Net Present Value (5 Cash Flows)

\[NPV=CF_0+\frac{CF_1}{(1+r)}+\frac{CF_2}{(1+r)^2}+\frac{CF_3}{(1+r)^3}+\frac{CF_4}{(1+r)^4}+\frac{CF_5}{(1+r)^5}\]

Variables

NPVnet present value (currency)

CF0initial cash flow at period 0 (currency)

CF1cash flow at period 1 (currency)

CF2cash flow at period 2 (currency)

CF3cash flow at period 3 (currency)

CF4cash flow at period 4 (currency)

CF5cash flow at period 5 (currency)

rdiscount rate per period (decimal)

Description

What is this formula?

Net Present Value (NPV) calculates the value today of a series of future cash flows discounted at a required rate of return.

This 5-cash-flow version is an explicit form designed for calculators that do not support summation notation or dynamic cash flow lists.

A positive NPV indicates that the investment is expected to generate value above the required return, while a negative NPV indicates that the investment may destroy value.

When to use it

Use this formula to evaluate investment projects, business decisions, financial assets, capital budgeting alternatives, and cash flow scenarios with up to five future periods.

Example

A project requires an initial investment of $10,000 and generates five annual cash flows.

Data:

CF0 = -10,000

CF1 = 2,500

CF2 = 3,000

CF3 = 3,500

CF4 = 3,000

CF5 = 2,000

Discount Rate = 10% = 0.10

Formula:

NPV=CF0+CF1/(1+r)+CF2/(1+r)^2+CF3/(1+r)^3+CF4/(1+r)^4+CF5/(1+r)^5

Substitution:

NPV=-10,000+2,500/(1.10)+3,000/(1.10)^2+3,500/(1.10)^3+3,000/(1.10)^4+2,000/(1.10)^5

NPV=1,340.06

Result:

Net Present Value = $1,340.06

Interpretation:

Because NPV is positive, the project is expected to create value above the required return.

Applications

Capital budgeting

Investment analysis

Project evaluation

Business valuation

Financial planning

Cost-benefit analysis

Note

This formula is a practical explicit version of the general NPV equation. It is limited to five future cash flows to remain compatible with fCalc and avoid implicit summation. For projects with more periods, additional explicit cash flow terms or specialized financial software may be required.