- Email: [email protected]
The impact of switching costs on vendor financing
Finance Research Letters 6 (2009) 236–241
Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
The impact of switching costs on vendor financing q M. Martin Boyer a,c, Karine Gobert b,c,* a
HEC Montréal, Université de Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, QC, Canada H3T 2A7 Faculté d’administration and GREDI, Université de Sherbrooke, 2500 Boulevard de l’Université, Sherbrooke, QC, Canada J1K 2R1 c Cirano, 2020 University Ave., 25th Floor, Montréal, QC, Canada H3A 2A5 b
a r t i c l e
i n f o
Article history: Received 19 December 2008 Accepted 27 July 2009 Available online 3 August 2009 JEL classifications: G32 D92 D86 C73 Keywords: Trade credit Financing of the firm Hold-up Self-enforcing contracts
a b s t r a c t We show that vendor financing appears in equilibrium as the result of repeated trade interactions between a buyer and a supplier when changing supplier is costly. Competition between suppliers forces them to offer a rebate before the relationship is initiated and switching costs allow the buyer to borrow from the supplier in the first period and to roll over the debt until the end of the relationship. The sequence of transfers is similar to a longterm financing structure. Our model suggests that switching costs allow small business owners to smooth their dividend income by using vendor financing. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction Vendor financing occurs when two corporations, a supplier and a buyer, arrange for a schedule of payments that makes one of them the debtor of the other for some period of time. Trade credit is a form of vendor financing that delays the payment of delivered goods. Trade credit is an important source of firm financing, and especially so for small and medium-sized firms. Cuñat (2007) estimates that trade credit represents 17% of the average medium-sized British firm’s asset and 40% of its debt
q This research was made possible by a grant from the Social Science and Humanities Research Council of Canada. The continuing financial support of CIRANO is also appreciated. * Corresponding author. Address: Faculté d’administration and GREDI, Université de Sherbrooke, 2500 Boulevard de l’Université, Sherbrooke, QC, Canada J1K 2R1. Fax: +1 819 821 7934. E-mail addresses: [email protected] (M. Martin Boyer), [email protected] (K. Gobert).
1544-6123/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.frl.2009.07.001
M. Martin Boyer, K. Gobert / Finance Research Letters 6 (2009) 236–241
237
financing. He also reports that in the United States, trade credit represents 18% of total assets and 35% of total debt for small and medium-sized firms. Clearly these figures would be higher if all forms of vendor financing are taken into account. We model in this paper the relationship between a risk neutral supplier, who has perfect access to intertemporal financial markets, and a credit-constrained risk averse buyer who is not indifferent to the timing of his income. In a world where agents have a concave value function (i.e., they are risk averse) they will also have, in a dynamic setting, marked preferences for smoothing their consumption over time. This situation is particularly pertinent to a small business owner where his periodic consumption depends on the dividend generated by the firm. As a result, if a small business owner is risk averse and has limited access to financial institution liquidities that would allow him to smooth his dividend stream, then he would value any relationship with a trading partner that implicitly promises smoothing of his dividend through a long-term relationship. An important research question in the past 20 years has addressed the question of why supplier firms would act as a substitute to banks in extending credit to other firms. Petersen and Rajan (1997), using the database on small and medium-sized firms in the United States, find that small firms are most likely to use vendor financing if they are credit constrained.1 They support the substitution theory that firms use vendor financing only when other sources of borrowing have been exhausted. For Elliehausen and Wolken (1993) and Demirgüç-Kunt and Maksimovic (2001), however, trade credit should be seen as a complement to bank credit rather than a substitute. Financially sound firms obtain credit from banks that they extend to less healthy firms. This adds efficiency to the financial system when suppliers have a better information about their client’s creditworthiness (Smith, 1987; Biais and Gollier, 1997; Jain, 2001), and when they are less vulnerable to cash diversion (Burkart and Ellingsen, 2004) or default (Santos and Longhofer, 2003). The model we present in this paper builds on the enforcement power theory that is central to vendor financing (see Burkart et al., 2008; Cuñat, 2007). Suppliers have an advantage over banks because they have better ways to enforce repayment. In line with the contract theory result that it is in the agents’ best interest ex ante to find a way to credibly commit to their contractual relationship, our model introduces adjustment costs to the supplier’s input that induce the buyer to enter a relationship in which he is held up by the supplier. The hold-up situation acts as a precommitment mechanism that enables the relationship to last for more than one period. The supplier can then safely make value increasing transfers to the client at the beginning of the relationship. As the result of the transfers’ particular timing between the supplier and the client, vendor financing emerges as a byproduct of a contract imperfection. In contrast to previous literature that concentrates mostly on short term relationships, our approach has the distinct advantage of combining short term financing with long-term relationships between business partners. Our model therefore focuses on the timing of transfers in an economy where the supplier has a negotiation power but no market power. We generate vendor financing as a consequence of trade relationships instead of imposing a relationship where the client needs credit to operate his project as in Cuñat (2007). In a repeated buyer/supplier relationship with no bank and in the presence of imperfect contracting between the parties, we show how vendor financing appears in the equilibrium sequence of transfers. Cuñat (2007) shows that the trade credit pattern of transfers incorporates risk sharing at a premium. We abstract from this issue by removing all uncertainty in the buyer’s income. Our contribution is thus to present an extremely simplified contract where adjustment costs are sufficient to make a form of incomplete long term vendor financing self enforceable. The paper is structured as follows. In the next section we present the basic model and the first best solution to trade relationships. In the last Section, we show how vendor financing appears at the equilibrium of the self-enforcing relationship with switching costs.
1 See also Niskanen and Niskanen (2006), using firm data from Finland, and Hernandez-Canova and Martinez-Solano (2007) with Spanish data.
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2. The basic model Suppose a firm that has a widget-producing project that will last for T þ 1 periods denoted t ¼ 0 . . . T. This firm, which we shall refer to as the buyer for the remainder of the paper, produces in each period widgets that can be sold on the competitive market at some unit price p. The buyer’s production function displays constant marginal returns so that his marginal cost is c for all levels of production. Without loss of generality we normalize production to one unit. To produce this widget in every period, the buyer must acquire one unit of an intermediary good for which there are N potential suppliers. As suppliers compete in prices, N does not have to be large to entail competition among sellers. Every supplier faces a constant marginal cost of producing the intermediary good equal to c (the competitive reserve price). In every period, the contract between the buyer and one of the suppliers specifies a transfer pt from the buyer to the supplier for the delivery of one unit of the intermediary good. Suppliers provide intermediary goods that are differentiated. Hence, by choosing a particular supplier the buyer must make some costly adjustments to his production process. The buyer’s assets are, therefore, specific to the intermediary good used. We denote by a the adjustment cost to the input involved. This cost must be borne by the buyer each time he changes his production line to fit with one supplier’s particular intermediary good. In other words, changing supplier entails a switching cost for the buyer equal to a. We focus the paper on a relationship between the owner of a small or medium size business and a larger supplier. A small business is characterized by two elements. Firstly, it has one (or a few) owner whose wealth is mainly invested in the firm and who has therefore an undiversified portfolio of assets. Secondly, it has a constrained access to financial markets, so that transferring revenue from period to period or across states of the world is impossible. This gives our buyer a risk averse behavior so that he values smooth income (represented here by the dividend stream) over time.2 As a result we shall model the firm as having a concave value function to display aversion towards risky income and strong preferences for income smoothing. Let us define Vðdt Þ as the per period value of the buyer over the dividend dt generated by the production and selling of the widget. We have V 0 ðdt Þ > 0 and V 00 ðdt Þ < 0 with Vð0Þ ¼ 0. As a large corporation with well diversified owners, the supplier has a perfect access to financial markets so that she can transfer income across periods at no cost. This is modeled with a risk neutral value function for the supplier. We suppose that p c c a 0, so that, even in the first period, the buyer has no demand for intra-period financing. He is only constrained on intertemporal revenue transfers. If all payments are enforceable, the buyer and the seller will write a long term contract that is first best. This solution offers perfect dividend smoothing to the buyer. It specifies a sequence of transfers fpt gTt¼0 from the buyer to the supplier that maximizes the buyer’s value over the T periods, under the constraint that the supplier’s discounted payoff is at least equal to zero:
max ðp c p0 aÞ þ T t gt¼0
fp
T X
bt Vðp c pt Þ s:t:
t¼1
T X
dt fpt cg 0;
t¼0
where b and d are, respectively, the buyer’s and the seller’s discount factors. Perfect smoothing is characterized by
V 0 ðdtþ1 Þ d ¼ ; b V 0 ðdt Þ
t ¼ 0; . . . ; T 1
ð1Þ
with d0 ¼ p c p0 a and dt ¼ p c pt . That means that, for d > b, the buyer’s consumption profile is slightly decreasing. If d ¼ b, the buyer’s consumption is constant through time. The first best long-term trade solution is such that the supplier offers a long-term financing plan for the adjustment a paid in period 0. It is as if the supplier paid for the adjustment cost and the buyer was made to pay a P cg ¼ 0. Each period, the transfer covers for the cost c of such that a þ Tt¼0 dt fp constant transfer p 2
See Stulz (1984), Campbell and Kracaw (1987), and DeMarzo and Duffie (1995).
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the intermediary good plus a compensation for the one time adjustment cost a paid for by the supplier in the initial period. This compensation is the average value of a over the T periods, discounted at d, so that the supplier’s intertemporal discounted profit is equal to zero. If the long-term contract is enforceable, there is no reason why a deep-pocket supplier could not help her client finance a first period investment through a specifically tailored sequence of transfers. Therefore, vendor financing is an efficient alternative for credit constrained businesses if contracts are perfect. If, on the other hand, contracts are not enforceable, the first best outcome cannot be achieved. Since many relationships are specific, they involve unobservable terms. That makes contracts unenforceable by a third party. Consequently, a supplier will not extend credit unless he can rely on a collateral or an enforcement mechanism to prevent default. Hence, long term vendor financing will exist only through a self-enforcing (i.e. non-binding) sequence of contracts. If not, the buyer reverts to the competitive market in each period. We address the non-binding sequence of contracts in the next section. 3. Non-binding relationships Suppose that the buyer chooses a different supplier in every period. He therefore incurs in each period the adjustment cost a and pays the intermediary good’s supplier the competitive price c. Changing supplier every period is obviously sub-optimal. The incumbent supplier could offer the same price and make the buyer economize on the adjustment cost. Hence, she has an advantage over her competitors so that she can charge higher prices and still supply the good. We solve for the equilibrium sequence of contracts that maximizes the buyer’s intertemporal value and leaves each supplier with a zero profit over the length of her relationship with the buyer. The optimal sequence of contracts must be optimal starting in any period t. Thus, we recursively solve for the optimal sequence of contracts starting with the last period. At the beginning of period T, the price for the intermediary good on the competitive market is c. Trading with a new supplier would force the buyer to adjust his production process at cost a, so that his dividend would be dT ¼ p c c a. Hence, the incumbent supplier (who supplied the good in period T 1) can charge a price pT ¼ c þ a and still be the chosen supplier for period T.3 Hence, the supplier in the last period is the same as in the second-to-last period. The buyer’s value in this last period is Vðp c c aÞ. In period T 1, any supplier knows that if she gets the contract in T 1, she will be able to keep it ~ T1 as well in period T and charge pT ¼ c þ a. Hence, the competitive price charged in period T 1 is p such that
p~ T1 c þ da ¼ 0:
ð2Þ
~ T1 ¼ c da. The competitive price in period T 1 is then p However, the incumbent supplier in period T 1 can offer pT1 ¼ c da þ a and still have the contract because it allows the buyer to save on the adjustment cost a. Hence, the supplier that had the contract in period T 2 remains the supplier in periods T 1 and T and pockets the discounted sum of profits in both last periods:
PT1 ¼ a da þ da ¼ a:
ð3Þ
Suppose the same supplier can trade with the buyer in each period after t with transfers equal to ps ¼ c þ a da for all s ¼ t þ 1; t þ 2; . . . ; T.PThat supplier pockets a rent of ð1 dÞa every period that di ð1 dÞa þ dTt1 a ¼ a. In period t, the optimal conleaves her with a discounted profit Ptþ1 ¼ Tt2 i¼0 tract for the buyer is the one obtained on the competitive market where the supplier that obtains the ~ t c þ dPtþ1 0, contract will keep it until T. The binding participation constraint for the supplier, p ~ t ¼ c da. Consequently, the with Ptþ1 ¼ a, gives the competitive transfer price in t equal to p 3 We suppose that being indifferent between the prices charged by the incumbent supplier or her competitors, the buyer chooses to deal with the incumbent.
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~ t and still reincumbent supplier at t can offer the same contract to the buyer with transfer pt ¼ a þ p main the supplier until T. In period 0, there is no incumbent supplier. Since the supplier that receives the contract in t ¼ 0 can maintain her relationship with the buyer until T and secure a payoff valued da in period 0, competition induces all suppliers into proposing a rebate of da in period 0. The transfer in t ¼ 0 is then p0 ¼ c da; and the discounted total payoff from the contract for the supplier is P0 ¼ 0. Based on this reasoning, we find the following result for the procurement contract of the intermediary good. Result 1. The buyer maintains his relationship with the same supplier over the T periods. The price paid for the intermediary good in period t is pt with
p0 ¼ c da; pt ¼ c þ ð1 dÞa for all 0 < t < T; pT ¼ c þ a. The incumbent supplier charges ð1 dÞa over the competitive price from t ¼ 1 to t ¼ T 1 and she charges a over the competitive price in the last period. Looking at the contract in any period t > 0, it may appear as if there is a rent ð1 dÞa collected by the supplier. This rent is generated by the hold-up situation introduced by the existence of adjustment costs. Nevertheless, since there is competition on the market for the intermediary good, suppliers are willing to offer a first period rebate to secure the contract. This rebate of da makes the discounted value of the T period trade relationship equal to zero in period 0 for the supplier. Therefore, the equilibrium trade relationship is not the repeated transfer of the reserve price c. The specificity of the intermediary good induces the supplier into offering a rebate da in the first period. She then secures a payment higher than the market price c in all subsequent periods. This timing of payments offers the opportunity of vendor financing. It is as if the amount da was lent every period and repaid the next, at a constant rate r ¼ 1=d 1. The amount da extended in the first period by the supplier partly finances the buyer’s initial period investment a. The buyer then owes a the next period. The sequence of transfers is such that the debt is rolled over from period to period as long as the relationship lasts. The buyer borrows da in one period to help with the payment of a that he owes from the preceding period. In the last period, the buyer must reimburse the total due a. In other words, the buyer borrows each period an amount that allows him to delay the payment of the entire first period investment until the end of the relationship. The price of financing depends on the supplier’s discount rate d, which is dependent on her cost of funds so that r ¼ 1=d 1. Competition among suppliers drives the price down to the competitive price r. Even if the buyer had access to credit at a rate lower than r, the hold-up situation would force him to accept this financing arrangement at the supplier’s rate r. Of course, if the intermediate good market were not competitive, then the price paid by the firm for the good cum financing would be greater. The size of the adjustment cost is related to the amount a supplier can lend to her customer. The higher this cost, the more held up he is, and the more financing she can extend in the first period without risk of strategic default. Hence, we should expect vendor financing to be used more significantly in industries where suppliers and clients are in more symbiotic relationships. 4. Conclusions For a small business with a restricted access to credit, it is overly important to be able to smooth the first period cost of finding a supplier. Here, competition among suppliers and switching costs allow the buyer to borrow from his supplier in period 0 and to roll over the debt from period to period until a late reimbursement in the final period of the relationship. This loan provides working capital that, in turn, allows the buyer to optimally invest in other projects without having to apply for bank debt.
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Hence, the existence of a hold-up disadvantage for the buyer ends up being an opportunity to be offered financing. The switching cost acts as an imperfect binding mechanism and generates its own partial financing in guaranteeing a future reimbursement. This allows buyers to partly rely on vendor financing to optimally manage their working capital. Some typical trade contracts offer buyers a rebate for early payment. Late payers are then made to pay implicit rates of interest that can be very high. Why buyers would choose to pay such high interest rates is a puzzle about trade credit. In our simple model, on the contrary, we find that vendor financing is extended by suppliers at their own cost of financing. In our view, the firm can be offered generous discounts as long as the relationship has a future value for the supplier. This involves new openings for empirical testing. Burkart et al. (2008) found evidence that trade credit is more prevalent when the traded good is specific. Empirical testing should also find that long lasting trade relationships and the use of early discounts can be related to the specificity of the relationship between the buyer and the supplier. As opposed to the short term view of the problem which argues that the buyer needs bank financing to pay early and benefit from the discount, we would rather argue that the discount itself is a form of long-term financing that is the result of a symbiotic relationship between the buyer and the seller. References Biais, B., Gollier, C., 1997. Trade credit and credit rationing. Review of Financial Studies 10, 903–937. Burkart, M., Ellingsen, T., 2004. In-kind finance: a theory of trade credit. American Economic Review 94, 569–590. Burkart, M., Ellingsen, T., Giannetti, M., 2008. What you sell is what you lend? Explaining trade credit contracts. Review of Financial Studies, doi:10.1093/rfs/hhn096. Campbell, T.S., Kracaw, W.A., 1987. Optimal managerial incentive contracts and the value of corporate insurance. Journal of Financial and Quantitative Analysis 22, 315–328. Cuñat, V., 2007. Trade credit: suppliers as debt collectors and insurance providers. Review of Financial Studies 20, 491–527. DeMarzo, P.M., Duffie, D., 1995. Corporate incentive for hedging and hedge accounting. Review of Financial Studies 8, 743–771. Demirgüç-Kunt, A., Maksimovic, V., 2001. Firms as financial intermediaries – evidence from trade credit data. The World Bank, Policy Research Working Papers: 2696. Elliehausen, G.E., Wolken, J.D., 1993. The demand for trade credit: an investigation of motives for trade credit use by small businesses. Board of Governors of the Federal Reserve System (US), Staff Studies: 165. Hernandez-Canova, G., Martinez-Solano, P., 2007. Effect of the number of banking relationships on credit availability: evidence from panel data of Spanish small firms. Small Business Economics 28, 37–53. Jain, N., 2001. Monitoring costs and trade credit. The Quarterly Review of Economics and Finance 41, 89–110. Niskanen, J., Niskanen, M., 2006. The determinants of corporate trade credit policies in a bank-dominated financial environment: the case of Finnish small firms. European Financial Management 12, 81–102. Petersen, M.A., Rajan, R.G., 1997. Trade credit: theories and evidence. Review of Financial Studies 10, 661–691. Santos, J.A.C., Longhofer, S.D., 2003. The paradox of priority. Financial Management 32, 69–81. Smith, J.K., 1987. Trade credit and informational asymmetry. Journal of Finance 42, 863–872. Stulz, R.M., 1984. Optimal hedging policies. Journal of Financial and Quantitative Analysis 19, 127–140.
Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
The impact of switching costs on vendor financing q M. Martin Boyer a,c, Karine Gobert b,c,* a
HEC Montréal, Université de Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, QC, Canada H3T 2A7 Faculté d’administration and GREDI, Université de Sherbrooke, 2500 Boulevard de l’Université, Sherbrooke, QC, Canada J1K 2R1 c Cirano, 2020 University Ave., 25th Floor, Montréal, QC, Canada H3A 2A5 b
a r t i c l e
i n f o
Article history: Received 19 December 2008 Accepted 27 July 2009 Available online 3 August 2009 JEL classifications: G32 D92 D86 C73 Keywords: Trade credit Financing of the firm Hold-up Self-enforcing contracts
a b s t r a c t We show that vendor financing appears in equilibrium as the result of repeated trade interactions between a buyer and a supplier when changing supplier is costly. Competition between suppliers forces them to offer a rebate before the relationship is initiated and switching costs allow the buyer to borrow from the supplier in the first period and to roll over the debt until the end of the relationship. The sequence of transfers is similar to a longterm financing structure. Our model suggests that switching costs allow small business owners to smooth their dividend income by using vendor financing. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction Vendor financing occurs when two corporations, a supplier and a buyer, arrange for a schedule of payments that makes one of them the debtor of the other for some period of time. Trade credit is a form of vendor financing that delays the payment of delivered goods. Trade credit is an important source of firm financing, and especially so for small and medium-sized firms. Cuñat (2007) estimates that trade credit represents 17% of the average medium-sized British firm’s asset and 40% of its debt
q This research was made possible by a grant from the Social Science and Humanities Research Council of Canada. The continuing financial support of CIRANO is also appreciated. * Corresponding author. Address: Faculté d’administration and GREDI, Université de Sherbrooke, 2500 Boulevard de l’Université, Sherbrooke, QC, Canada J1K 2R1. Fax: +1 819 821 7934. E-mail addresses: [email protected] (M. Martin Boyer), [email protected] (K. Gobert).
1544-6123/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.frl.2009.07.001
M. Martin Boyer, K. Gobert / Finance Research Letters 6 (2009) 236–241
237
financing. He also reports that in the United States, trade credit represents 18% of total assets and 35% of total debt for small and medium-sized firms. Clearly these figures would be higher if all forms of vendor financing are taken into account. We model in this paper the relationship between a risk neutral supplier, who has perfect access to intertemporal financial markets, and a credit-constrained risk averse buyer who is not indifferent to the timing of his income. In a world where agents have a concave value function (i.e., they are risk averse) they will also have, in a dynamic setting, marked preferences for smoothing their consumption over time. This situation is particularly pertinent to a small business owner where his periodic consumption depends on the dividend generated by the firm. As a result, if a small business owner is risk averse and has limited access to financial institution liquidities that would allow him to smooth his dividend stream, then he would value any relationship with a trading partner that implicitly promises smoothing of his dividend through a long-term relationship. An important research question in the past 20 years has addressed the question of why supplier firms would act as a substitute to banks in extending credit to other firms. Petersen and Rajan (1997), using the database on small and medium-sized firms in the United States, find that small firms are most likely to use vendor financing if they are credit constrained.1 They support the substitution theory that firms use vendor financing only when other sources of borrowing have been exhausted. For Elliehausen and Wolken (1993) and Demirgüç-Kunt and Maksimovic (2001), however, trade credit should be seen as a complement to bank credit rather than a substitute. Financially sound firms obtain credit from banks that they extend to less healthy firms. This adds efficiency to the financial system when suppliers have a better information about their client’s creditworthiness (Smith, 1987; Biais and Gollier, 1997; Jain, 2001), and when they are less vulnerable to cash diversion (Burkart and Ellingsen, 2004) or default (Santos and Longhofer, 2003). The model we present in this paper builds on the enforcement power theory that is central to vendor financing (see Burkart et al., 2008; Cuñat, 2007). Suppliers have an advantage over banks because they have better ways to enforce repayment. In line with the contract theory result that it is in the agents’ best interest ex ante to find a way to credibly commit to their contractual relationship, our model introduces adjustment costs to the supplier’s input that induce the buyer to enter a relationship in which he is held up by the supplier. The hold-up situation acts as a precommitment mechanism that enables the relationship to last for more than one period. The supplier can then safely make value increasing transfers to the client at the beginning of the relationship. As the result of the transfers’ particular timing between the supplier and the client, vendor financing emerges as a byproduct of a contract imperfection. In contrast to previous literature that concentrates mostly on short term relationships, our approach has the distinct advantage of combining short term financing with long-term relationships between business partners. Our model therefore focuses on the timing of transfers in an economy where the supplier has a negotiation power but no market power. We generate vendor financing as a consequence of trade relationships instead of imposing a relationship where the client needs credit to operate his project as in Cuñat (2007). In a repeated buyer/supplier relationship with no bank and in the presence of imperfect contracting between the parties, we show how vendor financing appears in the equilibrium sequence of transfers. Cuñat (2007) shows that the trade credit pattern of transfers incorporates risk sharing at a premium. We abstract from this issue by removing all uncertainty in the buyer’s income. Our contribution is thus to present an extremely simplified contract where adjustment costs are sufficient to make a form of incomplete long term vendor financing self enforceable. The paper is structured as follows. In the next section we present the basic model and the first best solution to trade relationships. In the last Section, we show how vendor financing appears at the equilibrium of the self-enforcing relationship with switching costs.
1 See also Niskanen and Niskanen (2006), using firm data from Finland, and Hernandez-Canova and Martinez-Solano (2007) with Spanish data.
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2. The basic model Suppose a firm that has a widget-producing project that will last for T þ 1 periods denoted t ¼ 0 . . . T. This firm, which we shall refer to as the buyer for the remainder of the paper, produces in each period widgets that can be sold on the competitive market at some unit price p. The buyer’s production function displays constant marginal returns so that his marginal cost is c for all levels of production. Without loss of generality we normalize production to one unit. To produce this widget in every period, the buyer must acquire one unit of an intermediary good for which there are N potential suppliers. As suppliers compete in prices, N does not have to be large to entail competition among sellers. Every supplier faces a constant marginal cost of producing the intermediary good equal to c (the competitive reserve price). In every period, the contract between the buyer and one of the suppliers specifies a transfer pt from the buyer to the supplier for the delivery of one unit of the intermediary good. Suppliers provide intermediary goods that are differentiated. Hence, by choosing a particular supplier the buyer must make some costly adjustments to his production process. The buyer’s assets are, therefore, specific to the intermediary good used. We denote by a the adjustment cost to the input involved. This cost must be borne by the buyer each time he changes his production line to fit with one supplier’s particular intermediary good. In other words, changing supplier entails a switching cost for the buyer equal to a. We focus the paper on a relationship between the owner of a small or medium size business and a larger supplier. A small business is characterized by two elements. Firstly, it has one (or a few) owner whose wealth is mainly invested in the firm and who has therefore an undiversified portfolio of assets. Secondly, it has a constrained access to financial markets, so that transferring revenue from period to period or across states of the world is impossible. This gives our buyer a risk averse behavior so that he values smooth income (represented here by the dividend stream) over time.2 As a result we shall model the firm as having a concave value function to display aversion towards risky income and strong preferences for income smoothing. Let us define Vðdt Þ as the per period value of the buyer over the dividend dt generated by the production and selling of the widget. We have V 0 ðdt Þ > 0 and V 00 ðdt Þ < 0 with Vð0Þ ¼ 0. As a large corporation with well diversified owners, the supplier has a perfect access to financial markets so that she can transfer income across periods at no cost. This is modeled with a risk neutral value function for the supplier. We suppose that p c c a 0, so that, even in the first period, the buyer has no demand for intra-period financing. He is only constrained on intertemporal revenue transfers. If all payments are enforceable, the buyer and the seller will write a long term contract that is first best. This solution offers perfect dividend smoothing to the buyer. It specifies a sequence of transfers fpt gTt¼0 from the buyer to the supplier that maximizes the buyer’s value over the T periods, under the constraint that the supplier’s discounted payoff is at least equal to zero:
max ðp c p0 aÞ þ T t gt¼0
fp
T X
bt Vðp c pt Þ s:t:
t¼1
T X
dt fpt cg 0;
t¼0
where b and d are, respectively, the buyer’s and the seller’s discount factors. Perfect smoothing is characterized by
V 0 ðdtþ1 Þ d ¼ ; b V 0 ðdt Þ
t ¼ 0; . . . ; T 1
ð1Þ
with d0 ¼ p c p0 a and dt ¼ p c pt . That means that, for d > b, the buyer’s consumption profile is slightly decreasing. If d ¼ b, the buyer’s consumption is constant through time. The first best long-term trade solution is such that the supplier offers a long-term financing plan for the adjustment a paid in period 0. It is as if the supplier paid for the adjustment cost and the buyer was made to pay a P cg ¼ 0. Each period, the transfer covers for the cost c of such that a þ Tt¼0 dt fp constant transfer p 2
See Stulz (1984), Campbell and Kracaw (1987), and DeMarzo and Duffie (1995).
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the intermediary good plus a compensation for the one time adjustment cost a paid for by the supplier in the initial period. This compensation is the average value of a over the T periods, discounted at d, so that the supplier’s intertemporal discounted profit is equal to zero. If the long-term contract is enforceable, there is no reason why a deep-pocket supplier could not help her client finance a first period investment through a specifically tailored sequence of transfers. Therefore, vendor financing is an efficient alternative for credit constrained businesses if contracts are perfect. If, on the other hand, contracts are not enforceable, the first best outcome cannot be achieved. Since many relationships are specific, they involve unobservable terms. That makes contracts unenforceable by a third party. Consequently, a supplier will not extend credit unless he can rely on a collateral or an enforcement mechanism to prevent default. Hence, long term vendor financing will exist only through a self-enforcing (i.e. non-binding) sequence of contracts. If not, the buyer reverts to the competitive market in each period. We address the non-binding sequence of contracts in the next section. 3. Non-binding relationships Suppose that the buyer chooses a different supplier in every period. He therefore incurs in each period the adjustment cost a and pays the intermediary good’s supplier the competitive price c. Changing supplier every period is obviously sub-optimal. The incumbent supplier could offer the same price and make the buyer economize on the adjustment cost. Hence, she has an advantage over her competitors so that she can charge higher prices and still supply the good. We solve for the equilibrium sequence of contracts that maximizes the buyer’s intertemporal value and leaves each supplier with a zero profit over the length of her relationship with the buyer. The optimal sequence of contracts must be optimal starting in any period t. Thus, we recursively solve for the optimal sequence of contracts starting with the last period. At the beginning of period T, the price for the intermediary good on the competitive market is c. Trading with a new supplier would force the buyer to adjust his production process at cost a, so that his dividend would be dT ¼ p c c a. Hence, the incumbent supplier (who supplied the good in period T 1) can charge a price pT ¼ c þ a and still be the chosen supplier for period T.3 Hence, the supplier in the last period is the same as in the second-to-last period. The buyer’s value in this last period is Vðp c c aÞ. In period T 1, any supplier knows that if she gets the contract in T 1, she will be able to keep it ~ T1 as well in period T and charge pT ¼ c þ a. Hence, the competitive price charged in period T 1 is p such that
p~ T1 c þ da ¼ 0:
ð2Þ
~ T1 ¼ c da. The competitive price in period T 1 is then p However, the incumbent supplier in period T 1 can offer pT1 ¼ c da þ a and still have the contract because it allows the buyer to save on the adjustment cost a. Hence, the supplier that had the contract in period T 2 remains the supplier in periods T 1 and T and pockets the discounted sum of profits in both last periods:
PT1 ¼ a da þ da ¼ a:
ð3Þ
Suppose the same supplier can trade with the buyer in each period after t with transfers equal to ps ¼ c þ a da for all s ¼ t þ 1; t þ 2; . . . ; T.PThat supplier pockets a rent of ð1 dÞa every period that di ð1 dÞa þ dTt1 a ¼ a. In period t, the optimal conleaves her with a discounted profit Ptþ1 ¼ Tt2 i¼0 tract for the buyer is the one obtained on the competitive market where the supplier that obtains the ~ t c þ dPtþ1 0, contract will keep it until T. The binding participation constraint for the supplier, p ~ t ¼ c da. Consequently, the with Ptþ1 ¼ a, gives the competitive transfer price in t equal to p 3 We suppose that being indifferent between the prices charged by the incumbent supplier or her competitors, the buyer chooses to deal with the incumbent.
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~ t and still reincumbent supplier at t can offer the same contract to the buyer with transfer pt ¼ a þ p main the supplier until T. In period 0, there is no incumbent supplier. Since the supplier that receives the contract in t ¼ 0 can maintain her relationship with the buyer until T and secure a payoff valued da in period 0, competition induces all suppliers into proposing a rebate of da in period 0. The transfer in t ¼ 0 is then p0 ¼ c da; and the discounted total payoff from the contract for the supplier is P0 ¼ 0. Based on this reasoning, we find the following result for the procurement contract of the intermediary good. Result 1. The buyer maintains his relationship with the same supplier over the T periods. The price paid for the intermediary good in period t is pt with
p0 ¼ c da; pt ¼ c þ ð1 dÞa for all 0 < t < T; pT ¼ c þ a. The incumbent supplier charges ð1 dÞa over the competitive price from t ¼ 1 to t ¼ T 1 and she charges a over the competitive price in the last period. Looking at the contract in any period t > 0, it may appear as if there is a rent ð1 dÞa collected by the supplier. This rent is generated by the hold-up situation introduced by the existence of adjustment costs. Nevertheless, since there is competition on the market for the intermediary good, suppliers are willing to offer a first period rebate to secure the contract. This rebate of da makes the discounted value of the T period trade relationship equal to zero in period 0 for the supplier. Therefore, the equilibrium trade relationship is not the repeated transfer of the reserve price c. The specificity of the intermediary good induces the supplier into offering a rebate da in the first period. She then secures a payment higher than the market price c in all subsequent periods. This timing of payments offers the opportunity of vendor financing. It is as if the amount da was lent every period and repaid the next, at a constant rate r ¼ 1=d 1. The amount da extended in the first period by the supplier partly finances the buyer’s initial period investment a. The buyer then owes a the next period. The sequence of transfers is such that the debt is rolled over from period to period as long as the relationship lasts. The buyer borrows da in one period to help with the payment of a that he owes from the preceding period. In the last period, the buyer must reimburse the total due a. In other words, the buyer borrows each period an amount that allows him to delay the payment of the entire first period investment until the end of the relationship. The price of financing depends on the supplier’s discount rate d, which is dependent on her cost of funds so that r ¼ 1=d 1. Competition among suppliers drives the price down to the competitive price r. Even if the buyer had access to credit at a rate lower than r, the hold-up situation would force him to accept this financing arrangement at the supplier’s rate r. Of course, if the intermediate good market were not competitive, then the price paid by the firm for the good cum financing would be greater. The size of the adjustment cost is related to the amount a supplier can lend to her customer. The higher this cost, the more held up he is, and the more financing she can extend in the first period without risk of strategic default. Hence, we should expect vendor financing to be used more significantly in industries where suppliers and clients are in more symbiotic relationships. 4. Conclusions For a small business with a restricted access to credit, it is overly important to be able to smooth the first period cost of finding a supplier. Here, competition among suppliers and switching costs allow the buyer to borrow from his supplier in period 0 and to roll over the debt from period to period until a late reimbursement in the final period of the relationship. This loan provides working capital that, in turn, allows the buyer to optimally invest in other projects without having to apply for bank debt.
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Hence, the existence of a hold-up disadvantage for the buyer ends up being an opportunity to be offered financing. The switching cost acts as an imperfect binding mechanism and generates its own partial financing in guaranteeing a future reimbursement. This allows buyers to partly rely on vendor financing to optimally manage their working capital. Some typical trade contracts offer buyers a rebate for early payment. Late payers are then made to pay implicit rates of interest that can be very high. Why buyers would choose to pay such high interest rates is a puzzle about trade credit. In our simple model, on the contrary, we find that vendor financing is extended by suppliers at their own cost of financing. In our view, the firm can be offered generous discounts as long as the relationship has a future value for the supplier. This involves new openings for empirical testing. Burkart et al. (2008) found evidence that trade credit is more prevalent when the traded good is specific. Empirical testing should also find that long lasting trade relationships and the use of early discounts can be related to the specificity of the relationship between the buyer and the supplier. As opposed to the short term view of the problem which argues that the buyer needs bank financing to pay early and benefit from the discount, we would rather argue that the discount itself is a form of long-term financing that is the result of a symbiotic relationship between the buyer and the seller. References Biais, B., Gollier, C., 1997. Trade credit and credit rationing. Review of Financial Studies 10, 903–937. Burkart, M., Ellingsen, T., 2004. In-kind finance: a theory of trade credit. American Economic Review 94, 569–590. Burkart, M., Ellingsen, T., Giannetti, M., 2008. What you sell is what you lend? Explaining trade credit contracts. Review of Financial Studies, doi:10.1093/rfs/hhn096. Campbell, T.S., Kracaw, W.A., 1987. Optimal managerial incentive contracts and the value of corporate insurance. Journal of Financial and Quantitative Analysis 22, 315–328. Cuñat, V., 2007. Trade credit: suppliers as debt collectors and insurance providers. Review of Financial Studies 20, 491–527. DeMarzo, P.M., Duffie, D., 1995. Corporate incentive for hedging and hedge accounting. Review of Financial Studies 8, 743–771. Demirgüç-Kunt, A., Maksimovic, V., 2001. Firms as financial intermediaries – evidence from trade credit data. The World Bank, Policy Research Working Papers: 2696. Elliehausen, G.E., Wolken, J.D., 1993. The demand for trade credit: an investigation of motives for trade credit use by small businesses. Board of Governors of the Federal Reserve System (US), Staff Studies: 165. Hernandez-Canova, G., Martinez-Solano, P., 2007. Effect of the number of banking relationships on credit availability: evidence from panel data of Spanish small firms. Small Business Economics 28, 37–53. Jain, N., 2001. Monitoring costs and trade credit. The Quarterly Review of Economics and Finance 41, 89–110. Niskanen, J., Niskanen, M., 2006. The determinants of corporate trade credit policies in a bank-dominated financial environment: the case of Finnish small firms. European Financial Management 12, 81–102. Petersen, M.A., Rajan, R.G., 1997. Trade credit: theories and evidence. Review of Financial Studies 10, 661–691. Santos, J.A.C., Longhofer, S.D., 2003. The paradox of priority. Financial Management 32, 69–81. Smith, J.K., 1987. Trade credit and informational asymmetry. Journal of Finance 42, 863–872. Stulz, R.M., 1984. Optimal hedging policies. Journal of Financial and Quantitative Analysis 19, 127–140.