Online Calculator for NPV, IRR, Payback Period, and Graphs

This is a free online simulatorstrong> that allows you to calculate the Net Present Value (NPV), Payback Period (with and without discounting), Internal Rate of Return (IRR)strong>, and Profitability Indexstrong>. It also displays cumulative cash flow graphs (with and without discounting)strong>. This free professional calculator takes into account the residual value. It can be used by students and professionals.

NPV, IRR, and Payback Period Calculator with Graphs

Net Present Value (NPV) Calculation Details

This is the sum of discounted cash flows minus the initial investment. The residual value is a cash inflow in the last year of the project.

Profitability Index Calculation Details

This is the sum of discounted cash flows divided by the initial investment.

Internal Rate of Return (IRR) Calculation Details

This is the rate that makes the NPV equal to zero.

Payback Period without Discounting

This is the time when the cumulative cash flows equal the initial investment.

Cumulative Cash Flow Graph without Discounting

The payback period is the intersection point between the cumulative cash flow curve and the initial investment curve.

Payback Period with Discounting (First Method)

This is the time when the cumulative discounted cash flows equal the initial investment.

Cumulative Discounted Cash Flow Graph

The payback period is the intersection point between the cumulative discounted cash flow curve and the initial investment curve.

Payback Period with Discounting (Second Method)

This involves tracking the evolution of the NPV. The payback period is the time when the NPV equals zero.

NPV Evolution Graph

The payback period is the intersection point between the NPV curve and the x-axis.

What are the characteristics of an investment?

To make an investment choice, you need to understand certain concepts.

What is an investment?

An investment is an immediate outlay of money that will generate future cash inflows over several years or after several years. Generally, it is the acquisition of durable goods. For example, a company buying a machine, a person buying a house to rent...

How to calculate the cost of an investment?

The cost of an investment is equal to the purchase price of the investment items plus acquisition costs. It is a pre-tax recoverable cost.

Example: Delta company acquired PCs, software, and offices. Total price 30,000 euros, installation costs: 1,000 euros. So the cost of the investment will be 31,000 euros.

Project lifespan and equipment lifespan

The project lifespan is the time required for the project to be profitable. It varies depending on the projects and the field of activity.

The equipment lifespan depends on the nature of the equipment itself and may differ from the project lifespan. In addition, an investment can be composed of several elements with different lifespans (depreciation periods).

For example, the following investment: Purchase of a house to rent. The lifespan of the house is assumed to be 50 years. The project duration can be 10 years. Here the investor will study if his project is profitable after 10 years.

For more information on depreciation, its methods and to establish your plan online Depreciation Calculator

Future cash flows

An investment generates future cash inflows over several years, called Net Cash Flow. These flows are of two types:

1. Operating cash flows

These are the net revenues from the company's operations. They are also called Cash Flow from Operations. This is a concept different from net income. It is a matter of making the difference between the sum of cash inflows and the sum of cash outflows related to operations, including taxes. So we will exclude financial charges (related to the mode of financing) and depreciation (non-cash). The simplified formulas will be:

Cash Flow from Operations formula = Operating income - operating expenses

Cash Flow from Operations formula = Net income + Depreciation

For an investment related to the acquisition of a car for rent

We can calculate it differently: 10000-2000-1500 = 6500

2. Residual value cash flows

Sometimes, at the end of the project, the equipment used can be sold or its value can be estimated. The sale of this equipment represents a cash inflow. It is a cash flow.

For example, the following investment: Purchase of a building for rent for 200,000 euros. The project duration can be 10 years. It is estimated that this building will bring in 12,000 euros of rent each year and can be sold for 280,000 euros at the end of the tenth year. The residual value is 280000.

For example, the following investment: Purchase of PCs for 5000. The project duration can be 4 years. It is estimated that this project will generate 12,000 euros each year and that the PCs will be discarded at the end of the fourth year. The residual value is 0.

Discount rate

When talking about investment choice, we are actually talking about future cash flows. Generally, to study the profitability of an investment, we discount future amounts using a rate called the "discount rate". In fact, if we are in 2025 and we expect a cash inflow of 10,000 euros in 2030, we can say that this amount is worth 7,000 euros today.

What is the discount rate?

The discount rate is a rate used in finance to bring future cash flows back to their present value. It represents the opportunity cost of money, that is, the return that could be obtained by investing that money elsewhere in a safe manner. In other words, it is the rate at which future sums are "discounted" to compare them to present sums.

Why use a discount rate?

• Money has time value: A sum of money today is worth more than the same sum in the future, due to inflation, missed investment opportunities, and risk.
• Comparing heterogeneous cash flows: The discount rate makes it possible to compare cash flows that occur at different times.

How to choose a discount rate?

The choice of the discount rate is crucial, as it directly influences the net present value (NPV) of a project. There is no magic formula, but several methods are commonly used:

• Weighted Average Cost of Capital (WACC): This is the average rate of return required by the various providers of funds (shareholders, creditors). It reflects the overall cost of financing the company.
• Risk-free rate + risk premium: We take a risk-free rate (such as the Treasury bond rate) to which we add a premium to compensate for the specific risk of the project.
• Internal rate of return (IRR): This is the discount rate that makes the NPV equal to zero. It can be used as a discount rate for similar projects.

What are the investment decision criteria?

The investment decision is a complex one, influenced by a multitude of criteria. In addition to financial profitability, investors consider factors such as capital security, investment liquidity, alignment with their personal values, and environmental and social impact. Here we will explain the most commonly used criteria: Net Present Value (NPV), Internal Rate of Return (IRR), Profitability Index, Payback Period without discounting, and Payback Period with discounting.

Net Present Value (NPV)

NPV is a key financial evaluation tool that determines whether an investment is profitable. It measures the difference between the sum of a project's future cash flows, discounted to their present value, and the initial investment cost. In other words, NPV indicates the added value that a project generates.

Why use NPV?

• Investment decision: NPV allows you to compare different projects and select those that offer the best return on investment.
• Profitability assessment: It allows you to assess whether a project is likely to generate profits or losses.
• Considering the time value of money: NPV incorporates the fact that a sum of money today is worth more than the same sum in the future.

NPV formula

The NPV formula is as follows:
NPV = ∑ (Cash flow / (1 + discount rate)^t) - Initial investment

Where:

• ∑: Sum of all cash flows
• Cash flow: Amount of money entering or leaving the project at a given period
• t: Period (year)
• Discount rate: Rate used to bring future cash flows back to their present value
• Initial investment: Initial cost of the project

Imagine a project requiring an initial investment of €100,000 and generating net cash flows of €30,000 per year for 5 years. The discount rate is set at 10%.
The NPV is calculated as follows:
NPV = (30,000 / 1.1) + (30,000 / 1.1²) + ... + (30,000 / 1.1⁵) - 100,000

Interpretation of results

• Positive NPV: The project is profitable and generates value.
• Negative NPV: The project is likely to generate losses and is not recommended.
• Zero NPV: The project is neutral, it generates neither profit nor loss.

Example

For all the following examples, we will use the following scenario: an investment in a rental car. The investment cost is 30,000 euros. The project duration is 3 years. The net cash flows are successively 15,000, 12,000, and 10,000 euros. The residual value is 5,000 euros.

Case 1: Discount rate 15%

Year 3 includes two cash flows: an operating income of 10,000 and a residual value of 5,000

NPV = 31980-30000 = 1980 or 28692 +3288 -3000 = 1980

This is a profitable project since the NPV is positive. It allows for a return on investment greater than 15%

Case 1: Discount rate 25%

NPV = 27360-30000 = -2640

This is an unprofitable project since the NPV is negative.

Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is a key financial metric used to measure the profitability of an investment. It represents the discount rate that makes the net present value (NPV) of a project equal to zero. In other words, it is the average annual rate of return generated by an investment over its entire lifespan.

IRR is a valuable tool for comparing different investment projects. A higher IRR generally indicates a more profitable project. However, it's important to note that IRR does not consider the size of investments, unlike NPV.

Why use IRR?

• Comparing projects: IRR allows for easy comparison of the profitability of different projects, even if their initial investments and durations vary.
• Investment decision: An IRR higher than the cost of capital is generally considered an indicator of profitability.
• Performance evaluation: IRR can be used to evaluate the historical performance of an investment.

How to calculate IRR?

Generally, it is calculated using specialized software. To calculate it manually and find an approximate value, you need to find a random rate that generates a positive NPV and another rate that generates a negative NPV, then perform linear interpolation to find the rate that corresponds to an NPV of 0. For greater precision, these two rates should be close.

Rate: 15% ---> NPV = 1980
Rate: IRR ---> NPV = 0
Rate: 25% ---> NPV = -2640
IRR -15/25-15 = 0-1980/-2640-1980 so IRR = 19.29%.
For more precision, you can recalculate and test the rates 20% and 18% and redo the interpolation.

The software used on this page indicates an IRR of 18.96%.

Profitability Index

The profitability index is a financial indicator used to evaluate the performance of an investment. It measures the ratio of the cash flows generated by a project to the initial amount invested. In other words, it indicates how many euros are generated for every euro invested.

Profitability Index Formula

The profitability index is calculated as follows:

Profitability Index = Sum of discounted cash flows / Initial investment

Where:

• Sum of discounted cash flows: This is the sum of all cash flows generated by the project, discounted to their present value to account for the time value of money.
• Initial investment: This is the initial amount invested in the project.

Interpretation of the profitability index

Advantages of the profitability index

Limitations of the profitability index

Example of the profitability index

For the project with a cost of 30,000 and the sum of discounted net cash flows of 31,980, the profitability index is 31980/30000 = 1.066.

Payback Period

The Payback Period is a financial metric used to evaluate how long it takes for an investment to generate enough cash flow to recover its initial cost.

Why use the Payback Period?

• Simplicity: The Payback Period is easy to calculate and understand.
• Speed: It provides a quick idea of a project's liquidity.
• Risk: Projects with a shorter Payback Period are generally perceived as less risky.

Advantages and limitations of the Payback Period

Advantages

• Simplicity: Easy to understand and calculate.
• Focus on liquidity: Emphasizes the speed of investment recovery.

Limitations

• Ignores the time value of money: A dollar today is not worth a dollar in five years. However, the Payback Period can also be calculated with discounting.
• Does not consider post-recovery cash flows: A project may be very profitable after the Payback Period, but this is not considered.
• Less accurate for long-term projects: The Payback Period can be misleading for projects spanning several years.

How to calculate the Payback Period?

For each year, calculate the cumulative cash flow until it equals the investment cost. If this equality occurs between two years, calculate the exact time using linear interpolation, assuming that the cash flow of a year is spread evenly throughout the year but the residual value is received at the end of the year.

Example 1: Payback Period without discounting

Duration between 2 and 3 years

2 ans ---> 27000
x ans ---> 30000
3 ans ---> 37000
(x -2)/(3-2) =(30000-27000)/(37000-27000) --> x = 2.3
2 years , 3 months et 18 days

Example 2: Payback Period with discounting

Here, we use the discounted cash flows.

In this case, the discounted net cash flows are insufficient (less than 30,000). But there is a final special flow: the residual value: 3288, which brings the total cash flow to 31980. So the Payback Period will be 3 years.