How to Evaluate Investments: NPV vs IRR and Why Results May Contradict

When it comes to assessing the financial viability of a project or investment, financial analysts face a common dilemma: two widely used metrics —NPV and IRR— can lead to conflicting conclusions about the same project. Which one to trust? How to make the right decision? This article breaks down both tools, their mathematical foundations, practical limitations, and how to use them together for a comprehensive evaluation.

Key Metrics: Understanding NPV and IRR in Practice

Before resolving contradictions, it is essential to understand what each indicator measures. The Internal Rate of Return (IRR) represents the percentage return generated by an investment over its useful life. It is calculated as the discount rate that equates the present value of all future cash flows with the initial investment. Meanwhile, the Net Present Value (NPV) expresses in absolute monetary terms how much value an investment generates above its initial cost.

The fundamental difference: while IRR answers “what percentage return do I get?”, NPV answers “how much money in present value will I earn?”. These different questions can lead to contradictory answers.

Breaking Down the Net Present Value (NPV)

NPV calculates the difference between the present value of all expected future revenues and the initial investment, discounting each future flow according to a rate that reflects the opportunity cost of capital.

The fundamental formula is:

NPV = (FC₁ / ((1 + r)¹) + )FC₂ / ((1 + r)²( + … + )FCₙ / )(1 + r)ⁿ( - Initial Investment

Where:

• FC = expected cash flows in each period
• r = discount rate (cost of capital)
• n = number of periods

A positive NPV indicates that the project will generate more cash than invested, making the investment profitable. A negative NPV suggests losses.

) Practical Case: Positive NPV

A company invests $10,000 in a project that will generate $4,000 annually for five years. With a discount rate of 10%:

• Year 1: $4,000 / 1.10¹ = $3,636.36
• Year 2: $4,000 / 1.10² = $3,305.79
• Year 3: $4,000 / 1.10³ = $3,005.26
• Year 4: $4,000 / 1.10⁴ = $2,732.06
• Year 5: $4,000 / 1.10⁵ = $2,483.02

NPV = $15,162.49 - $10,000 = $2,162.49

The positive result validates the project as a viable investment.

( Practical Case: Negative NPV

A $5,000 deposit certificate promises $6,000 in three years at an annual interest rate of 8%:

PV = $6,000 / )1.08###³ = $4,774.84

NPV = $4,774.84 - $5,000 = -$225.16

The negative NPV indicates that the investment does not recover its initial cost in present value terms.

The Role of the Discount Rate in NPV Calculation

Choosing the discount rate is perhaps the most critical factor in NPV calculation, but it is also highly subjective. Investors may use various approaches:

Opportunity Cost: Compares expected profitability with similar risk-adjusted investment alternatives. If the project is riskier, the rate increases.

Risk-Free Rate: Uses the return on risk-free assets, such as treasury bonds, as a base.

Comparative Analysis: Studies standard industry discount rates.

Investor Experience: Intuition and past decision history also influence this choice.

Limitations of NPV Every Investor Should Know

Despite its usefulness, NPV has significant weaknesses:

Subjectivity in Discount Rate: Small changes can turn a positive NPV into negative, making results inconsistent depending on who performs the analysis.

Ignores Uncertainty and Risk: Assumes cash flow projections are accurate, ignoring inherent volatility.

Lacks Flexibility: Presumes all decisions are made upfront and does not allow adjustments during project execution.

Comparison of Sizes Issues: A large project may have a higher NPV than a smaller one even if less efficient, because it does not normalize for investment scale.

Inflation Effect Ignored: Future flows may be affected by inflation, which is not considered in the basic model.

Despite these limitations, NPV remains widely used in business practice because it is relatively simple to apply and provides concrete monetary results that facilitate comparison between investment options.

Understanding the Internal Rate of Return ###IRR(

IRR is the discount rate that makes the NPV equal to zero. Mathematically, it solves this equation:

0 = )FC₁ / ((1 + IRR)¹) + (FC₂ / ((1 + IRR)²) + … + )FCₙ / ((1 + IRR)ⁿ( - Initial Investment

Expressed as a percentage and used by comparing it against a reference rate )for example, the company’s cost of capital). If IRR exceeds the reference rate, the project is considered profitable.

IRR is particularly valuable for comparing projects of different sizes, as it provides a measure of relative profitability expressed in percentage terms, regardless of the invested amount.

The Pitfalls of Using IRR as the Sole Metric

IRR has limitations that can lead to incorrect decisions:

Multiple Solutions: In projects with unconventional cash flows (multiple sign changes(, there may be several IRRs, complicating interpretation.

Non-Conventional Cash Flows: IRR assumes an initial negative flow followed by positive flows. If patterns are more complex, the metric can be misleading.

Reinvestment Problem: Implicitly assumes that positive cash flows are reinvested at the IRR itself, which is rarely realistic, leading to overestimating profitability.

Dependence on Assumptions: Calculation depends on future projections that may not materialize, introducing systematic risk.

Magnitude Ignored: A small project with a high IRR may be less valuable in absolute terms than a larger one with a more modest IRR.

Despite these limitations, IRR remains a valuable tool, especially for projects with uniform cash flows over time. However, it should never be used in isolation.

Why NPV and IRR Can Contradict Each Other?

Conflicts between NPV and IRR mainly arise from differences in how both metrics treat timing and scale of cash flows.

Project Scale: A large project can generate a higher NPV but a lower IRR than a smaller one. NPV favors the larger project; IRR favors the smaller.

Timing of Cash Flows: If one project generates income mainly in later periods versus another with early income, the choice of discount rate influences the outcome disproportionately. High rates favor early income )benefiting projects with high IRR); low rates favor later income.

Flow Volatility: When the discount rate used in NPV is very high and flows are volatile, NPV can be negative while IRR remains positive.

Resolving Conflicts: How to Proceed

When facing contradictory evaluations between NPV and IRR:

1. Review Assumptions: Critically examine cash flow projections and the discount rate used. Are they realistic given the project context?

2. Adjust the Discount Rate: If a very high or low rate was used, recalculate considering the actual project risk.

3. Prioritize NPV: In case of irresolvable conflict, analysts typically give more weight to NPV because it reflects the absolute value created, which is what shareholders care about.

4. Consider Complementary Indicators: Use ROI (Return on Investment), payback period (payback), profitability index, and weighted average cost of capital (WACC) to obtain a richer perspective.

Direct Comparison: Fundamental Differences

Practical Recommendations for Investors

To make sound decisions, individual investors and companies should:

• Use Both Metrics Together: NPV indicates if a project adds value; IRR quantifies the relative efficiency of capital employed. Together, they offer a comprehensive perspective.

• Consider Personal Context: Factors such as long-term financial goals, risk tolerance, available budget, and diversification are as critical as numerical metrics.

• Validate Assumptions: Cash flow projections are estimates. Conduct sensitivity analysis by varying these assumptions to understand the range of possible outcomes.

• Incorporate Other Tools: ROI, payback period, and profitability index complement the analysis and reduce decision risks.

• Monitor Inflation: Adjust future flows to reflect realistic inflation effects over the investment horizon.

Frequently Asked Questions

What other indicators complement NPV and IRR?

ROI measures percentage profitability over the initial investment. The payback period indicates how long it takes for the project to generate enough cash to recover the investment. The profitability index divides the present value of future income by the initial investment. The WACC (weighted average cost of capital) reflects the company’s actual financing cost.

How does the discount rate impact both metrics?

Increasing the discount rate decreases NPV and generally reduces IRR when recalculated. Lowering the rate has the opposite effect. This sensitivity underscores why selecting the correct rate is so critical.

How to choose between multiple projects?

Compare their NPVs and IRRs simultaneously. Prioritize the project with the higher NPV (if the budget allows) or the higher NPV relative to invested capital. If capital constraints exist, it may be more efficient to select several smaller projects with high IRR than one large project with a higher NPV but lower efficiency.

Can a negative NPV be acceptable?

Only if there are strategic reasons: a project may have a negative NPV but be justified by its alignment with non-financial objectives or by generating valuable future opportunities. Such cases are exceptional.