There are two ways to assign a budget on the "Iterations" page: Assigning a budget to an iteration or assigning a budget to a work item.
Budgets are usually assigned to iterations or even whole releases. After you assign a budget to a iteration, you can go to the "Budgets" page, click on that budget, and verify that the iteration was added by looking in the Included section of the page. You can also view the list of included work items from that iteration. For more information about the "Budgets" page, see "Budgets" Page: Budgets Page Overview.
However, if you only want to bill a customer for certain work items in an iteration, you can simply exclude them from one budget and assign them to a different one by clicking on the "Budget" column dropdown arrow next to each work item row on the "Iterations" page (see more details, below). These work items will display in the Excluded section of that budget on the "Budgets" page. For more information on changing work item budgets, see "Times Explorer" Page: Single, Bulk-Assigning and Removing Budgets.
Please note that budgets are inherited. A budget that is assigned to a parent object will be used by all child objects as long as no other budget is assigned. Therefore, the assignment of different budgets to child items are considered exceptions to the inherited budget settings.
For example, if you assigned a budget to the whole release (Budget "A"), but you assign a different budget (Budget "B") to a product backlog item (PBI), somewhere deep inside this release (e.g. in release\iteration\parent PBI\child PBI), all times that have been recorded on that PBI or to its child items are then counted in Budget "B".
Important: The budget inheritance from a parent work item to child work items overrides the budget inheritance from an iteration to its work items.
Assigning a Budget to an Iteration
1. Sign in to your Team Services or Team Foundation Server account.
2. On the Time menu bar, click Iterations.
3. In the left pane, click the iteration name for which you want assign a budget.
4. At the top-right corner of the web page, click the Budget dropdown -> The list of budgets created on the "Budgets" page displays.
5. From the dropdown list, select the budget that you want to assign to the selected iteration.
Assigning a Budget to a Work Item
1. On the Time menu bar, click Iterations.
2. In the left pane, click the iteration name.
3. In the Budget column, click the row corresponding to the work item in the work items list -> The dropdown displays the list of budgets created on the "Budgets" page.
4. From the drop-down list, select the budget that you want to assign to the work item.