The steps below will derive the formula on page 23 of the paper.

annual interest rate = [((1)^(365/days borrowed))/ 1-discount rate] -1

Let r=annual interest rate, d/100=discount rate

We have the trade terms d/t1 Net t2

(a) Write the formula using the variables given (i.e. using r, d, t1, t2 assume there are 365 days in the year).

(b) Use a time line to illustrate the trade terms d/t1 Net t2

*--------------*--------------*

0 X

(c) Using the fundamental formula F V = P V (1 + r)t, write down an equation to solver for the annual effective annual interest rate.

(d) Arrange your solution to derive the formula on page 23 of the paper.

trade credit to Stocking Out. On R/DR's balance sheet, the dollars owed by Stocking Out are an asset called accounts receivable, while the trade credit appears on Stocking Out's balance sheet as a liability called accounts payable. Trade credit comes in a wide variety of terms, but there are two broad types of agreements.? Under a net contract, Stocking Out promises to repay R/DR after a fixed period of time; 30 days is the most common maturity, according to Chee Ng, Janet Smith, and Richard Smith's survey results. This contract would be described as net 30." Although the price Stocking Out pays for the goods will clearly be affected by R/DR's cost of providing credit to its customer, the net contract doesn't include an explicit loan rate. Alternatively, Stocking Out and R/DR may use a more complicated two-part contract, in which Stocking Out receives a discount for paying within a fixed period, but then must pay the full price for the remaining term of the contract. For example, if the terms of the trade credit are "2/10 net 30" the most common two-part contract in Ng, Smith, and Smith's survey - Stocking Out receives a 2 percent discount if it pays within 10 days of delivery (the discount period) but pays full price between days 11 and 30 (the net period). This sounds like a good deal for Stocking Out, and it is if the credit is repaid within the first 10 days. But this is a very expensive form of borrowing if the firm takes longer than 10 days to repay. The implicit annual interest rate for such borrowings is nearly 45 percent. To see this, think about Stocking Out's cost of missing its payment on the 10th day and paying 20 days later. It has effec- tively chosen to pay 2 percent for 20 days. Thought about differently, if Stocking Out had paid on the 10th day, it could have invested the 2 percent discount on the pricing of goods for 20 days. For the sake of comparison, the annualized interest rate on my credit card is 16.25 percent if I don't pay off the loan balance before the 15th of the month. We might also make a compari- son with the rate on a bank loan to a firm without broad access to financial markets. At a time when the prime rate was 4.25 percent, a collateralized loan with a face value of less than $100,000 carried a loan rate of 5.35 percent per Stocking Out? To a significant extent, R/DR's bank actually finances this credit.10 Petersen and Rajan report that larger and older firms typically have larger accounts receivable; that is, they are large suppliers of trade credit. It is reasonable to view a firm's age and size as indicators of its creditworthiness. 11 One interpretation of Petersen and Rajan's results is that larger and older firms have easier access to external finance; they, in turn, act as intermedi- aries and extend trade credit to other, riskier firms. An even more explicit link between R/DR's access to bank credit and its provision of trade credit is Petersen and Rajan's finding that firms with larger credit lines also have larger accounts receivable. In particular, firms that have drawn down a larger share of their credit lines have even larger accounts receivable, consistent with the view that creditworthy firms effectively finance their provision of trade credit with bank loans. 12 Jeffrey Nilsen's article exam- ines different firms' use of trade credit during periods of monetary contraction, year. Thus, trade credit is expensive compared with a bank loan for any borrower who doesn't pay within the discount period. Not surprisingly, the evidence indicates that firms strongly prefer to borrow from a bank if bank credit is available. For example, in their 1997 article, Mitchell Petersen and Raghuram Rajan show that firms with unused bank credit lines have signifi- cantly lower accounts payable - that is, they use less trade credit. Also, firms with long-term relationships with a bank use less trade credit. Suppliers Are Financial Intermediaries. How does R/DR finance its provision of credit to 10 See Loretta Mester, Leonard Nakamura, and Micheline Renault's paper for an account of banks' comparative advantage in providing financing for accounts receivable. 11 See Aubhik Khan's article for a summary of the evidence from the manufacturing sector that a firm's probability of survival increases with age and size. The formula for the annual interest rate is [1/(1-discount rate) in the varidus bewed) = (1.02) 08/20 Ng. Smith, and Smith's article documents the wide variety of trade credit terms. Interestingly, their survey data indicate that trade credit terms are much more standard- ized within industry groups than across industry groups. However, they don't make much progress in explaining cross-industry variation in contract terms. 12 Bank financing is not the sole external funding source through which R/DR might finance this credit. Large firms also bypass the banking system altogether by selling securities backed by the cash flows from their receivables; that is, they also act as intermediaries between financial markets and the firms to which they grant trade credit. In some industries, providers of trade credit also sell their receivables at a discount to firms known as factors, which specialize in enforcing repayment. Sec Shehzad Mian and Clifford Smith's article about the variety of institutions involved in financing trade credit. Survey of Terms of Business Lending, March 20, 2003. A small "prime plus" loan is a relevant basis for comparison because firms that borrow above prime don't have access to broader financial markets and view a commercial bank as their cheapest source of funds, www.phil.frb.org Business Review 03 2003 23 trade credit to Stocking Out. On R/DR's balance sheet, the dollars owed by Stocking Out are an asset called accounts receivable, while the trade credit appears on Stocking Out's balance sheet as a liability called accounts payable. Trade credit comes in a wide variety of terms, but there are two broad types of agreements.? Under a net contract, Stocking Out promises to repay R/DR after a fixed period of time; 30 days is the most common maturity, according to Chee Ng, Janet Smith, and Richard Smith's survey results. This contract would be described as net 30." Although the price Stocking Out pays for the goods will clearly be affected by R/DR's cost of providing credit to its customer, the net contract doesn't include an explicit loan rate. Alternatively, Stocking Out and R/DR may use a more complicated two-part contract, in which Stocking Out receives a discount for paying within a fixed period, but then must pay the full price for the remaining term of the contract. For example, if the terms of the trade credit are "2/10 net 30" the most common two-part contract in Ng, Smith, and Smith's survey - Stocking Out receives a 2 percent discount if it pays within 10 days of delivery (the discount period) but pays full price between days 11 and 30 (the net period). This sounds like a good deal for Stocking Out, and it is if the credit is repaid within the first 10 days. But this is a very expensive form of borrowing if the firm takes longer than 10 days to repay. The implicit annual interest rate for such borrowings is nearly 45 percent. To see this, think about Stocking Out's cost of missing its payment on the 10th day and paying 20 days later. It has effec- tively chosen to pay 2 percent for 20 days. Thought about differently, if Stocking Out had paid on the 10th day, it could have invested the 2 percent discount on the pricing of goods for 20 days. For the sake of comparison, the annualized interest rate on my credit card is 16.25 percent if I don't pay off the loan balance before the 15th of the month. We might also make a compari- son with the rate on a bank loan to a firm without broad access to financial markets. At a time when the prime rate was 4.25 percent, a collateralized loan with a face value of less than $100,000 carried a loan rate of 5.35 percent per Stocking Out? To a significant extent, R/DR's bank actually finances this credit.10 Petersen and Rajan report that larger and older firms typically have larger accounts receivable; that is, they are large suppliers of trade credit. It is reasonable to view a firm's age and size as indicators of its creditworthiness. 11 One interpretation of Petersen and Rajan's results is that larger and older firms have easier access to external finance; they, in turn, act as intermedi- aries and extend trade credit to other, riskier firms. An even more explicit link between R/DR's access to bank credit and its provision of trade credit is Petersen and Rajan's finding that firms with larger credit lines also have larger accounts receivable. In particular, firms that have drawn down a larger share of their credit lines have even larger accounts receivable, consistent with the view that creditworthy firms effectively finance their provision of trade credit with bank loans. 12 Jeffrey Nilsen's article exam- ines different firms' use of trade credit during periods of monetary contraction, year. Thus, trade credit is expensive compared with a bank loan for any borrower who doesn't pay within the discount period. Not surprisingly, the evidence indicates that firms strongly prefer to borrow from a bank if bank credit is available. For example, in their 1997 article, Mitchell Petersen and Raghuram Rajan show that firms with unused bank credit lines have signifi- cantly lower accounts payable - that is, they use less trade credit. Also, firms with long-term relationships with a bank use less trade credit. Suppliers Are Financial Intermediaries. How does R/DR finance its provision of credit to 10 See Loretta Mester, Leonard Nakamura, and Micheline Renault's paper for an account of banks' comparative advantage in providing financing for accounts receivable. 11 See Aubhik Khan's article for a summary of the evidence from the manufacturing sector that a firm's probability of survival increases with age and size. The formula for the annual interest rate is [1/(1-discount rate) in the varidus bewed) = (1.02) 08/20 Ng. Smith, and Smith's article documents the wide variety of trade credit terms. Interestingly, their survey data indicate that trade credit terms are much more standard- ized within industry groups than across industry groups. However, they don't make much progress in explaining cross-industry variation in contract terms. 12 Bank financing is not the sole external funding source through which R/DR might finance this credit. Large firms also bypass the banking system altogether by selling securities backed by the cash flows from their receivables; that is, they also act as intermediaries between financial markets and the firms to which they grant trade credit. In some industries, providers of trade credit also sell their receivables at a discount to firms known as factors, which specialize in enforcing repayment. Sec Shehzad Mian and Clifford Smith's article about the variety of institutions involved in financing trade credit. Survey of Terms of Business Lending, March 20, 2003. A small "prime plus" loan is a relevant basis for comparison because firms that borrow above prime don't have access to broader financial markets and view a commercial bank as their cheapest source of funds, www.phil.frb.org Business Review 03 2003 23