Return on investment
The return on investment (ROI) is a calculation used in business used to determine whether a proposed investment is wise, and how well it will repay the investor. It is calculated as the ratio of the amount gained (taken as positive), or lost (taken as negative), relative to the basis.
In mathematical terms, the ROI is (Vf - Vb) / Vb, where Vf is the final value and Vb is the basis. Interestingly, to compensate for a negative ROI one needs a positive ROI that is higher in magnitude. For example, to recoup a 50% loss one needs to realize a 100% gain.
The analysis of the return on investment is either done by statical or dynamical formal methods, which may be distinguished by the role of time in the model chosen. Dynamic models take account of the fact that a later date of payment may be valued inferior in a model with interest rates. In other words, static approaches can be regarded as sufficient, if the distribution of payments in each period may be assumed as equal to others. All basic ROI-Models as deterministic, for instance the well known TCO-model by the Gartners Group. Deterministic models assume the security of prediction. Abandoning this leads into the wide sphere of risk-aware-models, that are basically inspired by the mathematics of insurances.