Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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SECTION
10.7
Multiple Attribute Analysis: Identification and Importance
and used to select the best alternative. The criterion has been the maximization
of
the equivalent value
of
PW,
AW,
ROR, or the
B/C
ratio. As we are all aware,
most evaluations do and should take into account multiple attributes in
decision making. These are the factors labeled
as
noneconomic at the bottom
of
Figure
1-
I,
which descri bes the primary elements in performing an engineering
economy study. However, these noneconomic dimensions tend to be intangible
and often difficult, if not impossible, to quantify directly with economic and
other scales. Nonetheless, among the many attributes that can be identified, there
are key ones that must be considered in earnest before the alternative selection
process
is
complete. This and the next section describe some
of
the techniques
that accommodate multiple attributes
in
an engineering study.
Multiple attributes enter into the decision-making process in many studies.
Public sector projects are excellent examples
of
multiple-attribute problem solv-
ing. For example, the proposal to construct a dam to form a lake in a low-lying
area or to widen the catch basin
of
a river usually has several purposes, such as
flood control; drinking water; industrial use; commercial development; recre-
ation; nature conservation for fish, plants, and birds; and possibly other less ob-
vious purposes. High levels
of
complexity are introduced into the selection
process
by
the multiple attributes thought to be important
in
selecting an alterna-
tive for the dam's location, design, environmental impact, etc.
The left side
of
Figure 10-5 expands steps 4 and 5 to consider multiple attri-
butes. The discussion below concentrates on the expanded step 4, and the next
section focuses on the evaluation measure and alternative selection
of
step 5.
4-i
Attribute identification Attributes to be considered in the evaluation
methodology can be identified and defined by several methods, some much bet-
ter than others depending upon the situation surrounding the study itself. To seek
input from individuals other than the analyst
is
important; it helps focus the study
on key attributes. The following
is
an incomplete listing
of
ways
in
which key
attributes are identified.
• Comparison with similar studies that include multiple attributes.
• Input from experts with relevant past experience.
• Surveys
of
constituencies (customers, employees, managers) impacted by the
a
lt
ernatives.
• Small group discussions using approaches such
as
focus groups, brainstorm-
ing, or nominal group technique.
• Delphi method, which is a progressive procedure to develop reasoned con-
sensus from different perspectives and opinions.
As an illustration, assume that Continental Airlines has decided to purchase
five new Boeing 777s for overseas flights, primarily between the North American
west coast and Asian c
iti
es, principally Hong Kong, Tokyo, and Singapore. There
are approximately
8000 options for each plane that must be decided upon by en-
gineering, purchasing, maintenance, and marketing personnel at Continental be-
fore the order to Boeing
is
placed. Options range in scope from the material and
color
of
the plane's interior
to
the type
of
latching devices used on the engine
cowlings, and
in
function from maximum engine thrust to pilot instrument design.
365
366
CHAPTER
10
Making Choices:
The
Method,
MARR, and Multiple Attributes
An economic study based on the equivalent AW
of
the estimated passenger in-
come
per trip has determined that 150
of
these options are clearly advantageous.
But
other noneconomic attributes are to
be
considered before some
of
the more
expensive options are specified. A Delphi study was performed using input from
25 individuals. Concurrently, option choices for another, unidentified airline's re-
cent order were shared with Continental personnel.
From
these two studies it was
determined that there are
10
key attributes for options selection.
Four
of
the most
important attributes are
• Repair time: mean time to repair
or
replace
(MTTR)
if
the option is
or
affects
a flight-critical component.
• Safety: mean time to failure
(MTTF)
of
flight-critical components.
• Economic: estimated extra revenue
for
the option. (Basically, this is the at-
tribute evaluated by the
economy
study already performed.)
• Crewmember needs: some measure
of
the necessity and/or benefits
of
the op-
tion as
judged
by representative crew
members-pilots
and attendants.
The
economic attribute
of
extra revenue
may
be considered an indirect measure
of
customer satisfaction,
one
that is more quantitative than
customer
opinion/sat-
isfaction survey results.
Of
course, there
are
many other attributes that can be,
and are, used.
However
, the point is that the economic study may directly address
only one
or
a few
of
the key attributes vital to alternative decision making.
An attribute routinely identified by individuals and groups
is
risk. Actually,
ri
sk is not a stand-alone attribute, because it
is
a part
of
every attribute
in
one
form
or
another. Considerations
of
variation, probabilistic estimates, etc.,
in
the
decision-making process are treated later
in
this text. Formalized sensitivity
analysis, expected values, simulation, and decision trees are some
of
the tech-
niques useful
in
handling the risk inherent in an attribute.
4-2 Importance (Weights)
for
the Attributes Determination
of
the extent
of
im-
porlance for each attribute i results
in
a weight Wi that is incorporated into the final
evaluation measure.
The
weight, a number between 0 and 1,
is
based upon the ex-
perienced opinion
of
one individual
or
a group
of
persons familiar with the attrib-
utes, and possibly the alternatives.
If
a group is utilized to determine the weights,
there must be consensus among the members for each weight. Otherwise,
some
averaging technique must be applied to arrive at
one
weight value for each attribute.
Table
10
- 3
is
a tabular layout
of
attributes and alternatives used to perform a
multiple attribute evaluation. Weights
Wi
for each attribute are entered on the left
side.
The
remainder
of
the table
is
discussed as
we
proceed through steps 4 and 5
of
the expanded decision-making process.
Attribute weights are usually normalized such that their sum over all the al-
ternatives
is
1.0. This normalizing implies that each attribute's importance score
is
di
vided by the sum S over all attributes. Expressed in formula form, these two
properties
of
weights for attribute i (i =
1,
2,
...
, m) are
m
Normalized weights: I
Wi
= 1.0
i = )
[10.8]
SECTION 10.7 Multiple Attribute Analysis: Identification and Importance
TABLE
10-3
Tabular Layout
of
Attributes and Alternatives
Used for Multiple Attribute Evaluation
Alternativ
es
A
ttrib
u
tes
Wei
ghts
1
2 3
WI
2 W
z
3
W3
Value ratings V
ij
m
Wm
n
importance score;
Weight calculation:
W;
= - m
C-
,
---=
-------'--
.
2.:
importance score;
importance score;
S
1= 1
[10.9]
Of
the many procedures developed to assign weights to an attribute, an analyst is
likely to rely upon one which
is
relatively simple, such
as
equal weighting, rank
order, or weighted rank order. Each
is
briefly presented below.
Equal Weighting All attributes are considered to be
of
approximately the same
importance, or there is
no
rationale to distinguish the more important from the
less important attribute. This
is
the default approach. Each weight in Table
10-3
will be
l/m,
according to Equation [10.9]. Alternatively, the normalizing can be
omitted, in which case each weight is 1 and their sum is
m. In this case, the final
evaluation measure for an alternative will be the sum over all attributes.
Rank
Order The m attributes are placed (ranked) in order
of
increasing impor-
tance with a score
of
1 assigned to the least important and m assigned to the most
important. By Equation [10.9], the weights follow the pattern
l/S,
2/S,
.
..
,
m/S.
With this method, the difference
in
weights between attributes
of
increasing
importance
is
constant.
Weighted
Rank
Order The m attributes are again placed in the order
of
in-
creasing importance. However, now differentiation between attributes is possi-
ble. The most important attribute
is
assigned a score, usually 100, and all other
attributes are scored relative to it between
100 and O. Now, define the score for
each attribute as
s;,
and Equation [10.9] takes the form
[10.10]
This is a very practical method to determine weights because one or more
attributes can be heavily weighted
if
they are significantly more important than
the remaining ones, and Equation [10.10] automatically normalizes the weights.
For example, suppose the four key attributes in the previous aircraft purchase
367
368
CHAPTER
10
Making Choices: The Method, MARR, and Multiple Attributes
example are ordered: safety, repair time,
crewmember
needs, and economic.
If
repair time is only
half
as important as safety, and the last two attributes are each
half
as important as repair time, the scores and weights are as follows.
Attribute
Score
Weights
Safety
100
100/ 200 = 0.50
Repair time
50
50/ 200
= 0.25
Crewmember needs
25
25/ 200 = 0.125
Economic 25
25/ 200 = 0.125
-
Sum
of
scores and weights
200 1.000
There
are other attribute weighting techniques, especially for group processes,
such as utility functions, pairwise comparison, and others.
These
become in-
creasingly sophisticated,
but
they are able to provide an advantage that these
simple methods do not afford the analyst: consistency
of
ranks and scores be-
tween attributes and
between
individuals.
If
this consistency is important
in
that
several decision makers with diverse opinions about attribute importance are in-
volved
in
a study, a more sophisticated technique may
be
warranted. There
is
substantial literature on this topic.
4-3 Value Rating
of
Each Alternative, by Attribute This is the final step prior
to calculating the evaluation measure. Each alternative is awarded a value rating
V
ij
for each attribute i.
These
are the entries within the ceJls
in
Table 10-3.
The
ratings are appraisals by decision makers
of
how well an alternative will perform
as each attribute is considered.
The
scale for the value rating can vary depending upon what is easiest to under-
stand for those who do the valuation. A scale
of
0 to 100 can be used for attribute
importance scoring. However, the most popular
is
a scale
of
4
or
5 gradations about
the perceived ability
of
an alternative to accomplish the intent
of
the attribute. This
is
called a Likert scale, which can have descriptions for the gradations (e.g., very
poor, poor, good, very good), or numbers assigned between 0 and 10,
or
- 1 to + I,
or
- 2 to
+2.
The
last two scales can give a negative impact to the evaluation mea-
sure for poor alternatives.
An
example numerical scale
of
0 to
lOis
as follows:
If
You
Value
the
Alternative
As
Very
poor
Poor
Good
Very
good
Give
It
a Rating
between
the
Numbers
0-2
3- 5
6- 8
7-
10
It
is
preferable to have a Likert scale with four choices (an even number) so that
the central tendency
of
"fair" is not overrated.
If
we now build upon the aircraft purchase illustration to include value rat-
ings, the cells are filled with ratings awarded by a decision maker. Table
10-4
includes
example
ratings V
ij
and the weights
Wi
determined above. Initially, there
will be
one
such table for each decision maker. Prior to calculating the final
SECTION
10.
8
Evaluation Measure for Multiple Attributes
TABLE
10-4
Completed Layout for Four Attributes and Three
Alternatives for M
ul
tiple-Attribute Evaluation
Alternatives
Attributes
Weights
1 2
Safety 0.50 6
4
Repair 0.25
9 3
Crew needs 0.125 5
6
Economic 0.
125
5 9
3
8
I
6
7
evaluation measure R
j
, the ratings can be combined in some fashion;
or
a differ-
ent R
j
can be calculated using each decision
maker's
ratings. Determination
of
this evaluation measure is discussed below.
10.8
EVALUATION MEASURE FOR MULTIPLE ATTRIBUTES
The
need for an eva
lu
ation measure that accommodates multiple attributes is in-
dicated
in
step 5
of
Figure]
0-5.
This measure should be a single-dimension
number that effectively combines the different dimensions addressed by the at-
tribute importance scores
Wi
and the alternative value ratings
Vi'
The
result is a
formula to calculate an aggregated measure that can
be
used to select from two
or more alternatives.
The
result is often referred to as a rank-and-rate method.
This reduction process removes much
of
the complexity
of
trying to balance the
different attributes; however, it also eliminates
much
of
the robust information
captured by the process
of
ranking attributes for their importance and rating each
alternative's performance against each attribute.
There are additive, multiplicative, and exponential measures, but by far the
most commonly applied is the additive model.
The
most
used additive model is
the weighted attribute method.
The
evaluation measure, symbolized by R
j
for
each alternative},
is
defined as
"
~
= L
WYij
[10.11]
j = 1
The
Wi
numbers are the attribute importance weights, and
Vi)
is the value rating
by attribute i for each alternative
j.
If
the attributes are
of
equal weight (also
ca
ll
ed unweighted), all
Wi
= I
/m,
as determined by Equation [10.9]. This means
that
Wi
can be moved outside
of
the summation
in
the formula for Rj'
(If
an equal
weight
of
Wi
= 1.0
is
used for all attributes,
in
lieu
of
lim
, then the R
j
value is
simply the sum
of
all ratings for the alternative.)
The selection guideline is as follows:
Choose the alternative with the largest R
j
value. This measure assumes
that increasing weights
Wi
mean more important attributes and increas-
ing ratings
Vij
mean better performance
of
an
alternative.
Sensitivity analysis for any score, weight,
or
value rating
is
used to determine
sensitivity
of
the decision to it.
369
370
CHAPTER
10
Making Choices: The Method, MARR, and
Mu
ltiple Attributes
EXAMPLE
10.1 0
,~
An
interactive regional dispatching and scheduling system for trai
ns
has been in place
for several years at
MB+O
Railroad. Management and dispatchers ajike agree it is time
for
an
updated software system, and possibly new hardware. Discussions have led
to
three alternatives:
1.
Purchase new hardware and develop new customized software in-house.
2. Lease new hardware and use
an
ou
ts
ide contractor for software services.
3. Develop new software using
an
outside contractor, and upgrade specific hardware
components for the new
sof
tware.
Six attributes for alternative comparison have been defined us
in
g a Delphi process in-
volving decision makers from dispatching,
fie
ld operations, and train engineering.
I.
In
itial investment requirement.
2. Annual cost
of
hardware and software maintenance.
3.
Response
ti
me to "collision conditions."
4.
User interface
fo
r dispatching.
5.
On-train software interface.
6.
Software system interface with other company dispatching systems.
Attribute scores developed by the decision makers are shown
in
Table lO-5, using a
we.ighted rank-order procedure with scores between
0 and 100. Attributes 2 and 3 are
considered equa
ll
y the most important attr
ib
utes; a score
of
100
is
assigned to them.
Once each alternative had been detailed enough to judge the capabilities from the sys-
tem specifications, a three-person group placed value ratings on the three alternatives,
again using a rating scale
of
0 to 100 (Table lO-5).
As
an
example, for alternative 3, the
economics are excellent (scores
of
100 for both attributes J and 2), but the on-train soft-
ware interface is considered very poor, thus the low rating
of
10. Use these scores and
ratings to determine which alternative is the best
to
pursue.
TABLE
10-5
Attribute Scores and Alternative Ratings for Multiple-
Attribute Evaluation, Example
10.10
Value Ratings (0
to
100)
, V
ij
Attribute
Importance Alternative
Alternative
Alternative
Score
1 2 3
50 75 50 lOa
2
100
60
75
100
3 100 50 100
20
4
80
100
90
40
5 50
85
100
10
6
70 100 100 75
Total
450
CHAPTER SUMMA
RY
TABLE
10-6
Results forthe Weighted-Attribute Method, Example
10
.
10
R
j
= W ;V
;j
Att
ribute
Norma
lized
Alte
rnative
Alt
e
rn
at
ive
Alte
rnative
Weight
W; 1 2 3
I
0.11
8.3 5.5 1l.0
2 0.22 13.2
16
.5 22.0
3 0.22
1l.0
22.0 4.4
4
0.18 1
8.
0 16.2
7.2
5
0.11 9.4
1l.0
1.1
6 0.16 1
6.
0
16
.0 12.0
Totals
1.
00
75.9
87
.2 5
7.
7
Solution
Table
10
-6
incl
ud
es
th
e no
rm
alized weights for each attribute determined by Equa-
tion
[10.9];
th
e total is
1.
0, as required. The evaluat
ion
measure R
j
for
th
e weighted
attribute method is obtained by apply
in
g Equa
ti
on [10.11]
in
each a
lt
e
rn
a
ti
ve column.
For alte
rn
ative I,
R
J
= 0.
11
(7
5) + 0.22(60) + .. . + 0.16
(1
00
) = 75.9
When the totals are revi
ewe
d
fo
r
th
e largest measure, alternative 2 is
th
e best choi
ce
at
R2 = 87.2. Further detailing of this a
lt
e
rn
ative sho
ul
d be recomme
nd
ed to management.
Comment
Any econo
mi
c measure can be
in
corporated
in
to a multiple-
at
tribute evalua
ti
on using
thi
s me
th
o
d.
A
ll
measures
of
worth- PW, AW, ROR, B/C
-ca
n be
in
cluded; however,
their impact on
th
e
fin
al selec
ti
on w
ill
vary rela
ti
ve to
th
e importance
pl
aced on
th
e
noneconomic attributes.
CHAPTER SUMMARY
The best me
th
od to economically evaluate and compare mutua
ll
y exclusive al-
te
rn
a
ti
ves is usually either
th
e AW or
PW
method at the stated MARR. The
choice depe
nd
s, in part, upon
th
e equal
li
ves or unequal lives
of
th
e alterna
ti
ves,
a
nd
th
e patte
rn
of
th
e estimated cash
fl
ows, as summarized in Ta
bl
e
10
- 1. Public
sector projects are best compared us
in
g the
B/
C ra
ti
o, but
th
e economic equiv-
al
ency is s
ti
II
A W or
PW
-based. Once
th
e evaluation method
is
selected,
Table
10
- 2 (also printed at
th
e rear of
th
e text with section references) can be
used to determine
th
e eleme
nt
s a
nd
decision guideline
th
at must be implemented
371
372
CHAPTER
10
Making Choices: The Method, MARR, and Multiple Attributes
to correctly perform the study.
If
the estimated
ROR
for
the
se
lected alternative
is needed, it is advisable to determine
i':'
by
using the
IRR
function on a spread-
sheet after the A W
or
PW
method has indicated the best alternati ve.
The
interest rate at which the
MARR
is established
depends
principally upon
the
cost
of
capital and the mix between
debt
and equity financing.
The
MARR
should be set equal to the weighted average
cost
of
capital (WACC). Risk, profit,
and
other
factors can be considered after the A
W,
PW,
or
ROR
analysis
is
com-
pleted and prior to
final alternative selection.
If
multiple attributes,
which
include
more
than the
economic
dimension
of
a
study, are to be considered in making the alternative decision,
first the attributes
must be identified and their relative importance assessed.
Then
each alternative
can be value-rated for each attribute.
The
evaluation measure is determined us
in
g
a model such as the weighted attribute method, where the measure is calculated
by Equation [10
.1
1].
The
largest value indicates the best alternative.
PROBLEMS
Choosing the Evaluation Method
10.1
Wh
en two
or
more alternatives are
com-
pared usi ng the
PW
, A
W,
or
B/C method,
there are three circumstances
for
which
the length
of
time
of
the evaluation pe-
riod is the
same
for all alternatives. List
these three circumstances.
10
.2 For what evaluation methods IS it
mandatory that an incremental cash flow
se
ries analysis be performed to ensure
that the correct alternative
is
se
lected?
10
.3 Explain what
is
meant by the decision
guideline to
choose
the "numerically
largest value" when selecting the
one
best mutually exclusive alternative from
two
or
more alternatives.
10.4
For
the following situation, (a) determine
which evaluation m
et
hod
is
probably the
easiest and fastest to apply by hand and
by
co
mputer
in
order to select from the
five alternatives, and (b) answer the two
questions, using your chosen evaluation
method.
Truck
An independent dirt contractor must de-
termine which size
dump
truck to buy.
The
cash
flows estimated with each size truck
bed are tabulated.
The
MARR
is
18
% per
year, and all alternatives are expected to
have
a useful life
of
8 years. (1)
What
size
truck bed should be purchase
d?
(2)
If
two
trucks are to be purchased, what should
be the size
of
the second truck?
Bed Size,
Initial
Annual
Cubic
Invest-
AOe,
Salvage Revenue,
Meters
ment,
$
$/year
Value, $
$/year
8
-
10
,000 - 4,000
+2,
000 + 6,500
10
-
14
,000 - 5
,5
00
+ 2,500
+
10
,000
15
-18,000
- 7,000
+ 3,000
+
14
,000
20
- 24,000
- 11,000
+ 3,500 +20,500
25
-33,
000 -
16
,000
+ 6,000
+2
6,500
10
.5
Read
Problem 9.26. (a)
Det
er
mine
which evaluation method is probably
th
e
easiest and fastest to apply by hand and
by
computer
in
order
to
se
lect from the
two
alternatives. (b)
If
the evaluation
method you chose
is
different from that
used
in
Chapter
9, solve the problem
using your chosen evaluation method.
lO.6
For
what type
of
alternatives should the
capita
li
zed cost method be used for com-
parison? Give several examples
of
these
types
of
projects.
Working with
MARR
10.7 After
15
years
of
employment
in
the air-
line industry, John started his own con-
sulting
company
to use physical and
computer simulation
in
the analysis
of
commercial airport accidents on run-
ways.
He
estimates his average cost
of
new capital at 8% per year for physical
simulation projects, that is, where he
physically reconstructs the accident
using scale versions
of
planes, buildings,
vehicles, etc. He has established 12% per
year as his MARR.
(a) What (net) rate
of
return on capital
investments for physical simula-
tion does he expect?
(b) John was recently offered an inter-
national project that he considers
risky
in
that the information avail-
able
is
sketchy and the airport per-
sonnel do not appear to be willing
to cooperate on the investigation.
John considers this risk to be eco-
nomically worth at least an added
5% return on his money.
What
is
the
recommended
MARR
in
this situa-
tion, based upon what you have
learned
in
this chapter?
How
should
John consider the required return
and perceived risk factors when
evaluating this project opportunity?
10
.8 State whether each
of
the following in-
volves debt financing
or
equity financing.
(0) A bond issue for $3,500,000 by a
city-owned utility
PROBLEMS
373
(b) An initial public offering (IPO)
of
$35,000,000
in
common
stock for a
dot-com
company
(c) $25,000 taken from your retirement
account to pay cash for a new car
(d)
A
homeowner's
equity loan for
$25,000
10.9 Explain how the opportunity cost sets
the effective
MARR
when, because
of
limjted capital, only
one
alternative can
be selected from two
or
more.
10
.
10
The
board
of
directors
of
the Brazilia
Group
has less capital than needed to
fund a $6.2 million project
in
the
Middle
East. Had it been funded, an estimated
i*
of
18% per year would result. Corporate
MARR
= 15% has been applied for
before-tax analysis. With the available
$2.0 million in equity capital, a project
with an estimated i*
of
16
.6% is ap-
proved.
The
group president
just
asked
you to estimate the after-tax opportunity
cost that has been forgone. Assume you
collect the following information
in
preparation to
answer
him:
Effective federal tax rate
= 20% per year
Effective state tax rate =
6%
per year
Equation for overall effective tax rate =
state rate +
(I
- staterate)(federal rate)
(Hint: First develop a drawing similar
to Figure
1-6
for the Brazilia Group
situation.)
10.
ll
The
initial investment and incremental
ROR
values for four mutually exclusive
alternatives are indicated below.
Select the best alternative
if
a maximum
of
(a) $300,000, (b) $400,
000
, and
(c)
$700
,000
in
capital funds
is
available
and the
MARR
is the cost
of
capital,
whjch
is
estimated at 9%
per
year.
(d)
What
is the de facto
MARR
for these
alternatives if no specific
MARR
is
stated,
the available capital is
$400,000, and the
opportunity cost interpretation is applied?
374
CHAPTER
10
Making Choices: The Method, MARR, and Multiple Attributes
Incremental
Alternative
Initial
Rate
of
Rate
of
Alternative
Investment,
$
Return,
%
Return,
%
2
3
4
10. l2
1
0.
13
-
100
,000 8.8 for I to DN 8.8
- 250,000
12.5
for 2 to DN
12.5
- 400,000
I
1.
3 for 3
to
2
14
.0
- 550,000
8.1
for 4
to
3
10.0
State the recommended approach in es-
tablishing the
MARR
when other fac-
tors, such as alternative risk, taxes, and
market
ft
uctuations are considered
lJl
addition to the
cost
of
capital.
A partnership
of
four engineers operates
a duplex rental business. Five years ago
they purchased a block
of
duplexes, using
a
MARR
of
14% per year.
The
estimated
return at that time for the duplexes was
15
% per year, but the investment was
considered very
ri
sky due to the
poor
rental business
economy
in the city and
state overall. Nonetheless, the purchase
was made with 100% equity financing at
a cost
of
10% per year. Fortunately, the
return has averaged 18% per year
over
the 5 years. Another purchase opportu-
nity for more duplexes has now presented
itself, but a loan at
8%
per year would
have to be taken to make the investment.
(a)
If
the
economy
for rental property has
not changed significantly, is there likely
to be a tendency to now make the
MARR
hi
gher than, lower than,
or
the
same
as
that used previously?
Why?
(b)
What
is
the recommended way to consider the
rental business
economy
risk now that
debt cap
it
al would be involved?
D-E Mix
and
WACC
10.14 A new cross-country, trans mountain
range water pipeline needs to be built at
an estimated
fir
st cost
of
$200,000,000.
The
consortium
of
cooperating
compa
-
nies has not
fu
ll
y decided the financial
10
.
15
arrangements
of
this adventurous project.
The
WACC for similar projects has aver-
aged
10% per year.
(a) Two financing alternatives have
been identified.
The
first requires
an investment
of
60% equity funds
at 12% and a loan for the balance at
an interest rate
of
9%
per year.
The
second alternative requires only
20%
equity funds and the balance
obtained by a massive international
loan estimated to carry an interest
cost
of
12.5%
per
year, which is,
in
part, based on the geographic loca-
tion
of
the pipeline. Which financ-
ing plan will result
in
the smaller
average cost
of
capital?
(b) If the consortium
CFOs
have
de-
cided that the WACC must not ex-
ceed the 5-year historical average
of
10%
per
year, what is the maxi-
mum
loan interest acceptable for
each financing alternative?
A couple is planning ahead for their
child's college education. They can fund
part
or
all
of
the expected $]
00
,000
tuition cost from their own funds (through
an Education IRA)
or
borrow all
or
part
of
it.
The
expected return for their own funds
is 8% per year, but the l
oa
n is expected to
have higher interest rates as the amount
of
the
loan increases. Use a spreadsheet-
generated plot
of
the WA
CC
curve and the
estimated loan interest rates below to de-
termine the best
D-E
mix for the couple.
Loan
Amount,
$
10,000
25,000
50,000
60,000
75,000
100,000
Estimated
Interest
Rate,
%
per
year
7.0
7.5
9.0
10.0
12.0
18
.0