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.
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By introducing the risk premium into the discount rate, we find that the NPV decreases by $385,000 as a result of the positive DPVt values in the first 3 years of the project's practical implementation ($43,000 + $154,000 + $188,000). At the same time, introducing the risk premium also increases the NPV by $168,000 due to the negative DPVt values in years 4 and 5 [-$44,000 + (-$124,000)].
However, the question arises: does this method really take economic risk into account correctly? It is quite clear that reducing the absolute value of negative cash flows is a benefit.
Example of NPV estimation
Let us consider an example of NPV estimation taking into account risk in the denominator (risk premium rf is taken to be equal to 0%).
Years 0 1 2 3 4 5
Initial investment (I0), thousand USD 200
Risk-free annual discount rate rt', % 10 10 10 10 10
Risk premium rtp, % 0 0 0 0 0
Annual discount rate taking into account the risk premium rf + rtp, % 10 10 10 10 10
Positive cash flows (Xt), thousand USD 3300 2750 2650 2600 2525
Negative cash flows (Yt), thousand USD 2500 3500 2600 2550 2500
Net cash flows (CFt), thousand USD 800 – 750 50 50 25
Present value of net cash flows (excluding risk) PVt', thousand USD. 727 – 620 38 34 16
Present value of net cash flows (taking into account risk) PVt, thousand USD 727 – 620 38 34 16
The difference between the present value of net cash flows without and with risk [DPVt) f thousand USD. 0 0 0 0 0
Net present value (NPV) taking into account risk, thousand USD – 5
Thus, the risk premium (rt) was set at 0%. At the same time, the net present value NPV turned out to be negative, amounting to -5 thousand USD. Based on this, the project should not be implemented.
What will be the valuation of the investment project if we take into account the risk by setting the premium for it (rtp) at 9%? At first glance, it may seem that the NPV value would become even greater in absolute terms.
However, everything is quite the opposite. NPV will not become even more negative, the indicator will even go positive. Thus, the assessment of the investment project has changed not only quantitatively, but also qualitatively. Now it should be accepted, since NPV has become positive and amounted to 7,000 USD.
Let's calculate the indicator taking into account the risk in the denominator (risk premium rtp at 9%)
Years 0 1 2 3 4 5
Initial investment (I0), thousand USD 200
Risk-free annual discount rate rt', % 10 10 10 10 10
Risk premium rtp, % 9 9 9 9 9
Annual discount rate taking into account the risk premium rf + rtp, % 19 19 19 19 19
Positive cash flows (Xt), thousand USD 3300 2750 2650 2600 2525
Negative cash flows (Yt), thousand USD 2500 3500 2600 2550 2500
Net cash flows (CFt), thousand USD 800 – 750 50 50 25
Present value of net cash flows (excluding risk) PVt', thousand USD. 727 – 620 38 34 16
Present value of net cash flows (taking into account risk) PVt, thousand USD 627 – 530 30 25 10
The difference between the present value of net cash flows without and with risk [DPVt) f thousand USD. 55 – 90 8 9 6
Net present value (NPV) taking into account risk, thousand USD 7
Thus, including a risk premium in project evaluation calculations can lead to unexpected results. In this example, the DPVP value, which reflects economic risk, turns out to be so low in the second year (-90) that its absolute value is greater than the sum of all positive DPVt values in the remaining years (55 + 8 + 9 + 6 = 78 thousand USD). Consequently, introducing a risk premium led to an increase in the investment attractiveness of the project.
According to P.L. Vilensky, V.N. Livshits and S.A. Smolyak, in the presence of probabilistic uncertainty in the project assessment, the inclusion of a risk premium is not always the best solution. Sometimes, on the contrary, a correct risk assessment requires a reduction, rather than an increase, in the discount rate.