Final answer:
The nominal annual percentage cost of the firm's non-free trade credit can be calculated by annualizing the effective cost of a 3% discount foregone over the extended payment period of 60 days, with respect to a 365-day year.
Step-by-step explanation:
The question involves calculating the nominal annual percentage cost of delayed payments on trade credit. The terms given are 3/15, net 45, which means the firm can take a 3% discount if payment is made within 15 days, otherwise, the payment is due in 45 days. However, the firm pays after 60 days. The cost of not taking the discount, therefore, is the discount foregone, which equals 3% for the 45-day credit period (since after day 15, the discount opportunity is lost), plus the 15-day delay where the full invoice amount is due.
To calculate the nominal annual percentage cost, one must first find the effective cost for the extra 15 days (from day 45 to day 60), where the firm could have paid but did not. Since the firm forgoes a 3% discount, the effective interest rate for these 15 days is 3% for the delay. The annualized percentage cost can then be determined by annualizing this effective cost over a 365-day year.
Using the formula for the cost of trade credit, we get:
Discount Percentage: 3%
Discount Period: 15 days (from day 15 to day 30)
Credit Period without discount: 45 days
Days beyond: 60 - 45 = 15 days
The nominal annual percentage cost is calculated by annualizing the discount over the period where credit is extended without taking the discount, which is:
Nominal APR = (Discount / (100 - Discount)) * (365 / (Full Payment Period - Discount Period))
Plugging in the values:
Nominal APR = (3 / (100 - 3)) * (365 / (60 - 15))
This formula will yield the nominal annual percentage cost of the firm's non-free trade credit based on a 365-day year.