However, this is only one approach to accounting for risks under uncertainty. It is not universal. For example, professors Cheng Li and Joseph Finnerty note: "In some real-world situations, we can indeed estimate future revenues. However, such calculations cannot be absolutely accurate.
It is therefore advisable to take into how to add taiwan number on whatsapp account a certain level of risk. To do this, the future positive cash flows should be discounted at the rate for certain risk-equivalent securities or investments. This allows the NPV value to be calculated for any investment, regardless of the level of risk."
However, not all experts share this opinion. For example, P. L. Vilensky, V. N. Livshits and S. A. Smolyak express a critical attitude towards this approach:
"This method is often recommended in Western financial literature. It is actively used in practice. However, it is not the only correct one. In addition, this method lacks sufficient theoretical justification."
Examples of NPV calculations
Now let's look at the first example from the table below. Pay special attention to the row "Difference in present value of net cash flows without and with risk." Each value in this row is calculated as the difference between the present value of net cash flows (without risk - PVt') and the present value of net cash flows (with risk - PVt).
Years 0 1 2 3 4 5
Initial investment (I0), thousand USD 3000
Risk-free annual discount rate rt', % 10 10 10 10 10
Risk premium rtp, % 5 5 5 5 5
Annual discount rate taking into account the risk premium rf + rtp, % 15 15 15 15 15
Positive cash flows (Xt), thousand USD 2900 4500 4200 1500 500
Negative cash flows (Yt), thousand USD 1800 2300 2200 1900 1500
Net cash flows (CFt), thousand USD 1100 2200 2000 – 400 – 1000
Present value of net cash flows (excluding risk) PVt', thousand USD. 1000 1818 1503 – 273 – 621
Present value of net cash flows (taking into account risk) PVt, thousand USD 957 1664 1315 – 229 – 497
The difference between the present value of net cash flows without and with risk [DPVt) f thousand USD. 43 154 188 – 44 – 124
Net present value (NPV) taking into account risk, thousand USD 210
During the first 3 years, the difference between the present value of risk-free and risk-adjusted net cash flows (DPVt) remains positive and amounts to 43, 154, and 188 thousand USD, respectively. However, there are also negative values of DPVt in the fourth and fifth years, which amount to -44 and -124 thousand USD, respectively.
Why does accounting for risk reduce the absolute value of a project's discounted negative cash flows? The higher the risk premium, the smaller the impact of negative cash flows on NPV.