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

**. 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.***(see below)***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

**. In such cases, it is difficult to know which of the IRR estimates should be compared to the firm’s required rate of return.***(see below)*

**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.

“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

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.

“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.

“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.

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