Interpretation As Integral Transform
The time-discrete formula of the net present value
can also be written in a continious variation
where
- r(t) is the rate of flowing cash given in money per time, and r(t) = 0 when the investment is over.
Net present value can be regarded as Laplace- respectively 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 = ln(1 + i).
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 and phase shift between commodity price and supply offer) whereas real parts are responsible for representing the effect of compound interest (compare with damping).
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