Comparison of IRR vs NPV: In-depth analysis of two fundamental metrics for project evaluation

Introduction: Why confront these two tools?

When an individual investor or company must decide between different investment options, a critical question often arises: which indicator should be trusted more? The Internal Rate of Return (IRR) and the Net Present Value (NPV) are two metrics that often lead to contradictory conclusions about the same project. A project may look attractive due to a high IRR but show a modest NPV, or vice versa. This guide delves into both tools, their mechanisms, weaknesses, and how to use them correctly together.

The Internal Rate of Return (IRR): The percentage that explains everything

What does IRR really represent?

The Internal Rate of Return is the interest rate that equates a project’s initial expenditure with the future returns it will generate. Expressed as a percentage, IRR answers a simple but powerful question: what is the annualized return I truly get from this investment?

Unlike other metrics, IRR provides a directly comparable number. If a project has an IRR of 15%, it means your money grows at that rate over the project’s lifespan. This feature makes it intuitive: if the IRR exceeds your benchmark rate (such as Treasury bonds or your opportunity cost), the project deserves consideration.

Critical limitations of IRR that every investor should know

Multiple solutions problem: In investments with unconventional cash flows—i.e., alternating periods of income and expenses—the function can have multiple mathematical roots. This results in several possible IRRs, making interpretation confusing.

Non-standard cash flows: IRR works best when there is an initial negative cash flow (the investment) followed only by positive flows. When cash flows behave erratically or there are unexpected expenses in later years, IRR becomes less reliable.

Reinvestment assumption: The model implicitly assumes that positive cash flows are reinvested at the IRR rate itself. In reality, reinvesting at that rate may be impossible, leading to an overestimation of final returns.

Ignoring investment scale: IRR expresses relative performance but ignores the absolute size of the gain. A small project with a 50% IRR may generate less money than a large project with a 15% IRR.

Inflation and time value: IRR does not automatically adjust for the effect of inflation on future cash flows, potentially overestimating real profitability in inflationary contexts.

The Net Present Value (NPV): Measuring profit in real monetary terms

Definition and purpose of NPV

Net Present Value is the difference between the present value of all cash flows a project will generate and the initial outlay. In other words, it answers: how much money in today’s pesos will I earn (or lose) with this project after considering the time value of money?

A positive NPV indicates the investment will generate gains above your cost of capital; a negative NPV signals value destruction.

The NPV formula explained step-by-step

To understand how it’s calculated, consider the fundamental mathematical structure:

NPV = Σ [Cash Flow t / ((1 + Discount Rate))^t] - Initial Investment

Where:

• Cash Flow t = net money received in period t (year, month, etc.)
• Discount Rate = rate reflecting your opportunity cost of capital
• t = number of periods from now

This formula discounts each future cash flow to present value, sums them all, and subtracts the initial investment.

Practical example 1: A profitable project (Positive NPV)

Imagine your company considers a project requiring an initial investment of $12,000. It is expected to generate $3,500 annually over 5 years. The applicable discount rate is 9%.

Let’s calculate the present value of each cash flow:

• Year 1: $3,500 / (1.09)^1 = $3,211.01
• Year 2: $3,500 / (1.09)^2 = $2,945.88
• Year 3: $3,500 / (1.09)^3 = $2,701.74
• Year 4: $3,500 / (1.09)^4 = $2,477.00
• Year 5: $3,500 / (1.09)^5 = $2,271.56

Sum of present values: $13,607.19

NPV = $13,607.19 - $12,000 = $1,607.19

A positive NPV of $1,607.19 suggests the project adds value.

Practical example 2: An investment that does not compensate (Negative NPV)

Now consider a fixed-term deposit of $8,000 paying $9,200 after 3 years, with an annual interest rate of 7%.

Present value of the future payment: PV = $9,200 / (1.07)^3 = $7,516.02

NPV = $7,516.02 - $8,000 = -$483.98

The negative NPV indicates that, once adjusted for the time value of money, this investment destroys value.

Determining the discount rate: A critical factor

Choosing the discount rate is perhaps the most influential decision in calculating NPV. Several approaches can guide this choice:

Opportunity cost: What return could you get from an alternative risk similar investment? If you forgo an 8% return on bonds to invest in this project, that is your minimum rate.

Risk-free rate: Treasury bonds offer a riskless return. This is the floor; any risky project should offer a premium above.

Sector analysis: What rates are typically used in your industry? Standard sector practices can serve as reference.

Experience and intuition: Your market knowledge and risk appetite are valid considerations but should be grounded in data.

Limitations that weaken NPV reliability

Subjective discount rate: Small changes in this rate cause significant changes in NPV. A project with a positive NPV at 8% may turn negative at 12%.

Ignores uncertainty: The model assumes your future cash flow projections are accurate, whereas in reality, volatility and uncertainty always exist.

Strategic rigidity: NPV assumes all decisions are made today without future flexibility. It does not value options to change course during execution.

Comparison of projects of different sizes: A large project may have a higher absolute NPV simply due to scale, not necessarily because it is more efficient.

Inflation effect unmodeled: If nominal cash flows do not reflect inflation adjustments, the calculated NPV will be misleading.

Despite its limitations, NPV remains widely used because it translates profitability into real money—an understandable and comparable metric across different options.

Conflict resolution: When NPV and IRR contradict each other

It is common for projects to show a high IRR but low NPV, or vice versa. Reasons include:

Scale differences: A small project may have a high IRR but modest NPV because total gains are limited.

Divergent cash flow patterns: If a project generates modest early cash flows but significant later, IRR may be low (distant flows are discounted more), but NPV can be positive if a low discount rate is used.

Sensitivity to discount rate: Changes in this rate dramatically affect NPV but do not alter IRR (which is endogenous to the project).

In case of conflicts, it is recommended to:

1. Review underlying assumptions about cash flows and rates
2. Conduct sensitivity analysis (vary the discount rate to see how results change)
3. Consider the context: what matters more, relative performance (IRR) or absolute gain (NPV)?
4. Complement with additional metrics such as ROI, payback period, and profitability index

Direct comparison: NPV versus IRR

Complementary indicators for a holistic assessment

To avoid relying solely on NPV and IRR, consider these complements:

ROI (Return on Investment): Measures profit as a percentage of initial investment, useful for simple comparisons.

Payback period (Payback): How long will it take to recover your initial investment? Valuable for liquidity risk assessment.

Profitability Index (PI): Divides the present value of positive flows by the initial investment; projects with PI > 1 generate value.

Weighted Average Cost of Capital (WACC): Reflects the average financing cost; a more sophisticated discount rate considering debt and equity.

Frequently asked questions about NPV and IRR

Which should I use if I have to choose only one? NPV is generally preferred because it measures absolute value in real money. However, for comparing projects of different sizes, IRR offers a valuable relative perspective.

Why do my bank or advisor insist on using both? Because they provide complementary information. NPV answers “How much money will I earn?”; IRR answers “At what rate does my investment grow?”. Together, they offer a more complete view.

What happens if I change the discount rate? NPV will change proportionally (higher rate = lower NPV). IRR remains the same (project-specific), but your conclusion about project viability may change.

How do I choose among competing projects? Compare their NPVs (pick the highest) if you have unlimited capital. If capital is limited, use the Profitability Index (NPV / Initial Investment) to select the best combination.

Should I fully trust these metrics? No. They are powerful tools but based on future projections subject to error. Complement with qualitative analysis, risk assessment, strategic alignment, and managerial judgment.

Conclusion: Smart use of both metrics

NPV and IRR are not competitors but allies in your investment evaluation. NPV tells you how much value a project will create in real monetary terms; IRR shows the relative performance. Both depend critically on assumptions about future cash flows and discount rates, which introduces inherent uncertainty.

For sound investment decisions, use both metrics, consider their limitations, complement with other indicators, and always apply your market analysis, risk tolerance, and personal financial objectives. The most robust assessment integrates quantitative data with experienced qualitative judgment.