Arnold Inc.purchases merchandise on terms of 2/10 net 30, and it always pays on the 30th day.The CFO calculates that the average amount of costly trade credit carried is $375,000.What is the firm's average accounts payable balance? (Assume a 365-day year.)
A) $458,160
B) $482,273
C) $507,656
D) $534,375
E) $562,500

Question

Quizplus · Accepted Answer

The firm's average accounts payable balance is calculated by considering the cost of not taking the discount. The discount offered is 2/10 net 30, meaning if the payment is made within 10 days, a 2% discount is available; otherwise, the full amount is due in 30 days. Since the firm pays on the 30th day, it foregoes the discount, effectively borrowing $375,000 at a cost of 2% for 20 days (the difference between paying on the 10th day and the 30th day). To annualize this, we calculate the equivalent annual cost of this borrowing. The formula to find the average accounts payable balance, considering the firm is effectively paying an interest for not taking the discount, is:$$ \text{Average Accounts Payable} = \text{Costly Trade Credit} \times \left(1 + \frac{\text{Discount Percentage}}{1 - \text{Discount Percentage}} \times \frac{\text{Days in Year}}{\text{Discount Period} - \text{Net Period}}\right) $$Given:- Costly Trade Credit = $375,000- Discount Percentage = 2% or 0.02- Days in Year = 365- Discount Period = 10 days- Net Period = 30 daysPlugging the values into the formula:$$ \text{Average Accounts Payable} = 375,000 \times \left(1 + \frac{0.02}{1 - 0.02} \times \frac{365}{20}\right) $$$$ \text{Average Accounts Payable} = 375,000 \times \left(1 + \frac{0.02}{0.98} \times 18.25\right) $$$$ \text{Average Accounts Payable} = 375,000 \times \left(1 + 0.372959 \right) $$$$ \text{Average Accounts Payable} = 375,000 \times 1.372959 $$$$ \text{Average Accounts Payable} \approx 515,109.625 $$However, since this specific calculation does not match any of the provided options and the premise of the calculation was to illustrate the method, it seems there was a misunderstanding in the approach. The correct approach should focus on understanding that the costly trade credit represents the additional cost due to not taking the discount, and the average accounts payable balance would be higher than the costly trade credit due to the opportunity cost of not taking the discount. Given the options and the context, the correct answer should reflect the cost of foregoing the discount over the year, which would typically result in a higher payable balance than the base amount of costly trade credit. However, without the precise calculation matching the options, the explanation aimed to demonstrate the thought process behind calculating the impact of trade credit terms on accounts payable. The correct answer, based on the options provided and assuming a direct relationship between the costly trade credit and the average accounts payable balance that reflects a typical scenario of not taking early payment discounts, would ideally be chosen to reflect the understanding of these financial dynamics. Given the misunderstanding in the calculation, let's correct the approach:The correct approach involves understanding that the costly trade credit is a part of the average accounts payable balance, but without the exact formula or calculation directly leading to the options provided, the focus should be on the principles behind trade credit and its cost implications. The explanation aimed to navigate through these principles, albeit the final calculation did not align with the provided choices, indicating a need for recalibration in the calculation or a reevaluation of the assumptions made.