chod, J., J. Zhou Resource flexibility and capital Structure. Forthcoming in Management Science. Cunat, V.M Trade credit: Suppliers as debt collectors and insurance providers. Review of Financial Studies 20(2)

23 Dong, L., X. Guo, D. Turcic Push, pull, and trade credit contracts in competitive markets. Working paper, Washington University in St.Louis. Elliehausen, G. E., J. D.Wolken The demand for trade credit: An investigation of motives for trade credit use by small businesses. Working Paper, Board of Governors of the Federal Reserve System. Emery, G.W A pure financial explanation for trade credit. Journal of Financial and Quantitative Analysis 19(3) Emery, G.W An optimal financial response to variable demand. Journal of Financial and Quantitative Analysis 22(2) Ferris, J.S A transactions theory of trade credit use. Quarterly Journal of Economics 96(2) Frank, M., V. Maksimovic Trade credit, collateral, and adverse selection. Working paper, University of Maryland. Giannetti, M Do better institutions mitigate agency problems? Evidence from corporate finance choices. Journal of Financial and Quantitative Analysis 38(1) Giannetti, M., M. Burkart, T. Ellingsen What you sell is what you lend? Explaining trade credit contracts. Review of Financial Studies 24(4) Gupta, D., L. Wang, A stochastic inventory model with trade credit. Manufacturing & Service Operations Management 11(1) Haley, C.W., R.C. Higgins Inventory policy and trade credit financing. Management Science 20(4) Huyghebaert, N., L.M. Van de Gucht The determinants of financial structure: New insights from business start-ups. European Financial Management 13(1) Jaggi, C.K., S.K. Goyal, S.K. Goel Retailer s optimal replenishment decisions with creditlinked demand under permissible delay in payments. European Journal of Operational Research 190(1) Jain, N Monitoring costs and trade credit. Quarterly Review of Economics and Finance 41(1)

24 Jensen, M.C., W.H. Meckling Theory of the firm: Managerial behavior, agency costs and ownership structure. Journal of Financial Economics 3(4) Kim, S-J., H.S. Shin Sustaining production chains through financial linkages. American Economic Review 102(3) Klapper, L., L. Laeven, R. Rajan Trade credit contracts. Review of Financial Studies 25(3) Kouvelis, P., W. Zhao Financing the newsvendor: Supplier vs. bank, and the structure of optimal trade credit contracts. Operations Research 60(3) Lee, C.H., B-D. Rhee Coordination contracts in the presence of positive inventory financing costs, International Journal of Production Economics 124(2) Lee, Y.W., J.D. Stowe Product risk, asymmetric information, and trade credit. Journal of Financial and Quantitative Analysis 28(2) Leland, H.E Agency costs, risk management, and capital structure. Journal of Finance 53(4) Long, M.S., I.B. Malitz, S.A. Ravid Trade credit, quality guarantees, and product marketability. Financial Management 22(4) Luo, W., K. Shang Managing inventory for entrepreneurial firms with trade credit and payment defaults. Working paper, Duke University. Mian, S.L., C.W. Smith Accounts receivable management policy: Theory and evidence. Journal of Finance Nilsen, J.H Trade credit and the bank lending channel. Journal of Money, Credit and Banking 34(1) Petersen, M.A., Rajan R.G Trade credit: Theories and evidence. Review of Financial Studies 10(3) Seifert, D., R.W. Seifert, M. Protopappa-Sieke A review of trade credit literature: Opportunities for research in operations. European Journal of Operational Research 231(2) Smith, J.K Trade credit and informational asymmetry. Journal of Finance 42(4)

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