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The internal rate of return (IRR) is a capital budgeting method used by firms to decide whether they should make long-term investments.
The IRR is the return rate which can be earned on the invested capital, i.e. the yield on the investment.
A project is a good investment proposition if its IRR is greater than the rate of interest that could be earned by alternative investments (investing in other projects, buying bonds, even putting the money in a bank account). The IRR should include an appropriate risk premium.
Mathematically the IRR is defined as any discount rate that results in a net present value of zero of a series of cashflows.
In general, if the IRR is greater than the project's cost of capital, or hurdle rate, the project will add value for the company.



Net present value (NPV) is a standard method for financial evaluation of long-term projects. Used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met. By definition,
NPV = Present value of cash inflows - Present value of cash outflows. For its expression, see the formula section below.
Formula
Each cash inflow/outflow is discounted back to its PV. Then they are summed. Therefore

Where
t - the time of the cash flow
n - the total time of the project
r - the discount rate
Ct - the net cash flow (the amount of cash) at that point in time.
C0 - the capitial outlay at the begining of the investment time ( t = 0 )
If... It means... Then...
NPV > 0 the investment would add value to the firm the project should be accepted
NPV < 0 the investment would subtract value from the firm the project should be rejected
NPV = 0 the investment would neither gain nor lose value for the firm the project could be accepted as shareholders obtain required rate of return


Payback Period

Payback period in business and economics refers to the period of time required for the return on an investment to "repay" the sum of the original investment. For example, a $1000 investment which returned $500 per year would have a two year payback period. It is intuitively the measure that describes how long something takes to "pay for itself"; shorter payback periods are obviously preferable to longer payback periods (all else being equal). Payback period is widely used due to its ease of use despite recognized limitations, described below.
The expression is also widely used in other types of investment areas, often with respect to energy efficiency technologies, maintenance, upgrades, or other changes. For example, a compact fluorescent light bulb may be described of having a payback period of a certain number of years or operating hours (assuming certain costs); here, the return to the investment consists of reduced operating costs. Although primarily a financial term, the concept of a payback period is occasionally extended to other uses, such as energy payback period (the period of time over which the energy savings of a project equal the amount of energy expended since project inception); these other terms may not be standardized or widely used.
Payback period as a tool of analysis is often used because it is easy to apply and easy to understand for most individuals, regardless of academic training or field of endeavour. When used carefully or to compare similar investments, it can be quite useful. As a stand-alone tool to compare an investment with "doing nothing", payback period has no explicit criteria for decision-making (except, perhaps, that the payback period should be less than infinity).
The payback period is considered a method of analysis with serious limitations and qualifications for its use, because it does not properly account for the time value of money, inflation, risk, financing or other important considerations. Alternative measures of "return" preferred by economists are internal rate of return and net present value. An implicit assumption in the use of payback period is that returns to the investment continue after the payback period. Payback period does not specify any required comparison to other investments or even to not making an investment.