LaTeX
0=\sum_{t=0}^{n}\frac{CF_t}{(1+IRR)^t}Variables
- CF_t: cash flow
- IRR: internal rate of return
- t: time index
How to use this formula
Defines an internal rate of return as a discount rate that makes NPV zero.
Important notes
- Multiple sign changes can create multiple IRRs.
- Numerical root finding is usually required.
Quick example
Solve the NPV equation for IRR rather than rearranging algebraically.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Multiple sign changes can create multiple IRRs.
- For the Internal Rate of Return Equation, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Internal Rate of Return Equation, 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
Solve the NPV equation for IRR rather than rearranging algebraically.
Common mistakes
- When copying Internal Rate of Return Equation, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Internal Rate of Return Equation with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Internal Rate of Return Equation 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
0=\sum_{t=0}^{n}\frac{CF_t}{(1+IRR)^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 Internal Rate of Return Equation used for?
Defines an internal rate of return as a discount rate that makes NPV zero.
Can I copy this formula as LaTeX?
Yes. Copy 0=\sum_{t=0}^{n}\frac{CF_t}{(1+IRR)^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.