The answer is because, using the indirect method of preparing a cash flow statement, you are trying to adjust net income (loss) ("NI") to net cash provided by operations.
Basically, any noncash gain or loss that's included in NI needs to adjust NI to get to net cash provided by operations.
In this case, it appears that the AR was not, "written off," but was reserved for via bad debt expense. Well, the cash collection of that is going to be shown in the cash flow statement as increase/decrease in accounts receivable.
In other words, it appears you are incorrectly trying to associate the cash collection with the bad debt expense and those don't go hand in hand (assuming that the AR was not written off with a JE that Dr Bad Debt Expense).
The "gain" here (the reversal of previously recorded bad debt expense) is included in net income, but is non-cash. As such, you need to subtract it from NI, as it was increasing NI, but was non-cash. It is conceivable that this could be buried in the change in accounts receivable altogether. But, since the expense was broken out, it would be consistent to show the reversal on the cash flow statement as well.
Or, look at it this way: If you are recording the expense in the SOCF, why wouldn't you record the recovery? It would seem strange to have that be a one-way street.
If the AR was actually written off with the bad debt expense, the receivable would first need to be restored in the AR aging, then the cash applied to it. The restoration of AR should generate a reversal of bad debt expense on the SOCF as well.
If you have any questions, let me know
