**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.

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**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