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project analysis under cert

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1
Ch 6 Project Analysis Under
Certainty
Methods of evaluating projects when
the future is assumed to be certain.
2
Introduction
The ideal investment decision making technique
is Net Present Value.
N P V measures the equivalent present wealth
contributed by the investment.
NPV is given in
NPV relates directly to the firm’s goal of
wealth maximization
employs the time value of money
can be used in all types of investments

can be adjusted to incorporate risk.
3
Other Project Evaluation Techniques:
Slide I
Discounted Cash Flow Techniques
Internal Rate of Return – calculates the
discount rate that gives the project an
NPV of $0. If the IRR is greater than
the required rate, the project is
accepted. IRR is given as % pa.

IO
IRR
CF


IRR
CF
NPV

+
+
+
=

)1()1(
)(0$
2
2
1
1
4
Other Project Evaluation Techniques:
Slide II
Modified Internal Rate of Return – calculates
the discount rate that gives the project an NPV
of $0, when future cash flows can be re-invested
at the Re-Investment Rate, a rate different from
the IRR. If the MIRR is greater that the
required rate, the project is accepted. MIRR is
given as % pa.
IO
IRR
RIRCF
IRR
RIRCF

NPV
nn

+

+
+

=


)1(
)1(
)1(
)1(
)(0$
2
)1(
2
1
1
5
Other Project Evaluation Techniques:
Slide III
Non-Discounted Cash Flow Techniques
Accounting Rate of Return- measures the ratio of
annual average accounting income to an asset base
value. ARR is given as % pa.

= % pa.


Payback Period – measures the length of time
required to retrieve the initial cash outlay.
PB is given as number of years.
6
Selection of Techniques: Slide I
NPV is the technique of choice; it satisfies the
requirements of: the firm’s goal, the time value of
money, and the absolute measure of investment.
IRR is useful in a single asset case, where the cash
flow pattern is an outflow followed by all positive
inflows. In other situations the IRR may not rank
mutually exclusive assets properly, or may have
zero or many solutions.
7
Selection of Techniques: Slide
II

MIRR is useful in the same situations as the IRR,
but requires the extra prediction of a re-
investment rate.

ARR allows many valuations of the asset base,
does not account for the time value of money, and
does not relate to the firm’s goal. It is not a
recommended method.

PB does not allow for the time value of money,
and does not relate to the firm’s goal. It is not a
recommended method.

8
The Notion of Certainty

Certainty allows demonstration and evaluation of the
capital budgeting techniques, whilst avoiding the
complexities involved with risk.

Certainty requires forecasting, but forecasts which are
certain.

Certainty is useful for calculation practice.

Risk is added as an adaption of an evaluation model
developed under certainty.
9
Investment Cash Flow Timing
End Of Year cash flow timing is assumed.
Capital Flows
0 1 2 3 4 5
Initial Later Terminal

Outlay. Outlay Flow

Operating Flows
0 1 2 3 4 5

Operating Flows.
10
The NPV Process: Slide I


Net annual cash flows are forecast
for each year of the project.
EOY 0
-900
EOY 1
300
EOY 2
380
EOY 3
600


The discount rate is then applied.
-900
1
)06.1(
300
+
2
)06.1(
380
+
3
)06.1(
600
+
11
The NPV Process: Slide II

The NPV is calculated.

$503.77$338.19$283.01-$900
NPV = $ 224.97 Positive: the project is acceptable.
12
Other NPV Applications:
Slide I
Asset
Retirement:
Asset
Replacement:
13
Other NPV Applications:
Slide II

Optimum cycle length within a replacement chain.
At EOY:
3 6 9 12 15

OR ?

4 8 12 16
14
Other NPV Applications:
Slide III
Correct ranking of mutually exclusive projects.
Where projects have different outlays.
Where projects have different lives.
15
Net Present Value
THE model to use in all investment evaluations.
Other criteria, such as IRR, MIRR, ARR, and

Payback may be used as complementary
measures.
The End

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