The present value of cash flow postnumbero and prenumerando
It is considered that receipts (payments) are made either at the beginning of the period or at the end, i.е. they are not distributed within the period, but are concentrated on one of its boundaries. In the first case, the flow is called the "preremerando" stream, and in the second case it is called "postnumerando".
In practice, the flow of "postnumerando" became more widespread, this flow underlies the methods of analysis of investment projects.
With regard to the distribution of cash flows, in practice they are most often distributed unevenly over time and therefore it is more convenient to conditionally classify all receipts by the end of the period. Thanks to this agreement, equal time periods are formed, which makes it possible to develop convenient formalized evaluation algorithms. The flow of "prenumerando" is important in analyzing the initial investment or accumulation (reserving funds) for subsequent investment.
☛ Note that the method of discounting "postnumerando" and "prenumerando" is used in the program, in calculating investment performance indicators, only for the present value of net investments , and does not apply to the cash flow of "net proceeds".
☛ Also, note that the choice of the method of discounting "postnumerando" and "prenumerando" is essential if the discounting step is "year", and does not significantly affect the results with the discounting step "month".
For example, if the discounting step is a year, it is assumed that the investment in the project will be concentrated or reserved at the beginning of the year and will be discounted with a "delay" of one year, in contrast to the cash flow of net proceeds, which are supposed to be more unevenly distributed in practice in time, and therefore it is more convenient to conditionally refer them to the end of the period.
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An example of discounting annuities "postnumerando" and "prenemerando":
| Periods | 1 | 2 | 3 | 4 | 5 | Total |
| The undiscounted cost of an annuity | 100 | 100 | 100 | 100 | 100 | 500 |
| The discounted value of postnumerando = CFn(1 + r)-n | 91 | 83 | 75 | 68 | 62 | 379 |
| The discounted value of prenumerando = CFn(1 + r)-(n-1) | 100 | 91 | 83 | 75 | 68 | 417 |
Thus, the variable of period n in the reduction formulas when using "postnumerando": CFn(1 + r)-n, respectively, when using "prenemerando" n = t - 1, where t is the current month of calculation. That is, in the first period, the given cash flow with "prenumarando" remains unchanged: CF1(1 + r)-0 = CF1.
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