# Net Present Worth (NPW) of a Cash Stream

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.

### Example - Investment In Renewable Energy - Discounted Cash Flow

- how to calculate discounted net present value in a typical renewable energy project

### 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

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Discount rate (%) |
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### 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.

#### 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 !

## Related Topics

### • Economics

Engineering economics - cash flow diagrams, present value, discount rates, internal rates of return - IRR, income taxes, inflation.

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### Discrete Compounding Cash Flow Formulas

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