Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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Future Worth Comparison
5.17 A remotely located air sampling station
can be powered by solar cells
or
by run-
ning an electric line to the site and using
conventional power. Solar cells will cost
$12,600 to install and will have a useful
life
of
4 years with no salvage value. An-
nual costs for inspection, cleaning, etc.,
are expected to be $1400. A new power
line will cost
$11,000 to install, with
power costs expected to be
$800
per
year.
Since the air sampling project will end in
4 years, the salvage value
of
the line is
considered to be zero. At an interest rate
of
10
% per year, which alternative should be
selected on the basis
of
a future worth
analysis?
5.
18
The
Department
of
Energy is proposing
new rules mandating a 20% increase
in
clothes washer efficiency by 2005 and a
35% increase by 2008.
The
20
% increase
is
expected to add
$100
to the current
price
of
a washer, while the 35% increase
will add
$240
to the price.
If
the cost for
energy
is
$80
per year with the 20% in-
crease
in
efficiency and $65 per year with
the 35% increase, which
one
of
the two
proposed standards
is
more economical
on
the basis
of
a future worth analysis at an
interest rate
of
10
% per year? Assume a
15-year life for all washer models.
5.19 A small strip-mining coal company
is
try-
ing to decide whether it should purchase
or
lease a new clamshell.
If
purchased, the
shell will cost $150,000 and is expected to
have a $65,000 salvage value in 6 years.
Alternatively, the
company
can lease a
clamshell for
$30,000 per year,
but
the
lease payment will have to
be
made at the
beginning
of
each year.
If
the clamshell
is
purchased, it will be leased to other strip-
mining companies whenever possible, an
activity that
is
expected to yield revenues
PROBLEMS
205
of$12
,000 per year.
If
the
company
's min-
imum
attractive rate
of
return is
15
% per
year, should the clamshell be purchased
or
leased on the basis
of
a future worth
analysis?
5.20
Three
types
of
drill bits can
be
used
in
a
certain manufacturing operation. A bright
high-speed steel (HSS) bit is the least
ex-
pensive to buy,
but
it has a shorter life than
either gold oxide
or
titanium nitride bits.
The
HSS bits will cost $3500 to buy and
will last for 3 months under the conditions
in
which they will be used.
The
operating
cost for these bits will be
$2000
per month.
The
gold oxide bits will cost $6500 to buy
and will last for 6 months with an operat-
ing cost
of
$1500
per
month.
The
titanium
nitride bits will
cost
$7000
to buy and will
last 6 months with an operating cost
of
$1200
per
month.
At
an interest rate
of
12%
per year, compounded monthly, which type
of
drill bit should be used on the basis
of
a
future worth analysis?
5.21
EI
Paso Electric is considering two alter-
natives for satisfying state regulations re-
garding pollution control for
one
of
its
generating stations. This particular station
is located at the outskirts
of
the city and a
short distance from Juarez, Mexico.
The
station is currently producing excess
VOCs
and oxides
of
nitrogen. Two plans have
been proposed for satisfying the regula-
tors. Plan A involves replacing the burners
and switching from fuel oil to natural gas.
The
cost
of
the option will be $300,000
initially and an extra $900,000
per
year
in fuel costs. Plan B involves going to
Mexico
and running gas lines to many
of
the "backyard" brickmaking sites that now
use wood, tires, and other combustible
waste materials for firing the bricks.
The
idea behind plan B is that by reducing the
particulate pollution responsible for smog
in
EI Paso, there would be greater benefit
206
CHAPTER 5 Prese
nt
Worth Analysis
to U.S. citizens than would be ac
hi
eve
d
through plan
A.
The
initial cost
of
plan B
will be $1.2 million for installation
of
the
line
s.
Additionally, the electric
company
would subsidize the cost
of
gas for the
brick makers to
th
e
extent
of
$20
0,
000
per
yea
r.
Ext
ra air monit
or
ing associated with
this plan will cost an additional $150,
000
per year.
For
a I O-year project period and
no sa
lv
age va
lu
e for either plan, which
one should be selected on the basis
of
a
future worth analysis at an interest rate
of
12
% per
yea
r?
Capitalized Costs
5.22
The
cost
of
pawtlllg the Golden
Gate
Bridge is
$4
00,000.
If
the bridge is painted
now and every 2 years her
eaf
ter, what is
the capita
li
zed
cost
of
painting at an inter-
est
rate
of
6%
per year?
5.23
The
cost
of
extending a certain road at
Yellowstone National
Park
is $
1.7
million.
Resurfacing and o
th
er maintenance are ex-
pected to cost $350,000 every 3 years. What
is the capita
li
zed
cost
of
the road at an
interest rate
of
6% per year?
5.24 Determine the capitalized cost
of
an ex-
penditure
of
$200,000 at time 0, $25,0
00
in
years 2 through 5, and $40,0
00
per year
from year 6 on. Use an interest rate
of
12
%
per year.
5.25 A city that is attempting to attract a profes-
sional footba
ll
team is planning to build a
new stadium costing
$2
50
mi
Ilion. Annual
upkeep is expected to amount to $800,000
per year.
The
artificial
turf
will have to
be replaced every 10 years at a
co
st
of
$950,000. Painting
eve
ry 5 years will
cost
$75,000.
If
the city expects to maintain the
facility indefinite
ly
, what will be its capi-
talized
cost
at an interest rate
of
8% per
year?
5.26 A certain manufacturing alternative has a
first cost
of
$82,000, an annual mainte-
nance
cost
of
$9000
, and a salvage value
of
$15,000 after its
4-year
life. What is its
capitalized cost at an interest rate
of
12
%
per year?
5.27
If
you
want
to be able to withdraw
$80,000
per
year forever beginning
30
years
from now, how much will you
have
to
have
in
your retirement account (that earns
8%
per
year interest) in (a) year 29 and
(b) year O?
5.28
What
is the capitalized cost (absolute
value)
of
the difference between the fo
l-
lowing two plans at an interest rate
of
10
%
per year? Plan A will require an expendi-
ture
of
$50
,000 every 5 years forever (be-
ginning
in
year 5). Plan B will require an
expenditure
of
$100,000 every 10 years
forever (beginning in year 10
).
5.29
What
is
the capitalized cost
of
expendi-
tures
of
$3,
000
,
000
now, $50,
000
in
months 1 through 12, $100,000
in
months
13
through 25, and $50,000 in months 26
through infinity
if
the interest rate
is
] 2%
per year, compounded monthly?
5.30
Compare
the following alternatives on
th
e
basis
of
their capitalized cost at an inter
est
rate
of
10% per year.
Petroleum-
Inorganic-
Based Based
Feedstock Feedstock
First cost, $
-250,
000 -
110
,0
00
Annual operating cost, - 130,000 - 65,000
$/year
Annual revenues,
400,000 270,000
$/year
Salvage value, $
50
,0
00 20,000
Life, years
6
4
5.31
An
alumna
of
Ohio State University
wanted to set up an endowment fund that
would award scholarships to female engi-
neering students totaling
$100,000 per
year forever.
The
first scholarships are to
be granted
now and continue each year for-
ever. How much must the alumna donate
now, if the endowment fund is expected to
earn interest at a rate
of
8% per year?
5.32 Two large-scale conduits are under consid-
eration by a large municipal utility district
(MUD).
The
first involves construction
of
a steel pipeline at a cost
of
$225 million.
Portions
of
the pipeline will have to be re-
placed every
40 years
at
a cost
of
$50 mil-
lion.
The
pumping and other operating
costs are expected to be $10 million per
year. Alternatively, a gravity flow canal
can be constructed at a cost
of
$350 mil-
lion.
The
M&O
costs for the canal are
expected
to
be $0.5 million per year.
If
both conduits are expected to last forever,
which should be built at an interest rate
of
10
% per year?
5.33 Compare the alternatives shown below on
the basis
of
their capitalized costs, using
an
interest rate
12
% per year, compounded
quarterly.
Alte
rnative
Alternative Alternative
E F G
First
- 200,000
- 300,000 - 900,000
cost, $
Quarterly
30,000 10,000 40,000
income,
$/quarter
Salvage 50,000 70,000 100,000
value, $
Life, years
2 4
00
Payback
Analysis
5.34 What
is
meant by no-return payback or
simple payback?
PROBLEMS
207
5.35 Explain why the alternative that recovers
its initial investment at a specified rate
of
return
in
the shortest time
is
not necessar-
ily the most economically attractive one.
5.36 Determine the payback period for an asset
that has a first cost
of
$40,000, a salvage
value
of
$8000 anytime within 10 years
of
its purchase, and generates income
of
$6000 per year.
The
required return
is
8%
per year.
5.37 Accusoft Systems is offering business
owners a software package that keeps
track
of
many accounting functions from
the company's bank transactions sales in-
voices.
The
site license will cost $22,000
to install and will involve a quarterly fee
of
$2000.
If
a certain small company can
save
$3500 every quarter and have the se-
curity
of
managing its books in-house,
how long will it take for the company
to
recover its investment at an interest rate
of
4%
per
quarter?
5.38 Darnell Enterprises constructed an addi-
tion to its building at a cost
of
$70,000.
Extra annual expenses are expected to be
$1850, but extra income will be
$14,000 per
year. How long will it take for the company
to recover its investment at an interest rate
of
10% per year?
5.39 A new process for manufacturing laser
levels will have a first cost
of
$35,000 with
annual costs
of
$17,000. Extra income as-
sociated with the new process is expected
to be
$22,000 per year.
What
is the pay-
back period at
(a) i = 0% and (b) i =
10
%
per year?
5.40 A multinational engineering consulting
firm that wants to provide resort accom-
modations to certain clients is considering
the purchase
of
a three-bedroom lodge
in
upper Montana that will cost $250,000.
208
CHAPTER 5
Pre
se
nt Worth Anal
ys
is
The
property
in
th
at area is rapidly appre-
ciating
in
value because people anxious to
get away from urban developments are
bidding up the prices.
If
the company
spends an average
of
$500 per month for
utilities and the inves
tm
ent increases at a
rate
of
2%
per month, how l
ong
would it
be
bef
ore the company could se
ll
the prop-
erty for
$100,000 more than it has in-
vested
in
it
?
5.41 A window frame ma
nuf
actur
er
is search-
in
g for ways to improve revenue from its
triple-insulated sliding windows, so
ld
pri-
mar
il
y
in
the far northern areas
of
the
United States. Alternative A is an increase
in
TV and radio marketing. A total
of
$300,000 spent n
ow
is
expected to in-
crease revenue by
$60,000 per year. Alter-
native B requires the same
in
vestment for
e
nh
ancements to the in-plant manufactur-
ing process that will improve the tempera-
ture retention properties
of
the seals
around each glass pane. New revenues
start slowly for this alternative at an esti-
mated
$
10
,
000
the first year, with growth
of
$15,000 per year as the improved prod-
uct ga
in
s reputation among builders.
The
MARR is 8% per year, and the maximum
evaluation period is
10
years for either
al
-
te
rn
at
iv
e.
Use both payback analysis and
present worth analysis at 8% (for
10 years)
to select the more economical alternative.
State
th
e reason(s) for any difference in
the alternative chosen between the two
analyses.
Life-Cycle Costs
5.42 A
hi
gh-technology defense contractor has
been asked by the
Pentagon to estimate
the life-cyc
le
cost (LCC) for a proposed
li
ght-duty support vehicle. Its
li
st of
items
in
cluded the following general
catego
ri
es:
R&D
costs (
R&D
),
nonrecur-
ring
in
vestm
ent
(N RI) costs, recurring
Year
o
I
2
3
4
5
6-
10
lion
1
8-20
5.43
invest
ment
(RI) costs, scheduled and un-
scheduled maintenance costs (Maint),
equipment usage costs (Equip), and
di
s-
posal costs (Disp). The costs (
in
millions)
for the
20-year life cycle a
re
as indicated.
Calculate the
LCC
at an interest rate
of
7% per year.
R&D NRI
RI
Maint
Equip
Disp
5.5 I.J
3.5
2.5
0.5 5.2
1.3
10
.5
3.1
10
.5
4.2
6.5
2.2
0.6
1.4
1.
6
2.7
3.5
1.5
3.6
5.3
7.8
8.5
2.7
A manufacturing software engineer at a
major aerospace corporation has been as-
signed the management responsibility
of
a
project to design, build, test, and
imple-
ment AREMSS, a new-generation auto-
mated scheduling system for routine and
expedited maintenance. Reports on
th
e
disposition
of
each service will also be en-
tered by field personnel, then filed and
archived by the system. The initial appli-
cation will be on existing Air Force in-
flight refueling aircraft. The system is
expected to be widely used over time for
other
ai
rcraft maintenance scheduling.
Once it is fully implemented, enhance-
ments will have to be made, but the sys-
tem is expected to serve as a worldwide
scheduler for up to
15
,0
00
separate air-
craft.
The
engineer, who
mu
st make a pre-
sentation next week
of
the best estimates
of
costs over a
20
-year life period, has de-
cided to use the life-cyc
le
cost approach
of
cost estimations. Use the following infor-
mation to determine the current
LCC
at
6% per year for the AREMSS scheduling
system.
Cost
in
Year ($ Millions)
Cost
Category
1 2 3 4 5 6
on
10
Field study 0.5
Design
of
system
2.1
1.2 0.5
Software design 0.6 0.9
Hardware
purchases
5.1
Beta testing
0.1
0.2
User's manual
development
0.1 0.1
0.2 0.2 0.
06
System impl
eme
n-
tation
1.3
0.7
Field hardware 0.4
6.0
2.9
Training trainers
0.3
2.5
2.5
0.7
Software upgrades
0.6 3.0
5.44
The
U.S. Army received two proposals for
a turnkey design-build project for barracks
for infantry unit soldiers
in
training. Pro-
posal A involves an off-the-shelf bare-
bones
de
sign and standard-grade construc-
tion
of
walls, windows, doors, and other
features. With this option, heating and
cooling costs will be greater, maintenance
costs will be higher, and replacement will
be sooner than for proposal B.
The
initial
cost for A will be
$750
,
000
. Heating and
cooling costs
wi
ll
average
$6000
per
month, with maintenance costs averaging
$2000 per month.
Minor
remodeling will
be required in years 5,
10
, and 15 at a cost
of
$\50
,000 each time
in
order to render
the units usable for
20
years. They will
have no salvage value.
Proposal B will include tailored design
and construction costs
of
$1.\
million ini-
tially, with estimated heating and cooling
costs
of
$3000 per month and mainte-
nance costs
of
$1000
per month.
There
will be no salvage value at the end
of
the
20-year
li
fe.
Which proposal should be accepted on
the basis
of
a life-cycle cost analysis,
if
the
interest rate is 0.5% per month?
18
3.7
PROBLEMS
209
5.45 A medium-size municipality plans to de-
velop a software system to assist
in
project
selection during the next 10 years. A I ife-
cycle cost approach has been used to
categorize costs into development, pro-
gramming, operating, and support costs for
each alternati ve. There are three alternati ves
under consideration, identified as A (tai-
lored system), B (adapted system), and C
(current system).
The
costs are summarized
below.
Use
a life-cycle cost approach to
identify the best alternative at 8% per year.
Cost
Alternative
Component
Cost
A Development $250,000 now,
$150,000 years 1
through 4
Programming
$45,000
now,
$35,0
00
years I, 2
Operation
$50,0
00
years I
through
10
Support $30,0
00
years I
through 5
B
Development
$
10
,000 now
Programming
$45,000
year 0,
$30,000
years I
through 3
Operation
$80,000 years I
through
10
Support $
40
,
000
years 1
through 10
c
Oper
ation
$175,
000
years I
through
10
Bonds
5.46 A mortgage bond with a face value
of
$10,000 has a bond interest rate
of
6%
per year payable quarterly.
What
are the
amount and frequency
of
the interest
payments?
5.47
What
is the face value
of
a municipal
bond that has a bond interest rate
of
4% per
year with semiannual interest payments
of
$800?
210
CHAPTER
5 PresenL Worth Analysis
5.48 What is the bond interest rate on a $20,000
bond that has semiannual interest payments
of
$1500 and a 20-year maturity date?
5.49
Whatis
the present worth
ofa
$50,000 bond
that has interest
of
10% per year, payable
quarterly? The bond matures
in
20 years.
The
interest rate
in
the marketplace is
10
%
per year, compounded quarterly.
5.50 What is the present worth
of
a $50,000
municipal bond that has an interest rate
of
4% per year, payable quarterly?
The
bond matures in
15
years, and the market
interest rate
is
8% per year, compounded
quarterly.
5.51 General Electric issued
1000 debenture
bonds 3 years ago with a face value
of
$5000 each and a bond interest rate
of
8%
per year payable semiannually.
The
bonds
have a maturity date
of
20 years from the
date they were issued.
If
the interest rate
in
the market place is 10%
per
year, com-
pounded semiannually, what is the present
worth
of
one bond to an investor who
wishes to purchase
it
today?
5.52 Charleston Independent School District
needs to raise
$200 million to refurbish
FE
REVIEW PROBLEMS
5.54
For
the mutually exclusive alternatives
shown below, determine which one(s)
should be selected.
Alternative
A
B
C
D
Present
Worth,
$
- 25,000
- 12,000
10,000
15
,000
its existing schools and build new ones.
The
bonds will pay interest semiannu-
ally at a rate
of
7%
per year, and they will
mature in
30
years. Brokerage fees asso-
ciated with the sale
of
the bonds will
be
$1
million.
If
the interest rate
in
the
marketplace rises to 8% per year, com-
pounded semiannually, before the bonds
are issued, what will the face value
of
the
bonds have to be for the school district to
net $200 million?
5.53 An engineer planning for his retirement
thinks that the interest rates in the market-
place will decrease before he retires.
Therefore, he plans to invest
in
corporate
bonds.
He
plans to buy a $50,
000
bond
that has a bond interest rate
of
12
% per
year, payable quarterly with a maturity
date
20
years from now.
(a) How much should he be able to sell
the bond for in 5 years
if
the market
interest rate is 8% per year, com-
pounded quarterly?
(b)
If
he invested the interest
he
received
at an interest rate
of
] 2% per year,
compounded quarterly, how much
will he have (total) immediately after
he sells the bond 5 years from now?
(a) Only A
(b) Only D
(c) Only A and B
(d)
Only C and D
5.55 The present worth
of
$50,000 now,
$10,000
per
year
in
years I through
15
,
and
$20,000 per year
in
years 16 through
infinity at 10% per year is closest to
(a) Less than $169,000
(b) $169,580
(c)
$173,940
(d)
$195,730
5.56 A certain donor wishes to start an endow-
ment at her alma mater that
wi
ll
provide
scholarship money
of
$40,000
per year be-
ginning
in
year 5 and
cont
inuing indefi-
nitely. If the university earns
10% per year
on the endowment, the
amount
she must
donate now is closest to
(a) $225,470
(b) $248,360
(c) $273,200
(d)
$293,820
5.57
At
an interest rate
of
10
% per year, the
amount you must deposit
in
your retire-
ment account each year
in
years 0 through
9
(i
.e.,
10
deposits) if you want to with-
draw $50,000 per year forever beginning
30
years from now
is
closest to
(a) $4239
(b) $4662
(c) $4974
(d)
$5471
Problems 5.58 through 5.60 are based on the
following estimates.
The
cost
of
money is
10
%
per year.
Initial cost, $
Annual
co
st, $/y
ear
Sa
lvage va
lu
e, $
Life, years
Machine X
- 66,000
-
10
,000
10
,000
6
Machine Y
- 46,000
- 15,000
24,000
3
5.58
The
present worth
of
machine X is closest
to
(a) $- 65,270
(b)
$-
87
,840
(c)
$-
10
3,9
10
(d)
$-
114
,3
10
FE
REVIEW
PROBLEMS
211
5.59 In comparing the machines on a pre
se
nt
worth basis, the present worth
of
machine
Y is closest to
(a)
$-65
,270
(b)
$-97
,840
(c)
$-103,910
(d)
$-
114
,310
5.60
The
capitalized cost
of
machine X is
clo
s-
est to
(a) $-
103
,910
(b) $- 114,310
(c) $- 235,990
(d)
$- 238,580
5.61 The cost
of
maintaining a public monu-
ment
in
Washington, D.C., occurs as peri-
odic outlays
of
$10,000 every 5 years.
If
the first outlay is now, the capitalized cost
of
the maintenance at an interest rate
of
10% per year is closest to
(
a)
$- 16,380
(b)
$-
26,380
(c) $- 29,360
(d)
$-41
,
050
5.62
The
alternatives shown below are to be
compared on the basis
of
their capita
li
zed
costs. At an interest rate
of
10% per year,
compounded continuous
ly
, the equation
that represents the capitalized
co
st
of
alter-
native A is
First
co
st, $
Annua
l
cost
, $/year
Sa
lv
age
va
lu
e, $
Life, years
Alternative
A
Alternative
B
-50
,000
-
10
,000
13,000
3
- 90,000
- 4,000
15
,000
6
(a) PW
A
= - 50,000 -
1O
,000(P/ A,
10.52%,6) -
37
,000(P/ F,I 0.52%,3)
+ 13,000(P / F, I 0.52%,6)
(b)
PW
A = -
50
,
000
-
IO
,
OOO(P
/ A,
10
.52%,3) +
13
,
OOO(P
/ F,
10.52%,3)
212
CHAPTER
5
Present Worth Analysis
(c)
PW
A
= [- SO,000(A/P,10.S2%,
3)-
10,000 +
13,000(A/F,10
.
S2
%,3)]/
0.IOS2
(
d)
PW
A = [-SO,OOO(A / P,
LO
%
,3
) -
10
,
000
+ 13,000(A/
F,10
%,3)]/ 0.1O
S.63 A corporate bond has a face value
of
$10
,
000
, a bond interest rate
of
6% per
year
payable semiannually, and a maturity
date
of
20
years from now.
If
a person pur-
chases the bond for
$9000
when the inter-
est rate
in
the marketplace is 8% per year,
compounded
semiannually, the size and
frequency
of
the interest payments the
person will receive are
closest
to
(a)
$270
every 6 months
(b)
$300
every 6 months
(c)
$360
every
6 months
(d)
$400
every 6 months
S.64 A municipal bond that was issued 3 years
ago has a face value
of
$SOOO
and a bond
interest rate
of
4% per
year
payable semi-
annually.
The
bond has a maturity date
of
EXTENDED EXERCISE
20
years
from
the date it was
issued
.
If
the
interest rate in the marketplace is 8% per
year,
compounded
quarterly, the value
of
n
that must
be
used in the PIA equation to
calculate the present worth
of
the bond
is
(a)
34
(b)
40
(c)
68
(d)
80
S.
6S
A
$10,000
bond
has an interest rate
of
6%
per
year
payable quarterly.
The
bond ma-
tures 1
S years from now. At an interest rate
of
8% per year,
compounded
quarterly,
th
e
present worth
of
the bond is represented
by which
of
the equations below
(a)
PW
=
ISO(P/A
,l.S%,60) + 10,000
(P
/
F,l.S
%,60)
(b)
PW
= ISO(P/
A,2
%,60) +
10
,
000
(P
/ F,2%,60)
(c)
PW
=
600(P/A,8%
,
lS)
+ 10,000
(P/F,8
%
,IS)
(d)
PW
=
600(P
/ A,2
%,
60) +
10
,
000
(P
/ F,2%,60)
EVALUATION OF SOCIAL SECURITY
RETIREMENT ESTIMATES
Charles
is
a senior
engineer
who
has worked for
18
years since he graduated
from college. Yesterday in the mail, he received a report from the
U.S. Social
Security Administration. In short, it stated that
if
he continues to earn at the
same
rate, social security will provide him with the following estimated monthly re-
tirement benefits:
• Normal retirement at age 66; full benefit
of
$IS00
per month starting at
age 66.
• Early retirement at
age
62; benefit reduced by
2S
% starting at
age
62.
•
Extended
retirement at age 70; benefit increased by
30
% starting at
age
70.
Char
les never thought much about social security; he usually thought
of
it as a
monthly deduction from his paycheck that helped pay for his parents' retirement
CASE
STUDY
benefits from social security. But this time he decided an analysis should be per-
formed. Charles decided to neglect the effect
of
the following over time: income
taxes, cost-of-living increases, and inflation. Also, he assumed the retirement
benefits are all received at the end
of
each year; that is, no
compo
unding effect
occurs during the year. Using an expected rate
of
return on investments
of
8%
per
year and an anticipated death
just
after his 85th birthday, use a spreadsheet to do
the fo
ll
owing for
Char
les:
I. Calculate the total future worth
of
each benefit scenario through the age
of
85.
2. Plot the annual accumulated future worth for each benefit scenario through
the
age
of
85.
The
report also mentioned that
if
Charles dies this year, his spouse is eligible at
full retirement age for a benefit
of
$1600
per
month for the remainder
of
her life.
If Charles and his wife are both
40
years old today, determine the following
about his wife's survivor benefits, if she starts at age 66 and lives through her
85th birthday:
3.
Present worth now.
4. Future worth for his wife after her 85th birthday.
CASE
STUDY
PAYBACK EVALUATION OF ULTRALOW-FLUSH TOILET PROGRAM
213
Introduction
Tn
many c
iti
es
in
the southwestern part
of
the United
States, water is being withdrawn from subsurface
aquifers faster than it
is
being replaced.
The
attendant
depletion
of
groundwater supplies has forced
some
of
these cities to lake actions ranging from restrictive
pricing policies to mandatory conservation measures in
residential, commercial,
an
d industr
ial
establishment
s.
Beginning
in
the mid-1990s, a city undertook a project
to encourage insta
ll
ation
of
ultralow-flush toilets
in
existing houses. To evaluate the cost-effectiveness
of
the program, an economic analysis was conducted.
unit), providing the toilet used no more than 1.6 ga
ll
ons
of
water
per
flush. There was no limit on the number
of
toilets any individual
or
business could have replaced.
Background
The
heart
of
the toilet replacement program involved a
rebate
of
75%
of
the cost
of
the fixture (up to $100 per
Procedure
To evaluate the water savings achieved (if any)
through the program, monthly water use records were
searched for 325
of
the household participants, repre-
sent
in
g a sample size
of
approximately 13%. Water
consumption data were obtained for
12
months before
and
12
months after installation
of
the ultralow-flush
toilets.
If
the house changed ownership during the
evaluation period, that account was not included
in
the evaluation. Since water
co
nsumption increases
dramatically during the hot summer months for lawn
watering, evaporative cooling,
car
washing, etc., only
214
CHAPTER 5
Present Worth Analysis
th
e winter months of December, Januar
y,
and February
were used to eva
lu
ate
wat
er consumption before
and
af
ter installation of the
toi
let. Before any calcu-
la
ti
ons were made,
hi
gh-vol
um
e water us
er
s (usually
bu
s
in
esses) were
sc
reened out by eliminating all
records whose av
er
age monthly consumption ex-
ceeded
50
C
CF
(I CCF = 100 cubic feet = 748 gal-
lons). Additionally, accounts which had monthly av-
erages of 2 CCF or less (either before or after
in
ta
ll
a
ti
on) were also eliminated because it was be-
li
eved
th
at such low consumption rates probably rep-
resented an abno
rm
al condition, such as a house for
sale w
hi
ch was vacant during pa
rt
of
the study
pe
ri
o
d.
The 268 records that remained after the
screening proce
dur
es were
th
en used to quantify the
effectiveness of
th
e program.
Results
Water Consumption
Monthly consumption before and after
in
stallation
of
the ultralow-flush to
il
ets was found to be 11.2 and
9. 1 CCF, respec
ti
vel
y,
for an average reduction
of
18.8%. When only
th
e months
of
January a
nd
Febru-
ary were used
in
the befo
re
and after calculations, the
respective values were
11.0 and 8
.7
CCF
, resulting
in
a water sav
in
gs rate
of
20.9%.
Economic Analysis
The fo
ll
owing ta
bl
e shows some
of
th
e program totals
through
th
e
fir
st I
Y.
years of the progra
m.
Program Summary
Number of househo
ld
s pa
rti
cipating
Number of toi lets re
pl
aced
Number
of
persons
Average cost of toilet
Average rebate
2466
4096
7981
$l15.83
$76.
12
The results
in
th
e previous sec
ti
on indicated monthly
water sav
in
gs of 2
.1
CCF. For
th
e average program
participan
t,
the payback period
/1.
1'
in
years with
/1.0
in-
terest considered is c
al
c
ul
ated us
in
g Equation l5.7].
net cost
of
toi lets +
in
stallation cost
n
l
}
=
----'..:....:...::.=-:--'--'-'...:.--'--"'----'--"--'--'--'---=...:..:...-
-
net annual
sa
vings for water and s
ew
er charges
The lowest rate
bl
o
ck
for water charges is $0.76 per
CCF. The s
ewer
surchar
ge
is $0.62 per CCF. Using
these values and a
$50 cost for installation, the pay-
back period is
(
115
.83 - 76.12) + 50
(2
.1
CCF/month
X 12 months) X
(0.76 +
0.62)/CCF
= 2.6 years
Less expensive toilets or lower installation cos
ts
would reduce the payback period accordingly, while
consideration
of
the time value
of
money would
lengthen
it.
From the standpoint
of
the utility which supplies
water,
thecostofthe
program must be compared against
the marginal cost of water delivery and wastewater
trea
tm
ent.
The
mar
ginal cost c may be represented as
cost
of
rebates
c =
---------------
volume
of
water not delivered
+ volume
of
wastewater not treated
The
ore
ti
call
y,
the reduction
in
water consumption
would go on for an infinite period
of
time, since
replacement wilI never be with a less efficient model.
But
for a worst-case condition,
it
is
assumed the toilet
would have a
"productiv
e"
life
of
only 5 years, after
which it would leak and not be repaired. The cost to
the city for the water not deljvered or wastewater not
treated would be
$76.12
c =
---
-
---~----------
(2.1 + 2.1
CCF/month)(l2
months)(5 years)
$0.302 $0.40
=
-----
or
CCF
LOOO
gallons
Thu
s,
unless the city can deliver water and treat the
resulting wastewater for less than
$0.40 per 1000
gallon
s,
the toilet replacement program would be
considered economically attractive. For the city, the
operating costs alone, that is, without the capital ex-
pense, for water and wastewater services that were not
expended
wereabout
$
l.l
0 per 1000 gallons, which far
exceeds $0.40 per 1000 gallons. Therefore, the toilet
replacement program was clearly very cost-effective.