Calculates the net present value of a series of cashflows using a constant interest rate.

If the timescale was yearly and the interest rate was 10% per annum, the syntax would be:

NPV(0.1, Cashflow)

If the rate is entered as a percentage-formatted line item, the result would be:

NPV(Rate, Cashflow)

In the latter case, the rate would be entered as 10%.

**What rate to use for monthly timescales?**

The rate is entered per period, so a 10% annual interest rate is equivalent to 0.7974% per month based on 12 equal periods.

(1+r)^{n}= 1.10 where ^{n} is the number of periods per year |

r = ((1.10) ^{1/12}) - 1 = 1.007974 or 0.7974% |

Whatever timescale is used for the cashflow, the NPV result is a single solution that does not require a timescale dimension. The NPV result is calculated based on cash flows over the entire span of the timescale.

NPV is the solution to the equation shown:

- Rate is the discount rate.
^{d}_{i}is the number of days from the start of the first time period^{P}_{i}is the payment in the ith period.- N is the number of payments in and out over the entire timescale.

## Syntax

NPV(d, c, [m, t]) where:

- d: Number: Discount Rate. Enter as a number, such as 0.1 meaning 10%
- c: Number: Cash flow. Must have at least one negative and one positive value
- m: The date of each transaction
- t: The name of the list containing the schedule of transactions

## Format

Input Format | Output Format |
---|---|

d: Number: percentage c: Number: Decimal m: The date of each transaction t: The name of the list containing the schedule of transactions |
Number |

## Arguments

The function uses the following arguments:

- d: Number: Numeric line item, property, or expression
- c: Number: Numeric line item, property, or expression
- m: Date: Hard-coded date, date variable, or line item
- t: Transaction List: List-formatted line item

## Constraints

The function has no constraints.

## Excel equivalent

## Example

#### NPV using Dates

NPV(Discount Rate, Cashflow, Date, Transactions)

- Discount Rate: Enter as a number, such as 0.1 meaning 10%. Alternatively input into a percentage-formatted variable in the module itself.
- Cashflow: Numeric cash values. Must have at least one negative and one positive value.
- Date: The date of each transaction
- Transactions: The name of the list containing the schedule of transactions.

**NPV Example using Dates**

In the example shown, a series of cash transactions and the dates are entered in the module named *Schedule*. This module has a list named *Transactions* as one of its dimensions. The *IRR *and *NPV *are calculated for each project.