Thereis no set formula for dividing the
revenueshortfall betweenusers.In this casethe
utility decidesto apportion 60Toof the shortfall
to residentialconsumersand 4OTa
to industrial/commercial consumersas follows:
Summary
. . Thg plcilg schedulefor this examplearea
is given in Table23.
This rate scheduleresultsin an annual cost
savingsof $9052 820for the utility from current
levelsand enablesexpansionto bê detayedby
sev-era,l
years. Peak period use dechneiby 26Vo
and off-peakuse by 21,70.With the addition of a
fixed connectioncharge,revenuesare sufficient
to recovertotal annual costs.
.60 x $13138300= $7 882980residential
connection charges
.40 x $13 138300 = $5 255320industrial/
commercial connection charges
The residential fixed connection charge per
customer works out as follows:
CASETWO: A MID-S|ZED
COMMUNtTy
$7882980/ 325000connections= $24.2iper
household
GeneralSetting
A total of $5 255 320 remains to be recovered from commercial/industrial water users.
The utility allocates 307aof this to the 200 large
volume industrial users:
. This water supply utility suppliesa midsrzedcommunity with a population of about
60 000. It has 37 500connectionsto the water
system,including 35 000residentialconnections
and 2 500small industrial/commercial establishments.The community operatesthe waterworks and is responsibleforàll expenses,
including operation,bill collection,administration, and regulation. In the most recentyear of
ope.ra
ti on,-the u tili ty deliv ered approximately 25
million cubic metresof water, with tZ million cubic metresdelivered during the peak period and
13 million delivered in the-off-pôakpôriod.
$5 255320x .30/ zffi = $7 883per large volume
industrial user
The remainr-ng $3 678724 is divided evenly
between the 4 000 smaller industrial/commercial establishments:
g3 678 320 / 4000 = $920per connection
Table 23
Summary of RateSchedule,Case 1
Off-peak charge
Peak charge
Fixed connection charge
Amount
$0.109,/m3
for all customers
$0.124lm3
for all customers
$24.25 per household
$920 per small industry or
commercial connection
$7883 per large volume industrial
connection
Period
Sept. 15 to May 15
May 15 to Sept. 15
Single annual charge
Basis
Marginal operating cost of water
Marginal capacity cost of water
Covers all other costs
supply
plus
Marginal cost of wastewater
treatment
supply
plus
Marginal operating cost of water
supply
plus
Marginal cost of wastewâter
treatment
u
L
t;
Table25 shows the itemized annual expenditure of the utility on operationsand maintenance.
Wateris withdrawn from an impoundment reservohon a river and delivered to the surroundingcommunityfollowing treatmentin a central
plant.Pumpingcostsare relatively high because
of the low elevationof the water source
relativeto the community served. Treatment
costsarealsoquite high. Peakperiod use in
June,July,August, and Septemberresultsin the
majordemandson the system.
Table 25
Water Supply Costs:Detailed Operations
and MaintenanceBudget, Case2
the
With an annual growth rate of 1.5Vo,
communitymust plan for expansionof its water
supplyover the long term. The next major capital expansionof the water systemwill occurin
fourto five years.
Budget
Salaries
Electricity
Chemicals
Vehicle operation
Equipment replacement
Wastewatergoesthrough a secondarytreatmentprocess.Total wastewatertreatedis about
25million cubic metres,similar in volume to the
amountof water supplied to customers.The initialcapitaloutlay was high for this system,but
regionalplanners feel that it has adequatecapacity for another10 years,given projectedgrowth
ratesof the community.
Provincial water taxes
Miscellaneous costs
Insurance
Total
Customerscurrently pay a flat rate for unlimitedaccessto water and for treatmentof
wastewater.
Table 24
Labour costs,which constitutethe most significant singleitem of the O&M budget, contain
both fixed and variablecomponents. The utility
estimatesthat about half of the labour work in
activitiesdependenton the amount of water delivered. Theseactivitiesinclude somemechanical repairs,systemmonitoring, quality control,
and purification. The remaining half of the
labour work in activitiessuch as regularly
Annual Water Supply Budget, Case2
Budget
Total
$3 350000
s2 500000
As in the previous example,many of the
O&M expendituresvary with water volume.
Chemicalcostsvary directly with pumpage and
thus fall whollv within the variable costcategory. Provinciâlwater taxesare also variable,
sincethe size of the tax varieswith the amount
of water intake.Pumping consumesmost of the
electricitycosts. Accordingly,9SToof this expenditure makesup an elementof variable cost.
Seventy-fivepercentof the equipment replacement costsare also variable,sincethey relateto
pump maintenance,a function of the âmount of
water pumped.
Annual costsfor the utility total $3.35million(Table24). This annual expenditurebudget
represents
the current cashrequirementsfor opand debt charges.The current water
erations
ratesmakeno provision for future capital expendituresrelatedto systemexpansion;this will requirea substantialcost increasewhen expansion
occurs.
$2 500000
850000
40 000
200000
10 000
ClassifyingCurrentCostsinto Fixed,Variable,and
DebtPayment
Current
Costsof WaterSupply
Operation and maintenance
Debt charges
$ 8400m
600000
110000
50 000
650000
55
Table 27
scheduledmaintenance,inspection,and administration,which are classified as fixed costs.
Annual WastewaterTreatmentBudget,
Case2
The remaining items on the operations
budget are fixed. Theseinclude vehicleoperation, insurance,and miscellaneouscosts.
Budget
Item
Variable costsaccordingly total $1 660000,
fixed costs$840000,and debt charges$850000
Oable 26).
Operation and maintenance
Debt charges
$1 670000
1 600000
Total
$3 270000
Table 26
Annual Variable,Fixed, and Debt Payment
Costs ($) for Water SuPPlY,Case2
Table 28
Item
Fixed
costs
Variable
costs
Total
costs
420000
570000
110000
840000
600000
110000
50 000
520000
650000
40 000
40 000
200000
10000
Salaries
Electricity
Chemicals
Vehicle operation
420000
30 000
Equipment replacement
Provincial water
taxes
Miscellaneous costs
Insurance
130000
Subtotal
Debt charges
840000 1 660000 2 500000
850000
850000
Total
50 000
200000
10000
WastewaterTreatmentCosts:Detailed
Operationsand MaintenanceBudget, Case2
Budget
Salaries
Chemicals
Other materials
Purchased services
Purchased repairs
Energy
General administration
1 690000 1 660000 3 350000
Total
$ 7000t)0
100000
300000
100000
30 000
400000
40 000
$ 1 670000
ClassifyingWastewaterTreatment Costs into
Fixed,Variable,and DebtPaYment
CurrentCosts of WastewaterTreatment
The utility's annual budget for wastewater
treatmentis shown in Table 27.This budget representscurrent cashrequirementsand doesnot
make a provision for future expansion.
Debt chargesare classifiedas fixed costsin
the short run. Other items from Table 28 that
fixed costsare generaladare considered1.00Vo
ministration,purchasedservices,and other
materials.
The operationand maintenancecostsin
Table27 shbuld be apportionedbetweenfixed
and variablecostsas was done in previous examples. A detailed breakdown of the operation
ànd maintenancecostsis given in Table28.
About 'l\Voof the salariedlabour is involved with activitiesthat are dependenton the
short-runvolume of wastewatertreated. Two
56
thirdsof.thepurchasedrepairsare for pump
andmachmerymaintenance/which is directly re_
latedto the volume of wastewater. About 10%
ofthechemicaluse is consideredvariable,with
theremaininggg9rc
fixed. Energyis the rnajor
variablecost,with 95Vovarjabtè. fne remaining
5%of the energyis used for fixed functions,
l!çltT lighting and heating. Variablecosrstotal
000and fixed costs(iniluding debt pay$515
ment)equal92755000 0able 29)."
Expalsion costswere defined as the equiva, .
lent annual payment of future expenditureson
capacityexpansion.Table30 shows the annual
expansioncostsbasedon the capital expendifure
plan for the water utility. An inierestràte of
72Vo,which is the current borrowing rate for the
utility, is used.The projectedcapital expendituresincludeallowancesfor inflation. The present value and equivalent annual paymentswere calculatedusing equations(2) âna (3) from
Chapter3.
Annual Variable, Fixed, and Debt payment
Costs ($) for Wastewater Treatment, Ôase 2
Debtpayment
Salaries
Chemicals
Othermaterials
Purchasedservices
Purchasedrepairs
Energy
Generaladministration
Total
1 600000
595000
90 000
300000
100000
10000
20 000
40 000
2755W
For any level of water demand or wastewater volume, the variablecostsare calculatedbv
multiplying the amount of water delivered or
treatedby the unit variablecost.This method of
calculationis used over the range of water delivery and wastewatervolumes specifiedin the section on determining total cost curves (p. Sg).
Calculating
ExpansionCostsovera Rangeof Water
Demand
Table 29
Fixed
costs
CalculatingVariableCostsover a Rangeof Water
Demand
Variable
costs
105000
10000
Total
costs
1 600000
700000
100000
300000
100000
20 000
380000
30 000
400000
40 000
Table 30
515000 3 270offi
ProjectedCapital Costs ($) of
Capacity Expansion,Case2
Year
Calculating
the Unit VariableCost
1
2
Theunit variablecost of water supply is
foundby dividing the total variablecostsbf
watersupply by the amount of water delivered
duringtheyear.The calculationis thus:
J
^
5
o
7
8
o
l0
$1660ffiO / 25000000m3= $0.066/m3
Theunit variable cost of wastewatertreat_
mentis found in a similar fashion,dividing the
totalvariablecostsof wastewatertreatmeritby
thevolumeof wastewatertreated:
Present value
at 12%
Equivalent annual
expansion cost
$515000/ 25ffiO000m3= $0.021lm3
JI
Water supply
costs
0
0
Wastewater
tfeatment costs
200000
500000
0
0
0
0
0
300000
0
200000
I 500000
300000
0
0
0
0
r 500000
| 434820
482960
253940
85 476
U
The annual expansion costs of $253 940 are
based on the current peak period water demand
of 12 million cubic mètres. In order to calculate
the costs at lower levels of water use, the effect
of a demand reduction on expansion plans must
be examined. By lowering demand, the need for
capacity expansion will be delayed. As outlined
inttrapter 3, delaying expansion will-reduce the
equivalent annual costs of financing the expansion.
treated. This volume is predicted to grow at a
per annum. For eachlong-term rerate of 1,.57o
duction in vôlume of 1"57o,the expansionplans
canbe delayedby one year, thus reducing-the
equivalentâttn,tâlexpânsioncosts(Table32)'
Table 32
Annual ExpansionCosts for Different
Volumes of WastewaterTreatment,Case2
The expansion plan for the rltility is based
on a projectèd annuâl increase of 7.5% in water
consùmption in both peak and off-peak periods'
Reducing demand by the equivalent of one
year's grôwth delays expansion for one year,.
ând reàuces financial costs accordingly. Table
31 shows the effect on the annual expansion
costs of incrementally reducing demand in peak
periods bv 1.SVofrom the current level. For each
ieduction in demand, expansion has been delaved, and the present values and equivalent annuat payments have been recalculated with the
rescheduled exPansion.
Wastewater treated
(m3)
Table 31
Annual ExpansionCostsfor Various Levels
of Peak Period Water SuPPlY,Case2
Water supplied
(mt)
Amortized annual
pa).rnent ($)
12000000
11820000
11 640000
11460000
11280000
253 940
226732
202 439
180 749
161383
11 100000
10920000
10740000
10 560000
10380000
7M092
128 654
114869
702 562
97 573
Amortized annual
payment ($)
25 000m0
24 625W
24 250000
23 875æ0
23 500000
85 476
76 318
68 141
60 840
54 322
23 125000
22 750WJ
22 375N0
22 000m0
21 625000
48 501
43 305
38 65
34 522
30 824
21 250000
20 87s000
20 500000
20 125000
19 750000
27 527
24 572
21 940
19 589
17 490
19 375000
19 000000
18 625000
18250000
17 875000
1 56 1 6
73 943
72 M9
1 11 1 5
9 924
17 500000
17 125000
16 750000
16375000
16 000000
I 861
7 912
70&
6 347
5 631
15 625000
15250000
14 875000
5 028
4 489
4 008
Determiningthe Total Cost Curves
The expansioncostsof wastewatertreatment over a range of wastewatervolume are calculatedin a similar manner. The presentannual
wastewaterexpansioncostsof 585476are based
on an annual volume of 25 million cubic metres
The analystshould now have sufficient information to calculatethree total costcurves:
peak period water supply, off-peak water sup-
58
ply,and wastewatertreatment. The procedure
basicallyinvolves adding up the variàble,fixed,
andexpansioncostsfor èachlevel of water supply or wastewatertreatment.
Table 34
Total Costs ($) of Off-PeakPeriod Water
Supply, Case2
In,thgpeak periods,total costsof water sup, .
pll.includecapacitycostsplus variablecosts
(Table33). In the ofi-peak period, costsinclude
variablecostsonly (Tablea4). ffre fixed costs
canbeincludedin eithercategoryor divided be_
tweencategorieswithout affeitirie the price cal_
culations.Following the procedule ouilined in
Chapter4, thelixed costsof water supply, including.the debt costs,are divided eqïàtiy Uetweenthepeak and off-peak periods. Thé
variablecostsare calculàtedtiy multiplying the
amountof water suppliedby lhe unit vâriàble
costof $0.0664per cubic mel.e.
Current
demand
(mt)
Total costsfor wastewatertreatmentare the
9u19f the variable,fixed, and expansioncosts
(Table35). Variable costsare thebroduct of the
unit variablecostof $0.021timesthe volumeof
Totd Costs lD oJ Pea* Petjoà )Ualc-r-9upp)V fae2
Expansion
COSTS
Fixed
costs
Variable
Total
costs
COSTS
253 940
226 732
202 439
180 749
161383
845000
845000
845000
845000
845000
796 800
784 848
772 896
760 9U
748 992
1 895 7û
1 856 580
1 820 335
1 786 693
11100000
10920m0
10740m0
10560000
l0 380000
lM 092
128 654
114 869
102562
91 573
845000
845000
845000
845000
845000
737 040
725 088
773 136
701 784
689232
1 726 132
1 698 742
7 673 005
1 648 746
1 625 805
10200000
10020000
9 840000
9 660000
9 480000
81 250
72 545
64n2
57 832
51 634
845000
845000
845000
845000
845000
677 280
665 328
6s3 376
647 424
629 472
r 603 530
1 582 873
1 563 1,18
1 532 3M
7 526 lM
9 300000
9 120000
8 940000
8 760000
8 600000
46 703
41 164
845000
845000
845000
845000
845000
ol/
605 568
593 676
587 664
569712
1 508 623
1 491 732
1 475 369
1 459 480
| 444 072
32 876
29 300
Total
13 000000
12 500000
12 000000
11 500000
11 000000
845000
845000
845000
845000
845000
863200
830000
7968ffi
763 600
730400
77æ2æ
1 675000
1 641800
1 608600
7 5754û
10 500000
10 000000
9 500000
9 000000
8 500000
845000
845000
845000
845000
845m0
697200
664000
630800
5976N
5644N
1 5422m
l 509000
1 4758n
1M2ffi
1 409400
COSTS
??fufufu1coslcurves {or water
supply and for wastewatertreatment
are displayed in Figure 42.
12000000
11820000
11640000
11460000
11280000
JO /J5
Variable
costs
wastewatertreated. Fixed costs,from
Table 29, total fi2755000. Expansion
costswere previously calculatedin
Table32.
Table 33
Current
demand
(mt)
Fixed
costs
Jll)
I /'J
59
J/5
Determining
the MarginalCost Curves
The analystcan now derive the
marginalcostcurvesfor peak period
water supp.ly,off-peakpèriodïater
supply/and wastewatertreatment.
Given the information containedin
the total costcurves,derivation of the
marginal cost curvesis quite straight_
forward.
The marginal cost fltrve of water
supply in the peak period,composed
ot ma.rginaloperatingcostsplus the
marginalcapacitycost,is foûnd bv
taking the slopeôf tne peak perioâ
water supply total costcurvé,and
plottingthe valueagainstthe volume
ot rvaterdelivered. This procedure
has beencarried out in Figure 43. At
any point along the x-axisin the lower
figure,the value of the marginalcost
Table 35
Total Costs ($) of WastewaterTreatment, Case 2
Volume
treated
(m3)
Expânsion
costs
Fixed
costs
Variable
costs
Total
costs
25 000m0
24 6250J0
24 250000
23 875û)0
23 500m0
85 476
76 318
68 141
60 840
54 322
2 755000
2 755000
2 755000
2 755000
2 7550m
515000
507275
499550
491825
484100
3 355476
3 338593
3 32269"1
3 307665
3 293 422
23 125000
22 750N0
22 375ùN
22 000m0
21 625000
48 501
43 305
38 4.65
'i22
34
30 824
2 7550m
2 755000
2 755Un
2 7550ùl
2 755000
476375
468650
460925
453200
M5 475
3 279876
3 26 955
3 254590
3 242722
3 23'I 299
21 250m0
20 875000
20 500000
20 r25 000
19750000
27 52r
24 572
21 940
19 589
17 490
2 755000
2 7550gJ
2 755000
2 755000
2 755000
437750
430025
422300
414575
406850
3 220271
3 26 597
3 199240
3 189164
3 1n 34)
19375ù)0
19 000000
18 625000
18250m0
17875ù)0
1 56 1 6
13 943
12 M9
1 11 1 5
9 924
2 755000
2 755000
2 755000
2 755000
2 755000
399125
39r 400
383675
375950
3æ 225
3 169741
3 160343
3 15L124
3 142065
3 133149
17500tto
17 125000
16750000
16375000
16m0 000
8 E61
7 912
7064.
6 307
5 631
2 755000
2 755000
2 755000
2 755000
2 755000
360500
352775
345050
337325
329600
3 124361
3 1 1 56 E 7
'107
3
114
3 098632
3 090232
15 625000
15250000
14 875000
5 028
4 489
4 ofhl
2 755000
2 755000
2 755oUJ
321875
314150
306425
3 081900
3 073639
3 0â5433
eachDeriod to reflect the relatrve
amount of wastewatertreated. In this
case,48Vaof the wastewater volume
occursin the peak demand period
from May to August and 527ooccurS
in the ofFpeakperiod fuomSeptember to April. Figure 45 shows the
breakdown of the annual marginal
coslcurve into the two periodi
based
on thesepercentages.
The marginal cost curve for
water supply in off-peak periods is
simply a straight line equal to the unit
variable cost of water supply of
$0.0664per cubic metre.
Combined Water Supply/Wastewater
TreatmentMarginalCost Curves
The combined off-peak marginal
cost curve is the summation of the
marginal operating cost and the marginal wastewatertreatment cost
orrve. A vertical summation of these
components(Fig. 46) gives the combined off-peak marginal cost curve.
This curve representsthe sum of the
marginal cos[ of supplying one additional unit of water and the marginal
costsof treatingthe increasein wastewater associatedwith the additional
unit of supply.
The combined peak period marginal cost curve is the summation of
the marginal cost curve for peak period water supply and the marginal
wastewatertreatment cost curve. A
vertical summation of thesetwo
curves gives a graphical representationof the combined marginal cost curve
(Fig.47).
is equal to the slope of the total cost function in
rho rrnnor fiorro
The annual marginal cost curve of wastewater treatment is derived in a similar manner.
The slope of the totâl cost curve for wastewater
treatméntis taken at a number of ooints on the
x-axisand plottedâgainstthe volumeof waste
water treated (Fig. aa). The annual marginal
cost curve can be broken down into peak and offpeakporiods,using the method desiribedin
Chapter 4. The basic shaperemains the samein
eachperiod, but the quantity scaleis reduced in
Determining
the DemandGurves
As in the first case,the utility hasno data
on which to basedemand estimation,and so the
genericdemand curves in Chapter 5 becomethe
basisfor rate setting. A demand elasticity of -.2
is selectedfor residential water demand. This is
slightly lower than the median elasticity in previous studies,but the rate settersfeel that the
warm climate and suburbannature of the
60
Tolal cost ol peak pèriod water supply
3.t
3.4
Tolal cosl ol waslewaler treatrnenl
3.3
Ê",
È
@ l r
3.0
Total cost ol off-peak period waler supply
2.9
1
6
r
t
t
Millions ot cubic melres
l0
Milllort3ot cubic melres
Figure42. Totalcostcurves,Case2.
1.5
l.a
Toial cosl of wastewaler lreatrnenl
3.3
Total cosl of peak p€riod water supply
-e
=
E
3.2
@
3.1
Marglnal cost ol waslewaler lrealment
Marginal cost of peak period waler supply
.}È
7
a
9
r0
tl
t?
r
?
r
Millionsof cubic melres
Figure43.
a
!
5
l
t
m
?
2
2
a
Millionsol cubic melres
Marginalcostfor peak periodwatersupply,
derivedfrom total cost curve.Case 2.
Figure44.
61
Marginal cost of wastewatertreatment,
derivedfrom total cost curve.Case 2.
â
Otf-peak marginal cosl
Peak marginal cosl
.?t
e
g
l
e
r
0
l2
9
MllliorB ol ojblc rnêlres
t
0
l
t
Millions ol cubic melres
Figure45. Peak and off-peakmarginalcosts of wastewatertreatment.Case 2.
Cornbined marginal cosl curve
Marginal cost ol waler supply
Marginal cost of water supply
.L
c
g
Marginal cosl of waslewaler lreatrnenl
9
r0
Millionsof cubic melres
Marginal cosl ol waslewaler trealment
Figure47.
population will result in a smallerresponseto
price variation.Similarly, an elasticityof -.3 for
industrial water demand is selected;this is
slightly lower than the average,but the rate setters feel that the numerous small establishments
found in the areado not have the samepossibilities for reducing water consumption that larger
firms have.
Millions ol cubic metres
Figure46.
Combinedwatersupply/wastewater
treatmentmarginalcost curve,
peak period,Case 2.
Combinedwatersupply/wastewater
treatmentmarginalcost curve,
off-peakperiod,Case 2.
62
During the peak period, which includes a
_
four-month period from June to September, resi_
dential consumption accounts for g'.4million cu_
bic metres of water. For 35 000 residential
connections,this is equivalent to a monthly de_
mand of about 60 cubic metres per household.
This corresponds to the fifth demand curve
shown in Figure 20, for which consumption at
zero marginal price is 60 cubic metres.^This de_
mand curve is then transformed back into total
consumption over the peak period by multiply_
ing monthly consum.ption pèr household li tire
number of months (4) and ihe number of connec_
tions (35 000).
Current industrial demand during the peak
period is 3.6 million cubic metres. Thùnalysts
nowconsult Figure 25 and interpolate an ap_
proximate demand curve with rèference to the
next to last demand curve, which intersectsthe
lower axis at 4.0 million cubic metres.This de_
c.uTVe
representsaggregate peak period in_
Told.
dustrialdemand, and when aàAed to the
residential demand curve, the total peak period
demand results (Fig. a8).
rroncublc metres, of which 9.1 million cubic me_
tres is due to residential demand and 3.9 million
cubic metres to industrial/commercial aerr.,unà.
The equivalent monthly demand is 32.Scubic
metres per household per month. A demand
curve that intersects the lower axis at 32.5 cubic
metres can then be interpolated with reference
to the first demand curvè in Figure 20. This de_
mand curve is transformed int6 aggregate resi_
dentialoff-peakdeTsttdby multfrïyiig by the
number of months (8) and-the number ôf ,"esi
dential connections (35 000).
The industrial/commercial demand of 3.9
million cubic metres at an elasticity of -.3 can
also be interpolated with referencé to the next to
last demand curve in Figure 25. Adding this de_
mand curve horizontally to the off-peaÈresiden_
tial demand curve gives the total off-peak
demand curve (Fig.+S).
waterdemand
I
\
Total
l2
c
g , -
Millionsol cubic melres
Figure49.
Off-peakperiodwater demand,Case 2.
Setting Peak Period prices at Intersection
of
MarginalCostand DemandCurve
The peak period price should be set at the
.
rntersectionof the peak period demand curve
and the combinedwater supply/wastewater
costcufve-forthe peak pe_
:l:itTîllT,rrginal
nod.
Notethat the peakperiodmarginalcôst
Mlllionsol cubic melres
Figure48.
Peakperiodwaterdemand.Case 2.
63