Npv
Npv(rate,values,I)
Computes the net-present value of a cash flow with equally spaced periods and constant discounting. The first parameter is an assumed discount rate per period. The second parameter, values, is an array indexed by I, where a positive value indicates an inflow (earnings) in that period, and a negative value represents an outflow (payment). Npv is computed as:
The first value is discounted as if it is one step in the future, rather than at the start. This is often not the most convenient convention, since the initial outlay for an investment often starts in the current time period. The convention is adopted by Analytica to match the convention used by Excel. With this convention, the full net-present value is actually obtained by adding the period-zero outlay to the Npv of all future cash flows, e.g.:
- Full_Npv := Initial_outlay + Npv(discountRate, futureFlows, Time)
It is common to have the current year flow in the first element of your values array. In this case, you can adjust the result that the first value is in the starting time period using:
- Npv(rate,values,I) * (1+rate)
Background
A dollar earned today will generally be worth more to you than a dollar earned at some point in the future. Conversely, a dollar spent now is generally more expensive than a dollar spent in the future. This time-value difference is a result of opportunities you may have to put that dollar to work -- e.g., investing in other projects, enjoying that dollar while you are alive, or placing the dollar in alternative investments -- along with inflation. To account for this time-value difference, it is common practice to discount future values. The discount rate is the rate per period that we discount a dollar in the future. If we obtain x dollars one time period in the future, then we would say that its present value is x / (1+r), where r is the discount rate. The net part of net-present value reflects that we are adding up the present values of all cash flows.
Npv is a good way to compare alternative investment options. Its primary limitation is the fact that is presupposes that you can identify the discount rate that applies to you. Because of its widespread use, many organizations are well aware of what their appropriate discount rate is. However, in general, the appropriate discount rate for you is not always obvious. In general, changing the discount rate will change the relative attractiveness of alternative investments, especially if the cash-flow structure of the investments is substantially different.
One practice that is often employed when using a net-present-value analysis is to repeat your analysis across a range of discount rates. This is referred to as a Parametric Analysis. You should use this parametric analysis to understand how your decision is impacted as the discount changes, and then use that understanding to guide your treatment of discount rate.
An alterative to Npv-analysis is the use of Internal Rate of Return (Irr). An Internal Rate of Return analysis avoids the need to select a discount rate a priori, but in general tends to suffer more downsides than a net-present-value analysis. While an Irr approach has some intuitive appeal, an Irr analysis should usually include a parametric Npv analysis also to avoid being mislead (the one exception is when the alternative investment options have almost identical structure).
Net-present value is well-suited to a Monte Carlo treatment of uncertainty. When uncertainty is present, the Expected Net Present Value (ENPV) is often used as a decision criteria. The ENPV is seen when viewing the mean view of an Npv result in Analytica, or obtained in an expression as
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