How to Use the NPV and IRR Formula to Evaluate Your Investments: Practical Guide to Financial Decision-Making

When facing an investment opportunity, you need to know if it’s truly worth it. How much money will it generate? How fast does your investment grow? These questions are answered with two fundamental metrics: Net Present Value (NPV) and Internal Rate of Return (IRR). Although both tools measure profitability, they do so differently, and understanding their different approaches is crucial for making solid investment decisions.

The Basics: Understanding Net Present Value (NPV)

What does NPV measure?

NPV answers a simple but powerful question: how much real money will I earn or lose today with this investment? It’s not just the money that will come in the future, but its discounted value in the present.

Imagine someone promises you $1,000 in one year. That future money isn’t worth the same as $1,000 in your hand today because you could invest that present money elsewhere. NPV adjusts all future cash flows to their value today, considering this economic reality.

How does it work?

The process is straightforward:

1. Project how much money the investment will generate each year
2. Determine a discount rate (the return you could get from a similar investment)
3. Bring all those future flows to their present value
4. Subtract the initial investment

If the result is positive, the investment yields net gains. If negative, you will lose money.

NPV formula explained step by step

The mathematical expression of NPV is:

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

Where:

• FC = Expected Cash Flow in each period
• r = Discount rate (your opportunity cost)
• n = Number of years

Each future flow is divided by )(1 + rate) raised to the power of the year. This simulates how money loses value over time.

Practical example: Positive NPV project

A company invests $10,000 in equipment. This equipment will generate $4,000 annually for 5 years. The discount rate is 10%.

Calculate the present value of each year:

• Year 1: 4,000 ÷ (1.10)¹ = 3,636.36
• Year 2: 4,000 ÷ (1.10)² = 3,305.79
• Year 3: 4,000 ÷ (1.10)³ = 3,005.26
• Year 4: 4,000 ÷ (1.10)⁴ = 2,732.06
• 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

With a positive NPV of $2,162.49, this project is profitable.

Another case: Investment with negative result

You invest $5,000 in a deposit certificate that pays $6,000 in 3 years, with an annual rate of 8%.

Present value of the $6,000 future amount: 6,000 ÷ (1.08)³ = 4,774.84

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

This negative NPV indicates that the investment does not compensate for the initial capital invested.

Deciphering the Internal Rate of Return (IRR)

What is IRR really?

IRR is the annual profitability percentage you get from your investment. It’s the discount rate that exactly equalizes all future flows with your initial investment, making NPV zero.

If the IRR of a project is 15%, it means your money grows at a rate of 15% per year. To decide if it’s attractive, compare this rate with alternative options: Do I earn more in Treasury bonds? Stocks? Other investments?

Why is IRR different from NPV

While NPV gives you an absolute amount of money (real gains in dollars), IRR provides a percentage. They are complementary perspectives: NPV measures total value created; IRR measures the growth rate of your money.

Choosing the Correct Discount Rate

Selecting the discount rate is critical because it determines how you value future flows. Here are three approaches:

1. Opportunity Cost What return could you get if you invested in another similar project? If you usually earn 8% in stable stocks, using 8% as the discount rate makes sense. If your new project is riskier, increase the rate to reflect that risk.

2. Risk-Free Rate Base Treasury bonds offer a virtually guaranteed return. This is your minimum starting point. Then add a premium for the additional risk of the project.

3. Sector Analysis Research what discount rates other companies in your industry use. This reference helps you stay aligned with industry standards.

The Real Limitations of NPV

Depends on subjective estimates

NPV requires projecting cash flows years ahead. If you are overly optimistic (or pessimistic), the analysis can be skewed. Markets change, competition emerges, technologies evolve.

Ignores uncertainty

NPV assumes your projections are exact and risk-free. In reality, cash flows can fluctuate significantly. A sensitivity analysis (checking how NPV changes if flows vary by 10%, 20%, 30%) is more realistic.

Does not capture strategic flexibility

NPV calculates everything as if decisions are made today and never change. But in practice, investors adjust strategies: they can halt unprofitable projects, expand successful ones, or change direction. Traditional NPV does not value this flexibility.

Has difficulty comparing projects of different scales

A project investing 1 million and generating $100,000 of NPV versus another investing $100,000 and generating $50,000 of NPV. Which is better? The first has a higher absolute NPV, but the second is more efficient.

Does not adjust for inflation

If inflation is 3% annually and you project flows without adjusting for it, your evaluation will be misleading. Nominal flows are worth less each year.

The Limitations of IRR

Sometimes multiple IRRs (or none)

When cash flows change signs multiple times (negative, positive, negative again), there can be several rates that make NPV = 0. This confuses the analysis.

Does not work with unconventional flows

IRR assumes a typical pattern: initial negative investment followed by positive returns. If there are interspersed negative flows (like major repairs midway through the project), IRR can mislead you completely.

Assumes reinvestment at the same rate as IRR

IRR assumes that all money received during the project is reinvested at the same IRR. In reality, you might only get 5% return in other investments.

Problems comparing different projects

Two projects with different durations and initial investments may have similar IRRs but create very different absolute value.

When NPV and IRR Contradict Each Other

It’s common for a project to have a high NPV but a low IRR, or vice versa. Which one to trust?

Example of conflict:

Project A: Investment of $10,000, very high returns at the end (NPV: $5,000, IRR: 12%) Project B: Investment of $100,000, steady returns each year (NPV: $8,000, IRR: 8%)

Project B has a higher NPV (more absolute money), but Project A has a higher IRR (grows faster).

The solution: When there is a conflict, prioritize NPV if:

• You have a limited budget (total value created matters)
• Your discount rate is reliable (reflects the true cost of capital)
• You need conservative decisions

Consider IRR if:

• Comparing projects of similar scale
• You are interested in the relative growth speed

Complementary Tools to NPV and IRR

Don’t rely solely on these indicators. Also use:

• ROI (Return on Investment): Measures percentage gain relative to initial investment
• Payback Period: How long to recover your initial money?
• Profitability Index: NPV divided by initial investment (measures efficiency)
• WACC (Weighted Average Cost of Capital): The most realistic discount rate for companies

Summary: NPV versus IRR

Conclusion: Make Informed Decisions

The NPV and IRR formulas are two lenses to view profitability. NPV shows how much money you will generate in terms of today. IRR shows how fast that money grows.

To evaluate an investment seriously:

1. Calculate both indicators with realistic projections
2. Compare with viable alternatives (other projects, bonds, stocks)
3. Adjust the discount rate according to the project’s actual risk
4. Review how results change if your projections vary
5. Combine with other analyses (ROI, payback period, qualitative analysis)
6. Consider your personal goals, risk tolerance, and time horizon

Neither NPV nor IRR are perfect predictions of the future. They are tools that reduce uncertainty by structuring your analysis. The best investors use both metrics together, understand their limitations, and make informed decisions considering the full context.