Choose language

PL, EN, ES, DE, FR, RU

# Profitability of investments: NPV (Net Present Value), PI (Profitability Index), IRR (Internal Rate of Return), DPP (Discounted Payback Period) - calculator

This calculator helps us check whether the planned investment will be profitable and whether the project should be accepted or rejected.
Thanks to the calculator, we can calculate:
NPV (Net Present Value) - sum of discounted net cash flows
PI (Profitability Index) - investment profitability
IRR (Internal Rate of Return) - internal rate of return
DPP (Discounted Payback Period) - discounted payback period
Value of discounted net cash flow for each period.

## Profitability of investments: NPV (Net Present Value), PI (Profitability Index), IRR (Internal Rate of Return), DPP (Discounted Payback Period)

%
YEARS

Year Income (CIF) Outcome (COF) Net cash flow (CF) Discounted cash flows (NCF)

Usefull information

Net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount rate. NPV accounts for the time value of money. It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications. More on Wikipedia.

Internal rate of return (IRR) is a method of calculating an investment’s rate of return. The term internal refers to the fact that the calculation excludes external factors, such as the risk-free rate, inflation, the cost of capital, or financial risk.
The internal rate of return on an investment or project is the "annualized effective compounded return rate" or rate of return that sets the net present value of all cash flows (both positive and negative) from the investment equal to zero. Equivalently, it is the discount rate at which the net present value of the future cash flows is equal to the initial investment, and it is also the discount rate at which the total present value of costs (negative cash flows) equals the total present value of the benefits (positive cash flows).
IRR accounts for the time preference of money and investments. A given return on investment received at a given time is worth more than the same return received at a later time, so the latter would yield a lower IRR than the former, if all other factors are equal. A fixed income investment in which money is deposited once, interest on this deposit is paid to the investor at a specified interest rate every time period, and the original deposit neither increases nor decreases, would have an IRR equal to the specified interest rate. An investment which has the same total returns as the preceding investment, but delays returns for one or more time periods, would have a lower IRR. More on Wikipedia.

Profitability Index (PI), also known as the investment profitability index - investment evaluation criterion, expressed as the quotient of the sum of discounted positive cash flows to the sum of discounted negative cash flows.
We mark the profitability index as PI. It is most often used in financial and insurance mathematics.
$$PI={\frac {\sum \limits _{t=0}^{n}{\frac {CIF_{t}}{(1+r)^{t}}}}{\sum \limits _{t=0}^{n}{\frac {COF_{t}}{(1+r)^{t}}}}}$$ where:

CIF (cash inflow) = positive cash flow in year t
COF (cash outflow) = negative cash flow in year t
r = cost of capital
n = number of years
When the PI profitability index is greater than 1, the project is initially accepted for implementation. The higher the PI value, the more profitable the investment appears to be. The profitability ratio is used to select the most effective from among several investment projects. PI is calculated only for projects with a positive NPV. More on Wikipedia.

Discounted payback period (DPP) is the amount of time that it takes (in years) for the initial cost of a project to equal to discounted value of expected cash flows, or the time it takes to break even from an investment. It is the period in which the cumulative net present value of a project equals zero. More on Wikipedia

## Users of this calculator also used

### Solving any systems with Cramer's Rule calculator

You can calculate step by step any system of linear equations, both homogeneous and inhomogeneous with any number of unknowns by the Cramer's method. As a result, in addition to the solution, you also get a complete analysis and presentation of calculations step by step.

### Fibonacci sequence calculator

Using the calculator, you can easily and quickly calculate the sum of the Fibonacci sequence, find a value or find the nth term.

### Laplace expansion, determinant of 4x4 matrix - calculator

With the help of the calculator you will calculate the determinant of the fourth degree matrix by the Laplace Expansion method. You will learn step by step how the calculations are performed and we will get explanations of each action. A useful tool for learning, consolidating, checking your own calculations and understanding the Laplace method.

### Vernam cipher - encoder / decoder

Vernam cipher online encoder and decoder. Encrypt and decrypt any cipher created in a Vernam cipher.

### Caesar cipher - encoder / decoder

Caesar cipher online encoder and decoder. Encrypt and decrypt any cipher created in a Caesar cipher. You can use any shift and additionally a key for more precise text encoding.

### Vigenère cipher - encoder / decoder

Vigenère cipher online encoder and decoder. Encrypt and decrypt any cipher created in a Vigenère cipher. You can use any shift and additionally a key for more precise text encoding.

### Basal metabolic rate (BMR) - calculator

Using the calculator, you will calculate the basic metabolic rate (BMR-basal metabolic rate) and the amount of calories needed to supplement, i.e. burned by the body on an empty stomach (in the morning, without a meal), in physical and mental peace.