Corporate Finance
IRR and payback
IRR is the discount rate that makes a project's NPV zero; payback measures how quickly the outlay returns.
Definition
The internal rate of return is the single discount rate at which a project's net present value equals zero. It expresses the project's return as a rate, which makes it easy to compare against a hurdle rate.
IRR has two well-known weaknesses: it ignores project scale, and unconventional cash flows can produce more than one IRR. The modified IRR (MIRR) and the payback period are used alongside it to cover those gaps.
Intuition
IRR answers 'what rate does this earn?'. NPV answers 'how much value does this add?'. When they disagree, value wins.
When to use it
- Communicating a project's return as a rate to non-specialists.
- Screening many small projects quickly, then ranking the survivors by NPV.
When not to use it
- Ranking mutually exclusive projects of different sizes: use NPV.
- Cash flows that change sign more than once, which can create multiple IRRs.
Formula
Internal rate of return
0 = Σ [CFₜ ÷ (1 + IRR)ᵗ] − C₀
The rate at which NPV is exactly zero.
Formula
Payback period
Full years before recovery + (Unrecovered ÷ Next-year cash flow)
How long until cumulative cash recovers the outlay, ignoring the time value of money.
Worked example
IRR and payback on the same project
Invest 120,000; receive 45,000, 50,000, 50,000, 40,000, 30,000 over five years.
- 1
Cumulative cash
45,000 then 95,000 then 145,000.
- 2
Locate payback
The outlay is recovered during year three.
- 3
Interpolate
2 + (120,000 − 95,000) ÷ 50,000 = 2.5 years.
- 4
Zero NPV
NPV falls to zero at an IRR of roughly 24.9%.
Payback is 2.5 years and the IRR is about 24.9%. Both are strong, and NPV at a 10% cost of capital is about +45,745.
Common mistakes
- Choosing the higher-IRR project when a larger project adds more NPV.
- Assuming a single IRR always exists.
- Treating payback as a measure of profitability: it ignores everything after recovery.
How it connects
contrasts with
Often confused, but different in an important way.
- NPV and IRR: A rate of return versus an amount of value.
relates to
Useful to study together, in either order.