## Issues in IRR

### A. IRR and Mutually Exclusive Projects

Mutually exclusive projects are those where selecting one precludes selecting the other (e.g., one plot of land usable for either Project S or Project L — choosing one rejects the other).

IRR can mislead with mutually exclusive projects because IRR is a percentage and ignores the scale of investment (the absolute quantum of money earned).

The core problem: A small project can show a high IRR yet add less to shareholder wealth than a larger project with a lower IRR. Choosing the high-IRR small project forgoes the extra NPV the larger project would have generated — reducing shareholders' wealth.

#### Why the conflict arises — reinvestment assumptions

NPV assumes interim cash flows are reinvested at the discount rate (logical, since all projects beating the discount rate are accepted).
IRR assumes reinvestment at the project's own IRR.
As a result, IRR favours projects with cash flows concentrated in early years over projects with larger later cash flows — even when the latter creates more wealth.

Resolution: Use NPV for the accept/reject ranking of mutually exclusive projects, or use MIRR, which removes the distorting reinvestment assumption.

> Caution: It is NOT safe to assume IRR is reliable even when the larger project also has the higher IRR — see Example 9, where Project A has both the larger investment and the higher IRR yet Project B is the wealth-maximizing choice at a 5% discount rate.

### B. Multiple IRR

When a project's cash flows change sign more than once during its life (a non-conventional cash flow pattern — e.g., outflow → inflows → a later major outflow), there can be more than one IRR.

Plotting discount rate (x-axis) against NPV (y-axis) gives a curve that crosses zero twice, producing two IRRs (IRR₁ and IRR₂).

Decision implication:

If the cost of capital is below both IRRs, a decision can still be made easily.
Otherwise the IRR rule becomes misleading: the project should be accepted only if the cost of capital lies between IRR₁ and IRR₂.

MIRR avoids the multiple-IRR problem entirely by collapsing all flows to a single terminal value.

Worked example

### Example 1

Example 8 — IRR ignores scale (mutually exclusive)

	Year 0	Year 1	IRR	NPV @ 10%
Project A	(₹1,00,000)	₹1,50,000	50%	₹36,360
Project B	(₹5,00,000)	₹6,25,000	25%	₹68,180

Project A's IRR (50%) beats B's (25%), but B's NPV is far higher. Since they are mutually exclusive, choosing A (because of IRR) sacrifices ₹68,180 − ₹36,360 = ₹31,820 of additional shareholder wealth. The larger project with the lower IRR maximises wealth. Decision: choose B (higher NPV).

### Example 2

Example 9 — even when the larger project has the higher IRR, NPV can disagree

Year	Project A (₹)	Project B (₹)
0	(9,00,000)	(8,00,000)
1	7,00,000	62,500
2	6,00,000	6,00,000
3	4,00,000	6,00,000
4	50,000	6,00,000

Project A has the larger investment AND the higher IRR: IRR(A) = 46%, IRR(B) = 35%.

But at a 5% discount rate, the NPVs reverse the ranking:

NPV(A) = ₹6,97,535
NPV(B) = ₹8,15,625

Project B has front-loaded less (its early cash flows are smaller), so it is penalised by IRR but rewarded by NPV. Decision: select Project B, despite its lower IRR — because IRR's reinvestment assumption overstates A. The anomaly is resolved by MIRR.

⚠️ Common exam mistakes

Always picking the higher-IRR project for mutually exclusive decisions — IRR ignores investment scale and can destroy wealth; use NPV.
Believing IRR is safe whenever the larger project also has the higher IRR — Example 9 shows it still can be wrong.
Not recognising non-conventional cash flows (more than one sign change) as the trigger for multiple IRRs.
With multiple IRRs, applying the simple 'accept if IRR > cost of capital' rule — the project is acceptable only when the cost of capital lies BETWEEN the two IRRs.
Confusing NPV's reinvestment-at-discount-rate assumption with IRR's reinvestment-at-IRR assumption — this difference is the source of the NPV/IRR conflict.

Reference:

Now that you've read this — what's next?

Move from understanding → mastery in 3 clicks. Each option below picks up from this lesson's topic.

🔥 Drill 5 Qs on this → ✍️ Adaptive practice →

Issues in IRR — Mutually Exclusive Projects & Multiple IRR

Worked example

⚠️ Common exam mistakes