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 = F₀ / (1 + i) ⁰ + F₁ / (1 + i) ¹ + F₂/ (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

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)

• Internal Rate of Return - IRR

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 !