Present worth with midlife replacement (NPW) calculator

Net present worth including replacement is calculated as −P0 + A × [1−(1+i)^(-n)]/i − C_R/(1+i)^t_R + S/(1+i)^n. Use the stated system boundary and matching input units.

\mathrm{NPW} = -P_{0} + \frac{A \times \left[1 - \left(1 + i\right)^{-n}\right]}{i} - \frac{C_{R}}{\left(1 + i\right)^{t_{R}}} + \frac{S}{\left(1 + i\right)^{n}}

Calculator

Enter the values you know and leave one box empty. Calculate finds the empty one, the result or any input.

Worked example

Given

$P_{0}$ = 45,000 $
$A$ = 16,000 $/year
$i$ = 0.08 —
$n$ = 6 year
$C_{R}$ = 6,000 $
$t_{R}$ = 3 year
$S$ = 2,000 $

\mathrm{NPW} = -45{,}000 + \frac{16{,}000 \times \left[1 - \left(1 + 0.08\right)^{-6}\right]}{0.08} - \frac{6000}{\left(1 + 0.08\right)^{3}} + \frac{2000}{\left(1 + 0.08\right)^{6}} \approx 25{,}463

Symbols and units

Symbol	Meaning	Unit
$\mathrm{NPW}$	net present worth including replacement	$
$P_{0}$	initial capital	$
$A$	annual operating saving	$/year
$i$	discount rate	—
$n$	study years	year
$C_{R}$	midlife replacement cost	$
$t_{R}$	replacement year	year
$S$	terminal salvage	$

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Results are estimates for study and screening. Check the inputs, units and assumptions before you use them for design, billing or contract decisions.