In
the case of longer-term projects, the time at which profits start accruing
can
have a bearing on the worth of future earnings. This is expressed by
an
important financial concept called the time
value of money. It states
that,
in general, money earned now is worth more than money earned at
some
time in the future, for two reasons:
1.
Additional return could have been obtained if the money had been
invested
in the intervening period.
2.
Purchasing power is reduced, due to inflation.
The
discount rate used is based on the required or desired
rate
of return, and may also include the expected rate of inflation over the
life
of the project. Applying discounting rates tends to show very clearly
that
projects generating a profit early in their life cycle are preferred to
projects
that generate profits much later in the future.
Discounted
cash flow takes into account the timing at which
expenditure
and profits rise, and shows the effective rate of return on the
total
investment over the life of the project.
When
evaluating the worth of the project, the desired rate of return can be set at
some boundary level. If
the
initial analysis and evaluation shows that this rate of return cannot
be
achieved, then the returns are likely to be too low and the project
will
not be worth pursuing. The method of calculating DCF is relatively
straightforward,
and can be easily adapted to spreadsheet methods.
An
alternative approach is to determine the discount rate that would
generate
a zero return over the complete life of the project. This is termed the internal rate of return (IRR). A hurdle rate can be set for the
IRR,
and
any project that cannot meet or exceed it is deemed to be not worth
pursuing
unless there are other important, nonfinancial factors.
When
the discounting process is
applied
to project cash flow, it produces the net
present value (NPV)
of
the proposed project at the given discount rate. (A project will have
an
NPV of zero at the IRR.) This is a popular method of establishing
the
worth of a project investment, with a positive NPV at the hurdle discount
rate
identifying a potentially viable project from a financial point
of
view.
In
addition to the NPV method, the discounted
cash flow return
(DCFR) approach
can be used. This approach is particularly suitable if
capital
is being borrowed to finance the project.
1.
NPV = (Cash inflows − Cash
outflows) ∗ Discount rate
where
Discount
rate = 1 / (1 + k
+ r)t
and
k = the
inflation rate
r = the
required or desired rate of return
t
= time period
2.
IRR = the discount rate at which NPV is
approximately equal to 0.
Example 1
Your
project organization has to decide whether or not to invest in a
project
opportunity. The following information is available to you:
Initial
cash outflow = $200,000 in the current year (year
0), and $100,000
in
the next year
Cash
inflows = $100,000 in year 1, $150,000 in
year 2, $175,000 in year 3,
and
$75,000 in year 4
Required
rate of return = 12%
Inflation
rate = 4%
a.
Calculate the NPV for this project.
b.
Calculate the IRR for this project.
Solution
The
discount factor and NPV for this example is given by
Discount
factor = 1 / (1 + k
+ r)t
= 1 / (1 + 0.04
+ 0.12)t for t = 0,
1, 2, 3,
and
4
NPV
= Net flow ∗ Discount
factor
a.
NPV (Table 6.1)
b.
IRR: Steps (Tables 6.2.1, 6.2.2, and 6.2.3)
1.
Assuming an inflation rate of 4 percent, try different rates of
returns
to calculate the NPV of the cash inflows.
2.
Subtract the cash outlay from the total NPV of the inflows.
3.
The rate at which the value from step 2 is close to zero is the IRR.
1.
Assuming an inflation rate of 4 percent, try different rates of
returns
to calculate the NPV of the cash inflows.
2.
Subtract the cash outlay from the total NPV of the inflows.
3.
The rate at which the value from step 2 is close to zero is the IRR.
There
is an important caveat, however, when using net present value to evaluate
projects.
The longer the project’s life or projected stream of revenues, the
less
precise this approach becomes.
• IRR
and NPV calculations typically agree (that is, make the same
investment recommendations)
only when projects are independent
of each other. If projects
are not mutually exclusive, IRR and NPV
may rank them differently.
The reason is that NPV employs a
weighted average cost of
capital discount rate that reflects potential
reinvestment, while IRR does
not. Because of this distinction, NPV
is generally preferred as a
more realistic measure of investment
opportunity.
• If
cash flows are not normal, IRR may arrive at multiple, conflicting
solutions, as is the case
when net outflows follow a period of net cash
inflows. For example, if it
is necessary to invest in land reclamation or
other incidental but
significant expenses following the completion of
plant construction, an IRR
calculation may result in multiple return
rates, only one of which is correct.
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