15. Trade accounts receivable

As of December 31, trade accounts receivable were as follows:

€ in millions	2012	2011
Trade accounts receivable	4,056	3,617
less allowance for doubtful accounts	406	383
Trade accounts receivable, net	3,650	3,234

All trade accounts receivable are due within one year.

The following table shows the development of the allowance for doubtful accounts during the fiscal year:

€ in millions	2012	2011
Allowance for doubtful accounts at the beginning of the year	383	317
Change in valuation allowances as recorded in the consolidated statement of income	251	216
Write-offs and recoveries of amounts previously written-off	-221	-154
Foreign currency translation	-7	4
Allowance for doubtful accounts at the end of the year	406	383

The following table shows the ageing analysis of trade accounts receivable and their allowance for doubtful accounts:

€ in millions	not overdue	up to 3 months overdue	3 to 6 months overdue	6 to 12 months overdue	more than 12 months overdue	Total
Trade accounts receivable	2,333	734	295	273	421	4,056
less allowance for doubtful accounts	24	60	39	61	222	406
Trade accounts receivable, net	2,309	674	256	212	199	3,650