# Net Present Worth - NPW - of a Stream of Payments

## Net Present Worth - NPW - or Value of a stream of payments

The present value of a stream of payments - Net Present Worth (NPW) or Net Present Value (NPV) -

can be calculated with a * discounting rate*

P = F_{0 }/ (1 + i)^{0 }+ F_{1 }/ (1 + i)^{1 }+ F_{2}/ (1 + i)^{2 }+ .... + F_{n}/ (1 + i)^{n }(1)

where

P = Net Present Worth (or Value)

F = cash flow in the future

i = discounting rate

*(1 + i) ^{n}* is known as the "

*compound amount factor*".

### Example - the Net Present Worth of an Investment Transaction with a variable Cash Flow

The Net Present Worth - *NPW* - of investing an amount of *1000* today and saving *250, 200, 300, 310 and 290 *the next *5* years - and selling the investment for *310 *in the last fifth year - at an interest or discount rate of *10%*, can be calculated as

P = (-1000)_{ }/ (1 + 0.1)^{0 }+ (250)_{ }/ (1 + 0.1)^{1 }+ (200) / (1 + 0.1)^{2 }+ (300) / (1 + 0.1)^{3}+ (310) / (1 + 0.1)^{4}+ (290 + 310) / (1 + 0.1)^{5 }

= 202

Net Present Worth is positive and the investment is profitable.

### Net Present Worth Calculator - Variable Cash Flow Stream

The calculator below can be used to estimate *Net Present Wort - NPW -* in an investment project with up to 20 periods and variable cash flows.

- money out - negative values
- money in - positive values

Period | Cash Flow | Cash Flow (discounted) |
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SUM | ||

Discount rate (%) | ||

### Net Present Worth Calculator - Investment with Fixed Cash Flow and Growth Rate

The calculator below can be used to calculate the Net Present Worth for a project with a fixed investment value and fixed return cash flows with a growth rate.

* Investment (money out - at period 0)*

* Fixed Cash Flow (money in - or saved - from period 1)*

* no. of periods (typical years)*

* Discount rate (% per period)*

* Growth rate (% per period - growth of Fixed Cash Flow)*

#### Example - Investing in a Solar Power System

An investment of *30000* in a solar power system saves an amount of *1000 *on the electricity bill the first year. The electricity price is in the future assumed to rise *10%* (growth rate) each year. The alternative use of the money is to invest in a savings account with *3%* interest rate (discount rate).

The lifespan of the solar power system is estimated to *20 years* (no. of periods).

Using these values in the calculator above gives

*P = 12819 *

*IRR = 6.1%*

- and the investment is profitable compared to the savings account.

Using the same values - but for a shorter lifespan of *15 years* - gives

*P = -3581*

*IRR = 1.6%*

- and the investment is not profitable compared to the savings account.

### Net Present Value - Spreadsheet

A flexible Net Present Value and Internal Rate Calculator in Excel spreadsheet format is available here!

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- de: Barwert Diskontsatz