VAN vs TIR: Master the calculations and key differences to make better investment decisions

Introduction: Why Every Investor Must Understand These Two Metrics

Deciding to invest requires more than intuition. Net Present Value (VAN) and Internal Rate of Return (TIR) are the pillars of financial analysis that distinguish profitable investments from those that generate losses. The challenge is that these two metrics often provide contradictory signals: a project may look attractive due to its VAN but show a lower TIR than another. That’s why it is essential to thoroughly understand how VAN and TIR are calculated, their real-world applications, and their limitations.

Understanding Net Present Value (VAN)

VAN answers a simple yet powerful question: how much is the money I will receive in the future worth today? It is the monetary measure of an investment’s net benefit, considering the value of money over time.

In practice, VAN takes all expected cash flows from an investment, discounts them to their present value using a discount rate, and subtracts the initial cost. A positive VAN means the investment will generate more money than initially invested. A negative VAN indicates the opposite: losses.

The formula and how VAN is calculated

The VAN equation is:

VAN = -Initial Investment + (Cash Flow 1 / ((1 + r)¹) + )Cash Flow 2 / ((1 + r)²( + … + )Cash Flow N / )(1 + r)ⁿ(

Where:

• Initial Investment: the outlay at the start of the project
• Cash Flows: projected income for each period
• r: the chosen discount rate
• n: number of periods

( Real cases: When VAN works

Scenario 1: Profitable project

A company invests $10,000 in a project that will generate $4,000 annually for 5 years. With a discount rate of 10%:

• Year 1: 4,000 / 1.10 = 3,636.36 dollars
• Year 2: 4,000 / 1.21 = 3,305.79 dollars
• Year 3: 4,000 / 1.331 = 3,005.26 dollars
• Year 4: 4,000 / 1.4641 = 2,732.06 dollars
• Year 5: 4,000 / 1.6105 = 2,483.02 dollars

VAN = -10,000 + 15,162.49 = 5,162.49 dollars

With a positive VAN of $5,162, the project is viable. The investment will generate that additional value.

Scenario 2: Project with negative VAN

A certificate of deposit requires $5,000 today and will pay $6,000 in 3 years, with an 8% discount rate:

Present value = 6,000 / )1.08)³ = 4,774.84 dollars
VAN = 4,774.84 - 5,000 = -225.16 dollars

The negative VAN indicates that the present value of the money is greater than what will be received, making the investment unattractive.

Choosing the discount rate: The heart of VAN calculation

The accuracy of VAN depends directly on the selected discount rate. Three main approaches are:

Opportunity cost: What return would be foregone if invested here? If you can get 12% elsewhere on a similar investment, that is your minimum reference.

Risk-free rate: Treasury bonds offer a safe floor, typically between 3-5%. A risk premium is added based on the investment.

Comparative analysis: What rate does your industry use? Established companies in mature sectors use different rates than tech startups.

Investor intuition and experience also play a role, but they should be backed by solid data, not replaced by it.

Limitations of VAN you should know

VAN is powerful but imperfect:

Despite this, VAN remains the most used tool because it translates analysis into concrete monetary terms, easy to compare.

Understanding the Internal Rate of Return ###TIR(

If VAN answers “how much money will I earn?”, TIR answers “what percentage return does that correspond to?”. It is the discount rate that makes VAN exactly zero.

In other words, TIR is the percentage yield that the investment will generate over its useful life. It is expressed as a percentage and compared with reference rates )such as bond yields, cost of capital, etc.(. If TIR exceeds the reference rate, the project is profitable.

) How TIR is calculated

Calculating TIR is more mathematically complex than VAN because it requires solving an equation where VAN = 0. There is no simple closed-form formula; iterative numerical methods or financial software are typically used.

The logic is: find the r rate that satisfies:

0 = -Initial Investment + (Cash Flow 1 / )(1 + r)¹### + (Cash Flow 2 / ((1 + r)²) + …

A project with a 15% TIR is more attractive than one with 8%, assuming similar risks.

Limitations of TIR you should understand

When do VAN and TIR give different answers?

It is common for one project to have a higher VAN but a lower TIR than another. This mainly occurs due to:

Scale differences: A large project may have a higher VAN but a lower TIR because the invested capital is larger.

Timing of flows: If a project concentrates gains at the end vs. evenly distributed, their metrics diverge significantly.

Sensitivity to discount rate: If the discount rate is very high and future flows are volatile, VAN can turn negative while TIR remains positive.

Recommendation: In contradictory cases, review assumptions about cash flows and adjust the discount rate to better reflect the project’s actual risk.

Comparing VAN and TIR: Their fundamental differences

Both metrics are essential. VAN provides the “what”: how much value is created. TIR provides the “how”: at what rate that value is created.

Beyond VAN and TIR: Complementary indicators

Although VAN and TIR are fundamental, they should never be the sole metrics in investment decisions:

• ROI )Return on Investment(: Simple return as a percentage of initial investment
• Payback Period: Time needed to recover the initial investment
• Profitability Index (PI): VAN divided by initial investment, useful for projects with limited budgets
• Weighted Average Cost of Capital )WACC(: Average financing cost, crucial for setting the discount rate

Practical guide to choosing between investments

When evaluating multiple projects:

1. Calculate both metrics for each project without exception
2. Rank by VAN if projects are similar in scale
3. Rank by TIR if invested amounts vary significantly
4. Review assumptions causing differences between VAN and TIR
5. Consider other factors: market risk, diversification, time horizon, liquidity needs
6. Select the project with the highest VAN, provided TIR exceeds the minimum reference rate