Net Present Worth (NPW) of a Cash Stream
The value of a stream of payments is called the Net Present Worth (NPW).
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 = F0 / (1 + i)0 + F1 / (1 + i)1 + F2 / (1 + i)2 + .... + Fn / (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
| Period | Cash Flow | Cash Flow (discounted) |
|---|---|---|
| 0 | ||
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| 9 | ||
| 10 | ||
| 11 | ||
| 12 | ||
| 13 | ||
| 14 | ||
| 15 | ||
| 16 | ||
| 17 | ||
| 18 | ||
| 19 | ||
| 20 | ||
| 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!
