

Paul McCoyne and Leo Goh, in the section on analyzing
business project plans, give the following definition:
«Discounted cash flows (DCF) is the net value of a project
in monetary terms, taking into account the change in
the value of money over time»
When calculating most of the integral indicators, discounted cash flow is used. Discounted Cash Flow (DCF) is a valuation technique used to analyze the attractiveness of a particular investment opportunity. The discounted cash flow analysis (DCF) uses the estimated future free cash flows and discounts them (most often using the weighted average cost of capital, WACC) to obtain their present value, in order to obtain adjusted estimates of the investment potential. If the value obtained from the analysis of discounted cash flows is higher than the current value of the investment, this investment opportunity is attractive. Discounted cash flow is calculated by the formula:
DCF = ∑ _{CFn} (1 + r)^{n}
Where:Sometimes this term is referred to as the "Discounted Cash Flows Model". Discounted cash flow models are a fairly powerful analysis tool, but do not forget that small changes or inaccuracies in the source data can lead to large distortions in project cost estimates.
For calculation of some indicators, for example, the payback period or the average rate of profitability, the usual (not discounted) cash flow is used. See the following example.
Payback period (PB) is the time when the amount of revenue generated by the project will cover the amount of investment. For example, consider the table with the calculation of the payback period.
Periods (years)  1  2  3  4  5  6  7  8  9  10  11  12 
Cash flow  30 000  25 000  17 000  29 000  19 000  14 000  25 000  25 000  14 000  21 000  19 000  14 000 
Cash flow (cumulative)  30 000  55 000  72 000  101 000  120 000  134 000  159 000  184 000  198 000  219 000  238 000  252 000 
Initial investment  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000 
Investments  Cash flow  110 000  85 000  68 000  39 000  20 000  6 000  19 000  44 000  58 000  79 000  98 000  112 000 
In this case, the payback period is 7 years.
To calculate the discounted payback period  DPB (Discounted Payback period), the cash flow is prediscounted, that is, the time for which the project's net present value (discounted) net cash flow exceeds the initial investment.
Periods (years)  1  2  3  4  5  6  7  8  9  10  11  12 
Cash flow  30 000  25 000  17 000  29 000  19 000  14 000  25 000  25 000  14 000  21 000  19 000  14 000 
Discounted cash flow (10% rate)  27 273  20 661  12 772  19 807  11 798  7 903  12 829  11 663  5 937  8 096  6 659  4 461 
Cash flow (cumulative)  27 273  47 934  60 706  80 514  92 311  100 214  113 043  124 705  130 643  138 739  145 399  149 859 
Initial investment  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000  140 000 
Investments  Cash flow  112 727  92 066  79 294  59 486  47 689  39 786  26 957  15 295  9 357  1 261  5 399  9 859 
To calculate the discount amount, for example, in the 5 period, the formula is used: CF_{5} = 19 000 / (1 + 0,1)^{5} = 11 798.
In this case, the discounted payback period is 11 years .
Such a big difference in calculating the payback periods in the PB and DPB in this example is explained simply: the shorter the payback period, the less the impact of the discount rate on cash flow, and vice versa ...
Therefore, if the project lasts long enough, with a relatively uniform cash flow, the "speed" of the project payback will decrease every year. For this reason, most of the projects that are considered by investors as the most preferable in terms of payback are in the payback period of up to 3 years. And, as a rule, in calculations, the step (calculation) of discounting is used  1 month, as well as the final figures are calculated, respectively, in months. Projects with a payback period of more than three years are usually a priori considered as projects with a high degree of investment risks.
Net Present Value  NPV (Net present value) is the amount of income that represents the estimate of the present value of future income. The net present value is the present value of future income, adjusted for the discount rate, less the present value of the initial (total) investment. If you use the DPB calculation table, the NPV calculated for the 12year period will be: 5 399 + 9 859 = 15 258 , respectively, the profitability index  PI (Profitability Index , PI) is equal to: 15 258/140 000 = 10.90% .
Internal rate of return  IRR (Internal Rate of Return),%  is the discount rate at which the total present value of income from investments is equal to the value of these investments. IRR is calculated as the discount rate at which NPV = 0. Internal rate of return is the second indicator after NPV, on the basis of which the attractiveness of investments is determined, and is the "selection" of the indicator, in which NPV = 0. This is done simply in the Excel table. In our case, this indicator (calculated for a period of 12 years) will be approximately equal to ≈ 11.5% .
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