In every business, investment appraisal is the very important part. Accounting rate of return (ARR), Payback period (PP), Net present value (NPV), Internal rate of return (IRR), and Profitability index (PI) are the different types of investment appraisal methods.
In investment decisions, time is a very vital feature. ARR and PP do not take into consideration the time value of money, and do not give an indication of the amount of capital investment required. NPV, IRR, PI are consider the time value of money and the discounted cash flow techniques. It measures the cash inflows and outflows of a project as if they occurred at a single point in time so that they can be compared in an appropriate way. These are the best methods to use for long-run decisions. Since, IRR and NPV incorporate all the cash flows and time value of money, these criteria can be used to reflect capital investment proposal’s strategic orientation.
It is often assumed that higher is better for both of the net present value and the internal rate of return.  It is usually stated that investments with higher IRR are more profitable than investments with lower IRR.
However, this is not essentially so.  In some situations, an investment with a lower IRR may be better, even judged on narrow financial grounds, than an investment with a higher IRR. This interactive lecture explores why and when this reversal takes place.
To review, both the NPV and the IRR require the idea of an income stream, so let’s start there. An income stream is a series of amounts of money. Each amount of money comes in or goes out at some specific time, either now or in the future.  The income stream represents the investment; the income stream is all you need to know for financial evaluation purposes.

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In real life, individuals, charitable institutions, and even for-profit businesses have social or other goals when selecting investments.  For businesses, the benefits of community good will are no less real for being difficult to measure precisely.  For enterprises with social as well as financial goals, the measures discussed here are still useful:  They tell you how much it costs you to advance your social goals.
In here, FIRMEX Corporation is allowing for undertaking two projects. The two projects will be evaluated using the discounted cash flow methods to decide on, which project is to be selected.
Net Present Value (NPV)
The Net Present Value analyzes the profitability of a project by discounting all expected future cash inflows and outflows to the present point in time, using the discount rate (Horngren, et al.,1997). Discount rate is the minimum acceptable rate of return on an investment. It is the return that the organization could expect to receive elsewhere for an investment of comparable risk.
NPV is a better method of appraising investment opportunities than Accounting rate of return (ARR) and Payback Period (PP), because it takes account of the time value of money and also includes all the relevant cash flows irrespective of when they are expected to occur (McLaney and Atrill, 2002).
Appraisal using NPV
NPV is positive when the discounted cash inflows exceed the discounted cash outflows, and so a proposal is acceptable if it has a positive NPV. When evaluating two or more mutually exclusive proposals, the one with the highest positive NPV should be accepted.
In the given case, NPV of ‘Project B’ is much higher than that of ‘Project A’. So, Project B is preferable.
Internal Rate Of Return (IRR)
Internal rate of return is another discounted cash flow technique. It is the discount rate at which the present value of expected cash inflows from a project equals the present value of expected cash outflows of the project. That is, IRR is the discount rate yielding a zero NPV (Upchurch, 1998).
Appraisal using IRR :
A project is accepted only if the internal rate of return exceeds the company’s cost of capital. If it is less than the cost of capital, the project should be rejected. While evaluating two competing projects, the one with the higher IRR should be selected.
In the given case, we will get two IRR values for ‘Project A’, and so this project cannot be evaluated using IRR. Whereas, the IRR of ‘Project B’ is much higher than the company’s cost of capital, and therefore it can be selected.
Profitability Index:
Profitability index is the total present value of future net cash flows of a project divided by the total present value of the net initial investment (Horngren, 1997). It measures the cash flow return per dollar invested. It is very useful in choosing among projects when the investment funds are limited, because it can identify the projects that will generate the most money from the limited capital available.
Conclusion:
NPV is the technically superior criteria, because IRR is calculated by trial and error method, and so the results are less precise. Also, IRR do not consider the size of the investment required and the gain/loss which will result from undertaking or not undertaking a project. It is therefore difficult to use IRR for comparing competing proposals, and there is a possibility that both NPV and IRR will give conflicting indications. IRR is also unable to cope with a change in the cost of capital during the life of a project. But, NPV can accommodate such a change. Another problem with IRR is that some projects may have more than one IRR, which makes it a meaningless criterion while evaluating that project.
In FIRMEX Corporation, Project ‘A ‘has got two IRR values. So, IRR cannot be used for evaluating this project. The other two criteria, NPV and profitability index are higher for Project ‘ B ‘. IRR for Project ‘B ‘ is also higher than the company’s cost of capital.