NPV risk definition
The Net Present Value (NPV) is a tool that allows determining the economic viability of a project. The NPV is equal to the disbursement of the initial investment of the project plus the present value of the future flows of said project. In such a way that if the NPV is positive, it indicates that the project is viable, since the present value of the flows is greater than the initial disbursement), and if it is negative, the project should be rejected as the present value of the flows is less than the initial investment.
The disbursement of the initial investment of the project takes a negative value (since it is a disbursement). For its part, the current value of the flows is equal to the cash flow of year ‘n’ divided by 1 plus the rate of return required for the project raised to year ‘n’.
So, the risks associated with the NPV can come from different routes.
a) Initial investment
When a project is launched there is usually an associated budget. However, said budget may be affected by implementation problems and may be greater than initially planned. In such a way that if the initial investment is greater, it may be that the current value of the flows does not cover said investment.
Initial investment higher than expected → lower NPV
b) Cash flow
Due to the fact that any project is an actor in the economy and this is not always predictable, the results of the cash flows do not have to be exact to those initially estimated.
At this point we must differentiate between two risks:
i) Amount
Appears when the amount of the estimated cash flows does not match the real one. The reason may be because the sales of the product have been lower than expected or because the costs have been higher.
Lower cash flow than expected → lower NPV
ii) Moment
Since the cash flows are their present value, the time variable (or moment of obtaining said flows) takes on relevant importance. This is why if there is a delay in obtaining a certain flow, its current value decreases, as it is updated to a longer period.
Delay in obtaining cash flow → lower NPV
c) Discount rate
The rate of return applied to obtain the NPV is equal to the minimum return required for the project. This minimum return depends on the investment alternatives that exist in the market at that time and, in particular, on the rate of return of so-called risk-free investments. This risk-free rate is usually represented by the 10-year bond of the country in which the investment is being made. Therefore, if the interest rates of the 10-year bond increase, the minimum return required for the project should also increase. If it rises, the current value of the flows will decrease, which may imply that the NPV becomes negative, with which the project would not be recommended.
Increase in interest rates → lower NPV
Although nothing is certain in economics except for volatility (any data is volatile), the estimated NPV at first may not coincide with the real NPV obtained for the reasons stated. However, there are tools that allow this volatility to be included in the forecasts, which can be:
• Creation of scenarios: different NPVs can be created based on different scenarios and give each one a probability of occurrence. In such a way that the resulting NPV will take into account the probability of each of the scenarios. Keep in mind that a scenario with a low probability of occurrence does not mean that it will not occur.
• Volatility of the variables: if we incorporate the volatility or standard deviation in each of the variables that affect the NPV, we will obtain an adjusted NPV. As an example, the NPV of a project with relatively certain flows will have less volatility than one with very erratic flows (cyclical company).
Xavier Brun is Doctor in Economic and Business Sciences and director of the UPF Barcelona School of Management (Pompeu Fabra University)
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