(LO2 _ LO1) Chap 3_1 Analysis Methods v1_43.pptx

CHAPTER 3: PROJECT
FINANCIALANALYSIS
FOREWORD:
This chapter is actually a continuation of the
previous one. However, it concerns more
complex lessons that are relevant to the
financial planning of projects.
1

CHAPTER 3, PART 1:
ANALYSIS METHODS
PREAMBLE:
Mathematics is of course the main skill that is
needed in the financial analysis of projects.
Algebra, arithmetics and calculus are the areas
of mathematics that are relevant to this.
2

Minimum Attractive Rate of
Return (MARR)
3
This is the minimum required interest rate which
is applied on a capital-based project.
The rate is based on, e.g.:
 Amount and source of money available for
investment
 Choices of projects available
 Perceived risk and uncertainties of
investment
 Estimated cost of administering projects over
short and long run

Return (MARR) (cont’d)
4
In other words, the MARR is the representation
of the opportunity costs from selecting one
project over the others.
Due to the consideration of risks, concerns and
returns, as well as balancing them against each
other,
 The MARR is also known as the hurdle rate.
A “hurdle” is an obstacle; in this case, the
obstacle is the aforementioned
consideration.

Return (MARR) (cont’d)
5
The calculations to perform the above are
known as capital rationing.
When an MARR is set, only the projects which
provide annual rate of return equal to or over
the MARR are shortlisted for further decision-
making.

CAPITAL RATIONING
6
Which method to be used depends on the
preferences of the project’s stakeholders.
There methods of capital rationing include:
 Present worth method
 Future worth method
 Annual worth method
 Internal rate of return method
 Payback period method
In financing, capital rationing is the act of
restricting the total amount of investment capital.

CAPITAL RATIONING (cont’d)
7
Cash outflows are considered as revenues.
 They are considered as “positive” flows (+).
Cash inflows are considered as expenses.
 They are considered as “negative” flows (–) .
For the purpose of this chapter,

8
Cash Flow Diagram for Equivalent
Worth
As this chapter involves equivalent values, the
arrow for the worth value is always a dashed line
in the direction of the net equivalent value.
PW
A
1 2 3 4
A A A
Period
0
The diagram below is an example which illustrates
this.

This method is based around finding the
equivalent worth of all expected cash flows
(revenues and expenses) relative to the present.
 This equivalent worth is known as the present
worth (PW).
9
Determining the present worth is done through
 Finding and summing the present value of all
cash flows at the present by using MARR as
the interest rate.

Relevance to engineering field:
 The present worth method is also known as
the “net present value” method (NPV).
10
 NPV is most useful if considerable capital
investment has to be spent at the beginning
of a project.
 Incidentally, almost all engineering projects
require capital investment because they
require physical resources and assets to be
prepared before the start of the project.

Example of where present worth method, or NPV, is
useful:
11
 An oil drilling platform cannot be used for
almost any other purpose, so investment on a
platform requires that its potential revenues be
more than the value of building the platform.

12
If PW > 0, the project is expected to be profitable.
If PW ≤ 0, the project is expected to be not worth
investing in.
Before illustrating the calculations, the following are
declared:
Let individual cash flows be Ck .
N is the number of cash flows.
The MARR is i.

13
The following example shows a cash flow diagram with
revenue flows (i.e. arrows directed above the period
axis).
N
CN
1 2 k
PW
C1 C2 Ck
MARR, i
Period
0
C0
C0 is usually a cash inflow instead of a cash outflow, but
for this example, it is a cash inflow.

14
C0 represents any costs that have been incurred before
the start of the project.
N
CN
1 2 k
PW
C1 C2 Ck
MARR, i
Period
0
C0
C0 is usually due to the costs for preparation or
enabling of the project.

Oil drilling is only possible because there was an oil
field that was identified earlier, e.g. seismic survey
for land-based oil fields.
15
 The identification of the oil field is a project
that has been completed before this
commercial drilling project started.

The previous project involved exploratory surveys and
collection of data and physical samples for confirmation of
the presence of the oil field.
• This project has costs too, but no immediate
revenues. (The data might be saleable later.)
16

17
Therefore, the project that comes after the enabling
project include the costs of the enabling project, so that
the revenues can pay off these costs.
N
CN
1 2 k
PW
C1 C2 Ck
MARR, i
Period
0
C0
The value of C0 has to be converted to its time-valued
amount at period 0 of this project.

18
Firstly, C0 has to be calculated from the financial
analysis of the previous project.
N
CN
1 2 k
PW
C1 C2 Ck
MARR, i
Period
0
C0
Then, the value of C0 has to be converted to its time-
valued amount at period 0 of this project.

19
Therefore, the present worth of the cash flows in the
example are:
       N
N
k
k
i
C
i
C
i
C
i
C
PW










1
....
1
....
1
1 1
1
0
0
 

 


N
k
k
k
i
C
PW
0 1
N
k 

0
Note: (1+i)0 = 1

20
MARR,
i
(1 + i )-10 Present
Worth
0% 1.00000 $ 1,000.00
5% 0.61391 $ 613.91
10% 0.38554 $ 385.54
20% 0.16151 $ 161.51
30% 0.07254 $ 72.54
Table of present worth of
cash flow of Ck = $ 1000
at k = 10 periods
Chart of present worth of cash
flow versus number of periods
By the way, this chart is not using a
timeline axis, i.e. this is not a cash-
flow diagram.
• The chart is only showing the
changes to the time-value of Ck
when the parameter of k
changes.

FUTURE WORTH (FW)
METHOD
21
This method is based around finding the equivalent worth
of all expected cash flows in the future.
 This equivalent worth is known as the future worth
(FW).
Determining the future worth is done through
 Finding the future value of all cash flows at a
certain point in the future by using MARR as the
interest rate.

22
The future worth method is useful to engineering projects
if there are existing assets that can be reused.
 These existing assets may need overhauls and repairs,
but the costs for these are lower than new purchases.
 Reusing existing assets requires analysis of the
benefits/revenues that can be had from reusing them for
another purpose.
 These other benefits/revenues have to be compared
with the benefits/revenues from having the existing
assets continue their original purpose.
Relevance to Engineering Field

Example of where future worth method is useful:
23
 This CNC machine is being upgraded with an
additional axis. The cost of the upgrade has to
be balanced against the benefits that it would
bring, and against the opportunity cost from
not letting the machine stay the way it was.

24
The future returns of the project are needed for the
following
1. Overhauls and repairs for the machine-based assets,
as mentioned earlier.
2. Upgrades for the machines, if any.
3. Disposal of the assets, if they are no longer worth
using for any future projects.
◦ Asset disposal can incur costs too, e.g. shipping assets
to second-hand buyers and transfer of licenses.
Relevance to Engineering Field
(cont’d)

25
FUTURE WORTH (FW)
METHOD (cont’d)
If FW > 0, the project is expected to be profitable.
If FW ≤ 0, the project is not expected to be worth the
investment.
Let individual cash flows be Ck .
N is the number of cash flows.
The MARR is i.

FUTURE WORTH (FW) METHOD
(cont’d)
26
N
1
CN
2 k
FW
C1
C2 Ck
MARR, i
Period
0
The following example shows a cash flow diagram with
revenue flows (i.e. arrows directed above the period
axis).
C0
In projects that use future worth analysis, C0 is usually
the cost of preparing pre-existing assets.

FUTURE WORTH (FW) METHOD
(cont’d)
Therefore, the future worth of the cash flows are:
27
   
    N
N
N
k
N
k
N
N
i
C
i
C
i
C
i
C
FW














1
....
1
....
1
1 1
1
0
0
 






N
k
k
N
k i
C
FW
0
1 N
k 

0
If FW ≥ 0, this means the project makes a loss if time
value of money is considered.
Note: (1+i)0 = 1

Reminder about Periodic Cash Flows
28
𝐴 = 𝑃𝐴
𝑖 1 + 𝑖 𝑁
1 + 𝑖 𝑁 − 1
The above equation can be rearranged to give the
value of A instead.
𝑃𝐴 = 𝐴
1 + 𝑖 𝑁
− 1
𝑖 1 + 𝑖 𝑁
This rearranged equation can be used to convert
an amount to a periodic equivalent value.

ANNUAL WORTH (AW) METHOD
29
The Annual Worth method is used to generate an
equivalent periodic series of cash flows over N
periods at an interest rate equal to MARR.
 The objective here is to calculate an
equivalent periodic value, i.e. AW.
 The Annual Worth here is calculated
differently from the periodic cash flows in
the previous chapter.
 The main difference is the inclusion of the
Capital Recovery (CR) term.

30
AW is equivalent annual revenues (AR) minus
equivalent annual expenses (AE), and minus
again the equivalent capital recovery (CR)
AW = AR – AE – CR
If AW = 0, the project is just sustainable.
If AW > 0, the project is economically profitable.
If AW < 0, the project is unsustainable.

31
CR is usually the conversion of the capital
investment I or pre-start cash flow (usually an
expense) Co into an equivalent periodic value.
N
CN
1 2 k
PW
C1 C2 Ck
MARR, i
Period
0
C0

32
N
1 2 k
CR
MARR, i
Period
0
C0 (or I)
CR CR CR
CR is an equivalent periodic expense cash flow
that represents the consumption or depreciation
of the capital investment I, or pre-start cost C0.

Capital Recovery (CR)
33
Capital Recovery is not exactly a cash flow.
It is closer to a book cost than cash cost.
This is because Capital Recovery is, e.g.:
 The paying back of the capital which would be
invested in the project, OR
 Depreciation of value in an asset which would
be used for the project.

Capital Recovery (CR) (cont’d)
34
However, Capital Recovery is presented as
periodic cash flows in order to
 Estimate whether the project can pay back the
investment, OR
 Estimate the salvage value of an asset at the
end of the project.
Capital Recovery is a practical application of
the Annual Worth method.

35
The equation for CR is:
AInvest is the equivalent periodic value of the
invested capital in the project.
AAsset is the equivalent periodic value of the
depreciation of the asset which is used for the
project.
Salv
Asset
Invest A
A
CR 
 /

36
IInvest is the value of the invested capital in the
project.
 
 
1
/
/
1
1
1












 N
N
Asset
Invest
Asset
Invest
i
i
i
I
A
The equation for AInvest or AAsset is:
IAsset is the initial value of the asset which is used
for the project, whichever applicable.

37
 
 
1
/
/
1
1
1












 N
N
Asset
Invest
Asset
Invest
i
i
i
I
A
The equation above is an adaptation of the P to A
equation in the previous chapter.
 
 
1
1
1
1












 N
N
i
i
i
P
A

38
ASalv is the equivalent periodic value that
represents the
 remaining value of the capital which has not
been consumed by the project or
 remaining second-hand value of the asset
which has been used for the project.
Salv
Asset
Invest A
A
CR 
 /

New oil drilling
platforms are expensive
to build.
 If the technical specs
of existing oil
platforms are
suitable, these oil
platforms may be
transferable to other
projects.
39
The key requirement for asset transfers like
these is that the costs of transfer must be lower
than the costs of making new assets.

In this case of
transferring oil
platforms,
 The size and shape of
the platform will
complicate transfers.
 Bigger platforms are
more difficult to
remove.
40
 Removal may also damage the oil platform.
 In the case of this example, the lower support of the
platform has been cut off through welding.
 The reliability of the platform may have been reduced
due to the removal.

41
The value of the salvage is usually represented
as S.
 The value depends on how useful the salvaged
asset is for the next project that it would be
used for.
 Its usefulness in turn depends on how much
its functions have been preserved and how
much reliability it has left.

42
The value of the salvage is usually represented
as S. (cont’d)
 The value is also deducted by the costs of the
removal of the asset from the previous project.
 For the salvaging to be feasible, S must be a
positive value.

43
ASalv is the equivalent periodic value converted
from S
 Since S occurs as the end of the project, i.e.
period no. N, the equation for future value
of periodic cash flows is rearranged and used
instead.

44
SInvest is the remaining value of the invested
capital in the project.
The equation for ASalv is:
SAsset is the remaining value (e.g. salvage value)
of the asset which is used for the project.
 
1
/
1
1








 


i
i
S
A
N
Asset
Invest
Salv

45
SInvest or SAsset occurs at the end of the project.
 
1
/
1
1








 


i
i
S
A
N
Asset
Invest
Salv
N is the number of periods in the project at
which interest is charged.

46
N
1 2 k
ASalv
MARR, i
Period
0
Sinvest/Asset
ASalv ASalv ASalv
The above is how SInvest or Sasset and Asalv appear
on a cash flow diagram.

47
The equation above is an adaptation of the F to A
equation in the previous chapter.
 
1
/
1
1








 


i
i
S
A
N
Asset
Invest
Salv
 
1
1
1








 


i
i
F
A
N

48
Leftover materials that are still usable are
considered as salvage too, and is best represented
as Asalv when accounting for them.
Surplus cement from the supplier is an example of
salvage from a construction project.

49
Disadvantage of FW, PW and
AW Methods
The main disadvantage of the FW, PW and AW
methods is that it assumes that the MARR is
applied throughout the entire project.
 It does not consider other interest rates.
 The focus on a positive amount in the final
calculation might cause possible risks and
opportunity costs represented by the interest
rates to be overlooked.

Internal Rate of Return
Method
50
If the cash flows for expenses and
revenues are known throughout the
timeline of a project,
 The equivalent interest rate which
results in present worth or future worth of
zero can be determined.
(A present worth or future worth of zero is
analogous to break-even in break-even
analyses.)

51
The equivalent interest rate which results
in a present worth (before start of project) or
future worth (at end of project) of zero is
known as the internal rate of return (IRR).
Method (cont’d)
Since the equivalent interest rate is
dependent on the cash flows, when it is
calculated:
 It may be positive (>0) or negative (<0), or
zero.

52
A positive IRR means that:
 The project will make a profit. (Higher
magnitude of IRR means higher profit.)
 And/or the project has more opportunities
(but also possibly more risks) than what is
expected.
Method (cont’d)
A negative IRR means that:
 The project will make a loss. (Higher
magnitude of IRR means higher losses.)
 The project has fewer opportunities than
desired and the payoff is likely not worth
the risks.

53
A zero IRR means that:
 The project is not likely to have factors
that can deviate from expectations.
 Zero IRR means that the project is just
decently profitable, but in return for having
more certainty in its outcome.
Method (cont’d)

54
The project owners or backers may express
their interest in the project as an interest
rate.
Method (cont’d)
For them to be confident in the feasibility of
the project,
 The IRR must be equal to or higher
than the desired interest rate. (This
interest rate is generally the MARR which
they have set.)

55
Let Rk be a revenue cash flow at time k.
Let Ek be an expense cash flow at time k.
Method (cont’d)
0 ≤ k ≤ N , where N is the total number of
periods
Let PWR be the absolute present worth of all Rk .
Let PWE be the absolute present worth of all Ek .
Let IRR be the interest rate common to both PWR
and PWE .

56
Method (cont’d)
   
   N
N
k
k
R
IRR
R
IRR
R
IRR
R
IRR
R
PW










1
...
1
...
1
1
1
1
0
0
 





N
k
k
k
R
IRR
R
PW
0 1

57
Method (cont’d)
   
   N
N
k
k
E
IRR
E
IRR
E
IRR
E
IRR
E
PW










1
...
1
...
1
1
1
1
0
0
 





N
k
k
k
E
IRR
E
PW
0 1
Likewise for PWE :

58
Method (cont’d)
   








N
k
k
k
N
k
k
k
IRR
E
IRR
R
0
0 1
1
Thus, to find IRR:
E
R PW
PW 
Take note that for a given k, there is not
necessarily both an Rk and an Ek ,
 So the above equation cannot be so easily
simplified.

Method (cont’d)
   










N
k
k
N
k
N
k
k
N
k IRR
E
IRR
R
0
0
1
1
Future worth can also be used instead,
E
R FW
FW 
The IRR should be the same in both cases.
if future-value calculations are more convenient.

60
Method (cont’d)
Using the equations, solve for IRR, using
iterative convergence (preferably with
computing software).
TIP: If the cash flows are periodic, find the
present/future worth of the periodic cash flows
using the A to P or the A to F equations in the
previous chapter.

61
Disadvantages of IRR Method
The main disadvantage of the IRR method is that it
does not include the MARR or other interest rates
in its calculations.
 The IRR method is however useful to test whether
the project will be profitable at all.
The second disadvantage of this method is that
each cash flow must be evaluated individually in
order to find IRR.
Without computing software, this will take a lot of time.
 Even with computing software, the computation that
is done is very repetitive and not efficient use of
computing power.

62
(cont’d)
Otherwise, the calculations diverge and the IRR
can never be determined.
The third and most significant disadvantage is
that:
 a break-even must be able to occur in the cash
flows,
 OR the cumulative revenues and expenses are
close to each other.

63
(cont’d)
The IRR method also requires a significant capital
investment.
 Without a significant capital investment, the
calculations will not converge to a net worth of
zero.
In other words, IRR method cannot be so easily
used for operations that are already underway
and are stable, e.g. making steady profits.
 IRR is best used for a project that is being
planned.

External Rate of Return
Method (cont’d)
64
The external rate of return method
 Includes other interest rates (usually
the MARR) in the calculations and,
 Calculate an additional interest rate to
compare equivalent worth of expenses
and revenues.
This additional interest rate is known as the
external rate of return.

Method (cont’d)
65
To calculate the external rate of return, the
following has to be done first.
 The revenue cash flows have to be
converted to their equivalent future worth
using the MARR or any other stipulated
interest rate.
 The expense cash flows have to be
converted to their equivalent present worth
using the MARR or any other stipulated
interest rate.

Method (cont’d)
66
The MARR or any other stipulated interest rate is
labeled as ε .
Let a revenue flow at period k be Rk .
Let an expense flow at period k be Ck .
Let the absolute future worth of all revenue flows
be FWR
Let the absolute present worth of all expense
flows be PWE

Method (cont’d)
67
Therefore, the future worth of the revenues with ε
as the interest rate is:
 






N
k
k
N
k
R R
FW
0
1 
And the present worth of the expenses with ε as
the interest rate is:
 

 


N
k
k
k
E
E
PW
0 1 

Method (cont’d)
68
FWR is not necessarily equivalent to PWE .
Instead, this method involves finding the interest
rate which can convert either one of them to be
equivalent to the other.
 This interest rate is the external rate of return,
ERR.

Method (cont’d)
69
Either of the two equations below can be used to
find ERR.
 N
E
R ERR
PW
FW 
 1
 N
R
E
ERR
FW
PW


1

Method (cont’d)
70
Therefore, solve for ERR:
1
1









N
E
R
PW
FW
ERR
Note that ERR is in fraction.
ERR
Period N
0
FWR
PWE

Method (cont’d)
71
With ERR found, compare it to ε (or MARR):
 If it is higher, the project is feasible and
profitable.
 If it is lower, the project is not feasible.
 If it is equal, it meets requirements but otherwise
is not a strong go-ahead for the project.
TIP: If the cash flows are periodic, find the
present/future worth of the periodic cash flows
using the A to P or the A to F equations in the
previous chapter.

Payback Period Method
72
The payback period method estimates the
number of periods to completely recover the
invested capital.
In other words, the payback period method
calculates the number of periods for revenue
flows to equalize expense flows, with interest
considered, and the invested capital.
 The interest rate must be known.

(cont’d)
73
There are two variants of this method:
 Simple payback
 This is used to provide a value which can
be used to check the results of the other
variant of the method.
 Time-valued payback
 This is the above method but with interest
rates and time factored in.

(cont’d)
74
Let a revenue flow be Rk at time period k.
Let an expense flow be Ek at time period k.
Let θ be the number of periods when equivalent Rk
balances equivalent Ek and I, time value considered.
Let I be the capital which has been invested in the
project.
Let α be the number of periods when enough Rk
flows balance Ek flows and I, time value not
considered.
Let i be the interest rate applied on the flows.

(cont’d)
75
Depending on the cash flows, θ may or may not be
equal to α.
• However, θ should be close to α in terms of
magnitude.
A very significant difference is a strong indicator
that a miscalculation has happened.

Simple Payback
76
The flows for revenues and expenses are
added/subtracted one by one until the net flow is equal
to or is greater than I.
The simple payback variant ignores the time value of
money, and any cash flow after the payback point.
  I
E
R
k
k
k 




0

Simple Payback (cont’d)
77
α is the period number for which the associated revenue
cash flow Rα , when included in the left side of the
equation above, finally results in the equation being ≥ I.
If time value of money is considered, the number of
periods for payback θ in the other variant of the
method should be higher than α.
  I
E
R
k
k
k 




0

Time-Valued Payback
78
θ is the period number for which the associated revenue
cash flow Rθ , when included in the left side of the
equation above, finally results in the equation being ≥ I.
   
I
i
E
i
R
k
k
k
k
k























0 1
1
The earlier equation is adapted to as follows, in order to
convert cash flows to their present worth:

(cont’d)
79
The value θ should be lower than α if the interest
rate is positive.
 Otherwise, there has been a miscalculation.
If the left side of the equation cannot be ≥ I, even
after θ has reached N, the project is not able to
pay back its investment in time.
(The payback period method is best done with a
spreadsheet.)

Evaluating Multiple
Alternatives
80
FOREWORD:
Meaning of “alternatives”:
A situation, such as the plan for an engineering
project, may have more than one solution.
 Each solution is considered an
“alternative”.
 Each alternative has to be compared against
the other alternatives.
 The best alternative is chosen.

Evaluating Multiple
Alternatives (cont’d)
81
The evaluation of multiple options for a project
requires the following:
1. The selection of one of the methods in the
previous slides.
 This method should be appropriate to the
analysis of all of the alternatives.
2. The method is applied to each alternative.
3. The results for each alternative is compared to
the results of the other alternatives.

Evaluating Multiple
Alternatives (cont’d)
82
4. The alternative with the best results is chosen.
If circumstances about a project change, the
entire analysis has to be repeated, e.g.:
• With the same method, if new but similar
options appear.
• With a different method, if completely
different options appear.

Returning to the example of an oil drilling platform…
83
 An oil drilling platform cannot be used for
almost any other purpose, but it can be towed
to another location to drill for oil elsewhere.

84
 Meaning of towed:
 “Towing” is the act of pulling a ship or
other object that is floating on water.
 The pulling is usually done by ships/boats
that are specifically made for this purpose.
 The costs of towing to different locations
have to be considered in the evaluation.

85
 There may be more than one location. (Each
location is considered an “alternative.)
 The oil drilling platform can only be at one
location, so the best location has to be
chosen.
 Therefore, evaluation of multiple
alternatives is needed.
 In this case, the oil drilling platform is
continuing its original purpose, so future
worth method is useful.

86
However, the oil drilling project may have
another option: using a drillship instead of a
drilling platform.
Drilling platform
Drillship

87
 However, the drillship operates differently
from drilling platforms.
 For example, the oil drilling platform is
meant to be semi-static, i.e. it stays on
location permanently.
 The drillship is an actual ship.
 The drilling platform is a semi-permanent
installation with securing cables and other
long-term supports.
 Drillships generally do not have these.
 Drillships are more vulnerable to bad
weather.

88
Therefore, the drillship and the oil drilling
platform have different considerations.
 When comparing the two of them, the
interest rates that are used should
consider the risks and opportunities
specific to either option.
 Drillships have to depend on its own systems
for balance, e.g.
 Ballasts filled such that the below-water
and above-water lines are at optimal
ratios for best stability.

89
 However, in both cases, capital investment is
needed in order to, for example:
 Refurbish/Modify and transfer the platform
to the drilling location
 Refurbish/Modify drillship and provide with
supplies for the staying at the drilling
location.
 Such a decision requires careful use of capital
investment to acquire/prepare either the drillship
or the platform before the start of the project.
 So, present worth method is most
appropriate for the comparison analysis.

90
 Meaning of “acquisition”:
 “Acquisition” is the buying of new assets.
 Usually, money is the price paid.
However, share ownership of the new
asset for the seller may also be another
form of payment.
 The verb of “acquisition” is “acquiring”.
 The costs of different ways of acquisition
have to be considered in the evaluation.

91
Oil drilling platforms require shipments of
supplies to come to it, whereas the drillship is able
to return to port if it cannot receive shipments.
Drilling platform
Drillship

92
Cash flow diagrams for each operational run of
oil drilling platforms
 would be longer in duration compared to
the cash flows diagrams for each operational
run of drillships, due to the semi-permanent
installation of the oil drilling platforms
However, for this to be possible, the oil drilling
platforms will require frequent shipments of
supplies from elsewhere.
 Oil drilling platforms may have more frequent
expenses in terms of shipments of supplies.

93
Differences between cash flow diagrams for
different options have to be converted into
equitable amounts for more objective
comparisons.
 The next sub-chapter concerns one of the
major differences between different plans,
which is the different number of periods.

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