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GLOSSARY · I

IRR

Corporate finance

4 min read

DEFINITION

Internal rate of return: the discount rate at which the net present value of all of a project's cash flows is zero. It turns a stream of cash flows into one annual rate, a return for an investment or a cost for a lease or loan.

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What IRR is

IRR answers one question: at what annual rate do the cash going out and the cash coming in exactly balance, once timing is taken into account? Working it out takes four steps.

1

Cash flows: list every amount in and out, with when it happens, including deposits, fees and any value at the end.

2

Trial rate: discount each flow at a trial rate and add them up to get the net present value (NPV).

3

Iterate: adjust the rate until NPV is zero. Spreadsheets do this with IRR, or XIRR when dates are irregular.

4

Compare: an investment's IRR should beat the hurdle rate. For a lease or loan, IRR is the cost, so lower is better.

IRR is easy to quote and compare, which is why it is widely used. It also has known blind spots, so it works best alongside NPV rather than in place of it.

When IRR is reliable

IRR gives a clear answer for simple cash flows. In other cases NPV at your cost of capital is the safer guide.

WHAT CHANGES

IRR works well

Lean on NPV instead

Cash flow pattern

One outflow, then inflows

Signs change more than once

Choosing between projects

Similar size and life

Different size or life

Reinvestment of cash

Realistic at the IRR

Only possible at a lower rate

Answer you get

A rate to compare

Value added in rupees

How to calculate IRR

Find the rate r for which CF₀ + CF₁ ÷ (1 + r) + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ = 0. There is no direct formula, so the rate is found by trial and error, which spreadsheet functions do for you.

Cost of a lease or loan.

Treat the amount financed as an inflow and each rental, deposit and fee as an outflow. The IRR is the cost. Compare offers on the same basis and after tax.

Known limits.

Cash flows that change sign more than once can give several IRRs or none. IRR also assumes interim cash earns the IRR, which flatters high-return projects.

Annualise a monthly IRR as (1 + monthly rate)¹² − 1, not monthly rate × 12.

Where IRR is used

Screening a warehouse automation project

ILLUSTRATIVE

A logistics company can spend ₹1 crore on sortation equipment that saves ₹30 lakh a year for five years, with no value at the end. The IRR is the rate that makes those savings worth exactly ₹1 crore today: about 15.2%. Its hurdle rate is 12%, so the project clears it. As a check, the NPV at 12% is ₹30 lakh × 3.6048 − ₹1 crore, or about ₹8.1 lakh, which is positive. Separately, the CFO compares a lease quote and a bank loan by working out the IRR of each one's cash flows to see which costs less.

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