(1)	$\begin{array}{l}\displaystyle \mbox{MIRR} = \left( \frac{ \sum_t FV[CF^+_t]}{-\sum_t PV[CF^-_t]}} \right)^{1/T} - 1 = (1+r) \cdot \left( \frac{ \sum_t PV_r[CF^+_t]}{-\sum_t PV_{r_f}[CF^-_t]}} \right)^{1/T} - 1\end{array}$

(2)	$\begin{array}{l}\displaystyle PV_{r_f}[CF^-] = \sum_{t=0}^T \frac{CF^-_t}{(1+r_f)^t}\end{array}$

(3)	$\begin{array}{l}\displaystyle FV_r[CF^+] = \sum_{t=0}^T CF^+_t \cdot (1+r)^{T-t} = (1+r)^T \cdot \sum_{t=0}^T \frac{CF^+_t}{(1+r)^t} = (1+r)^T \cdot PV_r[_t}{(1+r)^t} = (1+r)^T \cdot PV_r[CF^+]\end{array}$

where

$\begin{array}{l}T\end{array}$	total investment period	$\begin{array}{l}t\end{array}$	annual counter
$\begin{array}{l}r\end{array}$	reinvestment rate	$\begin{array}{l}r_f\end{array}$	financing rate
$\begin{array}{l}CF^+\end{array}$	positive cash flows	$\begin{array}{l}CF^-\end{array}$	negative cash flows
$\begin{array}{l}CF^+_0 = 0\end{array}$		$\begin{array}{l}CF^-_0 = I_0\end{array}$	initial investment
$\begin{array}{l}\displaystyle FV[CF^+]\end{array}$	future value of the positive cash flows	$\begin{array}{l}\displaystyle PV[CF^-]\end{array}$	present value of the negative cash flows

The usual practise is to give preferences to the Investment Projects with higher MIRR and make a direct comparison of MIRR against the Weighted Average Cost of Capital (WACC).

MIRR is similar to IRR in nature but free from some common IRR issues.

The corporate investment policy usually dictates that:

Investment Projects with MIRR < WACC should be rejected
Investment Projects with higher MIRR should have a financing priority over the Investment Projects with lower MIRR

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See also