## Conflict Between NPV and IRR

NPV and IRR can rank projects differently. The root cause is their different reinvestment assumptions about interim cash flows.

### The Reinvestment Assumption

Technique	Assumes interim cash flows are reinvested at...
NPV	the discount rate (cost of capital)
IRR	the project's own IRR

The NPV assumption is logical: NPV implies you accept any project earning more than the discount rate, so reinvesting freed-up cash at that rate is realistic.
The IRR assumption is often unrealistic — reinvesting at a high project IRR may not be achievable.
Consequence: projects with heavy cash inflows in early years are favoured by IRR (because those early flows compound at the high IRR), even when a project with later cash flows creates more wealth.

### Three Scenarios Causing Conflict

1. Scale / Size Disparity — IRR is a relative measure (a %), NPV is an absolute measure (₹). When projects differ greatly in size, rankings can contradict.

2. Time Disparity in Cash Flows — Total cash flows may be similar, but if one project front-loads inflows and another back-loads them, the two methods can rank them differently.

3. Disparity in Life (Unequal Lives) — Comparing mutually exclusive projects of different durations can produce conflicting rankings.

### Multiple IRR Problem

When a project's cash flows change sign more than once (e.g., outflow → inflows → a later major outflow), the IRR equation can have more than one solution — multiple IRRs.

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

### The Fix

Both the reinvestment problem and the multiple-IRR problem are overcome by the Modified Internal Rate of Return (MIRR), which explicitly reinvests interim flows at the cost of capital.

> Key takeaway: When NPV and IRR conflict for mutually exclusive projects, follow NPV — it directly measures the addition to shareholders' wealth.

Worked example

### Example 1

Example 9 — Higher IRR project is NOT the better project

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

Step 1 — Compute IRR of each project:

Project A: NPV ≈ 0 at r = 46%, so IRR(A) = 46%.
Project B: NPV ≈ 0 at r = 35%, so IRR(B) = 35%.

By IRR alone, Project A (higher IRR + larger investment) looks superior.

Step 2 — Compute NPV at the relevant discount rate of 5%:

Year	DF @5%	A: PV (₹)	B: PV (₹)
0	1.0000	(9,00,000)	(8,00,000)
1	0.9524	6,66,680	59,525
2	0.9070	5,44,200	5,44,200
3	0.8638	3,45,520	5,18,280
4	0.8227	41,135	4,93,620
NPV		6,97,535	8,15,625

Conclusion: At 5% cost of capital, Project B has the higher NPV (₹8,15,625 vs ₹6,97,535) and should be selected — even though Project A has the higher IRR (46%) and the larger investment.

Why: Project A's inflows are concentrated in early years, which the IRR method over-rewards via its high reinvestment assumption. Project B's later, larger inflows generate more real wealth at the true 5% reinvestment rate.

⚠️ Common exam mistakes

Assuming the project with the higher IRR is always the better choice — for mutually exclusive projects, follow NPV when the two methods conflict.
Forgetting that IRR assumes reinvestment at the IRR itself, not at the cost of capital — this biases IRR toward early-cash-flow projects.
Applying the simple IRR decision rule when cash flows change sign more than once, where multiple IRRs exist and the rule can be misleading.
Confusing the source of conflict — it stems from scale disparity, timing disparity, or unequal lives, not from arithmetic error.

Reference:

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Conflict between NPV and IRR (Reinvestment Assumption & Multiple IRR)

Worked example

⚠️ Common exam mistakes