IRR:

Internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero.

One popular use of IRR is in comparing the profitability of establishing new operations with that of expanding old ones.For example, an energy company may use IRR in deciding whether to open a new power plant or to renovate and expand a previously existing one. While both projects are likely to add value to the company, it is likely that one will be the more logical decision as prescribed by IRR.Any project with an IRR that exceeds the RRR will likely be deemed a profitable one, although companies will not necessarily pursue a project on this basis alone. Rather, they will likely pursue projects with the highest difference between IRR and RRR, as chances are these will be the most profitable.

NPV : Net Present Value

The difference between the present value of cash inflows and the present value of cash outflows. NPV is used in capital budgeting to analyze the profitability of a projected investment or project.

interesting reference:

http://www.mathsisfun.com/money/net-present-value.html

The following is the formula for calculating NPV:

where

C_{t} = net cash inflow during the period t

C_{o }= total initial investment costs

r = discount rate, and

t = number of time periods

A positive net present value indicates that the projected earnings generated by a project or investment (in present dollars) exceeds the anticipated costs (also in present dollars). Generally, an investment with a positive NPV will be a profitable one and one with a negative NPV will result in a net loss. This concept is the basis for the Net Present Value Rule, which dictates that the only investments that should be made are those with positive NPV values.

Discount Rate:

The interest rate charged to commercial banks and other depository institutions for loans received from the Federal Reserve Bank’s discount window. The discount rate also refers to the interest rate used in discounted cash flow (DCF) analysis to determine the present value of future cash flows. The discount rate in DCF analysis takes into account not just the time value of money, but also the risk or uncertainty of future cash flows; **the greater the uncertainty of future cash flows, the higher the discount rate.** A third meaning of the term “discount rate” is the rate used by pension plans and insurance companies for discounting their liabilities.

Overall

A similar issue arises when using IRR to compare projects of different lengths. For example, a project of a short duration may have a high IRR, making it appear to be an excellent investment, but may also have a low NPV. Conversely, a longer project may have a low IRR, earning returns slowly and steadily, but may add a large amount of value to the company over time.