IRR Calculator

What Is IRR?

The Internal Rate of Return (IRR) is the discount rate at which the net present value (NPV) of a series of cash flows equals zero. In plain English, it's the constant annual return that makes the project's inflows exactly repay its outflows. \[ 0 = \sum \frac{CF_t}{(1 + IRR)^{t}} \]

Where \(CF_t\) is the cash flow at period \(t\). This tool puts every cash flow into one list, treated as periods 1, 2, 3, … in order and discounted accordingly; the up-front investment is simply the first item (period 1).

IRR vs. NPV vs. ROI

• IRR — a rate, comparable directly to your hurdle rate (cost of capital, required return).
• NPV — a dollar amount, dependent on the discount rate you choose.
• ROI — a simple ratio, ignores the time value of money.

IRR is the rate where NPV equals zero, so they answer complementary questions.

Worked Example

A project costs $10,000 today and returns $3,000, $4,200 and $6,800 over the next three years:

\[ NPV(r) = -10000 + \frac{3000}{1+r} + \frac{4200}{(1+r)^{2}} + \frac{6800}{(1+r)^{3}} \]

Setting NPV = 0 and solving gives IRR ≈ 16.34% — the project's break-even annual return.

How We Solve It

IRR has no closed-form solution, so we use:

1. Newton-Raphson (fast, requires a reasonable starting guess). Convergence is quadratic near the root.
2. Bisection fallback if Newton-Raphson stalls. Robust but slower.

Both converge to within 1e-7 of the true IRR or terminate after 200 iterations.

Multiple IRRs

When cash flows switch sign more than once (e.g., one negative followed by positive, then negative again), the polynomial NPV(r) = 0 can have multiple real roots. In that case, IRR is ambiguous and you should fall back to NPV at your cost of capital.

Common Pitfalls

1. Reinvestment assumption: IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself, which is rarely true in practice. The Modified IRR (MIRR) fixes this by using a separate reinvestment rate.
2. Scale blindness: A $1,000 project returning $2,000 has the same 100% IRR as a $1M project returning $2M. Always compare to scale and NPV.
3. Timing matters: IRR rewards projects that return money early, which can bias you away from long-horizon value creation.
4. Hurdle rate comparison: IRR is only useful compared to your required return. A 15% IRR is bad if your cost of capital is 12%; great if it is 8%.

When to Use IRR

• Comparing mutually exclusive projects with similar scale and timing.
• Communicating returns to non-financial stakeholders (IRR is intuitive as a percentage).
• Quick screening before a full NPV / DCF analysis.

For capital budgeting and valuation, prefer NPV as the primary metric and use IRR as a sanity check.

How to fill this tool in and read the results

This tool has only one input method: enter all cash flows in the same list, treated as periods 1, 2, 3, … in order and discounted accordingly. There is no separate "initial outlay" box — the up-front investment is just the first item in the list (a negative number means an outflow). The bottom of the list always keeps one empty input; typing in it adds a new row automatically, and "Bulk set" lets you paste a whole series at once.

Why does the Net Present Value (NPV) show 0? The NPV shown is recomputed at the IRR the solver found. By definition, IRR is the discount rate that makes NPV = 0, so NPV(IRR) is necessarily ≈ 0 (a few cents of residual is just the convergence tolerance). This number is there to confirm the solver actually converged to a root — it does NOT mean the project loses money. To judge "do it or not", discount at your own cost of capital (required return) — that NPV may be positive or negative. This tool currently only shows NPV (at the IRR).

What is the Initial Guess (%)? It is the starting search point for the numeric solver (Newton-Raphson), expressed in % (default 10 means 10%). IRR has no closed-form solution, so the solver iterates from near this number to find the root. For normal projects, leaving the default 10% converges to the true IRR; only when it reports "no solution" or the cash flows change sign multiple times (multiple IRRs) does a different guess closer to your expectation help. Once converged, the guess does not change the true IRR.

About This Tool

IRR is solved with Newton-Raphson followed by a bisection fallback. NPV at the solved rate is reported to confirm convergence. The chart shows each period's cash flow as a coloured bar (green inflow, red outflow) and the cumulative cash flow as an amber line so you can see when the project breaks even.