Internal Rate of Return (IRR)

What is IRR?

The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of an investment’s cash flows equal to zero. Practically, IRR is an estimated annualized rate of return for a project or investment that accounts for the timing of cash inflows and outflows.

Formula

Set NPV = 0 and solve for IRR:

0 = NPV = Σ (Ct / (1 + IRR)^t) − C0

where:
* Ct = net cash flow at period t
* C0 = initial investment (usually a negative outflow)
* t = time period (1…T)

Because IRR appears in the denominator for each period, it must usually be found iteratively (trial-and-error) or by using software.

How to calculate IRR

1. List all cash flows in chronological order, including the initial outlay (negative).
2. Use an iterative solver to find the discount rate that makes NPV = 0.
3. Tools:
4. Excel: =IRR(range) for regular periodic cash flows.
5. Excel: =XIRR(values, dates) for irregular timing.
6. Excel: =MIRR(values, finance_rate, reinvest_rate) computes a modified IRR (assumes different financing and reinvestment rates).

Interpretation and uses

• IRR represents the annualized growth rate an investment is expected to generate.
• Common uses:
• Capital budgeting — compare projects and prioritize those with higher IRR.
• Comparing projects to a company’s cost of capital (WACC) or required rate of return (RRR).
• Evaluating buybacks, real estate, private investments, and money-weighted returns (MWRR).
• IRR rule: accept a project if IRR > required rate (e.g., cost of capital); reject if IRR < required rate.

IRR and WACC / RRR

• WACC = weighted average cost of capital; it’s the typical benchmark for projects.
• A project with IRR > WACC is expected to create value; firms often require IRR > RRR (which may be set above WACC to reflect risk or opportunity cost).
• Compare IRR to other market or investment alternatives when setting thresholds.

Comparison with other metrics

• IRR vs. CAGR:
• CAGR uses only beginning and ending values to compute a smooth annual growth rate.
• IRR handles multiple interim cash flows and timing differences.
• IRR vs. ROI:
• ROI measures total percentage gain/loss over the entire holding period (does not annualize or account for timing).
• IRR annualizes returns and incorporates time value of money.

Limitations and pitfalls

• Multiple IRRs: non‑conventional cash flows (sign changes more than once) can produce multiple IRR solutions.
• No IRR: if all cash flows are the same sign (always negative or always positive), no real IRR will make NPV = 0.
• Reinvestment assumption: IRR implicitly assumes interim cash flows are reinvested at the IRR itself. MIRR can be used to assume different reinvestment/finance rates.
• Scale and timing: IRR alone can mislead when comparing projects of different sizes or durations (a small, short project may have higher IRR but lower absolute NPV).
• Sensitivity to forecasts: IRR depends on projected cash flows, which are uncertain—use scenario and sensitivity analysis alongside IRR.

Example

A company with a 10% cost of capital evaluates two projects:

Project A
* Initial outlay: −$5,000
* Year 1: $1,700
* Year 2: $1,900
* Year 3: $1,600
* Year 4: $1,500
* Year 5: $700
IRR ≈ 16.61%

Project B
* Initial outlay: −$2,000
* Year 1: $400
* Year 2: $700
* Year 3: $500
* Year 4: $400
* Year 5: $300
IRR ≈ 5.23%

Decision: With a 10% cost of capital, accept Project A (IRR > 10%) and reject Project B (IRR < 10%).

Practical guidance

• Use IRR alongside NPV, WACC, and scenario analysis—not as the sole decision rule.
• For non‑standard cash flows or when reinvestment assumptions matter, use XIRR (irregular timing) or MIRR (modified reinvestment assumptions).
• When comparing projects, consider both IRR and absolute returns (NPV), as well as project scale, risk, and duration.

Key takeaways

• IRR is the discount rate that sets NPV to zero and estimates an investment’s annualized return.
• It’s useful for ranking projects, but has limitations (multiple solutions, reinvestment assumption, sensitivity to forecasts).
• Combine IRR with NPV, WACC/RRR comparisons, and scenario analysis to make well‑rounded capital allocation decisions.