Practical Guide: Understanding the Internal Rate of Return (IRR) and Net Present Value (NPV) for Better Investment Decisions

Why the choice between IRR and NPV is crucial for your investments

The decision to invest capital is one of the most critical moments for anyone looking to grow their wealth over the long term. However, many investors face a confusing dilemma: how to determine if a project will truly generate profits? The answer is not straightforward. The Internal Rate of Return (IRR) and the Net Present Value (NPV) are two fundamental financial metrics that can sometimes contradict each other. A project may look attractive based on IRR but less profitable according to NPV, or vice versa. That’s why understanding both indicators is essential to properly evaluate any investment opportunity and avoid decisions that may lead to regret later.

What is the Internal Rate of Return (IRR) and how does it work?

IRR is the interest rate that makes the present value of future cash flows equal to the initial investment cost. In other words, it’s the annual return percentage you expect to earn from a project over its entire lifespan.

When using IRR as an analysis tool, you compare it with a reference rate (such as the yield of a Treasury bond or your opportunity cost). If IRR exceeds that reference rate, the project is attractive. If it’s lower, it probably isn’t worth investing.

The main advantage of IRR is that it provides a relative measure of profitability in percentage, making it easier to compare projects of different sizes. A small project with 50% IRR might be potentially better than a large project with 15% IRR, even if it generates less absolute money.

What is the Net Present Value (NPV) and why does it matter?

NPV is a measure of the total economic benefit generated by an investment. Specifically, it’s the present value of all expected future cash flows minus what you invest today.

The calculation works like this: you project how much money you will receive each year from the investment, apply a discount rate (which reflects the cost of money over time), convert all those future flows to present value, and then subtract your initial investment.

If the result is positive, the investment will generate more money than you spent. If negative, you will lose money. A positive NPV indicates that the project adds value to your wealth; a negative NPV means it destroys value.

NPV formula (NPV)

The mathematical expression of NPV is:

NPV = (Cash Flow Year 1 / ((1 + Discount Rate)¹) + )Cash Flow Year 2 / ((1 + Discount Rate)²( + … + )Cash Flow Year N / )(1 + Discount Rate)ᴺ( - Initial Investment

Where:

• Initial Investment: the money you disburse at the start
• Cash Flows: the money you expect to receive each year
• Discount Rate: the percentage reflecting the cost of time and risk

It’s important to recognize that these future flows and the discount rate are estimates. Their accuracy will determine the reliability of your analysis.

Practical cases: positive vs negative NPV

( Scenario 1: When NPV is positive

A company is evaluating a project requiring an investment of $10,000. It expects to receive $4,000 annually for 5 years. Using a discount rate of 10%, the calculations are:

• Present value Year 1: $4,000 / )1.10)^1 = $3,636.36
• Present value Year 2: $4,000 / ###1.10(^2 = $3,305.79
• Present value Year 3: $4,000 / )1.10(^3 = $3,005.26
• Present value Year 4: $4,000 / )1.10(^4 = $2,732.06
• Present value Year 5: $4,000 / )1.10(^5 = $2,483.02

NPV = -$10,000 + $3,636.36 + $3,305.79 + $3,005.26 + $2,732.06 + $2,483.02 = $2,162.49

Result: The positive NPV of $2,162.49 suggests that the project is viable and will add value.

) Scenario 2: When NPV is negative

Consider an investment of $5,000 in a certificate of deposit that will pay $6,000 at the end of the third year, with an interest rate of 8%:

Present value of the payment: $6,000 / (1.08)^3 = $4,774.84

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

With a negative NPV of -$225.16, this investment is not profitable. The money you will receive in the future does not justify what you invest today. It’s a clear rejection signal.

Main limitations you should know about IRR

IRR, although useful, has several important restrictions:

Multiple possible IRRs ###No convexity(: In complex projects with irregular cash flows, there may be more than one IRR, making it difficult to know which to use.

Only works with conventional cash flows: If cash flows change sign multiple times )positive and negative alternations(, IRR can give misleading results.

Reinvestment problem: IRR assumes you will reinvest all positive flows at the same IRR rate. In reality, you probably won’t achieve that return on future reinvestments.

Does not reflect the actual size of gains: A project with IRR of 50% but only $1,000 net profit may be inferior to one with IRR of 20% but $100,000 profit.

Sensitivity to changes: Slight adjustments in the discount rate can significantly change IRR, affecting your conclusion.

Despite these limitations, IRR remains valuable especially for projects with uniform flows and no drastic changes. For final decisions, always combine it with other indicators like NPV, ROI, or payback period.

The weaknesses of Net Present Value )NPV(

NPV also has limitations you cannot ignore:

The discount rate is subjective: Two investors may use different rates and reach opposite conclusions. There is no universal “correct” rate.

Ignores uncertainty: NPV assumes your cash flow projections are exact and that there are no unforeseen risks. In reality, markets are unpredictable.

Does not account for flexibility: Assumes all investment decisions are made at the start. If you need to change strategy midway, NPV does not consider it.

Not comparable between projects of different sizes: A project requiring $100,000 with an NPV of $50,000 seems better than one of $10,000 with an NPV of $8,000, but the second is relatively more profitable.

Ignores inflation: NPV does not automatically adjust cash flows for future inflation effects, which can bias your results.

Despite these drawbacks, NPV remains the most used tool in financial analysis because it provides a concrete answer in monetary terms. It’s easy to understand: if NPV is positive, the investment is profitable. If negative or close to zero, it’s not. That’s why many companies prefer it, although they always complement it with other metrics.

How to select the correct discount rate?

The discount rate is crucial because small changes can turn a negative NPV positive or vice versa. To choose it wisely, consider these approaches:

Opportunity cost: What return could you get investing in something similar with comparable risk? That’s your minimum required rate.

Risk-free rate: Start with the yield of safe instruments like Treasury bonds. It’s your baseline reference.

Sector analysis: Research what rate similar companies in your industry use. It gives you a market perspective.

Your own experience: Your knowledge of past projects and actual results can inform future decisions.

Choosing the right discount rate requires careful reflection because it determines whether your project appears profitable or not.

Resolving conflicts: what to do when NPV and IRR contradict each other?

It’s common for a project to have an attractive IRR but a negative NPV, or vice versa. When this happens, don’t rely solely on one indicator.

First step: Review your assumptions carefully. Is the discount rate you used realistic? Are your cash flow projections conservative or overly optimistic?

Second step: Adjust the discount rate. If your initial rate was very high, it might have artificially depressed the NPV while IRR remained positive. A lower rate could reveal a more realistic negative NPV.

Sensitivity analysis: Test your model with different discount rates )10%, 15%, 20%( to see how results change. This shows how robust the project is.

When indicators conflict, it’s a sign you need to investigate further before investing your money.

Comparative table: key differences between NPV and IRR

Complementary indicators to enhance your analysis

To make more solid investment decisions, don’t rely solely on NPV and IRR. Also consider:

ROI )Return on Investment(: Measures what percentage of profit you get over the invested amount. Simple and direct.

Payback period )Payback(: How long does it take to recover your initial investment? Important for liquidity measurement.

Profitability index: Divides the present value of future flows by the initial investment. Useful for comparing small projects.

Weighted Average Cost of Capital )WACC(: Calculates the average cost of financing your investment )debt and equity(. Provides a more accurate discount rate.

Frequently asked questions

Why use NPV and IRR together if they give different results? Precisely because they contradict each other. NPV tells you if you’re making money in absolute terms; IRR tells you your percentage return. Both perspectives are valuable for a complete decision.

How does a higher discount rate affect a negative NPV? A higher rate reduces the present value of future flows, making NPV more negative or less positive. This is another reason why selecting this rate is critical.

Should I always choose the project with the highest IRR? Not necessarily. A project with 40% IRR but only $5,000 profit might be worse than one with 15% IRR but $500,000 profit. Consider the absolute value, not just the percentage.

What if both indicators suggest not to invest? If both NPV and IRR indicate the project isn’t profitable, it’s a very clear signal. Look for better opportunities.

Final conclusions for your next investment

NPV and IRR are complementary tools, not competitors. NPV answers “How much money will I earn?”; IRR answers “At what speed will my money grow?”.

Both have limitations because they are based on future cash flow projections and discount rates, inherently uncertain factors. A project with a negative NPV according to one analysis can turn positive if your initial assumptions were too pessimistic.

Before investing, conduct a thorough analysis: review your assumptions, validate your projections, compare with other options, consider your risk tolerance and alignment with your personal financial goals. Don’t rely on a single number. The best investors use multiple tools, seek complementary perspectives, and recognize that investing always involves risk and uncertainty.