LaTeX
NPV=\sum_{t=0}^{n}\frac{CF_t}{(1+r)^t}Variables
- CF_t: cash flow at time t
- r: discount rate
- n: final period
How to use this formula
Sums discounted cash flows including the initial investment.
Important notes
- Cash-flow signs must be consistent.
- NPV depends on the selected discount rate.
Quick example
An initial outflow is usually CF0<0.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Cash-flow signs must be consistent.
- For the Net Present Value, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Net Present Value, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- Match the interest rate to the compounding period, convert percentages to decimals, and keep cash-flow timing consistent.
Worked example
An initial outflow is usually CF0<0.
Common mistakes
- When copying Net Present Value, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Net Present Value with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Net Present Value in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
NPV=\sum_{t=0}^{n}\frac{CF_t}{(1+r)^t}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Net Present Value used for?
Sums discounted cash flows including the initial investment.
Can I copy this formula as LaTeX?
Yes. Copy NPV=\sum_{t=0}^{n}\frac{CF_t}{(1+r)^t} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.