A firm is offered trade credit terms of 2/8, net 45 days. The firm does not take the discount, and it pays after 58 days. What is the effective annual cost of not taking this discount? (Assume a 365-day year.)

Question

Quizplus · Accepted Answer

First, we need to calculate the cost of not taking the discount. To do this, we need to find the effective annual interest rate (EAR) that is equivalent to the trade credit terms.

The formula to calculate EAR is: 
EAR = (1 + (Discount / (1 - Discount)) ^ (365 / (Days Payable - Discount Period))) - 1

where, 
Discount = percentage discount offered 
Days Payable = total number of days in the credit period

Substituting the given values, we get: 
Discount = 2% = 0.02 
Days Payable = 45

EAR = (1 + (0.02 / (1 - 0.02)) ^ (365 / (45 - 2))) - 1 
    = 0.2095 or 20.95%

So, the cost of not taking the discount is 20.95% per year.

Next, we need to adjust this cost for the number of days of delay in payment. Since the firm pays after 58 days instead of 45 days, it incurs an additional 13 days of interest cost.

The formula to adjust the cost for delay is: 
Adjusted Cost = (Cost of not taking the discount / (1 - Discount)) ^ (365 / Days Delayed) - 1

Substituting the values, we get: 
Cost of not taking the discount = 20.95% 
Discount = 2% = 0.02 
Days Delayed = 58 - 45 = 13

Adjusted Cost = (0.2095 / (1 - 0.02)) ^ (365 / 13) - 1 
            = 0.1589 or 15.89%

Therefore, the effective annual cost of not taking the discount and paying after 58 days is 15.89%.

The best choice is D, 15.89%.

A Firm Is Offered Trade Credit Terms of 2/8, Net