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Net Present Value (NPV) Tutorial

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Net Present Value (NPV) Tutorial

Key Snapshots

NPV Formulas

The generalised NPV formula is:

    \[NPV = PV - I\]

Where NPV refers to the Net Present Value, PV refers to the Present Value, and I represents an initial investment.

NPV formula for single cash flow:

    \[NPV =\frac{CF_t}{(1+r)^t} - I\]

Here, NPV represents the Net Present Value. CF_t reflects a cash flow that occurs at time t, r represents the appropriate discount rate, and I denotes the initial investment.

NPV formula for multiple cash flows:

    \[NPV = \sum_{t=1}^n \frac{CF_t}{(1+r)^t} - I\]

Here, NPV represents the Net Present value.

CF_t reflects a cash flow that occurs at time t

r represents the appropriate discount rate

n denotes the final time period (the time period in which the final cash flow is earned)

I denotes the initial investment.

If the cash flow stream is an annuity, then the NPV formula for multiple cash flows can transform into this:

    \[NPV = \frac{CF}{r} \left(1 - \frac{1}{(1+r)^n}\right) - I\]

If the cash flow stream is a (constant) perpetuity, then the NPV formula for multiple cash flows transforms into this:

    \[NPV = \frac{CF}{r} - I\]

Relevant NPV formulas on Excel®:

  • PV
  • NPV

NPV Use Cases

The NPV is relevant for:

  • Capital Budgeting / Investment Appraisal
  • Estimating the Yield to Maturity (YTM) of bonds
  • Stock and company valuation

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