From Microsoft:
Excel uses an iterative technique for calculating XIRR. Using a changing rate (starting with guess), XIRR cycles through the calculation until the result is accurate within 0.000001 percent. If XIRR can't find a result that works after 100 tries, the #NUM! error value is returned. The rate is changed until: 
where:
di = the ith, or last, payment date.
d1 = the 0th payment date.
Pi = the ith, or last, payment.
Good Luck! I use an HP calculator.
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