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What is the nominal and effective cost of trade credit under the credit terms of \(3 / 15\) net \(30 ?\)

Short Answer

Expert verified
The nominal cost is 3.093%, and the effective annual cost is 86.86%.

Step by step solution

01

Understanding Credit Terms

The credit terms provided are \(3/15\), net \(30\). This means the buyer receives a \(3\%\) discount if they pay within \(15\) days. Otherwise, the full invoice amount is due in \(30\) days.
02

Calculate the Discount Percentage

The discount percentage is directly given in the terms, which is \(3\%\).
03

Determine the Length of the Credit Period

The total credit period is \(30\) days, and the discount period is \(15\) days. The length of the period without discount is \(30 - 15 = 15\) days.
04

Calculate the Nominal Cost of Trade Credit

The nominal cost of not taking the discount can be calculated using the formula:\[ \text{Nominal Cost} = \frac{3\%}{100\% - 3\%} = \frac{0.03}{0.97} \approx 0.03093 \text{ or } 3.093\% \]
05

Annualizing the Nominal Cost

To find the effective annual rate, we need to annualize the nominal cost since these cost adjustments occur every \(15\) days:\[ \text{Effective Annual Cost} = \left(1 + 0.03093\right)^{\frac{365}{15}} - 1 \approx 1.8686 - 1 = 0.8686 \text{ or } 86.86\% \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Nominal Cost
Understanding the nominal cost of trade credit is crucial when analyzing credit terms. In the given problem, the credit terms of 3/15 net 30 mean a buyer can enjoy a 3% discount if payment is made within 15 days. It's important to note that if the discount is not taken, the payment is due in 30 days.

The nominal cost essentially represents the implied cost of not receiving this discount. Here's how it works:
  • The discount percentage in our scenario is 3%.
  • The formula to calculate the nominal cost when opting to forgo the discount is:\[ \text{Nominal Cost} = \frac{\text{Discount Percent}}{100\% - \text{Discount Percent}} = \frac{3\%}{100\% - 3\%} \]
  • Substitute the values, \( \frac{0.03}{0.97} \), and you'll find a nominal cost of approximately 3.093%.
This percentage indicates the cost — in terms of the interest rate — of choosing not to take the early payment discount within the terms provided.
Effective Annual Rate
The effective annual rate (EAR) helps in understanding the real economic cost of not taking trade discounts over a year. By taking the nominal cost and converting it to an annual rate, you get a better perspective on the implications.

For the credit terms 3/15 net 30 given, the nominal cost is computed approximately as 3.093%. These terms suggest that the loan period repeats every 15 days if the discount is not taken.
  • The formula to convert the nominal rate to an EAR is:\[ \text{Effective Annual Rate} = \left(1 + \text{Nominal Rate}\right)^{\frac{365}{\text{Period}}} - 1 \]
  • Plugging in our values, we get \( \left(1 + 0.03093\right)^{\frac{365}{15}} - 1 \).
  • This simplifies to an effective annual rate of approximately 86.86%.
This high percentage reflects the substantial benefit of taking the discount under the described terms versus deferring payment.
Credit Terms
Credit terms are a significant part of purchase agreements between businesses. They define when and how payments should be made. In the scenario of 3/15 net 30,
  • The number '3' represents a 3% discount offered by the seller.
  • '15' indicates the number of days you have to pay the invoice with the discount potential.
  • 'Net 30' implies that if not paid within the early discount period, the full invoice amount is due in 30 days.
These terms urge buyers to make their payment within 15 days to avail of the discount, which ultimately reduces their purchase costs. However, if the discount isn’t taken, the nominal and effective costs exemplify the expense of delaying the payment until day 30. Thus, it often pays to utilize the discount if cash flow allows.

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Most popular questions from this chapter

The Prestopino Corporation is a leading U.S. producer of automobile batteries. Prestopino turns out 1,500 batteries a day at a cost of \(\$ 6\) per battery for materials and labor. It takes the firm 22 days to convert raw materials into a battery. Prestopino allows its customers 40 days in which to pay for the batteries, and the firm generally pays its suppliers in 30 days. a. What is the length of Prestopino's cash conversion cycle? b. At a steady state in which Prestopino produces 1,500 batteries a day, what amount of working capital must it finance? c. By what amount could Prestopino reduce its working capital financing needs if it was able to stretch its payables deferral period to 35 days? d. Prestopino's management is trying to analyze the effect of a proposed new production process on the working capital investment. The new production process would allow Prestopino to decrease its inventory conversion period to 20 days and to increase its daily production to 1,800 batteries. However, the new process would cause the cost of materials and labor to increase to \(\$ 7\). Assuming the change does not affect the receivables collection period (40 days) or the payables deferral period \((30\) days), what will be the length of the cash conversion cycle and the working capital financing requirement if the new production process is implemented.

Dorothy Koehl recently leased space in the Southside Mall and opened a new business, Koehl's Doll Shop. Business has been good, but Koehl has frequently run out of cash. This has necessitated late payment on certain orders, which, in turn, is beginning to cause a problem with suppliers. Koehl plans to borrow from the bank to have cash ready as needed, but first she needs a forecast of just how much she must borrow. Accordingly, she has asked you to prepare a cash budget for the critical period around Christmas, when needs will be especially high. Sales are made on a cash basis only. Koehl's purchases must be paid for during the following month. Koehl pays herself a salary of \(\$ 4,800\) per month, and the rent is \(\$ 2,000\) per month. In addition, she must make a tax payment of \(\$ 12,000\) in December. The current cash on hand (on December 1 ) is \(\$ 400\), but Koehl has agreed to maintain an average bank balance of \(\$ 6,000-\) this is her target cash balance. (Disregard till cash, which is insignificant because Koehl keeps only a small amount on hand in order to lessen the chances of robbery.) " The estimated sales and purchases for December, January, and February are shown below. Purchases during November amounted to \(\$ 140,000\). $$\begin{array}{lcr} & \text { SALES } & \text { PURCHASES } \\ \hline & & \\ \text { December } & \$ 160,000 & \$ 40,000 \\ \text { January } & 40,000 & 40,000 \\ \text { February } & 60,000 & 40,000 \end{array}$$ a. Prepare a cash budget for December, January, and February. b. Now, suppose Koehl were to start selling on a credit basis on December 1 , giving customers 30 days to pay. All customers accept these terms, and all other facts in the problem are unchanged. What would the company's loan requirements be at the end of December in this case? (Hint: The calculations required to answer this question are minimal.)

A large retailer obtains merchandise under the credit terms of \(1 / 15,\) net \(45,\) but routinely takes 60 days to pay its bills. Given that the retailer is an important customer, suppliers allow the firm to stretch its credit terms. What is the retailer's effective cost of trade credit?

The text identifies three principal components that jointly comprise the cash conversion cycle. The cash conversion cycle is defined as the average length of time a dollar is tied up in current assets, and it is determined by the interaction between the inventory conversion period, receivables collection period, and the payables deferral period. Ideally, a company wants to minimize the cash conversion cycle as much as possible. In some circumstances, a firm has a comparative advantage in working capital management because of the nature of its business. This cyber-problem looks at two competing booksellers. Barnes and Noble Inc. is a hybrid between the traditional brick and mortar retailer and the Internet retailer. However, approximately 85 percent of its revenues are generated in the traditional retail setting, which will lead us to consider it a traditional retail firm. Amazon.com, on the other hand, represents the new wave of Internet retailing. The success of Amazon.com has spawned the flood of specialty retailing into the Internet marketplace. We will look at the cash conversion cycles of these companies and their implications. For this cyberproblem, you will be accessing information from the web sites for Barnes and Noble Inc. and Amazon.com at http://www.shareholder.com/bks and http://www.amazon.com, respectively. a. Go to Barnes and Noble's web site, and click on "Annuals." Now that you are in the annual report gallery, click on "1999 Annual Report. (HTML version)" to view the 1999 annual report. Click on "1999 Financial Review" and then click on "Consolidated statements of Operations." From the income statement, write down the annual sales and cost of goods sold for \(1999 .\) Assuming a 365 -day year, what are the average daily sales and purchases for Barnes and Noble Inc.? b. Go back one screen and click on "Consolidated Balance Sheets." Write down the 1999 balances shown for the firm's inventories, accounts receivable, and accounts payable. Using this information plus that from part a, calculate its inventory conversion period, receivables collection period, and payables deferral period. c. What is Barnes and Noble's cash conversion cycle? d. Now, access Amazon's web site. Scroll to the bottom of the page, and click on "About Amazon.com." Next, click on "Investor Relations," and then click on "Annual Reports \& Financial Documents." Click on 1999 Annual Report on Form \(10-\mathrm{K},\) and scroll down until you see Amazon's Consolidated Statement of Operations. Find the annual sales and cost of goods sold. Again, assuming a 365 day year, calculate the average daily sales and purchases for Amazon. e. Scroll up a page until you see Amazon's Consolidated Balance Sheets. Record 1999 balances for inventories, accounts receivable, and accounts payable. Use this information to calculate Amazon's inventory conversion period, receivables collection period, and payables deferral period. f. Calculate Amazon's cash conversion cycle. g. Compare the cash conversion cycles of Barnes and Noble and Amazon. What factors are responsible for these differences? Are these differences firm specific, or are they consequences of the nature of the businesses in which these firms operate? h. Interpret your results. Explain in words what the cash conversion cycles you calculated mean for these companies.

The Zocco Corporation has an inventory conversion period of 75 days, a receivables collection period of 38 days, and a payables deferral period of 30 days. a. What is the length of the firm's cash conversion cycle? b. If Zocco's annual sales are \(\$ 3,421,875\) and all sales are on credit, what is the firm's investment in accounts receivable? c. How many times per year does Zocco turn over its inventory?

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