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IRR (Internal Rate of Return) is the discount rate that makes the Net Present Value (NPV) of a series of cash flows equal to zero. It is the foundational return metric from which XIRR is derived, and it is conceptually distinct from CAGR.
Formula
NPV = Σ [ CFt / (1 + r)t ] = 0, solve for r
Where: CFt = cash flow at period t (negative for outflows, positive for inflows), t = period number (assumes equal intervals), r = IRR (annualised if periods are years).
IRR assumes equal time intervals between cash flows. When cash flows occur at irregular real-calendar dates (as in SIP investments), the generalised form — XIRR — is used. XIRR replaces the integer exponent t with (di − d0)/365, enabling day-precise discounting.
IRR vs. CAGR vs. XIRR
| Metric | Cash Flow Pattern | Time Intervals | When to Use |
|---|---|---|---|
| CAGR | Single in, single out | Not applicable | Lumpsum investment return |
| IRR | Multiple, periodic | Equal (annually, monthly) | Annual project cash flows (academic/corporate finance) |
| XIRR | Multiple, irregular | Actual calendar dates | SIP portfolios, real-world MF transactions |
For most individual investors in Indian mutual funds, XIRR is the correct metric. IRR is primarily relevant in corporate capital budgeting (evaluating project NPVs with annual cash flows) and real-estate investment analysis.
How IRR is Solved
IRR has no closed-form algebraic solution for n > 2 cash flows. It is computed iteratively via Newton-Raphson or bisection. Excel's =IRR(values) and =XIRR(values, dates) implement Newton-Raphson internally. The algorithm starts with an initial guess (default 10%), computes NPV, adjusts r toward zero NPV, repeats until convergence (typically <20 iterations). Multiple IRRs can exist if the cash flow series changes sign more than once — a known limitation in complex project finance not typically encountered in MF portfolio analysis.
Worked Example
A project requires ₹10,00,000 upfront and returns ₹3,50,000 per year for 4 years (equal annual cash flows — IRR is the right tool, not XIRR).
Solve: −10,00,000 + 3,50,000/(1+r) + 3,50,000/(1+r)² + 3,50,000/(1+r)³ + 3,50,000/(1+r)⁴ = 0
Excel =IRR({-1000000, 350000, 350000, 350000, 350000}) → r ≈ 14.96%
This means the project earns 14.96% p.a. on the invested capital. Compared to an 8% borrowing cost, the project creates positive economic value. CAGR applied here would be incorrect because there are four separate cash inflows, not one terminal value.
IRR and SEBI MF Disclosures
SEBI mandates CAGR for lumpsum performance disclosures (Circular 2021/647). For SIP illustrations, XIRR is mandated. Pure IRR is not referenced in SEBI MF regulation — it lives in SEBI's Infrastructure Investment Trust (InvIT) and Real Estate Investment Trust (REIT) disclosure frameworks, where project-level cash flows follow regular intervals more closely.
Caveats
IRR implicitly assumes that intermediate cash flows are reinvested at the same IRR rate — often unrealistic for high-IRR projects. Modified IRR (MIRR) corrects this by specifying a separate reinvestment rate. For MF analysis, XIRR avoids the reinvestment assumption issue by working with actual market valuations at each date.
Related terms: XIRR, CAGR, Rolling Returns, Total Return.
Primary source: Brealey, Myers & Allen, "Principles of Corporate Finance" (IRR and NPV framework); SEBI InvIT Regulations 2014 for IRR-based project disclosure: sebi.gov.in — InvIT Regulations 2014.
Past performance is not indicative of future returns. Mutual fund investments are subject to market risks. Read all scheme-related documents carefully. ARN-314872. APMI APRN-01658. Content is informational and not investment advice.