## Internal Rate of Return (IRR)

IRR is the discount rate at which NPV of the project equals zero—the break-even cost of capital.

> Solve for r in:

> Σ [CFt ÷ (1+r)^t] = Initial Outflow

Decision Rule:

IRR > WACC (Cost of Capital) → Accept
IRR < WACC → Reject

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### Advantages

#	Advantage
1	Incorporates Time Value of Money
2	Considers all cash flows throughout the project's life
3	Intuitively comparable to cost of capital—managers immediately understand 'project earns 18% vs. 12% cost'
4	Aligned with shareholder wealth maximisation objective

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### Limitations

#	Limitation	Detail
1	Tedious calculation	Requires trial and error (interpolation) to find the rate; no closed-form solution for multi-period cases
2	Misleading for unconventional cash flow patterns	Multiple sign changes in cash flows can produce multiple IRRs
3	Reinvestment rate assumption is unrealistic	IRR assumes interim cash flows are reinvested at the IRR itself, which is usually not achievable
4	Can conflict with NPV for mutually exclusive projects	IRR may rank a smaller-but-efficient project above a larger wealth-creating project

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> IRR vs. NPV for mutually exclusive projects: When IRR and NPV rankings conflict, always follow NPV—it directly measures wealth addition. IRR is best used as a supplementary communication tool.

Worked example

### Example 1

A project costs ₹1,00,000 and generates ₹60,000 in Year 1 and ₹70,000 in Year 2. At 20%: PV = 60,000/1.2 + 70,000/1.44 = 50,000 + 48,611 = 98,611 (NPV = −1,389). At 18%: PV = 60,000/1.18 + 70,000/1.3924 = 50,847 + 50,273 = 1,01,120 (NPV = +1,120). IRR ≈ 18 + [1,120/(1,120+1,389)] × 2 = 18 + 0.89 ≈ 18.9%. If WACC = 12%, accept the project.

### Example 2

Project A: cost ₹1,00,000, NPV ₹20,000, IRR 25%. Project B: cost ₹5,00,000, NPV ₹80,000, IRR 20%. IRR favours A; NPV favours B. If mutually exclusive and the firm has sufficient funds, choose B—it adds ₹80,000 to wealth vs. ₹20,000. This conflict arises from scale difference, a known limitation of IRR.

⚠️ Common exam mistakes

Accepting a project simply because IRR is high without comparing it to WACC—the cost of capital is the correct hurdle, not an arbitrary threshold.
Using IRR to rank mutually exclusive projects without cross-checking with NPV—IRR rankings can mislead when project sizes differ.
Assuming there is always a unique IRR—projects with multiple cash flow sign changes (e.g., large decommissioning costs at end) can have multiple valid IRRs.
Confusing IRR's reinvestment assumption with NPV's—NPV implicitly assumes reinvestment at WACC (realistic); IRR assumes reinvestment at IRR (often unrealistic).

Reference:

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Internal Rate of Return (IRR) — Merits and Limitations

Worked example

⚠️ Common exam mistakes