On the Tools / Options / Calculation menu set Iterations to one
Set up a new cell, lets say in A1, that is equal to itself plus 1 (yes, it is a circular reference)
Each time you calculate, by pressing key F9, you will see the value in A1 increase by one.
Put your formula inside an IF statement so that the your formula only executes when the A2 is equal to one; and is equal to itself when A1 is not equal to one.
So for example:
Lets say your formula is in A2 your formula would be =If(A2=1,Today(),A2)
You can test this for yourself using Excel's Now function formatted to show minutes and seconds.
To reset the New Cell back to one, click in the formula bar and hit enter. (ie - re-enter the formula)
This should work provided you are not using Solver elsewhere in the work book.
Also note, that if you have other circular references in the workbook, Excel will not flag them as such.