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# Net present value(NPV), the basics

Computations:
 Summary: Net Yields: 140726 Installment Credits: 84993 Net Present Values: 74408 Pension by lump sum payment: 54432 Repayment Plan: 37421 Savings Plans: 24766 Early repayment charge: 2298 Performance of the system

## The net present value, residual value or current value

The net present value tells you the value of a pending sequence of payments at today's time.

It answers the question, what is the fair price for a contract that still brings certain payments. For example, the termination of a lease contract before it expires. Or the sale of a security with some disbursements pending. It is thus the typical question for the secondary market of fund portions.

## Comparison net yield

To determine the value of a sequence of pending payments you need to indicate a comparison net yield, which could be obtained alternatively with the capital. One could call this comparison net yield or the capital costs if one needs to borrow the money. This comparison net yield should contain a risk impact, which covers the uncertainty of the payments that can be received. For example one could take the net yield (approx. 4%) of government notes as the comparison net yield and add some points for the higher risk. Mostly you will use comparison yields from 4-10%. Where 4% represents very safe investment and 10% an investment in a business with certain risks.

## The formula

NPV = Sum of (payments /((1 + comparison yield)powers duration))

NPV= net present value
Comparison yield: eg. 6% = 0.06
Duration: the time between the purchase date and the date of a payment in years. One year is thus 1 and one day 1/365 or 1/365.25.
The formula in a mathematical expression:
```                N
NBW(B, t, r) = Sum B[i]/(1+r)^t[i]
i=0

```
here:
B[i] is the i.th payment amount.
r is the indicated comparison yield.
t[i] is the time between the beginning (e.g. buy) and a date of a payment. The unit of the time can be arbitrarily selected. However, one must select years as unit for the time to obtain the net yield per year or per annum (p.a.).
Summary: to obtain the NPV you simply build the sum of all payments whereby the worth of payments, with a maturity in the future, is reduced as a function of the time and the comparison yield. With a comparison yield from 0% the net present value is equal to the sum of all still pending payments. The more detailed article Future and Present Value of Money is available at invest-faq.com.

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