Factoring

Sir i have a doubt in this quesion

The finance director of Widnor Co has been looking to improve the company’s working capital management.
Widnor Co has revenue from credit sales of $26,750,000 per year and although its terms of trade require all credit
customers to settle outstanding invoices within 40 days, on average customers have been taking longer. Approximately
1% of credit sales turn into bad debts which are not recovered.
Trade receivables currently stand at $4,458,000 and Widnor Co has a cost of short-term finance of 5% per year.
The finance director is considering a proposal from a factoring company, Nokfe Co, which was invited to tender to
manage the sales ledger of Widnor Co on a with-recourse basis. Nokfe Co believes that it can use its expertise to
reduce average trade receivables days to 35 days, while cutting bad debts by 70% and reducing administration costs
by $50,000 per year. A condition of the factoring agreement is that the company would also advance Widnor Co 80%
of the value of invoices raised at an interest rate of 7% per year. Nokfe Co would charge an annual fee of 0·75% of
credit sales.
Assume that there are 360 days in each year.

Sir here if the Company plans to use the services of the factor then the bad debts will be cut by 70%. So the savings here is 267,500*70% = $187,250. But the rest 30% is a cost to the company right? So it should be included as a cost but then in the answer they have not accounted for the 267,500*30% = $80,250 of bad debts cost.
They have just considered the bad debts saving and not the cost. May i know why?