Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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SECTION 13.3 Spreadsheet Application- Using Excel's SOLVER
Even though the preceding examples treat two alternatives, the same type
of
analysis can be performed for three or more alternatives.
To
do so, compare the al-
ternati ves in pairs to
fi
nd their respecti ve break even points. The results are the ranges
through which each alternative is more economical. For example, in Figure
13-8,
if
the output
is
less than 40 units per hour, alternative 1 should be selected. Between 40
and 60, alternative 2
is
more economical; and above 60, alternative 3 is favored.
If
the variable cost relations are nonlinear, analysis is more complicated.
If
the
costs increase or decrease uniformly, mathematical expressions that allow direct
determination
of
the breakeven point can be developed.
13.3 SPREADSHEET
APPLICATION-USING
EXCE~S
SOLVER
FOR
BREAKEVEN ANALYSIS
This section focuses on the utilization
of
Excel's optimIzmg tool SOLVER
for basic breakeven analysis. We have used this tool previously with excellent suc-
cess in speeding up the
solution-Section
12.4 on the linear programming model
formulation to select from independent projects, and
Section 11.3 to find the re-
placement value for a defender asset
in
a replacement study. The latter is an appli-
cation
of
SOLVER for breakeven analysis. Some discussion about SOLVER is in-
cluded here in case it has not been used in previous chapters. Further discussion
of
its use can be found
in
Appendix A, Section A.4, and the Excel help system.
SOLVER is on the "Tools" toolbar
of
Excel.
(If
SOLVER is not on the com-
puter, click
"add-ins" on the Tools menu to receive installation directions.) Fun-
damentally, it
is
designed to perform breakeven and "what if?" analysis. This is
a tool that demonstrates the real advantages
of
using a computer for engineering
economic analysis. The
SOLVER template is shown in Figure 13-9. Two pri-
mary cell designations
of
SOLVER are the target cell and changing cells.
Target
cell-This
is
the cell that sets the objective. For example, to find the
rate
of
return, we can set PW =
O.
On the spreadsheet, the NPV function is
set to
O. The target
is
the cell with the NPV function in it. The target cell
must contain a formula or function. The entry may be maximized, mini-
mized, or set to a specific value, such as
O.
If
specified, the value must be a
number, not a cell reference. In breakeven analysis, the target cell is com-
monly set equal to the value
of
another cell, for example, equating the
PW
Solver Parameters
Da
455
Figure 13- 9
Excel's SOLVER
template used
to
perform
breakeven analysis and
many other
"what if?"
analyses.
456
~
E·So
lv
e
CHAPTER
13
Breakeven Analysis
values
of
two alternatives. This
is
the spreadsheet equivalent
of
equating
two relations for breakeven analysis.
Changing
cells-This
is the cell (or cells) where SOLVER will make the
changes. These are the decision variables.
One or more cells are identified
that are directly or indirectly affected
by
the target cell. SOLVER changes
the value
of
this cell until a solution is found that results
in
the target cell,
as
specified. Clicking "Guess" will display all the cells that can be changed
once the target cell is identified.
Constraints-These
are limits placed on the target and changing cells
to
set
bounds on cell values while
SOLVER is looking for a solution
to
match the
target cell value.
Cheryl is a project engineer
in
the ANCO Division
of
Federal-Mogul. She
is
searching for
a replacement
fo
r an aging testing machine for after-market windshield wiper blades. One
of
her engineering technicians found two equivalent machines that have fundamentally the
same estimates, except for the expected life.
X Microsoft Excel
1!I(';iJ
Ei
Ei
le
~dit
~iew
Insert
FQrmat
.....=.
..,.,.-
...,:;,.
_
;:::.".
_ -=,.,:-.
11
a Example
13
.5 (Fig
13
·
101
I!lIiIEi
A
B C
0 E
F
MA
RR
10%
2
3
Al
ternative
#1
#2
-$9,000 -$9,000
$3,
000 $3,000
$2
00
$3
00
4 6
Actual CF
A
c
t
u
a
l
CF
~
9
0
$
(9,000)
$ (9,000
=$
C$S
10
1 $
3,
000
$ 3,000
11
2 $ 3,000 $ 3,000
12 3
$
3,000
$
3,000
13
4
$
3,
200 $ 3,000
$ 3,000
$ 3,300
13.24%
24.68%
- PMT($B$I ,C7, - (NPV($B$1,CIO:CIS)+C9»
$204
$972
$1,389 $6,626
- PV($B$I ,LCM($B$7,$C$7),
-C
18)
Ready
Figure
13-10
Spreadsheet comparison
of
two alternatives for wltich SOLVER
is
used for breakeven analysis, -
Example 13.5.
SECTION 13.3
First cost, $
Net cash flow, $/year
Salvage, $
Life, years
Spreadsheet
Application
~
U
s
ing
Excel's SOLYER
Machine
#1
$- 9000
3000
200
4
Machine
#2
$-9000
3000
300
6
Cheryl knows that #2 is the better choice due to its longer life. However, she judges the
features
of
alternative # I as much better. She has decided to perform breakeven analysis to
determine what alterations in estimated values are necessary to make the two machines
economically indifferent. The MARR is
10% at the ANCO Division. Use the spreadsheet
in Figure
13
-
10
and the SOLVER tool to explore breakeven values for (a) the first cost
of
machine
#1
a
nd
(b)
th
e n
et
cash flow for machine #1.
Solution by Computer
The
spreadsheet (Figure
13
-
10)
is
developed
in
cell reference format in preparation for
any type
of
breakeven or sensitivity analysis.
For
example, the PY functions
in
row
19
use
#1
tf2
-
$6,
564
-$9
,000
$
3,000
$3
,000
Solver
Paramete.~
, '
DEI
$
200
$
300
4 6
Actual
CF
Ac
tu
al
CF
S!l.tTarget
Cell:
1$6
$
19
Oil
Equal
To:
('
!l:!.ax
('
MI[)
r.
'i;ll
ue
of: 16626
0
-$6,
564
-$
9
,00
0
1
$3
,000
$3,000
2
3000
3000
3
3000
300
0
to
the
C
onstraints
::
~'_-~
-~0'
...
C',
4 $3,
200
3
000
5
3000
6
$3
,
300
30.
05%
24
.
68%
.
Q.elete
$
972
$
972
$6
,
626
$6,
626
Enter
(a) Initial cost for alternative
#1
Figure 13-11
Excel's SOLVER used to perform breakeven analysis on alternative #1: (a) first cost and (b) net cash
flow
, E
xample
13
.
5.
tielp
457
458
Enter
Figure 13-11
(Continued).
CHAPTER
13
Breakeven Analysis
3 3000,
4 3000
5 3000
6 $3,300
24.89% 24.68%
$972 $972
$6,626
~
$6,626
an embedded least common multiple function LCM(B7,C7). With this addition, SOLVER
can be used
to
examine the estimated lives, and the
PW
values will be correct for unequal
lives.
(a) Figure
13
-
11a
presents the SOLVER solution for
PI'
The target cell
(B
19) is the PW
of
machine
#1
at the MARR. It is set equal
to
the value
of
PW
2
= $6626. The
changing cell (B4)
is
the decision variable PI' The breakeven value is
PI
= $6564.
The interpretation is that if machine
#1
can be purchased for $6564, the two alter-
natives are economically equal. This represents a required reduction
in
the first cost
of
$9000 - 6564 = $2436.
(b) Figure
13
- 11b targets cell B19 again with the same value PW
2
= $6626, but now
the changing cell (decision variable) is B5, the net cash
flow
for machine #1. Since
the NCF values
in
cells B 1 0 through B
13
are determined with reference to the value
in
cell
B5
, they
all
change to the breakeven value
of
$3769. The salvage
of
$200 is
added to NCF in cell B
13.
The interpretation
is
that if the estimated annual net cash
flow can be raised from
$3000 to $3769, the alternatives are economically equal
with a first cost
of
$9000 for both.
PROBLEMS
459
CHAPTER SUMMARY
The
breakeven
point
for a variable X for
one
project is
expressed
in terms
such
as unjts
per
year
or
hours
per
month.
At
the breakeven
amount
QBE'
there
is
in-
difference to accept
or
reject the project.
Use
the following
decision
guideline
:
Single Project
(Refer
to
Figure
13-2.)
Estimated quantity is larger than Q
BE
-7
accept
project
Estimated
quantity is smaller than Q
BE
-7
reject
project
For
two
or
more
alternatives,
determine
the breakeven
value
of
the
common
vari-
able
X.
Use
the
following
guideline to
select
an alternative:
Two
Alternatives
(Refer
to
Figure
13-7.)
Estimated level
of
X is
below
breakeven
-7
select
alternative with the
higher
variable
cost
(larger slope)
Estimated
level
of
X
is
above breakeven
-7
select alternative with the
lower
variable
cost
(smaller
slope)
Breakeven
analysis between
two
alternatives is
accomplished
by
equating
the
PW
or
A W relations and sol ving for the
parameter
in question.
The
SOLVER
tool
is
very effective
in
performing
fast,
accurate
breakeven analyses on a computer.
PROBLEMS
Breakeven
Analysis
for
a
Project
13.1
The
fixed costs
at
Harley
Motors
are
$1
miIJion annually.
The
main
product
has revenue
of
$8.50
per unjt and $4.25
variable cost.
Determine
the
following.
(a)
Breakeven
quantity
per
year.
(b
) Annual profit
if
200,000
units are
sold and
if
350
,
000
units are sold.
Use
both an
equation
and a
plot
of
the revenue and total cost relations
to answer.
13.2
If
both linear and nonlinear
revenue
and
total
cost
relations are
considered
, state
at least
one
combination
of
mathematical
relations for which there
could
easily be
exactly two breakeven points.
13
.3 A metallurgical
engineer
has
estimated
that
the
capital
investment
for recov-
ering
valuable
metals (nickel, silver,
gold
, etc.) from a
copper
refinery
'S
wastewater
stream will be $15 million.
The
equipment
will
have
a useful life
of
10 years
with
no
salvage value.
The
amount
of
metals currently dis-
charged
is 12,
000
pounds
per
month.
The
monthly
operating
cost
is represented
by
$(4,100,000)£1
8,
where
£ is the effi-
ciency
of
metal recovery in decimal
form.
Determine
the
minimum
removal
efficiency required for the
company
to
break
even,
if
the
average
selling price
of
the metals is
$250
per
pound.
Use
an
interest rate
of
1 % per month.
13.4
For
the
estimates
below,
calculate
the
following.
(a)
Breakeven
quantity
per
month.
(b)
Profit (loss)
per
unit
at
sales levels
that
are 10%
above
and 10% below
breakeven.
460
CHAPTER
l3
Breakeven Analysis
(c) Plot average cost per unit for quan-
tities ranging from 25% below to
30% above breakeven.
r = $39.95 per unit
v = $24.75 per unit
FC
= $4,000,000 per year
13.5 Develop a plot
of
the average cost per
unit versus production quantity for the
houseware appliance assembly depart-
ment
of
Ace-One, Inc., that has a fixed
cost
of
$160,000
per
year and a variable
cost
of
$4.00 per unit; use it to answer the
following questions.
(a)
At
what quantity
is
a $5 per unit
average cost justified?
(b)
If
the fixed cost increases to
$200,000, plot the new curve on the
same graph and estimate the quan-
tity that justifies an average cost
of
$6 per unit.
13.6 A call center
in
India used
by
U.S. and
U.K. credit card holders has a capacity
of
1,400,000 calls annually. The fixed cost
of
the center
is
$775,000 with an average
variable cost
of
$2 and revenue
of
$3
.50
per call.
(a) Find the percentage
of
the capacity
that must be placed each year to
break even.
(b) The center manager expects to ded-
icate the equivalent
of
500,000
of
the 1,400,000 capacity to a new
product line. This is expected to in-
crease the center's fixed cost to
$900,000,
of
which 50% will be al-
located to the new product line. De-
termine the average revenue per call
necessary to make
500,000 calls the
breakeven point for only the new
product. How does this required
revenue compare with the current
center revenue
of
$3.50
per
call?
1
3.
7 For the last 2 years, the Homes-r-US
company has experienced a fixed cost
of
$850,000 per year and an (r - v) value
of
$1.25 per unit. International competition
has become severe enough that some
financial changes must be made to keep
market share at the
cunent
level. Perform
a graphical analysis, using Excel, that esti-
mates the effect on the breakeven point if
the difference between revenue and vari-
able cost per unit increases somewhere
between 1 % and 15%
of
its current value.
If
fixed costs and revenue per unit remain
at their current values, what must change
to make the breakeven point go down?
13.8 (This is an extension
of
Problem 13.7.)
Expand the analysis performed in
Prob-
lem 13.7, where a change in variable
cost per unit is examined. The financial
manager estimates that fixed costs will
fall to
$750,000 when the required
production rate to break even is at or
below
600,000 units. What happens to
the breakeven points over the
r - v
range
of
1 % to 15% increase
as
evaluated
previously?
13
.9 An automobile company
is
investigating
the advisability
of
converting a plant that
manufactures economy cars into one that
will make retro sports cars. The initial
cost for equipment conversion will be
$200 million with a 20% salvage value
anytime within a 5-year period. The cost
of
producing a car will be $21,000, but it is
expected to have a selling price
of
$33,000
(to dealers). The production capacity for
the first year will be
4000 units.
At
an
interest rate
of
12% per year, by what uni-
form amount will production have to in-
crease each year
in
order for the company
to recover its investment in 3 years?
13
.10 Rod, an industrial engineer manager with
Zema Corporation, has determined via the
least squares method that the annual total
cost per case
of
producing its top-selling
drink can best be described by the qua-
dratic relation TC
= 0.001Q2 +
3Q
+
2,
and that revenue is approximately linear
with r = $25 per case. Rod asks you to do
the following.
(a) Tabulate the profit function between
the values
of
Q = 5000 and 25,000
cases. Estimate the maximum profit
and the quantity at which it occurs.
(b) Find the answers
to
part (a)
by
using
an
Excel graph.
(c) Determine an equation for Qmax' the
quantity at which the maximum
profit should occur, and determine
the amount
of
the profit at this point
for the
TC
and r identified by the
manager.
13.11 A civil engineer has been promoted to
managerofengineered public systems.
One
of
the products
is
an
emergency intercept
pump for potable water.
If
the tested water
quality or volume varies by a preset per-
centage, the pump automatically switches
to preselected options
of
treatments or
water sources. The manufacturing process
for the pump had the following fixed and
variable costs over a I-year period.
Variable
Fixed
Costs,
Costs,
$
$/Unit
Administrative 30,000 Materials 2500
Salaries and Labor 200
benefits: 20%
of
350,000
Equipment
100,000 Indirect labor
2000
Space, utilities, etc. 55,000 Subcontractors
800
Computers:
1/3
of
150,000
(a) Determine the minimum revenue
per unit to break even at the current
production volume
of
5000 units
per year.
(b) Ifselling internationally and to large
corporations
is
pursued, an increased
production
of
3000 additional units
will be necessary. Determine the
revenue
per
unit required if a profit
goal
of
$500,000
is
set for the entire
product line. Assume the cost esti-
mates above remain the same.
PROBLEMS
461
Breakeven Analysis Between Alternatives
13.12 A Yellow Pages directory company must
decide whether it should compose the ads
for its clients inhouse or pay a production
company to compose them.
To
develop
the ads inhouse, the company will have
to purchase computers, printers, and
other peripherals at a cost
of
$12,000.
The
equipment will have a useful life
of
3 years, after which it will be sold for
$2000.
The
employee who creates the
ads will be paid
$45,000 per year. In ad-
dition, each ad will have an average cost
of
$8 to prepare for delivery to the
printer. A total
of
4000 ads are antici-
pated for the next few years. Alterna-
tively, the company can outsource ad
development at a fee
of
$20 per ad re-
gardless
of
the quantity. The current in-
terest rate is 8% per year. What
is
the
breakeven amount, and which alternative
is economically better?
13
.
13
An engineering firm can lease a measure-
ment system for
$1000 per month or pur-
chase one for
$15,000. The leased system
will have no monthly maintenance cost,
but the purchased one will cost
$80 per
month. At an interest rate
of
0.5% per
month, how many months must the sys-
tem be required to break even?
13.14 Two pumps can be used for pumping a
corrosive liquid. A pump with a brass im-
peller costs
$800 and is expected to last
3 years. A pump with a stainless steel im-
peller costs
$1900 and will last 5 years. A
rebuild costing
$300 will be required
after
2000 operating hours for the brass
impeller pump while an overhaul costing
$700 will be required for the stainless
steel pump after
8000 hours.
If
the oper-
ating cost
of
each pump is
$1
per hour,
how many hours per year must the pump
be required to justify the purchase
of
the
more expensive pump?
Use an interest
rate
of
10% per year.
462
CHAPTER
13
Breakeven
Analy
s
is
13.
15
Two bids have been received to repave a
commercial parking lot. Proposal 1 in-
cludes new curbs, grading, and paving at
an initial
cost
of
$250
,000.
The
life
of
the
parking lot surface constructed
in
this
manner
is
expected to be 4 years with
annual costs for maintenance and repaint-
ing
of
pavement markings at $3000. Pro-
posal 2 offers
pavement
of
a significantly
higher quality with an expected life
of
8 years.
The
annual maintenance cost will
be negligible for the pavement, but the
markings will have to be repainted every
2 years at a cost
of
$3000. Markings are
not repainted the last
year
of
its expected
life
under
proposal
2.
If
the
company's
current
MARR
is
12% per year, how
much can it afford to
spend
on proposal
2 initially so the two break
even?
13. 16 Jeremy
is
evaluating the operational costs
of
the manufacturing processes for spe-
cific components
of
a wireless
home
secu-
rity system.
The
same
components are
produced at plants
in
New
York (NY) and
Los Angeles (LA).
The
records for the last
3 years from NY report a fixed
cost
of
$400,
000
per year and a variable cost
of
$95 per unit
in
year I, decreasing by $3
per unit per year.
The
LA reports indicate
a fixed
cost
of
$750,000 per year and a
variable
cost
of
$50
per unit, increasing by
$4
per unit per year.
If
the trends continue,
how many units must be
produced
in
year 4 for the two processes break even?
Use an interest rate
of
10
%
per
year.
13.17 Alfred Home Construction
is
considering
the purchase
of
five dumpsters and a trans-
port truck to store and transfer construc-
tion debris from building sites.
The
entire
rig
is
estimated to have an initial cost
of
$125,000, a
lifeof8
years, a
$5000
salvage
value, an operating
costof$40
per day, and
an annual maintenance
cost
of
$2000
.
Alternatively, Alfred can obtain the
same
services from the city as needed at each
construction site for an initial delivery cost
of
$125 per
dumpster
per site and a daily
charge
of
$20
per day per dumpster. An
estimated 45 construction sites will need
debris storage throughout the average
year.
The
minimum attractive rate
of
re-
turn is 12% per year.
(a)
How
many days
per year
mustthe
equi
pment
be
requ ired to
just
break even? (b)
If
the expected usage
is
75 days
per
year, which option- buy
or
lease-should
be
selected based on
this economic analysis? Determine the
expected annual
cost
of
this decision.
13.18
Machine
A has a fixed
cost
of
$40
,
000
per
year
and a variable cost
of
$60
per
unit.
Machine
B has an unknown fixed
cost, but with this process
200
units can
be
produced each month at a total vari-
able
cost
of
$2000.
If
the total costs
of
the
two
machines
break even at a production
rate
of
2000
units per year,
what
is
the
fixed
cost
of
machine
B?
13.19 A waste-holding lagoon situated near the
main plant receives sludge daily. When
the lagoon
is
full, it is necessary to remove
the sludge to a site located 8.2 kilometers
from the main plant. Currently, when the
lagoon
is
full, the sludge
is
removed by
pump
into a
tank
truck and hauled away.
This
process requires the use
of
a portable
pump
that initially
cost
$800
and has an
8-year life.
The
company
pays a contract
individual to operate the
pump
and over-
see
environmental and safety factors at
a rate
of
$100
per day, but the truck and
driver must be rented for
$200
per day.
The
company has the option to install a
pump
and pipeline to the remote site.
The
pump would have an initial
cost
of
$1600
and a life
of
10
years and will
cost
$3 per
day to operate.
The
company
's
MARR
is
10% per year.
(a)
If
the pipeline will
cost$12
per meter
to construct and will have a 10-year
life, how many days per year must
the lagoon require pumping to jus-
tify construction
of
the pipeline?
(b)
If
the company expects to pump the
lagoon once per week every week
of
the year, how much money can it
af
-
ford to spend now on the
lO
-year-life
pipeline to just break even?
Use
of
SOLVER for Breakeven Analysis
13
.20 Develop a spreadsheet using cell reference
format for the estimates of
Problem 13.15
where two proposals for repaving a com-
mercial parking lot are evaluated. Answer
the following questions, using
SOLVER.
(a) How much can the company afford
to spend on proposal 2 initially so the
two break even? (This is the same
question posed
in
Problem 13.15.)
(b) Assume that P2 =
$-400,000
is the
actual cost
of
proposal 2 and that
PI = $- 250,000 is correct. Use
the results
of
the analysis above to
determine if the annual costs
of
proposal 1 for maintenance and re-
painting can be reduced enough to
make it a
vi
able option.
13.21
Ajeans
manufacturing company
is
evalu-
ating the purchase
of
a new automatic cut-
ting machine with fuzzy-logic features.
The machine will have a first cost
of
$40,000, a life
of]
0 years, and no salvage
value. The maintenance cost
of
the
ma
-
chine
is
expected to be $2000 per ye
ar.
The
machine will require one operator at a total
cost
of
$30 per hour. A total
of
2500 yards
of
material can be cut each hour by the ma-
chine. Alternatively, if human labor
is
used, six workers, each earning
$1
4 per
hour, are required
to
cut 2500 yards per
hour. The
MARR
is
8% per year. Deter-
mine the minimum yards per year to justify
the purchase
of
the automatic machine.
Use (a) hand and (b) computer solution.
13.22 This
is
an extension to Problem
13
.
2l.
Assume this
is
a North American com-
pany that elected to move some
of
its
cutting operations to Asia when domestic
commercial interest rates were high at
PROBLEMS
463
8% per year and Asian labor rates aver-
aged $14 per hour. Now the machinery
will cost
$80,000 with the other estimates
remaining the same, the interest rate is
6% per year, and Asian labor costs an av-
erage
of
$25 per hour. Further assume the
company elected earlier to stay with
human cutting operations since the gar-
ment line for which the analysis was done
had an annual production rate
of
about
300,000 yards. Recalculate the new
breakeven point, and determine
if
the ear-
lier
"human cutters" decision is still valid.
13.23 A 3-year-old house can be purchased for an
excellent price
of
$100,000. Remodeling
costs immediately after purchase are esti-
mated to be
$12,000. Taxes will be $3800
per year, utilities will cost $2500 per year,
and the house must be repainted every
6 years
atacostof$1000
. At present, resale
houses are selling for
$60 per square foot,
but this price has been increasing, a trend
that
is
expected to continue, by $1.50 per
square foot per year. The
2500-square-
foot house can be continually leased for
$12,000 per year from this year until it is
sold. A return
of
8% per year is expected
if
the investment is made. (a) Determine how
long the purchaser must own and lease the
house to break even and the anticipated
selling price at breakeven time.
(b) Use
Excel to approximate the breakeven years
and estimated selling price.
13.24 Bovay Medical Labs is evaluating the
alternatives
of
complete and partial
in-house diabetes and associated blood
sugar testing labs, instead
of
outsourcing
samples to an independent laboratory for
analysis. The alternatives and associated
costs are as follows:
Complete lab inhouse:
If
the inhouse
lab is completely equipped, the
initial cost will be
$50,000. A part-
time technician will be employed
at an annual equivalent salary
of
$26,000. Cost
of
chemicals and
464
CHAPTER
13
Breakeven Analysis
supplies is estimated at
$10
per
sample.
Partial lab inhouse:
The
lab can be
partially equipped at an initial cost
of
$35,000.
The
part-time techni-
cian will have an annual equivalent
salary
of
$10,000.
The
cost
of
in-
house sample analysis will be only
$3 per
samp
le.
However
, since
some tests cannot be conducted in-
house, outside testing will be re-
quired at an average cost
of
$40 per
sample for all samples.
Complete outsourcing:
The
cost aver-
ages $120 per sample analyzed.
Any laboratory
equipment
purchased
will have a life
of
6 years.
If
the
MARR
is
10
% per year, determine the number
of
samples that must be tested each year to
justify (a) the complete lab and (b) the
partial lab. (c) Plot the total cost lines for
all three options, and state the range
of
samples for which each option will have
the lowest cost.
(d)
If
Bovay expects to
test
300
samples per year, which
of
the
three options
is
the best economically?
13
.25 The chief engineer
of
Domingo County
is
considering two methods for lining water-
holding tanks. A bituminous coating can be
applied at a cost
of
$8000.
If
the coating is
CASE STUDY
touched up after 3 years at a cost
of
$1
000,
its life can be extended another 3 years.
As an altel11ative, a plastic lining may be
installed with a useful life
of
15
years.
If
the discount rate is 4% per year, how much
can
be
spent for the plastic I ining so that the
two methods
just
break even? Solve (a)
by
hand and (b) by computer.
13.26 A building contractor is evaluating two al-
ternatives for improving the exterior ap-
pearance
of
a small commercial building
that he
is
renovating.
The
building can be
completely painted at a cost
of
$2800.
The
paint is expected to remain attractive for
4 years, at which time repainting is neces-
sary. Every time the building is repainted,
the cost will increase by 20% over the pre-
vious time. As an altel11ative, the building
can be sandblasted now and every
10
years
at a cost
40%
greater than the previous
time.
The
remaining life
of
the building is
expected to be 38 years.
The
MARR
is I 0%
per year. What is the maximum amount that
can be spent now on the sandblasting alter-
native for the two alternatives to
just
break
even? Use present worth analysis (a)
by
hand and (b) by computer to answer this
question. (c) Use the spreadsheet to find the
breakeven value
if
the cost increase for
sandblasting can be reduced from
40
% to
30%,
or
even 20%, each 10 years.
WATER TREATMENT
PLANT
PROCESS COSTS
Introduction
Aeration and sludge recirculation have been practiced
for many years at municipaJ
mld
industrial water treat-
ment plant
s.
Aeration is used primarily for the physical
removal
of
gases or volatile compounds while sludge
recirculation can be beneficial for turbidity removal
and hardness reduction.
When the advantages
of
aeration and sludge recircu-
lation
in
water treatment were first recognized, energy
costs were so low that such considerations were seldom
of
concern
in
treatment plant design and operation. With
the lO-fold increase in electricity cost that occurred
in
some localities, however, it became necessm'y to review
the cost-effectiveness
of
all water treatment processes
that consume significant amounts
of
energy. This study