Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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SECTION 8.6 Incremental ROR Analysis
of
Multiple, Mutually Exclusive Alternatives
3. The incremental cash
flow
series, column 3, and Ili* for 8-to-A comparison is
determined from
0 = - 275,000 -
(-200
,000) + (35,000 - 22,000)(PIA,lli*,30)
= -
75
,000 +
13
,000(PIA,
lli
*,
30)
4. From the interest tables, look
up
the PIA factor
at
the
MARR
, which is
(PIA,
10
%,
30) = 9.4269. Now, any PIA value greater than 9.4269 indicates that
the
Ili* will be less than
10
% and is unacceptable.
The
PIA factor
is
5.7692, so B
is acceptable. For reference purposes,
Ili* = 17.28%.
5. Alternative B is justified incrementally (new defender), thereby eliminating
A.
6. Comparison D-to-B (steps 3 and 4) results
in
the PW relation 0 =
-75,000
+
7000(PIA,lli*,30) a
nd
a PIA va
lu
e
of
10.7143 (Ili* = 8.
55
%
).
Location D
is
eliminated, and only alternative B remains; it
is
selected.
Comment
An
a
lt
ernative must always be incrementally compared with
an
acceptable alternative,
and the do-nothing alternative can end
up
being the only acceptable one. Since C was
not justified in this example, location A was not compared with
C.
Thus, if the B-to-A
comparison had n
ot
indicated that B was
in
crementally
ju
stified, then the D-to-A com-
parison would
be
correct instead
of
D-to-B.
To demonstrate how important it is to apply the
ROR method correctly, consider the
following.
Tf
the i*
of
each alternative
is
computed initially, the results by ordered al-
ternati ves are
Location I C I A I
BID
i*,
% 9.
63
10.49 12.35 11.56
Now apply only the
fir
st criterion stated earlier; that is, make the largest investment that
has a MARR
of
10
%
or
more. Location D
is
selected.
But
, as shown above, this
is
the
wrong selection, because the extra investment
of
$75,000 over location B will not earn
the MARR.
Tn
fact, it will earn only 8.55%.
For service alternatives (costs only), the incremental cash flow is the differ-
ence between costs for two alternatives. There is no do-nothing alternative and
no step 2
in
the solution procedure. Therefore, the lowest-investment alternative
is the initial defender against the next-lowest investment (challenger). This pro-
cedure
is
illustrated
in
Example 8.7 using a spreadsheet solution for equal-life
service alternatives.
EXAMPLE 8.7 t
As the
film
of
an oil spill from an at-sea tanker moves ashore, great
lo
sses
occm
for aquatic
life as
well as shoreline feeders and dwellers, such as birds. Environmental engineers and
lawyers from several international petroleum corporations and transport companie
s-
Exxon-Mobil, BP, Shell, and some transporters for OPEC producers- have developed
295
296
~
E·So
lv
e
CHAPTER 8
Rate
of
Return Analysis: Multiple Alternatives
TABLE
8-7
Costs for Four A
lt
e
rn
a
ti
ve
Machines, Example 8.7
Machi
ne
1 Machine 2 Machine 3 Machine 4
First cost, $
- 5,000
-6,
500
-
10
,0
00
- 15,000
Annual operating cost, $
-3,
500 - 3,200
-3
,000 - 1,400
Salvage value, $
+ 500 + 900
+700
+ 1,000
Life, years
8 8 8 8
a plan
to
strategically locate throughout the world newly developed equipment that is
substantially more effective than manual procedures
in
cleaning crude oil residue from
bird feather
s.
The Sierra Club, Greenpeace, and other international environmental interest
groups are in favor
of
the initiative. Alternative machines from manufacturers
in
Asia,
America, Europe, and Africa are available with the cost estimates in Table 8-7. Annual cost
estimates are expected
to
be high
to
ensure readiness at any time.
The
company represen-
tatives have agreed to use the average
of
the corporate MARR values, which results in
MARR
=
13
.5%. Use a computer and incremental ROR analysis
to
determine which man-
ufacturer offers the best economic choice.
Solution
by
Computer
Fo
ll
ow the procedure for incremental ROR analysis outlined prior to Example 8.6. The
spreadsheet in Figure
8-6
contai
ns
the complete solution.
1.
The
alternatives are already ordered
by
increasing first costs.
2. These are service alternatives, so there
is
no comparison
to
DN
,
si
nce i* values ca
nn
ot
be
calculated.
3. Machine 2 is the first challenger to machine 1; the incremental cash
fl
ows for the
2-to-l comparison are
in colunm D.
4. The 2-to-l comparison results
in
t!..i
* = 14.57%
in
cell D17 by applying the IRR
function.
5.
This return exceeds
MARR
= 13.5%, so machine 2
is
the new defender (ce
ll
D
19
).
The
compa
ri
son continues for 3-to-2
in
cell E17 where the return
is
very negative at
t!..i
* =
- 18.77%; machine 2 is retained as the defender. Fina
ll
y the 4-to-2 comparison has
an
incremental ROR
of
13.60%, which is slightly larger than MARR = 13.5%. The concl
u-
sion
is
to purchase machine 4 because the extra investment is (marginally) justified.
Comment
As
mentioned earlier, it
is
not possible to generate a PW
vs.
i graph for each service alter-
native because a
ll
cash flows are negative. However,
it
is
possible to generate
PW
vs.
i
graphs for the incremental series
in
the same fashion
as
we have done previousl
y.
The
curves
wi
ll
cross the PW = 0 line at the
t!..i*
values determined by the IRR functions.
The spreadsheet does not include logic to select the better alternative at each stage
of
the solution. This feature could be added at each comparison using the Excel IF-operator
and the correct arithmetic operations for each incremental cash flow and
t!..i
* values. This
is too time-consuming; it
is
faster for the analyst to make the decision and then develop the
required functions for each comparison.
SECTION 8.7 Spreads
he
et
Application- PW,
AW,
and ROR Anal
ys
es
All
in
One
~
lot
ierosoft E Keel
!lriI
t3
11
E Hample
8.7
!Iii! t3
A
1
MA.R
R =
2
3
I
Year
Ma
chine 1
Ma
chine 2 Machine 3 Machine 4
~
Initial
in
vestment
-
$5
,000 -$6,500 -$10,000
-$15,000
5 Annual
co
st
-$3,500 -$3,200 -$3,000 -$1,400
6
Sa
lva e va
lu
e $500 $900
$700 $1,000
7 ROR compar
is
on 2 to 1 3 to 2 4 to 2
8
Incremental inv
es
tment 0
-$1
,500 -$3,500 -$8,500
9
In
cremental cash flow $300
$2
00
$1,800
10
2 $300 $200 $1,800
3 $300 $200 $1,800
4
$300 $200 $1,8
00
5
$300 $200 $1,800
6 $300 $200
$1,SOO
7 $300 $200 $1,800
8 $700 $0 $1
,9
00
14.57%
Y
es
2
Read',
Figure
8-6
Spreadsheet solution
to
select from
fo
ul' service alternatives, Example 8.7.
Selection from multiple, mutually exclusive alternatives with unequal
li
ve
s
using
t1i
* va
lu
es requires that the incremental cash flows be evaluated over the
LCM
of
the two alternatives being compared. This is another application
of
the
principle
of
equal-service comparison,
The
spreadsheet application
in
the next
section illustrates the computations,
It
is always possible to rely on
PW
or
AW analysis
of
the incremental cash
flows at the
MARR
to make the selection. In other words,
don't
find
t1i*
for each
pairwise comparison; find
PW
or
AW at the
MARR
instead.
However
, it
is
still
necessary to make the comparison over the
LCM
number
of
years for an incre-
mental analysis to be performed correctly.
8.7 SPREADSHEET
APPLICATION-PW,
AW,
AND
ROR
ANALYSES
ALL
IN
ONE
The following spreadsheet example combines many
of
the economic analysis
techniques we have learned so
far-(
in
ternal)
ROR
analysis, incremental
ROR
analysis,
PW
analysis, and A W analysis. Now that the
IRR
,
NPV
, and PV functions
297
298 CHAPTER 8 Rate
of
Return Analysis: Multiple Alternatives
are mastered, it
is
possible to perform a wide variety
of
evaluations for multiple
alternatives
on
a single spreadsheet.
To
better understand how the functions are
formatted and used, their formats must be developed by the reader,
as
there are
no
cell tags provided in this example. A nonconventional cash flow series for which
multiple
ROR values may be found, and selection from both mutually exclusive
alternatives a
nd
independent projects, are included in this example.
EXAMPLE
8.8
.,;:
'
m
E·Solve
In
-flight telephones provided at airline passenger seats are an expected service by many cus-
tomers. Delta Airlines knows it will have to replace
15,000 to 24,000 units in the next
few
years
on
its Boeing 737, 757, and some 777 aircraft. Four optional data-handling features
which build upon one another are available from the manufacturer, but at
an
added cost per
unit. Besides costing more, the higher-end options (e.g., satellite-based plug-in video ser-
vice) are estimated to have longer lives before the next replacement is forced by new, ad-
vanced features expected
by
flyers. All four options are expected to boost annual revenues
by varying amounts. Figure
8- 7 spreadsheet rows 2 through 6 include all the estimates for
th
e four options.
(a) Using MARR = 15%, perform ROR, PW, andAW evaluations to select the one level
of
options which is the most promising economically.
(b)
If
more than one level
of
options can be selected, consider the four that are described
as
independent projects.
If
no budget limitations are considered at this time, which
options are acceptable
if
the MARR is increased to 20% when more than one option
may be implemented?
Solution
by
Computer
(a) The spreadsheet (Figure 8-7) is divided into six sections:
Section 1 (rows
1,
2): MARR value and the alternative names (A through D)
in
increasi
ng
order
of
initial cost.
Secti
on
2 (rows 3 to 6): Per-unit net cash flow estimates for each alternative.
These are revenue alternatives with unequal lives.
Section 3 (rows 7 to 20): Actual and incremental cash flows are displayed here.
Section 4 (rows
21
, 22): Because these are
all
revenue alternatives,
i*
values
are determined by the IRR function.
If
an alternative passes the MARR test
(i* >
15
%
),
it is retained and a column
is
added to the right
of
its actual cash
flows so the incremental cash flows can be determined. Columns F and H
were inserted to make space for the incremental evaluations. Alternative A
does not pass the
i*
test.
Section 5 (rows
23
to 25): The IRR functions display the
1':;.i*
values in columns
F and
H. Comparison
of
C to B takes place over the LCM
of
12 years. Since
1':;.i
~
_ B
= 19.42% > 15%, eliminate B; alternative C is the new defender and
D is the next challenger. The final comparison of D to
Cover
12 years results
in
1':;.if;
-c
= 11.23% < 15%, so D is eliminated. Alternative C is the chosen
one.
SECTION 8.7
Spreadsheet App
li
cation- PW,
AW
, and ROR Analyses A
ll
in One
X Microsoft
EHcel
1lIr.J
x
$2.000 $3.000 $3.000
$3
.500
$0
$200
$3
00 $1,000
B
DID
I
ncrE-
m
e-nta
l
investmen
t ·6000 ·9000 -$2
.0
00 -$8.000
In
Cl
ement.a
1
cash
fl
ow
2000 30
00
$0
$5
00
ove'
the
lCM 2000 3000
$0
$500
2000 3000 3000
$0
$500
3200 3000
$6
,
80
0
3500
$500
3000
$0
3500 $500
3300 -$8,700 3500
$9.200
$0
3500 $5
00
$6.800
3500
$500
$0
35
00 $5
00
10 $0 3500
$500
to
$5
00
Ready
Fi
gure
8-7
Spreadsheet analysis us
in
g ROR, PW, a
nd
AW
methods for
un
equal-b
fe
, reve
nu
e alte
rn
atives,
Ex
ample 8.8.
Sec
ti
on 6 (rows 26 to 29): These include
th
e AW and PW analyses. Th
eA
W value
over the
li
fe
of
each alte
rn
a
ti
ve is calculated using
th
e PMT f
un
c
ti
on at the
MARR with an embedded
NPY
fun
c
ti
o
n.
Also,
th
e PW value is determined
from the AW va
lu
e for 12 years us
in
g
th
e PY function. For bo
th
measures, al-
te
rn
ative C has the nume
ri
cally largest value, as expected.
Conc
lu
sion: All me
th
ods result
in
the same, correct choice of alte
rn
a
ti
ve C.
(b) S
in
ce each option is indepe
nd
ent of the others, and there is no budget limitation at
th
is
time, each i* value
in
row 21
of
Figure 8- 7 is compared
to
MARR = 20%. This
is a comparison of each o
pti
on with
th
e do-nothing alternative.
Of
th
e four, options
Ba
nd
C have i* > 20%. They are acceptable; the o
th
er
tw
o are no
t.
Comment
In
part (a), we sho
ul
d have applied
th
e two multiple-root sign tests to
th
e
in
cremental cash
fl
ow se
ri
es for
th
e C-to-B comparison. The selies
it
self has three sign changes, and the
cum
ul
ative cash
fl
ow series starts nega
ti
vely and also has three sign changes. Therefore,
f--
----{
up to thr
ee
real-number roots may exist. The IRR f
un
c
ti
on is applied
in
ce
ll
F23 to obtain
'--
______
...Y
299
300
PROBLEMS
CHAPTER 8 Rate of Return Analysis: Multiple Alternatives
~
i
t
-
B
= 19.42% without using the net-investment procedure. This action assumes that the
reinvestment assumption
of
19.42%
fo
r positive net-investment cash flows
is
a reason-
ab
le one.
If
the MARR = 15%, or some other earning rate, were more appropriate, the net-
investment procedure would have to be applied to determine the composite rate, which
would be different from 19.42%. Depending upon the reinvestment rate chosen, alternative
C
mayor
may not be incrementally justified against B. Here, the assumption
is
made that
the
~i*
value
is
reasonable, so C
is
justified.
CHAPTER
SUMMARY
Just
as
present worth, annual worth, and future worth methods find the best al-
ternati ve from among several, incremental rate
of
return calculations can be used
for the same purpose.
In
using the ROR technique, it is necessary to consider the
incremental cash flows when selecting between mutually exclusive alternatives.
This was not necessary for the
PW,
AW,
or FW methods. The incremental
in
-
vestment evaluation is conducted between only two alternatives at a time begin-
ning with the lowest initial investment alternative.
Once
an
alternative has been
eliminated, it
is
not considered further.
If
there is no budget limitation when independent projects are evaluated using
the
ROR method, the ROR value
of
each project is compared to the MARR. Any
number, or none,
of
the projects can be accepted.
Rate
of
return values have a natural appeal
to
management, but the ROR analy-
sis is often more difficult
to
set
up
and complete than the
PW,
AW
, or FW analysis
using an established MARR. Care must be taken
to
perform a ROR analysis
conectly on the incremental cash flows; otherwise
it
may give inconect results.
Understanding Incremental
ROR
the first $30,000 and 14% on the remain-
ing
$70,000?
8.1
If
alternative A has a rate
of
return
of
10%
and alternative B has a rate
of
return
of
18%, what
is
known about the rate
of
re-
turn on the increment between A and B
if
the investment required
in
B
is
(a) larger
than that required for A and
(b) smaller
than that required for A?
8.2 What is the overall rate
of
return on a
$100,000 investment that returns 20% on
8.3 Why is
an
incremental analysis necessary
when you are conducting a rate
of
return
analysis for service alternatives?
8.4
If
all
of
the incremental cash flows are
negative, what is known about the rate
of
return on the incremental investment?
8.S Incremental cash flow is calculated
as
cast
flow
B
-
cash flow
A'
where B represents
th
alternative with the larger initial invest-
ment.
If
the two cash flows were switched
wherein B represents the one with the
smaller initial investment, which alterna-
tive should be selected
if
the incremental
rate
of
return
is
20% per year and the com-
pany's
MARR
is
15
% per year? Explain.
8.6 A food processing company
is
considering
two types
of
moisture analyzers.
The
com-
pany expects an infrared model to yield a
rate
of
return
of
18
% per year. A more ex-
pensive microwave model will yield a rate
of
return
of
23% per year.
If
the company's
MARR
is
18% per year, can you deter-
mine which model(s) should be purchased
solely on the basis
of
the rate
of
return in-
formation provided if
(a) either one or
both analyzers can be selected and
(b)
only
one can be selected? Why or why not?
8.7 For each
of
the following scenarios, state
whether an incremental investment analy-
sis would be required to select an alterna-
tive and state why or why not. Assume that
alternative
Y requires a higher initial in-
vestment than alternative X and that the
MARR
is
20% per year.
(a) X has a rate
of
return
of
28% per
year, and
Y has a rate
of
return
of
20% per year.
(b)
X has a rate
of
return
of
18% per
year, and
Y has a rate
of
return
of
23% per year.
(c) X has a rate
of
return
of
16% per
year, and
Y has a rate
of
return
of
19
% per year.
(d)
X has a rate
of
return
of30
% per year,
and
Y has a rate
of
return
of
26% per
year.
(e) X has a rate
of
return
of
21
% per
year, and
Y has a rate
of
return
of
22% per year.
8.8 A small construction company has
$100,000 set aside
in
a sinking fund to
PROBLEMS
301
purchase new equipment.
If
$30,000 is in-
vested at
30%, $20,000 at 25% and the re-
maining
$50,000 at 20% per year, what
is
the overall rate
of
return on the entire
$100,000?
8.9 A total
of
$50,000 was available for in-
vesting in a project to reduce insider theft
in
an appliance warehouse. Two alterna-
tives identified as
Y and Z were under con-
sideration.
The
overall rate
of
return on the
$50,000 was determined to be
40
%, with
the rate
of
return on the $20,000 increment
between
Y and Z at
15
%.
If
Z is the higher
first-cost alternative,
(a) what is the size
of
the investment required in Y and
(b)
what
is the rate
of
return on Y?
8.
10 Prepare a tabulation
of
cash flow for the
alternatives shown below.
Machine
A
Machine
B
First cost, $
Annual operating cost, $/year
Salvage value, $
Life, years
- 15,000
- 1,600
3,000
3
-
25
,000
- 400
6,000
6
8.
11
A chemical company is considering two
processes for making a cationic poly-
mer.
Process A will have a first cost
of
$100,000 and an annual operating cost
of
$60,000. Process B will have a first cost
of
$165,000.
If
both processes will be ade-
quate for 4 years and the rate
of
return on
the increment between the alternatives
is
25%, what is the amount
of
the operating
cost for process
B?
Incremental
ROR
Comparison
(Two Alternatives)
8.
12 When the rate
of
return on the incremental
cash flow between two alternatives
is
ex-
actly equal to the MARR, which alterna-
tive should be
selected-the
one with the
higher
or
lower initial investment? Why?
302
CHAPTER
8 Rate
of
Return Analysis: Multiple Alternatives
8.13 A consulting engineering firm is trying to
decide
whether
it should purchase Ford
Explorers
or
Toyota
4Runner
s for
com-
pany principals.
The
models
under
consid-
eration would
cost
$29,
000
for the Ford
and
$
32
,
000
for the Toyota.
The
annual
operating cost
of
the
Explorer
is expected
to be
$200
per
year
less than that
of
the
4Runner.
The
trade-in values after 3 years
are estimated to
be
50%
of
first
cost
for
the
Explorer and
60
%
for
the Toyota. (a)
What
is the rate
of
return relative to that
of
Ford,
if
the Toyota is selected? (b)
If
the firm's
MARR
is ] 8%
per
year
, which
make
of
vehicle should it buy?
8.14 A plastics
company
is considering two in-
jection molding processes.
Process X will
have a first
cost
of
$600,000
, annual costs
of
$200
,000, and a salvage value
of
$100,000 after 5
year
s. Process Y will
have a
first
cost
of
$800
,
000
, annual costs
of
$150,000, and a salva
ge
value
of
$
230
,
000
after 5
year
s. (a)
What
is the rate
of
return on the increment
of
inves
tment
between the two? (b)
Which
process
should the
comp
any select on the basis
of
a rate
of
return analysis,
if
the
MARR
is
20
% per
year
?
8.
15
A
company
that manufactures amplified
pressure transducers is trying to
decide
be-
tween the machines shown below.
Com-
pare them
on
the basis
of
rate
of
return,
and determine which should be selected
if
the
company
's
MARR
is
15
%
per
year.
First cost, $
Annual operating
co
st, $/y
ear
Ove
rh
a
ul
in
year 3, $
Ove
rh
a
ul
in
year 4, $
Salvage va
lu
e, $
Lif
e, years
Variable
Speed
- 250,000
- 231,000
- 39,000
50,000
6
Dual
Speed
- 225,000
- 235,000
- 26,000
10
,000
6
8.16
The
manager
of
a
canned
food processing
plant is trying to
decide
between two la-
beling machines.
Determine
which should
be
selected on the basis
of
rate
of
return
with a
MARR
of
20
%
per
year.
Machine A Machine B
Fi
rst
co
st, $ -
15
,000 - 25,000
Annual operating cost, $/year
Salvage value, $
- 1,600
3,000
2
- 400
4,000
4 Life, years
8.
17
A solid
waste
recycling
plant is consider-
ing two types
of
storage bins.
Determine
which should
be
selected on the basis
of
rate
of
return.
Assume
the
MARR
is
20%
per year.
Alternative
P
Alternative
Q
Fi
rst cost, $
- 18,000
- 35,000
Annual operating
-4,000
- 3,600
cost, $/year
Salvage value, $
1,000 2,700
Life, years 3
6
8.18
The
incremental cash flow between alter-
natives J and
K is estimated below.
If
the
MARR
is
20
%
per
year
, which alternative
should
be
selected on the basis
of
rate
of
return?
Assume
K requires the extra
$90
,
000
initial investment.
Year
o
1-3
4-9
10
Incremental
Cash
Flow,
$(K
- J)
- 90,000
+
10
,000
+20,000
+ 5,000
8.19 A
chemical
company
is considering two
processes for isolating
DNA
material.
The
incremental
cash
flow between two alter-
natives
J and S is as shown.
The
company
uses a
MARR
of
50% per year.
The
rate
of
return on the incremental cash flow below
is
less than 50%, but the company
CEO
prefers the more expensive process.
The
CEO
believes she can negotiate the initial
cost
of
the more expensive process down-
ward. By how much would s
he
have to
reduce the first cost
of
S, the higher-cost
alternative, for it to have an incremental
rate
of
return
of
exactly 50%?
Year
o
1
2
3
Incremental
Cash Flow, $(S - J)
- 900,000
400,000
600,000
850,000
8.20 Alternative R has a
fir
st cost
of
$100,000,
annual
M&O
costs
of
$50,000, and a
$20,000 salvage value after 5 years. Alter-
native S has a first cost
of
$175,000 and a
$40,000 salvage value after 5 years, but its
annual
M&O
costs are not known. Deter-
mine the
M&O
costs for alternative S that
would yield an incremental rate
of
return
of
20
% per year.
8.21 The incremental cash flows for alterna-
tives M and N are shown below. Deter-
mine which should be selected, using an
A W-based rate
of
return analysis.
The
MARR
is
12
% per year, and alternative N
requires the larger initial investment.
8.22
Incremental
Year Cash Flow, $(N -
M)
o
1- 8
9
-
22
,000
+4,000
+ 12,000
Determine which
of
the two machines
below should be selected, using an A W-
based rate
of
return analysis, if the
MARR
is
18
% per year.
PROBLEMS
303
Semiautomatic
Automatic
First cost, $
-40
,000
- 90,000
Annual cost, $/year
Salvage value, $
Life, years
-100,000
5,000
2
-95,000
7,000
4
8.23
The
incremental cash flows for alterna-
tives X and
Yare
shown below. Calculate
the incremental rate
of
return per month,
and determine which should be selected,
using an AW-based rate
of
return analysis.
The
MARR
is
24%
per year, compounded
monthly, and alternative Y requires the
larger initial investment.
8.24
8.25
Month
o
1-23
24
Incremental
Cash Flow, $(Y -
Xl
-
62
,000
+4,000
+
10
,000
The
incremental cash flow between alter-
natives
Zl
and
Z2
is shown below (Z2 has
the higher initial cost).
Use
an AW-based
rate
of
return equation to determine the in-
crementa] rate
of
return and which alterna-
tive should
be
selected,
if
the
MARR
is
17% per year.
Let
k = year I through 10.
Year
o
1-10
Incremental
Cash Flow, $(Z2 - Z1)
-4
0,000
9000
- 500k
Two roadway designs are under considera-
tion for access to a permanent suspension
bridge. Design
lA
will cost $3 million to
build and
$100,000 per year to maintain.
De
sign
IB
will cost $3.5 million to build
and
$
40
,000
per
year to maintain. Use an
A W-based rate
of
return equation to deter-
mine which design is prefeITed. Assume
n =
10
years and the
MARR
is
6% per year.
304
CHAPTER
8 Rate
of
Return
Analysis:
Multiple
Alternatives
8.26 A
manuf
acturing company is
in
need
of
3000 square meters for expansion because
of
a n
ew
3-year
contract it
ju
st won.
The
company
is considering the purchase
of
land for $50,000 and er
ec
ting a temporary
metal structure on it at a
cost
of
$90
per
square meter. At the end
of
the 3-year pe-
riod, the
company
ex
pects to be able to
se
ll
the land for $55,
000
and the building
for $60,
000
. Alternatively, the company
can lease space for $3 per square meter
per month, payable at the beginning
of
each year.
Use
an AW-based rate
of
return
equation to determine which alternative
is
pref
erred.
The
MARR
is
28% per year.
8.27 Four mutually exclusive service alternatives
are under consideration for automating a
manufacturing operation.
The
alternatives
were ranked
in
order
of
in
creasing initial
investment and then compared by incre-
mental investment rate
of
return analysis.
The
rate
of
return on each increment
of
in-
vestment was less than the
MARR.
Which
alternative should be selected?
Multiple-Alternative Comparison
8.28 A metal plating
company
is considering
four different methods for recovering by-
product heavy metals from a manufactur-
in
g site's liquid waste.
The
investment
costs and incomes associated with each
method have been estimated. All methods
have an 8-year life.
The
MARR
is
11
%
per
year. (a)
If
the methods are independent,
because they can be implemented at dif-
ferent plants, which ones are acceptable?
(b)
If
the methods are mutually exclusive,
determine which
one
method should be
selected, using a ROR evaluation.
First
Salvage
Annual
Method
Cost,
$
Value, $
Income,
$/year
A - 30,000
+ 1,000 + 4,000
B - 36,000
+2,000 + 5,000
C
- 41,000
+ 500 + 8,000
D -
53
,000 - 2,000 +
10
,500
8.29 Mountain Pass
Canning
Company
has de-
termined that
anyone
of
five machines
ca
n
be used
in
one
phase
of
its canning opera-
tion.
The
costs
of
the machines are esti-
mated below, and all machines have a
5-year life.
If
the
minimum
attractive rate
of
return is 20%
per
year, determine the
one
machine that should be selected on the
basis
of
a rate
of
return analysis.
Annual
Operating
Machine
First
Cost,
$
Cost,
$/year
1
-31,000
-
18
,000
2 -
28
,000 - 19,500
3
-3
4,500
-
17
,000
4 - 48,000 - 12,000
5
-
41
,000
-
15
,500
8.30 An independent dirt contractor
is
trying to
determine which size
dump
truck to buy.
The
contractor knows that as the bed size
increases, the net
income
increases, but he
is uncertain whether
the
incremental ex-
penditure required for the larger trucks is
ju
stified.
The
cash flows associated with
each size truck are estimated below.
Th
e
contractor's
MARR
is
18
% per year, a
nd
all trucks are expected to have a u
sef
ul
life
of
5 years. (a)
Determine
which size truck
should be purchased. (b)
If
two trucks
of
different size are to
be
purchased, what
should be the size
of
the second truck?
Truck Initial Annual
Bed
Size, Invest-
Operating
Salvage
Annual
Cubic
ment,
Cost,
Value,
Income,
Meters
$
$/year
$
$/year
8
-30,000
-
14
,000
+ 2000 + 26,500
10
- 34,000 -
15
,500
+ 2500 + 30,000
15
- 38,000
- 18,000
+ 3000
+
33
,500
20
- 48,000
-2
1,000
+3500
+40,500
25
- 57,000
-26
,000
+4600
+49,00(