# The internal rate of return (IRR) and the net present value (NPV)

Categories: Values

The internal rate of return (IRR) and the net present value (NPV) techniques are 2 investment decision tools that satisfy the 2 major criteria for the correct evaluation of capital projects. This criterion is that the techniques should incorporate the use of cash flows and the use of the time value of money. This makes them viable techniques for evaluating investment proposals.

The Net Present Value is one of the techniques that are used by firms when evaluating which investment proposals to take on board and which ones to reject.

The net present value is calculated by discounting all flows to the present and subtracting the present value of all inflows.

As cited by Petrochilos G 2004, the Net Present Value principle advises us to invest in the project as long as its Net Present Value is positive, and reject the investment suggestion if its Net Present Value is negative.

The reason given by Petrochilos G, 2004, is that when the flow of future returns is discounted at the cost of capital, and gives a positive NPV, the project can cover both interest and depreciation charges, and thus, the positive NPV represents a clear profit, which increases the wealth of the firm.

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In the case of a negative NPV, the condition as referred to by Petrochilos, tells us that we shall lay yourself open to a loss in our internal venture opportunity, thus, should not invest, but consider, instead, using the outer opportunities by lending any money in the capital market.

Formula:Wheret - The time of the cash flowN - The total time of the projectr - The discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk.

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)Ct - the net cash flow (the amount of cash) at time t (for educational purposes, C0 is commonly placed to the left of the sum to emphasize its role as the initial investment.).

The net present value of an investment tells you how this investment compares either with your alternative investment or with borrowing, whichever alternative you prefer.

The NPV uses the discount rate which is the interest rate used to evaluate the project. This discount rate represents the cost of the funds used also known as the opportunity cost of the capital.

After calculating the NPV if the value is positive that means that the project is financially feasible because after the cash inflows are added and discounted at the cost of capital and the cash outflow is deducted, there will still be something leftover. This would make any such proposal a good investment opportunity.

If after the calculations the net present value is negative, this means that the project is not a very good investment opportunity while if the NPV is 0, the project could be considered as it is on the border line of being viable. This is because it is just earning back the cost of the capital that would be invested in it.

For example if a company wanted to introduce a new product line, the new product will have startup costs, operational costs, and incoming cash flows over a certain period of time. This project will have an immediate (t=0) cash outflow of 0.000, which might include among others machinery, and employee training costs. Other cash outflows for years are expected to be 000 per year. Cash inflows are expected to be ,000 per year for the period estimated. The required rate of return is 10%.

The sum of all these present values is the net present value, which equals \$8,881. Since the NPV is greater than zero, the corporation should invest in the project.

The Internal Rate of Return is another technique that is used when evaluating investment proposals. But just like the NPV it satisfies the criteria required for the correct evaluation o0f capital projects by using cash flows as well as the time value of money.

The Internal Rate of Return is the discount rate where the Net Present Value is zero. Internal rate of return (IRR) is a rate of return on an investment. The IRR of an investment is the interest rate that will give it a net present value of zero.

The IRR is calculated by a trial and error processStarting with a guess at the IRR, r, the process is as follows:The NPV is calculated using r.

To find the internal rate of return, one needs to find the values of r that satisfies the following equation:YearCash Flow0-1001+302+353+404+45Internal Rate of Return (IRR)IRR = r,IRR = 17.09%Net Present Value (NPV)Thus using r = IRR = 17.09%,If the NPV is close to zero then r is the IRR.

If the NPV is positive r is increased.

If the NPV is negative r is decreased.

This technique looks for the interest rate that equals the present value of inflows and outflows.

The IRR technique use the accept/reject criteria of comparing the IRR with the cost of capital which is based on comparing the internal rate of return to the cost of the capital of the project.

If the IRR is less than the capital then that project should be rejected because it is not very feasible. If the Internal Rate of Return is larger than the capital required for the project, it should be accepted while if the IRR is just equal to the capital then the project could be considered because it is at the very least earning its cost of capital and should therefore be accepted at the margin.

When evaluating any investment proposals, the NPV technique and the IRR technique usually provide results that are in sync with each other in regards to any single proposal. This means that in many cases it is clear after calculating both the NPV and IRR of any project whether it should be accepted for investment or rejected.

This is because for most projects if the NPV is greater than 0, the IRR is usually greater than the cost of capital making it a viable project. Also where the NPV is equal to zero, the IRR equals the capital putting the project on the margin as it is just able to cover the cost of its capital. In instances where the NPV is less than 0, the IRR is less than the capital so such a venture is not very financially viable and as such should be rejected.

This sync between the results from the NPV and IRR techniques is especially true in cases where the proposals being analysed are independent of each other. In such cases, both the NPV and IRR will give consistent results. This means that a company can invest in 2 projects and run them at the same time just as long as they are do not require the same resources, pass both the NPV and IRR tests and the company has enough funds to invest in both projects at the same time.

Sometimes the results from the NPV and the IRR may contradict each other. This usually happens in cases where a firm is analysing proposals for projects that are mutually exclusive to each other. In such circumstances, the results from the NPV and the IRR may be conflicting which gives rise to a question on which proposal should be accepted and which should be rejected.

These differences in results from the NPV and IRR method can be brought about as a result of a number of circumstances.

The first one of the reasons for such results can be that there is a difference in the initial costs required to set up the different projects that are being analysed. This means that since the initial capital required to set up each project is different from the other, the NPV and IRR values when calculated will tend to conflict and not give conclusive results on which projects should be accepted or which should be rejected.

Another circumstance that can lead to conflicting NPV and IRR values is that the different projects may have different shapes of their subsequent cash inflow streams. For example for one project it could have big cash inflows in its early stages while another project could have small cash inflows in its early stages which then go on increasing overtime. This difference in the shape of their cash flows will lead to the conflict in the NPV and IRR test results for such projects.

These conflicting results of the IRR and the NPV tests occur as a result of implicit reinvestment assumption. The formula for calculating the NPV assumes that cash inflows are automatically reinvested at the cost of capital while the IRR assumes that cash inflow is reinvested at the Internal Rate of Return. This will then result in 2 different set of results for the NPV and IRR tests.

Another scenario where the IRR and NPV may give conflicting results is where the 2 projects being analysed have significantly contradictory cash inflow shapes. Although the initial outlays for 2 mutually exclusively project maybe the same, the shape they take after that may be different. For example for one project, the cash inflow may start out slowly and then gradually build itself up while for the second project it may have a big cash inflow initially that will then decline overtime. In such a circumstance the NPV and IRR tests will give you conflicting results on which of the 2 projects you should accept and which one you should reject.

Furthermore, you may have a problem using the NPV and IRR techniques if the projects you are analysing have unconventional cash flows. Under normal circumstances a project would have a conventional cash flow where cash out flows are followed by a number of cash inflows for the remaining time period of the project. In this case, the only change that occurs is from negative flows (outflow) to the positive flows (inflows. In projects where this does not happen and instead the project started with positive flows (cash inflows) that are then transcending into negative flows (.outflows). In this situation, if the IRR technique is used 2 analyse such projects, it will give 2 different IRR results which can be confusing but if you use the NPV method to analyse the same project, you get one single answer.

The IRR technique should not be used to analyse proposals for projects that have different durability. This is because it does not make assumptions that positive cash flows are reinvested into any project and as such if you use it to analyse 2 different projects with 2 different durations, you will end up with 2 IRR values which make it difficult to decide which of them to reject or which one you should invest in. Many analysts will then use the Modified Internal Rate of Return as it gives them a better understanding of how efficient any project will be in contributing to its discounted cash flows.

Furthermore, the IRR technique is not very effective in circumstances where there are many sign changes before the cash flows for example where a positive cash flow is followed by a negative cash flow then a positive then a negative and so on. In situations like this, there will be many IRR values for a single project which will lead to confusion on the true value of investing in such a project. Examples of such projects are strip mines and nuclear power plants because they have large cash outflows at the end of the project.

Another weakness of the IRR technique is that it does not show the actual annual profitability of a project. This is because although the IRR technique assumes that cash inflows are reinvested into the project at the rate of return, the intermediate cash flows are almost never reinvested and as such the actual IRR will always be lower. The intermediate cash flows include things such as the value of return on stocks and bank deposits. This weakness can be rectified by using the modified internal rate of return which has an assumed reinvestment rate usually at the cost of the capital. As such if you use only the IRR to determine how profitable your investment will be, you may not get an accurate value.

Many people consider, the NPV as a better technique in comparison to the IRR because projects with the highest NPV will give the highest present value for the business and since the ultimate financial goal of any firm is to maximise its stockholder抯 wealth, this makes it quite effective as an investment decision tool. This is because it helps you choose the projects that will ultimately give you the most return if you decide to invest in them.

Furthermore, the fact that NPV assumes reinvestment of the cash inflows at the cost of capital while IRR assumes reinvestment of cash inflows at the rate of return. This makes NPV a more realistic technique on which an investment decision should be made .This is because intermediate cash inflows are almost never reinvested at the rate of return and as such this misconception that all cash inflows are reinvested at the rate of return will give an unrealistic view of the actual annual profitability of a project.

In some situations where the after calculating the NPV and IRR of 2 projects, one has the higher NPV while the other has the higher IRR, a crossover method is sometimes used to determine which is the most viable option of the 2. If the Cross Over Point is greater than the IRR then you choose the project with higher NPV and if the Cross Over Point is less than the IRR value then you opt for the project with higher IRR value.

Because of the many weaknesses of the IRR technique, many analysts consider NPV to be the more accurate of the 2 methods. This does not necessarily make NPV the more popular of the 2 as despite its weaknesses many investment analysts still opt to use the IRR technique. This is because they prefer to compare investment proposals by percentages given by IRR than actual cash amounts got by using the NPV. IRR is usually more effective in determining whether a single project is worth investing in rather than comparing 2 mutually exclusive projects to determine which is better for investment.

In conclusion, both the NPV and IRR techniques are important tools in the decision making process in determining which projects a firm should invest in and which ones they should reject. They give the analyst an idea of the future earning potential of projects and as such make investment decisions easier. Whether the techniques are used together or separately will depend on the nature of the projects being analysed. This will go a long way in easing the investment decision making process.

## Bibliography

1. Chris Mulhearn, Howard. R. Vane, James Eden, (2001), 慐conomics for business, Palgrave Foundations, London: pages 127-131.
2. Joseph.G.Nellis and David Parker, (1992), 慐ssence of business economics, prentice hall, London: page 150-151.
3. Evan, Dorla A and Shawn. Forbes, 1993, 揇ecision making and Display Methods. The case of prescription and practice in capital budgeting, the engineering Economist, page 87-92.
4. Petrochilos. A. George, (2004), 慚anagerial Economics A European Text, Palgrave Macmillan, pg 315McGuigan et al. 2002, Managerial Economics: Applications, Strategy and TacticsSalvator, e D. 2003, Managerial Economics in a Global Economyhttp://en.wikipedia.org/wiki/Net_present_valuehttp://www.investopedia.com/terms/n/npv.asp
Updated: Nov 01, 2022