Net Present Value - Interpretation As Integral Transform

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).

Read more about this topic:  Net Present Value

Famous quotes containing the words integral and/or transform:

    Painting myself for others, I have painted my inward self with colors clearer than my original ones. I have no more made my book than my book has made me—a book consubstantial with its author, concerned with my own self, an integral part of my life; not concerned with some third-hand, extraneous purpose, like all other books.
    Michel de Montaigne (1533–1592)

    He had said that everything possessed
    The power to transform itself, or else,
    And what meant more, to be transformed.
    Wallace Stevens (1879–1955)