Find the annual internal rate of return of an investment. Use Fixed for a level deposit or withdrawal plus an ending balance, or Irregular for a different cash flow each year.
Default results
| Tab | Inputs | IRR |
|---|---|---|
| Fixed | $10,000 → $15,000, 2 years 6 months, $100/month withdrawn at period end | 29.768% |
| Irregular | $50,000, then −$10,000 / $30,000 / $50,000 | 12.446% |
Examples
Default fixed cash flow
Invest $10,000, hold 2 years 6 months, withdraw $100 at the end of each month, and finish with $15,000. IRR is 29.768% per year. Withdrawals total $3,000, total return is $8,000, and gross return is 80.000%.
Machine purchase (irregular years)
A $40,000 machine returns $10,000, $20,000, and $30,000 at the ends of years 1–3. IRR is 19.438%. Its NPV is positive at a 12% required return and negative at 20%; risk and project scale still require separate review.
Same 50% ROI, different IRR
Two $100,000 projects each return $150,000 over five years (50% ROI). Front-loaded cash flows (5 / 20 / 25 / 40 / 60 thousand) have IRR 11.290%. Back-loaded cash flows (0 / 10 / 30 / 30 / 80 thousand) have IRR 10.259%.
Formula
IRR is the rate r that sets net present value to zero. Times are in years:
NPV = Σ CF_t / (1 + r)^t = 0
CF₀ is the initial investment (an outflow). Later cash flows are deposits (outflows), withdrawals (inflows), or the ending balance at the holding date.
On the Fixed tab, complete periods are floor((years + months/12) × payments per year). A leftover fraction of a year still discounts the ending balance,
but does not add another deposit. Beginning-of-period cash flows include one
extra payment at t = 0.
Gross return is total return divided by capital (the initial investment plus any extra deposits or further investments).
Weekly and biweekly holdings assume a 52-week year (52 weeks or 26 two-week periods).
Interpreting IRR
IRR is a mathematical root, not an accept-or-reject recommendation. Cash flows that change sign more than once can have multiple real IRRs or none; this solver returns one root found from its search sequence and does not enumerate every root. Compare NPV at an appropriate required return and consider scale, risk, financing constraints, and mutually exclusive alternatives before using IRR in a decision.