Editing Net present value (section)

== Interpretation as integral transform ==
The time-discrete formula of the net present value
: <math>\mathrm{NPV}(i,N) = \sum_{t=0}^{N} \frac{R_t}{ (1+i) ^{t}}</math>

can also be written in a continuous variation
: <math>\mathrm{NPV}(i) = \int_{t=0}^\infty (1+i)^{-t} \cdot r(t) \, dt</math>
where
:''r''(''t'') is the rate of flowing cash given in money per time, and ''r''(''t'')&nbsp;=&nbsp;0 when the investment is over.

Net present value can be regarded as [[Laplace transform#Formal definition|Laplace-]]<ref>{{cite journal |last1=Buser |first1=Stephen A. |title=LaPlace Transforms as Present Value Rules: A Note |journal=The Journal of Finance |date=March 1986 |volume=41 |issue=1 |pages=243–247 |doi=10.1111/j.1540-6261.1986.tb04502.x }}</ref><ref>{{cite journal |first1=Robert W. |last1=Grubbström |title=On The Application of the Laplace Transform to Certain Economic Problems |journal=Management Science |volume=13 |issue=7 |date=March 1967 |pages=558–567 |doi=10.1287/mnsc.13.7.558 |jstor=2627695 }}</ref> respectively [[Z-transform#Definition|Z-transformed]] cash flow with the [[integral operator]] including the complex number ''s'' which resembles to the interest rate ''i'' from the real number space or more precisely ''s''&nbsp;=&nbsp;ln(1&nbsp;+&nbsp;''i'').

: <math>F(s) = \left\{ \mathcal{L} f\right\}(s) = \int_0^\infty e^{-st} f(t) \,dt </math>

From this follow simplifications known from [[cybernetics]], [[control theory]] and [[system dynamics]]. Imaginary parts of the [[complex number]] ''s'' describe the oscillating behaviour (compare with the [[pork cycle]], [[cobweb theorem]], and [[phase shift]] between commodity price and supply offer) whereas real parts are responsible for representing the effect of compound interest (compare with [[Damping ratio|damping]]).