Comparison of Net Present Value and Internal Rate of Return Methods

By Jackie, Researcher

Topic: Education

Area of discussion: Cost & Management Accounting

Chapter: Capital Budgeting & Cost Analysis

The objective of this posting is to discuss, explain, and justify the superiority of NPV over the IRR. We will look into the conditions which make IRR method becomes inappropriate for usage purpose (i.e. the IRR’s technical shortcoming).

Introduction

Net Present Value Method

It calculates the expected monetary gain or loss from a project by discounting all expected future cash inflows and outflows back to the present point in time using the required rate of return. In other words, it is the present value of the net cash inflows less the present value of the net cash outflows (if any), and then minus the project’s initial investment outlay. A positive NPV indicates that an investment should be accepted, while a negative value indicates that it should be rejected. A zero NPV calculation indicates that the firm should be indifferent to whether the project is accepted or rejected.

Internal Rate of Return Method

It is the rate of return promised by an investment project over its useful life. It is sometimes referred to simply as the yield on a project. The internal rate of return is computed by finding the discount rate that equates the present value of a project’s cash outflows with the present value of its cash inflows. In other words, the internal rate of return is the discount rate that results in a net present value of zero. The decision rule is that if the IRR is greater than the opportunity cost of capital, the investment is acceptable as it is profitable and will yield a positive NPV. Alternatively, if the IRR is less than the cost of capital, the investment should be rejected as it is unprofitable and will result in a negative NPV. When the IRR is equal to the opportunity cost of capital, the firm should be indifferent to whether the project is acceptable or rejected.   

Comparison of Net Present Value and Internal Rate of Return Methods

In many situations the internal rate of return method will result in the same decision as the net present value method. In the case of conventional projects (in which an initial cash outflow is followed by a series of cash inflows) that are independent of each other (i.e. where the selection of a particular projects does not preclude the choice of the other), both NPV and IRR rules will lead to the same accept/reject decisions. However, there are also situations where the IRR method may lead to different decisions being made from those that would follow the adoption of the NPV procedure. 

Mutually exclusive projects 

If projects are mutually exclusive (i.e. the acceptance of one project excludes the acceptance of another project), it is possible for the NPV and the IRR methods to suggest different rankings as to which project should be given priority. For example, choosing one out of three possible factory locations. When evaluating mutually exclusive projects, the IRR method is prone to indicate wrong decisions (i.e. incorrectly rank projects) due to its reinvestment assumptions especially when dealing with unequal lives or unequal levels of initial investment outlay. For instance, compare an investment of £ 10,000 that yields a return of 50 per cent with an investment of £15,000 that yields a return of 40 per cent. If only one of the investments can be undertaken, normally managers will choose the project which has the highest IRR, but bear in mind that in actual fact, the first investment will only yield £5,000 but the second investment will yield £6,000. Thus, if the objective is to maximize the shareholders’ wealth the NPV provides the correct measure.

Percentage returns 

We can sum NPVs of individual projects to calculate a NPV of a combination or portfolio of projects as NPV method is expressed in monetary terms, not in percentages. For example, Project Alpha consists of two smaller projects: South (NPV = £12,500) and West (NPV = £7,500). Then, the NPV of Project Alpha will be £20,000. In contrast, IRRs of individual projects cannot be added or averaged to represent the IRR of a combination of projects.

Volatile cost of capital 

NPV method can also be used when the cost of capital varies over the life of a project. For instance, Vortex Plc has made an initial investment of £10,000 and expected to receive cash inflow as much as £25,000 in year 1 when the cost of capital is 12%, followed by another cash inflow of £18,000 when the cost of capital is 10% in year 2 and finally, £5,000 cash inflow in year 3 when the cost of capital is 8%. Then, the NPV can be calculated as £31,163 (see below). It is not possible to use IRR method in this case. This is because different cost of capital in different years means that there is no single cost of capital that the IRR (a single figure) can be compared against to decide whether the project should be accepted or rejected. 

Reinvestment assumptions 

The assumption concerning the reinvestment of interim cash flows from the acceptance of projects provides another reason for supporting the superiority of the NPV method. The implicit assumption if the NPV method is adopted is that the cash flows generated from an investment will be reinvested immediately at the cost of capital (i.e. the returns available from equal risk securities traded in financial markets). However, the IRR method makes a different implicit assumption about the reinvestment of the cash flows. It assumes that all the proceeds from a project can be reinvested immediately to earn a return equal to the IRR of the original project. This assumption is likely to be unrealistic because a firm should have accepted all projects which offer a return in excess of the cost of capital, and any other funds that become available can only be reinvested at the cost of capital.

Unconventional cash flows 

When the signs of the cash flows switch overtime (i.e. when there are outflows, followed by inflows, followed by additional outflows and so forth), it is possible that more than one IRR may exist for a given project. In other words, there may be multiple discount rates that equate the NPV of a set of cash flows to zero (see below). In such cases, it is difficult to know which of the IRR estimates should be compared to the firm’s required rate of return.

Additional readings, related links and references:

“Perils of the Internal Rate of Return”: This is an extremely good link. It heavily focuses on discussion with clear and detailed examples. Calculations and graphs are all provided. This is highly recommended for those who are doing a research project on this issue or doing revision for coming exams.

http://www.sambaker.com/econ/invest/invest.html

“Which is a better measure for capital budgeting, IRR or NPV?”: This site is suitable for beginner. It provides a brief explanation, examples and concepts. It can give you a quick understanding.
http://www.investopedia.com/ask/answers/05/irrvsnpvcapitalbudgeting.asp#axzz2Favl7l6v

“Chapter 6 - Investment decisions - Capital budgeting”: Well, this site looks like an e-book to me. The good thing about this link is it offers more detailed calculations instead of theories. Complete formulas are given too. 

http://www.fao.org/docrep/W4343E/w4343e07.htm

“Net Present Value Vs Internal Rate Of Return (NPV & IRR) & Excel Calculations For DCF”: If you prefer to learn via hearing instead of reading, then this might suit you. 

http://www.youtube.com/watch?v=aziR2zNtPHk

“How to calculate NPV and IRR in Excel”: The voice is clear, good explanation and most importantly, it is a step-by-step tutorial approach.

http://www.youtube.com/watch?v=kCnwCplibAk