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\mbox{MIRR} = \left( \frac{ \sum_t FV[CF^+_t]}{-\sum_t PV[CF^-_t]}} \right)^{1/T} - 1 = (1+r) \cdot \left( \frac{ \sum_t PV_r[CF^+_t]}{-\sum_t PV_{r_f}[CF^-_t]}} \right)^{1/T} - 1
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 PV_{r_f}[CF^-] = \sum_{t=0}^T \frac{CF^-_t}{(1+r_f)^t}



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FV_r[CF^+] = \sum_{t=0}^T CF^+_t \cdot (1+r)^{T-t} = (1+r)^T \cdot \sum_{t=0}^T \frac{CF^+_t}{(1+r)^t} =  (1+r)^T \cdot PV_r[_t}{(1+r)^t} =  (1+r)^T \cdot PV_r[CF^+]]



where

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bodyT

total investment period

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bodyt

annual counter

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bodyr

reinvestment rate

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bodyr_f

financing rate

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body--uriencoded--CF%5e+

positive cash flows
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body--uriencoded--CF%5e-


negative cash flows

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body--uriencoded--CF%5e+_0 = 0


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body--uriencoded--CF%5e-_0 = I_0

initial investment

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body--uriencoded--\displaystyle FV[CF%5e+]

future value of the positive cash flows

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body--uriencoded--\displaystyle PV[CF%5e-]

present value of the negative cash flows

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