Cash collections and bad debt expense issues: why we don't exclude bad debt expense?

Hello!

Below I post an example on computing the cash collections based on the information in the company’s report, when we don’t actually have any more details. I wonder why we don’t have to exclude bad debt expense (or provision for doubtful accounts) in this calculation?

Here is how I understand it:

During the accounting period a company makes sales, and at the end of the period, when it prepares the income statement, it includes the bad debt expense (or provision for doubtful accounts) as an expense on the income statement. Within the accounting period this bad expense is recorded as a Credit to Allowance for Doubtful accounts account, and as a Debit to the Bad Debt Expense account.

So, simplifying a lot:

Gross Profit = Revenue - Bad Debt Expense

Revenue = Cash sales + Ending balance of Accounts Receivalbes

Ending balance of Accounts Receivalbes = Beginning balance of Accounts Receivalbes + Non-cash sales - Write-offs

Therefore, if a company included Bad Debt Expense in the Income Statement, it should mean that the company did not collect this amount as cash, nor it thinks it will collect it. So, why when we compute cash collections we take the gross Accounts Receivable amount, and not the net one, which is minus Allowance for Doubtful Acconts, or why we at least don’t subtract the Bad Debt expense? Please, see example below for more details about my question.

Cash collections = Gross Accounts Receivable Beginning balance + Revenue - Write-offs - Ending balance

Example:

Accounts Receivable Beginning balance, net of Allowance of 220 = 7,826

Accounts Receivable Ending balance, net of Allowance of 1021 = 12,930

Provision for doubtful accounts in the income statement = 1,558

Revenue = 149,270

(1) Find write-offs:

Beginning balance of Allowance for DA + Provision for DA - Ending balance of Allowance for DA =

= 220 + 1,558 - 1021 = 757

(2) Cash collections (formula above) = Gross Accounts Receivable Beginning balance + Revenue - Write-offs - Ending balance =

= 8,046 + 149,270 - 757 - 13,951 = 142,608

It means that the company collected 142,608, but this amount completely ignores the Bad Debt expense reported on the income statement. Shouldn’t this amount be reduced by Provision for doubtful accounts in the income statement = 1,558?

Thank you very much!