Question Help Needed – Receivables

Hi there,

I have been working through a question on the acca website (extra constructed questions) and even though I see the solution I am still unsure why the answer is what it is. I will paste the question below with the solution:

Question:
KXP Co is an e-business which trades solely over the internet. In the last year the company had sales of $15 million. All sales were on 30 days’ credit to commercial customers.

Extracts from the company’s most recent statement of financial position relating to working capital are as follows:

Trade receivables 2,466,000
Trade payables 2,220,000
Overdraft 3,000,000

In order to encourage customers to pay on time, KXP Co proposes introducing an early settlement discount of 1% for payment within 30 days, while increasing its normal credit period to 45 days. It is expected that, on average, 50% of customers will take the discount and pay within 30 days, 30% of customers will pay after 45 days, and 20% of customers will not change their current paying behaviour.

KXP Co has an overdraft facility charging interest of 6% per year.

Calculate the net benefit or cost of the proposed changes in trade receivables policy and comment on your findings.

Solution:
Current receivables = $2,466,000

Receivables paying within 30 days = 15m x 0·5 x 30/365 = $616,438
Receivables paying within 45 days = 15m x 0·3 x 45/365 = $554,795
Receivables paying within 60 days = 15m x 0·2 x 60/365 = $493,151
Revised receivables = 616,438 + 554,795 + 493,151 = $1,664,384

Reduction in receivables = 2,466,000 – 1,664,384 = $801,616
Reduction in financing cost = 801,616 x 0·06 = $48,097

Cost of discount = 15m x 0·5 x 0·01 = $75,000

Net cost of proposed changes in receivables policy = 75,000 – 48,097 = $26,903

Now what I am confused with is that in the question it states that 20% of customers do you change their payment method however it doesn’t state in the question what there usual payment method is. How are we to assume they pay in 60 days as suggested in the solution?
Secondly for the net cost of the proposed changes I would have thought that this would be the cost of the discount plus the finance costs because both are putting the company in a disadvantageous position at face value (in that, the company has to discount sales hence reducing profits and cash).

Thank you.