Early settlement discounts for receivables question

Hi sir,

May I please ask a question about early settlement discounts for receivables?

In the text book, there is this question:
Company A offers a cash discount of 2.5% to receivables if clients pay debts within one month. The usual credit period taken is three month.
What is the effective annualised cost of offering the discount and should it be offered, if the bank would loan the company at 18% pa.

The provided answer is:
Discount as a percentage of amount page = 2.5/97.5 = 2.56%
Saving is 2 months, thus, the no. of periods = 12/2 = 6 in a year
Annualised cost of discount % is: [(1+2.56%)^6]-1 = 16.38%
The loan rate is 18%, thus it would be worthwhile offering the discount.

However, if I apply the receivables balance to the scenario to verify the result, my calculation shows that the loss from the discount cannot be offset by the benefit from receiving the early settlement. Could you help me find out what went wrong in my calculation? Thanks!

My calculation:
Assuming the company’s sales revenue was $20m the last year, with receivables to be $4m at the year end. Other conditions are not changed, the following will show:

Step 1: calculate the cost of discount:
$20m of revenue x 2.5% discount = $500,000

Step 2: Benefit of having the early settlement:
(1) The current receivables balance is $4m, while the cost of financing when the credit period is 3 months and cost of bank rate 18%:
$4m x 18% interest = $720,000
(2) The new receivables balance, if the new credit period is applied:
$20m of revenue x 1/12 = $1,666,667
The cost of financing this new receivables:
$1,666,667 x 18% interest = $300,000
The saving if the early settlement is applied: (1) less (2)
$720,000 – $300,000 = $420,000

Step 3: compare the savings from Step2 and the loss from the discount from Step 1:
Total loss $500,000 – $420,000 = $80,000

From this perspective, there would have been made a loss of $80,000 if the discount of 2.5% is provided to clients, contrary to the answer provide by the text book.

Could you tell me what went wrong in my calculation? Thanks!