IRR, and where it misleads

The internal rate of return is the discount rate at which NPV equals zero:

$\sum_{t=0}^{n} \frac{C_t}{(1+IRR)^t} = 0$

The rule: accept if IRR exceeds the cost of capital.

For a conventional project — one outflow followed by inflows — this gives the same accept/reject answer as NPV, which is why it survives. The trouble starts everywhere else.

Why people prefer it

It is a percentage, so it needs no discount rate to compute and it compares to one intuitively. "This project returns 23%" is a sentence anyone understands; "this project creates ₹18 crore of value" invites an argument about the discount rate.

That convenience is also the problem: a percentage says nothing about size.

Failure one: it ranks by rate, not by value

Work the problem.

	Cost	Return	IRR	NPV at 10%
A	₹1 cr	₹1.5 cr	50%	₹0.36 cr
B	₹50 cr	₹65 cr	30%	₹9.09 cr

A has a far higher IRR. B creates twenty-five times more value.

Take B. You cannot spend a percentage. If both can be done, do both; if only one, the objective from chapter 1 is value, and B wins by a distance.

The general rule: IRR is a valid accept/reject screen and an invalid ranking tool. Any time projects differ in scale or in timing, ranking by IRR can be wrong.

Failure two: the reinvestment assumption

IRR's arithmetic implicitly assumes intermediate cash flows are reinvested at the IRR itself. For a project with a 40% IRR, that assumes every rupee it throws off earns 40% until the end.

If 40% opportunities were freely available, the firm would already be doing them. The assumption inflates the attractiveness of projects with early, large cash flows.

NPV makes the more defensible assumption: reinvestment at the cost of capital — the rate actually available.

Failure three: multiple IRRs, or none

A polynomial can have as many roots as it has sign changes. A project whose cash flows change sign more than once — an outflow, then inflows, then a large outflow for decommissioning or a mid-life overhaul — can have two or more IRRs, both mathematically correct and neither meaningful.

Some projects have no real IRR at all.

Mining, nuclear and heavy infrastructure routinely have this shape. Where cash flows change sign more than once, IRR should not be computed, let alone used.

Failure four: the lending-versus-borrowing sign flip

For a project that takes money in first and pays out later — an advance received against future obligations — the rule reverses: such a project is acceptable when IRR is below the cost of capital.

The formula gives no warning. A rule that silently inverts for a subset of cases is a rule that will eventually be applied the wrong way round.

MIRR, and why it is only a partial fix

Modified IRR discounts outflows at the cost of capital and compounds inflows at a stated reinvestment rate, then solves for the rate linking them. It fixes the reinvestment assumption and the multiple-root problem.

It does not fix the ranking problem, because it is still a percentage. The scale issue is inherent to any rate-based measure, not to IRR specifically.

When to use it anyway

IRR is genuinely useful in three places:

Communication. It is understood by audiences who will not engage with NPV.

Screening. For conventional projects of similar scale, ranking by IRR and by NPV usually agrees.

As a sensitivity measure. The gap between IRR and the cost of capital is a margin of safety: a project with an IRR of 11% against a 10% cost of capital is one revision away from being value-destroying.

Use it alongside NPV, never instead of it. Where they disagree, NPV is right.

The point

IRR is the discount rate at which NPV is zero, and for a conventional project it gives the same accept/reject answer. As a ranking tool it fails, because a percentage ignores scale — a 50% return on ₹1 crore creates less value than a 30% return on ₹50 crore. It also assumes reinvestment at itself, produces multiple answers when cash flows change sign more than once, and silently inverts for borrowing-type projects.