NPV vs IRR: Choosing the Right Project Evaluation Method

Introduction: The Two Pillars of Project Evaluation

A finance manager presents two projects to the board. “Project A has an IRR of 25%, and Project B has an IRR of 18%,” she says. “But Project B has a higher NPV.”

The board is confused. Which project is better?

This scenario plays out in boardrooms across India. NPV and IRR are the two most important capital budgeting tools, yet they can give conflicting signals. Understanding when and why they differ—and which to trust—is essential for sound investment decisions.

Net Present Value (NPV) Explained

Definition

NPV is the sum of present values of all cash flows associated with a project, including the initial investment.

Formula

$$NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t} = -Initial\ Investment + \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t}$$

Calculation Example

Project Data:

• Initial investment: ₹100 lakh
• Cash flows: ₹35 lakh per year for 4 years
• Required return: 12%

NPV Calculation:

$$NPV = -100 + \frac{35}{1.12} + \frac{35}{1.12^2} + \frac{35}{1.12^3} + \frac{35}{1.12^4}$$

$$NPV = -100 + 31.25 + 27.90 + 24.91 + 22.24$$

$$NPV = ₹6.30\ lakh$$

Decision Rule

What NPV Represents

• Absolute value creation in rupee terms
• Wealth addition to shareholders
• Present value of economic profit

Internal Rate of Return (IRR) Explained

Definition

IRR is the discount rate that makes the NPV of a project equal to zero. It represents the project’s actual rate of return.

Formula

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

IRR must be solved through trial and error (or Excel/calculator).

Calculation Example

Same Project:

• Initial investment: ₹100 lakh
• Cash flows: ₹35 lakh per year for 4 years

Finding IRR:

At 15%: NPV = ₹-0.07 lakh At 14.9%: NPV ≈ ₹0

IRR ≈ 14.9%

Decision Rule

What IRR Represents

• Percentage return on investment
• Break-even discount rate
• Internal earning power of project

NPV vs IRR: Head-to-Head Comparison

Summary Table

Key Differences

1. Absolute vs Relative

• NPV gives absolute value (₹ lakh)
• IRR gives relative return (%)

2. Reinvestment Assumption

• NPV assumes reinvestment at required return (realistic)
• IRR assumes reinvestment at IRR (often unrealistic)

3. Scale Consideration

• NPV accounts for project size
• IRR ignores scale (a 50% return on ₹1 lakh vs ₹100 lakh)

When NPV and IRR Agree

Independent Projects with Conventional Cash Flows

Conventional Cash Flow: One sign change (negative initially, then positive)

Year:    0       1       2       3       4
CF:    -100    +30     +35     +40     +45

For such projects:

• If NPV > 0, then IRR > Required Return
• If NPV < 0, then IRR < Required Return
• Decision is the same!

Example

Project Alpha:

• Investment: ₹80 lakh
• Annual CF: ₹25 lakh for 5 years
• Required return: 10%

Analysis:

• NPV = ₹14.77 lakh ✓
• IRR = 16.9% ✓

Decision: Both methods say Accept!

When NPV and IRR Conflict

Scenario 1: Mutually Exclusive Projects with Different Scales

Project A:

• Investment: ₹50 lakh
• NPV: ₹15 lakh
• IRR: 25%

Project B:

• Investment: ₹200 lakh
• NPV: ₹40 lakh
• IRR: 18%

Which is correct?

If you can only do one: Choose Project B (higher NPV = more wealth)

The extra ₹150 lakh invested earns more than the required return.

Scenario 2: Different Cash Flow Timing

Project X: Early cash flows

Year:    0      1      2      3
CF:    -100   +60    +50    +30

Project Y: Late cash flows

Year:    0      1      2      3
CF:    -100   +20    +40    +100

At 10% required return:

• Project X: NPV = ₹22.4 lakh, IRR = 25.8%
• Project Y: NPV = ₹24.2 lakh, IRR = 22.1%

NPV Profile (Crossover):

At low discount rates: Y has higher NPV At high discount rates: X has higher NPV Crossover rate ≈ 14.5%

Decision depends on required return:

• If required return < 14.5%: Choose Y (NPV is correct)
• If required return > 14.5%: Both methods agree on X

Scenario 3: Different Project Lives

Short Project (3 years):

• Investment: ₹100 lakh
• NPV: ₹25 lakh
• IRR: 22%

Long Project (6 years):

• Investment: ₹100 lakh
• NPV: ₹40 lakh
• IRR: 18%

IRR misleads: Higher IRR for short project doesn’t account for:

• What happens after 3 years?
• Reinvestment opportunities

NPV is correct: Use equivalent annual annuity or assume project repetition.

The Multiple IRR Problem

Non-Conventional Cash Flows

When cash flows change sign more than once, multiple IRRs can exist.

Example: Oil Well Project

Year 0: -₹50 lakh (drilling)
Year 1: +₹200 lakh (oil revenue)
Year 2: -₹150 lakh (cleanup/abandonment)

Two sign changes → Potentially two IRRs

Solving: IRR = 20% and IRR = 50%

Problem: Which IRR to use?

Solution:

1. Use NPV instead
2. Use Modified IRR (MIRR)
3. Apply decision rule to NPV profile

NPV Profile for Multiple IRRs

NPV
 ↑
 |      /\
 |     /  \
 |----/----\---- Required Return
 |   /      \
 |  /        \
 | /          \
 +---------------→ Discount Rate
    IRR₁     IRR₂

Decision: Accept if required return is between the two IRRs (where NPV > 0)

Modified Internal Rate of Return (MIRR)

Why MIRR?

MIRR addresses IRR’s reinvestment assumption problem.

How MIRR Works

1. All negative cash flows → Discounted to present at financing rate
2. All positive cash flows → Compounded to terminal year at reinvestment rate
3. MIRR → Rate connecting PV of costs to FV of benefits

Formula

$$MIRR = \left(\frac{Terminal\ Value\ of\ Inflows}{PV\ of\ Outflows}\right)^{1/n} - 1$$

Example

Project:

Year 0: -₹100 lakh
Year 1: +₹40 lakh
Year 2: +₹50 lakh
Year 3: +₹60 lakh

Assumptions:

• Required return: 12%
• Reinvestment rate: 12%

Terminal Value of Inflows: $$TV = 40(1.12)^2 + 50(1.12)^1 + 60 = 50.18 + 56 + 60 = ₹166.18\ lakh$$

MIRR: $$MIRR = \left(\frac{166.18}{100}\right)^{1/3} - 1 = 18.5%$$

Interpretation: More realistic than IRR because it uses achievable reinvestment rate.

Practical Guidance: Which Method to Use?

Decision Framework

Best Practice: Use Both

Step 1: Calculate NPV

• Is project worth doing? (NPV > 0?)
• How much value added?

Step 2: Calculate IRR

• What’s the return?
• How much cushion above required return?

Step 3: If they conflict

• Trust NPV for value maximization
• Investigate why they differ

NPV and IRR in Indian Practice

Corporate Usage

Observation: Indian companies use multiple methods (not just one)

Why IRR is Popular

Despite theoretical limitations:

• Easy to communicate to board
• Intuitive for non-finance managers
• Benchmarking across projects
• Quick mental calculation

Adapting to Indian Context

Higher Discount Rates:

• Indian risk-free rate: 6-7%
• Equity risk premium: 5-7%
• WACC often 12-16%

Impact:

• More projects rejected
• NPV more sensitive to rate
• IRR margin of safety matters

Common Mistakes to Avoid

Mistake 1: Using IRR for Mutually Exclusive Projects

Wrong: “Project A has 22% IRR vs 18% for B, so choose A” Right: Compare NPVs; larger NPV = more value

Mistake 2: Ignoring Scale

Wrong: “₹1 crore at 30% IRR beats ₹10 crore at 20% IRR” Right: ₹10 crore at 20% creates more value

Mistake 3: Not Checking for Multiple IRRs

Wrong: Using IRR without checking cash flow pattern Right: Verify conventional cash flows; use MIRR if needed

Mistake 4: Misunderstanding Reinvestment Assumption

Wrong: “IRR of 25% means I’ll earn 25% on everything” Right: IRR assumes reinvestment at 25% (often unrealistic)

Key Takeaways

1. NPV = Absolute value creation – Best for maximizing shareholder wealth
2. IRR = Percentage return – Great for communication
3. They usually agree – For independent, conventional projects
4. NPV wins conflicts – Especially for mutually exclusive projects
5. Watch for multiple IRRs – With non-conventional cash flows
6. MIRR is more realistic – Better reinvestment assumption
7. Use both methods – NPV for decision, IRR for insight

Disclaimer

This article is for educational purposes only. Investment decisions should be based on comprehensive analysis including factors beyond NPV and IRR. Consult financial professionals for specific investment decisions. This is not investment advice.

Frequently Asked Questions

Q: If NPV is better, why do companies still use IRR? A: IRR is intuitive, easy to communicate, and allows quick comparison. Most companies use both.

Q: Can IRR be negative? A: Yes, if project loses money. Negative IRR means NPV is negative at any positive discount rate.

Q: What if IRR equals required return? A: NPV = 0. Project earns exactly what shareholders require—neither creates nor destroys value.

Q: How do I handle inflation? A: Be consistent—use nominal cash flows with nominal rate, or real cash flows with real rate.

Q: Which method do IIMs teach as primary? A: NPV is taught as theoretically superior, but both are extensively covered.

Q: What if my Excel shows #NUM! for IRR? A: Likely non-conventional cash flows with multiple sign changes. Use NPV or provide guess value.

NPV and IRR are not competitors—they’re complementary tools. Like a doctor using both blood pressure and pulse, a good financial analyst uses both NPV and IRR to get a complete picture. Master both, understand their differences, and know when each is most appropriate.