Summary: An internal rate of return (IRR) of an investment or financing project with cash flow \((a_ 0,a_ 1,a_ 2, \dots,a_ n)\) is usually defined as a rate of interest such that \(a_ 0+a_ 1(1+r)^{- 1}+\cdots+a_ n(1+r)^{-n}=0\). If the cash flow has one sign change then the previous equation has a unique solution \(r>-1\). Generally the IRR does not extend to fuzzy cash flows, as it can be seen with examples [see \textit{J. J. Buckley}, Fuzzy Sets Syst. 21, 257-273 (1987; Zbl 0613.90017)]. We show that under suitable hypotheses a unique fuzzy IRR exists for a fuzzy cash flow.