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.

See Also

• XNpv
• Irr, XIrr