Methods of calculation of indicators of investment effectiveness in simple examples
Paul McCoen and Leo Goh, in the section on analyzing business plans, give the following definition: “Discounted cash flows (DCF) are the net cost of a project in monetary terms, taking into account changes 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:CFn – the amount of cash flow for n periods;
r – the discount rate (for example, the weighted average cost of capital, WACC) can be used as the discount rate;
n – the number of periods for which cash flows occur.
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.
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Calculation example payback period
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.
Example of calculating the discounted payback period and other indicators
To calculate the discounted payback period - DPB (Discounted Payback period), the cash flow is pre-discounted, 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: CF5 = 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 12-year 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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