Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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8.31 An
eng
in
eer
at Anode
Meta
ls is consider-
ing the projects below, a
ll
of
which can be
consider'ed to last
in
definitel
y.
If
the
com
-
pany
's
MARR
is
15
% per year, determjne
Annual
First
Cost
, $
Income
, $
/year
A
- 20,000
+3,
000
B - 10,000
+ 2,000
C
- 15,000
+2,
800
D - 70,000 + 10,000
E - 50,000
+6,
000
8.32 Only one
of
four different machines
is
to
be purchased for a certa
in
production
process. An engin
eer
performed the fol-
low
in
g analyses to select the b
est
ma-
Initial
cost,
$
Annual
cost
,
$/year
Annual savings,
$/yea
r
ROR,%
Machines
compared
Incremental
investment
, $
Incremental
cash flow,
$/year
ROR
on
increment
, %
- 44,000
- 70,000
+8
0,000
18.6
8.33 The
fo
ur alternatives desc
ri
bed bel
ow
are
be
in
g eva
lu
ated.
(a) If the pr
oposa
ls are indepen
de
nt,
w
hi
ch sho
ul
d be selected when the
MA
RR
is 16% per year?
PROBLEMS
305
which should be selected (a) if they are
independent and (b)
if
th
ey
are mutua
ll
y
exclusive.
Alt
ernative
's
Rate
of
Return, %
15
20
18.7
14.3
12
chin
e.
All machines are assumed to h
ave
a J O-year
li
fe. Which machine, if an
y,
should the
co
mpany select if its
MA
RR is
(a)
12% per year and (b) 20%
per
year?
Machi
ne
2
3
4
-60
,000 - 72,000
-98
,000
-64
,000
-6
1,000 - 58,000
+ 80,000
+8
0,000 + 82,000
23.4
2
to I
- 16,000
+ 6,000
35.7
23.1
20.8
3
to 2
4
to 3
-
12
,000
-26,000
+3,
000
+5,000
2
1.
4
14.
1
(b)
If
the proposals are mutua
ll
y exclu-
sive, which
one
should be selected
when the
MA
RR is 9% per year?
(c)
If
the proposals are mutua
ll
y exclu-
sive, which one sho
ul
d be selected
wh
en the
MAR
R is 12% per year?
I
ncremental
Rate
of
Return, %,
When
Compared
with
Alternative
Alternative
Initial
Investment,
$
Rate
of
Return,
%
A B C
A
B
C
D
- 40,000
- 75,000
- 100,000
- 200,000
29
15
16
14
I
7
10
20
13
12
306
CHAPTER
8 Rate
of
Return Analysis: Multiple Alternatives
8.34 A rate
of
return analysis was initiated for
the infinite-life alternatives below.
(a) Fill
in
the blanks
in
the incremental
rate
of
return column on the incre-
mental
cashftow
portion
of
the
table.
(b)
How much r
eve
nue is associated
with each alternative?
Alternative's
Alternative's
Alternative
Investment,
$
Rate
of
Return, %
E
- 20,000
20
F
-3
0,000
35
G
- 50,000
25
H - 80,000 20
8.35 A rate
of
return analysis was initiated for
the infinite-life alternatives below.
(a)
Fill
in
the blanks
in
the alternative's
rate
of
return column and incre-
mental rate
of
return columns
of
the
table.
Alternative's
Alternative's
Alternative
Investment,
$ Rate
of
Return, %
E
F
G
H
- 10,000
- 25,000
- 30,000
- 60,000
FE
REVIEW PROBLEMS
25
30
8.36 Alternative I requires an initial investment
of
$20,000 and wi
ll
yield a rate
of
return
of
15% p
er
year. Alternative C, which re-
quires a $30,000 investment, will yield
20% per year. Which
of
the following
statements
is
true about the rate
of
return
(c)
What
alternative should be selected
ifthey
are mutually exclusive and the
MARR
is 16%?
(d)
What
alternative should be selected
if
they are mutually exclusive and
the
MARR
is
11
%?
(e) Select the two best alternati ves at a
MARRof
19
%.
Incremental
Rate
of
Return, %,
on
Incremental Cash Flow
When
Compared
with
Alternative
E F
G H
11.7
11.7
(b)
What
alternative should be select
ed
if
they are independent and the
MARR
is 21 % per year?
(c)
What
alt
erna
tive should be selected
if they are mutual I y exclusi ve a
nd
the
MARR
is
24%
per
year?
Incremental Rate
of
Return, %,
on
Incremental Cash Flow
When
Compared
with
Alternative
E F G H
20
20
4
4
on the $10,
000
increment?
(a)
It
is greater than
20%
per
year.
(b)
It
is exactly 20% per year.
(c)
It
is between 15% and 20% per year.
(d)
It is less than
15
% per year.
8.37
The
rate
of
return for alternative X is
18
% per year and for alternative Y is
17
% per year, with Y requiring a larger initial
investment.
If
a company has a minimum
attracti ve rate
of
return
of
16% per year,
(a)
The
company should select alterna-
tive
X.
(b)
The
company shou
ld
select alterna-
tive
Y.
(c) The company should conduct an in-
cremental analysis between X and
Y
to select the economically better
alternative.
(d)
The company should select the do-
nothing alternative.
8.
38
When one
is
conducting an ROR analysis
of
mutually exclusive service projects,
(a) All the projects must be compared
against the do-nothing alternative.
(b) More than one project may be selected.
(c) An incremental investment analysis
is
necessary to identify the best one.
(d)
The
project with the highest incre-
mental
ROR should be selected.
8.39 When one
is
comparing two mutually ex-
clusive a
lt
ernatives by the
ROR
method,
if
the rate
of
return on the alternative with
the higher first cost
is
less than that
of
the
lower first-cost alternative,
(a)
The
rate
of
return on the increment
between the two is greater than the
Initial
Alternative
FE
REVIEW PROBLEMS
307
rate
of
return for the lower first-cost
alternative.
(b)
The
rate
of
return
on
the increment
is
less than the rate
of
return for the
l
ower
first-cost alternative.
(c)
The
higher first-cost alternative may
be the better
of
the two alternatives.
(d)
None
of
the above.
8.40
The
incremental cash flow between two
alternatives is shown below.
Year
Incremental
Cash Flow, $
o - 20,000
1-
10
+3,000
10
+400
The
equation(s) that can
be
used to cor-
rectly solve for the incremental rate
of
re-
turn is (are)
(a) 0 = - 20,000 +
3000(A
/ P,i,
1O)
+
400(PIF
,i,
1O)
(b) 0 =
-20,000
+
3000(A
/ P,
i,10)
+
400(AI
F ,i,
10)
(c) 0 =
-20
,
000(A
/ P,i,10) + 3000 +
400(PI
F,i,
I 0)
(d)
0 =
-20,000
+
3000(P
/ A,i,
1O)
+
400(PI
F,i,
1 0)
Questions
8.41
through 8.43 are based on the fol-
lowin
g.
The five alternatives are being evaluated
by the rate
of
return method.
Incremental
Rate
of
Return,
%,
When
Compared
with
Alternative
Alternative
Investment,
$
Rate
of
Return,
% A B
C
D E
A
-
25
,000 9.6
28
.9
19
.7 36.7 25.5
B
-
35
,000
15.1
1.5
39.8
24.7
C
- 40,000
13.4
49.4
28.0
D - 60,000 25.4
- 0.6
E
- 75,000
20.2
308
CHAPTER 8
Rate
of
Return Anal
ys
i
s:
Multiple Alte
rn
a
ti
ves
8.41
If
the alternatives are independent and the
MARR
is 18%
per
year, the
one
(s) that
should be selected
is
(are)
(a)
Only
D
(b)
Only
D and E
(c) Only B, D, and E
(d ) Only E
8.42
If
the alternatives a
re
mutually exclus
ive
and the
MARR
is
15
%
per
year
, the alter-
native to sele
ct
is
EXTENDED EXERCISE
(a) B
(b) D
(c) E
(d
)
None
of
them
8.43
If
the alternatives are mutually
ex
clusive
and the
MARR
is 25% per year, the alter-
native to select is
(
a)
A
(b) D
(c) E
(d
)
Non
e
of
them
INCREMENTAL
ROR
ANALYSIS
WHE
N ESTIMATED
ALTERNATIVE LIVES
ARE
UNCERTAIN
Mak
e-to-Specs is a software system under development by
ABC
Corporation. It
will be able to translate
di
gital versions
of
three-dimensional computer models,
containing a wide variety of part shapes with machined and highly finished (ultra-
smooth) surfaces.
The
product
of
the system is the numerically controlled
(NC
)
machine
code
for the
part's
manuf
acturing. Additionally, Make-to-Specs will build
the code for super-fine finishing of surfaces with continuous control
of
the finish-
ing
ma
chines. There are two alterna
ti
ve computers that can provide the
se
rver
function for
th
e
sof
tware interfaces and
shar
ed database updates
on
the manufac-
turing floor while M
ak
e-to-Specs is operating
in
parallel mode.
The
server first c
ost
and estimated contribution to annual net cash flow are summarized below.
F
ir
st cost, $
Net cash
fl
ow, $/year
Li
fe
, years
Server
1
$
100
,000
$35,000
3 or 4
Server
2
$200,000
$50,000
year I, plus $5000 per year
for years
2,
3, and 4 (gradient).
$70,000 m
ax
imum for years 5 on, even if
th
e server is replaced.
5 or 8
Th
e life estimates were developed by two different individuals: a
de
sign engi-
neer and a
manuf
acturing mana
ge
r.
They
have asked that at this stage
of
the proj-
ect, a
ll
analyses be performed using both
lif
e estimates for each system.
Questions
Us
e co
mputer
analysis to answer the f
ollowing
:
1.
If
the
MARR
= 12%, which
se
rver should
be
s
elected
? Use the
PW
or
AW
method to
mak
e
th
e
se
lection.
CASE STUDY
309
2.
Use
in
cremental ROR analysis to decide between the servers at MARR =
12%.
3. Use any method
of
economic analysis to display on the spreadsbeet the
va
lu
e
of
the incremental ROR between server 2 with a life estimate
of
5 years and a life estimate
of
8 years.
CASE STUDY 1
SO MANY OPTIONS. CAN A
NEW
ENGINEERING GRADUATE HELP
HIS FATHER?I
Background
"I don
't
know whether to sell
it
, expa
nd
it
, lease it, or
what.
But
I don't think we can keep doing the same
thing for many more years. What I really want
to
do is
to keep
it
for 5 more years, then sen it for a bundle,"
E
lm
er Kettler sa
id
to his wife Janise,
th
e
ir
son, John
Kettler, a
nd
new daughter-in-l
aw,
Suzanne Gestory,
as
they were gathered arou
nd
the dinner table. Elmer was
sha
rin
g thoughts on Gulf Coast Wholesale Auto Parts,
a company he has owned and operated for 25 years
on the southern out
sk
irts
of
Houston, Texas. The busi-
ness has exce
ll
ent contracts for parts supply with sev-
eral national retailers operat
in
g
in
the area- NAPA,
AutoZone, O'Re
ill
y, a
nd
Advance
,.
Additionally,
Gulf Coast operates a rebuild shop serving these same
retailers for major automo
bil
e component
s,
such
as carburetors, trans
mi
ssion
s,
a
nd
a
ir
cond
itioning
compressors.
At
hi
s home after dinner, John decided
to
help his
fa
th
er with an important and difficult decision: What to
do with
hi
s business? John gr
ad
uated
ju
st l
as
t year with
an
engineering degree from a major state university
in
Texas, where he completed a course
in
engineering
economy.
Part
of
hi
s job at Energcon Industries
is
to
perform basic rate
of
return and present worth analyses
on energy management proposals.
Options
Over the next few weeks, Mr. Kettler out
lin
ed five
options, including his favorite
of
selling in 5 years. John
summarized a
ll
the estimates over a lO-year horizo
n.
The options and estimates were given to Elmer, and he
agreed with them.
Option #1:
Remove rebuild. Stop operating
th
e rebuild
shop a
nd
concentrate on selling wholesale parts. The
removal
of
the rebuild operations and
th
e switch to an
"a
ll
parts house" is expected to cost $750,000
in
the
first yea
r.
Overall revenues will drop
to
$1
million the
first year with
an
expected 4% increase per year there-
after. Expenses are projected at
$0.8 million the first
year, increasing 6% per year thereafter.
Option #2:
Contract rebuild operations. To get the re-
build shop ready for
an
operations conu·actor to take
over will cost
$400,000 immediately.
If
expenses stay
th
e same for 5 years, they will average $1.4 million
per year, but they can be expected
to
ri
se to $2 million
per year
in
year 6 and thereafter. Elmer thinks rev-
enues under a contract arrangement can be $
1.4
mil
-
lion
th
e first year and
ri
se 5% per year for
th
e duration
of
a 1 O-year contract.
Option #3:
Maintain status quo
and
sell out after 5 years.
(Elmer's personal favorite.) There
is
no cost now, but the
'Ba ed upon a study by Mr. Alan
C.
Stewart, Consultant, Communica
ti
ons a
nd
Hi
gh Tech Solutions Eng
in
e
er
ing,
Accenture
LLP.
310
CHAPTER 8 Rate
of
Return Analysis: Multiple Alternatives
current trend
of
negative net profit will probably con-
tinue. Projections are $1.25 million per year for ex-
penses and $1.15 million per year
in
revenue. Elmer
had an appraisal last year, a
nd
the report indicated Gulf
Coast Wholesale Auto
Parts is worth a net $2 million.
E
lm
er's
wish
is
to
sell out completely after 5 more
years at this price, and to make a deal that the
new owner pay
$500,000 per year at the end
of
year 5
(sale time) and the
~ame
amount for the next 3 years.
Option #4: Trade-out. Elmer has a close friend
in
the
antique auto parts business who is making a
"killing,"
so he says, with e-commerce. Although the possibility
is
risky, it is enticing to Elmer
to
consider a whole new
line
of
parts, but still
in
the basic business that he
already understands. The trade-out would cost an esti-
mated
$1
million for Elmer immediately. The 10-year
horizon
of
annual expenses and revenues is consider-
ably higher than for his current business. Expenses
are estimated at $3 million per year and revenues at
$3.5 million each year.
Option #5: Lease arrangement.
Gulf
Coast could
be leased
to
some turnkey company with Elmer re-
maining the owner and bearing part
of
the expenses
for building, delivery trucks, insurance, etc.
The
first-cut estimates for this option a
re
$1.5 million to
get the business ready now, with annual expenses
at
$500,000 per year and revenues at $ l million per year
for a I
O-year contract.
CASE STUDY 2
Case Study Exercises
Help John with the analysis by doing the following:
1.
Develop the actual cash flow series a
nd
incre-
mental cash flow series (in
$1000 units) for all
five options in preparation for an incremental
ROR analysis.
2. Discuss the possibility
of
multiple rate
of
return
values for all the actual and incremental cash
flow series. Find any mUltiple rates
in
the range
0[0
to
100
%.
3.
If
10hn's father insists that he make 25% per year
or
more on tbe selected option over the next
10
years, what should he do? Use all the meth-
ods
of
economic analysis you ha ve learned so far
(PW, AW, ROR) so 10hn's father can understand
the recommendation
in
one way
or
another.
4.
Prepare plots
of
the
PW
vs. i for each
of
the five
options. Estimate the breakeven rate
of
return
between options.
5. What
is
the minimum amount that must be re-
ceived
in
each
of
years 5 through 8 for option #3
(the one Elmer wants) to be best economically?
Given this amount, what does the sale price have
to
be
, assuming the same payment alTangement
as presented in the description?
PW ANALYSIS WHEN MULTIPLE INTEREST RATES ARE PRESENT
2
Background
Two engineering economy
st
udents, Jane and Bob,
could not agree on what evaluation tool should be
used
to
select one
of
the following investment plans.
The cash flow series are identical except for their
signs. They recall that a
PW
or
AW
equation should be
set up
to solve for a rate
ofreturn.lt
seems that the two
investment plans should have identical
ROR value(s).
It may be that the two plans are equivalent and should
both be acceptable.
2Co
ntributed
by
Dr.
Tep Sas
lri
(former Associate Professor, Industrial Engineering, Texas A&M University).
Year Plan A
Plan B
0
$+1900
$-1900
1
-500
+500
2
-8
000
+8000
3
+6500
-6500
4
+400
- 400
Up
to this point in class, the professor has dis-
cussed the present worth and annual worth methods
at a given MARR for evaluat
in
g alternatives. He
explained the composite rate
of
return method during
the last class. The two students remember that the pro-
fessor said,
"The calculation
of
the composite rate
of
return is often computationally involved.
If
an
actual
ROR is not necessary, it
is
strongly recommended that
the
PW or A W at MARR be used to decide
00
project
acceptability."
Bob admitted that it is not very clear
to
him why
the simplistic
"
PW
at MARR"
is
strongly recom-
mended. Bob is
un
sure how to determine if a rate
of
return
is
"not necessary."
He
said
to
Jane, "Since the
composite
ROR technique a
lw
ays yields a unique
ROR value and eve
ry
student has a calculator or a
computer with a spreadsheet system on it, who cares
about the computation problem? I would always per-
form the composi
te
ROR method." Jane was more
cautious and suggested that a good analysis star
ts
with a simple, common-sense approach. She sug-
gested that Bob inspect the cash flows and see if he
could pick the better plan just through observation
of
the cash
flow
s.
Jane also proposed that they
u'y
every
method they had learned so
far.
She said, "
If
we ex-
periment with them, I think we may understand the
real reason that the
PW
(or
AW)
at the MARR method
is
recomme
nd
ed over the composite rate
of
return
method."
CASE STUDY
311
Case Study Exercises
Given their discussion, the following are some ques-
tions Jane and Bob need to answer. Help them develop
the answers.
1.
By simply inspecting the two cash
flow
patterns,
determine which
is
the preferred plan. In other
words,
if
someone is offering the two plans,
which one do you
think might obtain a higher
rate
of
return?
2.
Which plan is the better choice if the MARR
is
(a)
15
% per year and (b) 50% per year? Two ap-
proaches should be taken here: First, evaluate
the two options using
PW
analysis at theMARR,
ignoring the multiple roots, whether they exist or
not. Second, determine the internal rate
of
return
of
the two plans. Do the two cash flow series
have the same
ROR values?
3.
Perform an incremental ROR analysis
of
the two
plans. Are there still multiple roots
to
the incre-
mental cash flow series
th
at limit Bob's and
Jane's ability to make a definitive choice?
If
so,
what are they?
4. The students want
to
know
if
the composite ROR
anaJys.
is
will consistently yield a logical and
unique decision
as
the MARR value changes.
To
answer this question, find out which plan should
be accepted if any end-of-year released cash flows
(excess project funds) earn at the following three
reinvestment rates. The MARR rates change also.
(a) Reinvestment rate
is
15
% per year; MARR
is
15
% per year.
(b) Reinvestment
is
at
45
% per year; MARR
is
15% per year.
(c) Reinvestment rate and MARR are both
50% per year.
(d)
Explain your findings about these three dif-
ferent rate combinations to Bob and Jane.
9
w
«
I
u
Benefit/Cost Analysis
and Public Sector
Economics
The
evaluation
methods
of
previous chapters are usually
applied
to
alterna-
tives in
the
private sector,
that
is,
for-profit
and
not-for-profit
corporations
and
businesses. Customers, clients, and
employees
utilize
the
installed alter-
natives. This
chapter
introduces
public
sector
alternatives and
their
economic
consideration. Here
the
owners
and
users (beneficiaries) are
the
citizens
of
the
government
unit-city,
county, state, province,
or
nation.
Government
units
provide
the
mechanisms
to
raise (investment) capital and
operating
funds
for
projects
through
taxes, user fees,
bond
issues, and loans. There are substan-
tial differences
in
the
characteristics
of
public
and
private
sector
alternatives
and
their
economic
evaluation,
as
outlined
in
the
first section. Partnerships
of
the
public
and
private
sector
have
become
increasingly
common,
especially
for
large infrastructure
construct
ion projects such
as
major
highw
ays,
power
generation
plants,
water
resource
developments,
and
the
like.
The
benefit/cost
(B/C) ratio was
developed,
in part,
to
introduce
ob
jecti
v-
ity
into
the
economic
analysis
of
public
sector
evaluation, thus
reducing
the
effects
of
politics
and
special interests. However,
there
is
always
predictable
disagreement
among
citizens (individuals and groups)
about
how
the
bene-
fits
of
an
alternative
are
defined
and
econom
ically
va
lu
ed.
The
different
formats
of
B/C
analysis, and associated
disbenefits
of
an
alternative, are
discussed here.
The
B/C
analysis can use
equivalency
computations
based
on
PW,
AW,
or
FW values.
Performed
correctly,
the
benefit/cost
method
will
always select
the
same
alternative
as
PW, AW, and
ROR
analyses.
A
public
sector
project
to
enhance freeway
lighting
is
the
subject
of
the
case study.
LEARNING OBJECTIVES
Purpose: Understand public sector economics; evaluate a project and compare alternatives
using the benefit/cost ratio
method.
Public sector
B/C
for
single project
Alternat
ive selection
Multiple
alternatives
This
chapter
will help you:
1.
Identify
fundamen
tal differences
between
pub
lic
and
private
sector
eco
n
omic
al
te
rn
atives.
2.
Use
the
benefit/cost
ratio
to
evaluate a single
pro
j
ect
.
3. Select
the
better
of
two
alternat
ives using
the
incremental
B/C
ratio
method.
4.
Se
l
ect
th
e best from multiple
alt
e
rn
at
ives
us
i
ng
the
incremental
B/C
me
th
od.
314
I Sec.5.5 I
Capitalized cost
CHAPTER 9 Benefit/Cost Analysis and Public Sector Econ
om
ics
9.1 PUBLIC SECTOR PROJECTS
Public sector projects are owned, used, and financed by the citizenry
of
any gov-
ernment level, whereas projects in the private sector are owned by corporations,
partnerships, and individual
s.
The
products and services
of
private sector proj-
ects are used by individual customers and clients. Virtually all the examples in
previous chapters have been from the private sector. Notable exceptions occur
in
Chapters 5 and 6 where capitalized cost was introduced as an extension to
PW
analysis for long-life alternatives and perpetual investments.
Public sector projects have a primary purpose to provide services to the citi-
zenry for the public good at no profit. Areas such as health, safety, economic
welfare, and utilities comprise a majority
of
alternatives that require engineering
economic analysis. Some public sector examples are
Hospitals and clinics
Parks and recreation
Utilities: water, electricity, gas,
sewe
r, sanitation
Schools: primar
y,
secondary,
community colleges, universities
Economic development
Convention centers
S ports arenas
Transportation:
hi
ghways, bridges,
waterways
Police and fire protection
Courts and prisons
Food stamp and rent relief programs
Job training
Public housing
Emergency relief
Codes and standards
There are significant differences in the characteristics
of
private and public sector
alternati ves.
Characteristic
Public
sector
Private
sector
Size
of
investment
Larger Some large; more medi
um
to sma
ll
Often alternatives developed to serve public needs require large initial invest-
ments, possibly distributed over several years. Modern
hi
ghways, public trans-
portation systems, airports, and flood control systems are examples.
Life estimates
Longer
(30-
50+
years)
Shorter (2-25 years)
The
long lives
of
public projects often prompt the use
of
the capitalized cost
method, where infinity
is
used for n and annual costs are calculated as A = P(i).
As n gets larger, especially over 30 years, the differences in calculated A values
become small. For example, at
i = 7%,
th
ere will be a very small difference
in
30 and 50 years, because
(AI
P,7%,30) = 0.08059 and
(AI
P,7%,50) = 0.07246.
Annual cash
fl
ow
es ti mates
No
profit; costs, benefits,
and
di
sbenefits, are est
im
ated
Revenues contr
ib
ut
e
to profits; costs are est
im
ated