Net Present Value (NPV) Tutorial
The generalised NPV formula is:
Where refers to the Net Present Value, refers to the Present Value, and represents an initial investment.
NPV formula for single cash flow:
Here, represents the Net Present Value. reflects a cash flow that occurs at time , represents the appropriate discount rate, and denotes the initial investment.
NPV formula for multiple cash flows:
Here, represents the Net Present value.
reflects a cash flow that occurs at time
represents the appropriate discount rate
denotes the final time period (the time period in which the final cash flow is earned)
denotes the initial investment.
If the cash flow stream is an annuity, then the NPV formula for multiple cash flows can transform into this:
If the cash flow stream is a (constant) perpetuity, then the NPV formula for multiple cash flows transforms into this:
Relevant NPV formulas on Excel®:
NPV Use Cases
The NPV is relevant for:
- Capital Budgeting / Investment Appraisal
- Estimating the Yield to Maturity (YTM) of bonds
- Stock and company valuation
- Video tutorial on IRR: Internal Rate of Return (IRR) Tutorial
- Course on Investment Appraisal / Capital Budgeting: Investment Appraisal Course
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