Lecture # 13 investment alternatives i

Lecture # 13
Investment Alternatives
PW and AW methods
1 Dr. A. Alim

• One of the important functions of financial
management and engineering is the creation
of “alternatives”.
• If there are no alternatives to consider then
there really is no problem to solve!
• Given a set of “feasible” alternatives,
engineering economy attempts to identify the
“best” economic approach to a given problem.
2
Material used in this lecture is sourced from “Engineering Economics”, 6th ed. McGraw Hill, © 2005 ,
by L. Blank and A. Tarquin, and also from Engineering Economics 4N04 class notes, McMaster
University © 2001-2007.

Assessing Alternatives
• Feasible Alternatives
Feasible Set
Mutually Exclusive Set Independent SetOR
3

Four Types of Categories:
In addition to the two outcomes listed earlier:
• Mutually Exclusive Set
• Independent Project Set
We may also have two additional outcomes:
• The single Project.
• The “Do Nothing” (DN) option
4

The Single Project
• Called “The Unconstrained” Project selection
problem
• No comparison to competing or alternative
projects
• Acceptance or Rejection is based upon
specified criteria
5
Material used in this lecture is sourced from “Engineering Economics”, 6th ed. McGraw Hill, © 2005 , by
L. Blank and A. Tarquin, and also from Engineering Economics 4N04 class notes, McMaster University ©
2001-2007.

Do Nothing Option
• The firm may decide to reject all alternatives and decide to do
nothing.
• Therefore, the do nothing is always “an option”.
• In that case, the company maintains the current approach and
simply invest their funds at MARR (e.g. in a bank) until a decision
is made at a future date.
• In projects involving safety or legal aspects, the do nothing is not
considered.
6

Independent Project Set
Funds exist to allow the selection of all
feasible alternatives.
Each project is judged independently of
the others, i.e. same as single project.
An interesting case of “partially
independent” project set occurs when
funds exist for some but not all feasible
alternatives. We will discuss this case
later, under optimization.
7
2001-2007.

Mutually Exclusive (ME) Set
Only one of the feasible (viable)
projects can be funded.
Once selected, the others in the set
are “excluded”.
Each of the identified feasible
(viable) projects is (are) considered
an “alternative”.
8
2001-2007.

Example
Distillation tower
to separate
L-L extraction to
separate
Solid adsorption
to separate
Stream with
mixed
components
Funds exist for only one alternative !
Mutually Exclusive (ME) Set
9
2001-2007.

Cash Flow Types for Projects
 Revenue – each alternative generates costs and
revenues over the estimated life of the project.
 Selection criterion: Select the alternative that
maximizes the economic measure of merit (PW
or AW)
 Service – each alternative has only current and
future costs over the estimated life of the
project.
minimizes the economic measure of merit,
which is a cost-based measure (PW or AW)
10
Material used in this lecture is sourced from “Engineering Economics”, 6th ed. McGraw Hill, © 2005 , by L. Blank and A. Tarquin, and also from
Engineering Economics 4N04 class notes, McMaster University © 2001-2007.

How do we choose among alternatives ?
Basically, any of the profitability measurements could be used:
PW (or AW): * Reject a revenue project if PW (or AW) at
MARR is negative. Reject a service project
if PW of cost is more than a preset level.
* Select the project with the most favorable
PW or AW among alternatives.
PBP: * Reject a project if PBP>PBP (ref)
* Pick the shortest PBP among alternatives
* Not recommended, and must never be the
only method used.
11

Examples
• Calculate PW of each alternative at MARR
• Selection criterion: Select alternative with
most favorable PW value, that is,
numerically largest PW value (most positive)
PW1 PW2 Select
$-1,500 $-500 2
-2,500 500 2
2,500 1,500 1
Note : Not
the absolute
value
12
Material used in this lecture is sourced from “Engineering Economics”, 6th ed. McGraw Hill, © 2005 , by L. Blank
and A. Tarquin, and also from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.

How do we choose among alternatives ?
In addition, we can also use the ROI or DCFRR method :
ROI: Reject a project if ROI<MARR
DCFRR (IRR): Reject a project if DCFRR<MARR
Among alternatives, it is not always true that the highest ROI
or DCFRR is the most preferred. If we are to use the ROI or
the DCFRR methods then we must apply incremental analysis
among alternatives.
13

Summary - How do we choose among alternatives ?
PW or AW: Select the most positive (profit/cash
flow) or least negative (cost)
PBP : Not recommended as sole method.
ROI or DCFRR: May be used, but must apply
incremental analysis.
14
Material used in this lecture is sourced from “Engineering Economics”, 6th ed. McGraw Hill, ©
2005 , by L. Blank and A. Tarquin, and also from Engineering Economics 4N04 class notes,
McMaster University © 2001-2007.

15
Material used in this lecture is sourced from “Engineering Economics”, 6th ed. McGraw Hill, ©
2005 , by L. Blank and A. Tarquin, and also from Engineering Economics 4N04 class notes,
McMaster University © 2001-2007.
Let’s discuss details of PW and AW in this class. Next class
we will address the ROI and the DCFRR approaches and
the concept of incremental analysis.

PW analysis of Investment
Alternatives
• Alternatives must be compared at the same
project life.
• For Alternatives with unequal lives, we apply the
“lowest common multiple”
• LCM – Evaluate the alternatives over the lowest
common multiple of lives, e.g. lives of 4 and 6
years, use n=12
and assume re-investment at same cash flow
estimates.
16
2001-2007.

LCM Approach
The assumptions for the analysis of
different-life alternatives are a follows:
1.The service provided by the alternatives
will be needed for the LCM of years or
more.
2.The selected alternative will be
repeated over each life cycle of the LCM
in exactly the same manner.
3.The cash flow estimates will be the
same in every life cycle.
17

LCM Example – Cost projects
Example 5.14, page 246, Contemporary Engineering Economics,
C.S.Park, 4th edition, Pearson Prentice Hall, 2007.
18
A certain mail-order firms wants to install an automatic mailing system to handle product
Announcements and invoices. The firm has a choice between two different types of
machines. The two machines are designed differently, but have identical capacities and
Do exactly the same job. The $12,500 semiautomatic model A will last three years. The
Fully automatic model B will cost $15,000 and last four years.
The expected cash flows for the two machines including maintenance, salvage, and tax
Effects, are as follows:
model A model B
Number of years 3 4
Initial cost $12,500 $15,000
Annual expenses $5,000 $4,000
Salvage value $2,000 $1,500
If the MARR is 15%, using the PW method, which machine should the firm purchase?
NOTE: This is a service project with two alternatives having different service lives.

20
Clearly, model B is the better choice.

The use of Annual Worth (AW) for
selecting among alternatives
• AW may be used instead of PW to
select among alternatives!
• Recall the criterion discussed
earlier, depending on type of cash
flows in the project.
21

Cash Flow Types for Projects
 Revenue – each alternative generates costs and
revenues over the estimated life of the project.
maximizes the economic measure of merit (PW
or AW)
 Service – each alternative has only current and
future costs over the estimated life of the
project.
minimizes the economic measure of merit,
which is a cost-based measure (PW or AW)
24

The use of Annual Worth for selecting
among alternatives
• Popular Analysis Technique
• Easily understood-results are
reported in $/time period
– Eliminates the LCM problem
associated with the present worth
method
– Only have to evaluate only one life
cycle of a project
23

Previous example – Solution using the AW method
24
Recall we calculated PW for one cycle for each model:
For model A, PW(15%) = - $22,601
Hence AW = -$22,601(A/P,15%,3) = -$9,899
For model B, PW(15%) = - $25,562
Hence AW = -$25,562(A/P,15%,4) = -$8,953
Hence, model B is the better choice

• 3 investments. Need to evaluate profitability of each.
• Use ROI, PBP, NPV, and DCFRR.
• Assume straight line depreciation.
• Tax rate is 35%
• MARR is 15%
• Use MARR as interest rate for time value of money.
• Ignore land value.
Example (Evaluating alternatives using AW):
Modified example 8-3, Peters, page 331
25

Investment
#
Fixed
capital
$
Working
capital
$
Salvage
value
$
Service life,
years
GI – E
$
1 100,000 10,000 10,000 5 See yearly
tabulation
2 170,000 10,000 15,000 7 64,615
(constant)
3 210,000 15,000 20,000 8 73,846
(constant)
For investment # 1:
Year 1 2 3 4 5
GI – E
$
46,154 47,692 55,385 61,539 66,154
26
Material used in this lecture is sourced from “Engineering Economics”, 6th ed. McGraw Hill, © 2005 , by L. Blank and A. Tarquin, and also
from Engineering Economics 4N04 class notes, McMaster University © 2001-2007.

27

Comparing investments 1,2, and 3 on AW basis:
PW of CFAT (one cycle) n years AW of CFAT
Investment 1 38,509.00$ 5 $11,487.83
Investment 2 36,378.00$ 7 $8,743.83
Investment 3 39,133.00$ 8 $8,720.79
Investment 1 has the highest AW, hence we select it.
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(Evaluating alternatives using AW), Example 6.4 page 157, Blank and
Tarquin, 7th ed. McGraw Hill, 2012.:
29

31

Advantages of AW
* Easier to calculate, uses only one cycle. No
need for LCM calculation.
* Applicable to a variety of engineering economy
studies:
– Breakeven Analysis
– Economic Value Added analysis (EVA)
– Asset Replacement
32

Lecture # 13 investment alternatives i

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