- Email: [email protected]
Generalised sensitivity charts
Engineering
Costs and Production
Elsevier Science
Publishers
Ecor&omics,
B.V., Amsterdam
8 (1984)
55 - 115
- Printed
in The Netherlands
GENERALISED SENSITIVITY CHARTS Ivan V. Klumpar * Massachusetts
Institute
of Technology,
One of the most important parts of the economic evaluation of industrial processes is sensitivity analysis. It assesses the effect on the process economics of various engineering and economic parameters. A widely used method of sensitivity analysis starts with defining a base or reference case and determining its economics in terms of a criterion, such as cost or profitability. Subsequently, one parameter at a time is varied over a range of values, and the corresponding changes in the selected criterion are estimated. In some cases, the investigator varies two related parameters at the same time. Assume, for example, that it is desired to investigate the effect on profitability of plant capacity, with all other independent variables unchanged. A higher capacity implies the increase in two parameters, capital cost and production, as opposed to the increase in production at constant capital, which can be denoted as attaining higher plant productivity. Capital and production are two distinct parameters. The former, an economic variable, affects cash flow primarily during the construction period; while production, an engineering variable, may have a major impact only after start-up. Rarely are more than two selected parameters varied at the same time in sensitivity analysis. The purpose of this analytical tool would be defeated, as the individual effects would become blurred. The variation of a *Currently
with
0167-188X/84/$10.00
Sturtevant,
Inc.,
Boston,
MA
1984 Elsevier Science
(U.S.A.).
Publishers
Cambridge,
MA (U.S.A.1
parameter (e.g., production) changes, of course, a certain number of other parameters (e.g., raw material consumption), but this change can be considered secondary. The remaining parameters (e.g., raw material cost per pound) are not affected. Mathematically, the latter can be considered independent variables together with the varied parameter (production); while the other parameters, subject to secondary change (raw material consumption), are dependent variables. In using sensitivity analysis, it should be kept in mind that this mathematical model is a convenient simplification of the real life. In most sensitivity analysis applications, the preferable economic criterion is profitability because it allows the measurement, with one yardstick, of the effects of both capital and operating costs. Profitability analysis has been lately done almost exclusively using yardsticks based on discounted cash flow, such as net present value, discounted cash flow rate of return (DCF-RR), etc. However, for back-of-the-envelope calculations, return on investment (ROD is still widely used. In a typical sensitivity analysis, a number of independent parameters is investigated, the profitability being calculated for several values of each. Accordingly, sensitivity analysis exceeds profitability analysis in the volume of computations by one or two orders of magnitude. To speed up routine sensitivity analyses, a set of generalized charts was developed that allows the determination of the B.V.
56 approximate DCF-RR sensitivity of any industrial process to 13 selected engineering and economic parameters. Upon classifying industrial processes into seven categories, it was found that the’ DCF-RR of any process within a category approximately conforms to a general correlation of a selected set of independent parameters if both the DCF-RR and each parameter are expressed as ratios to their relative variables. A set of reference parameter values is defined as a selected set of values that constitute a reference case with a reference DCF-RR value. The approach is discussed in detail elsewhere [ l-31. Process categories are defined, based on the concept of the variable, semivariable, and fixed components of operating cost. The variable component is proportional to plant capacity and includes such items as raw materials. The fixed component, such as overhead, is a constant, independent of capacity within the range of sensitivity analysis. The semivariable component varies directly with
capital cost, but is affected less by capacity changes. Accordingly, it is expressed as a capital factor. If the capital is $100 million and the capital factor lo%, the semivariable cost is $10 million per year. A typical semivariable item is maintenance cost. The process categories are defined according to the extent to which the components control operating cost (see Table 1). TABLE 1 Process Category
Number
1 2 3 4 5 6 I
categories
Name of controlling component(s)
All three Semivariable Variable Fixed Semivariable and fixed Variable and fixed Variable and semivariable
Component expressed as Percent Operating Cost Variable
Semivariable
Fixed
33.3 4 92 4 4
33.3 92 4 4 48
33.3 4 4 92 48
48
4
48
48
48
4
TABLE 2 Definitions
and assumptions
Term
Text
Base Case
A combination of parameters selected by the user of the charts as a basis for the sensitivity analysis. The Base Case DCI: rate of return must be known to the user.
Capital (Cost)
Equals depreciable life.
Capital Factor
Represents all capital charges against operating cost excluding a percentage of C. Reference cases assume K = 10%.
Category
Used to classify processes according to whether variable, or two of them, or all control operating cost. See Table 1.
Depletion
Allowance
Depreciable
Capital
Depreciation
Life
DCF Rate of Return
Symbol
capital (cost). Charts assume capital outlay in the first year of venture depreciation. semivariable
Expressed or fiied
as
costs,
Amount by which taxable income may be decreased by law for certain processes. Relative A is expressed as a percentage of sales. Reference cases assume A = 0. See Capital (Cost). Period of time during which capital may be written off for tax purposes by law. Charts are based on straight line depreciation and reference cases assume D = 12 years. Discounted-cash-flow DC&RR” of 10,20,
rate of return and 30%.
or DW-RR.
Reference
cases assume a “reference
Expense
See Investment
Fixed Cost
Operating cost component that can be assumed independent of capital and production rate within a limited range, as long as the number of trains doesn’t change. Fixed cost is a sum of such items as supervision, most operating labor, and some overhead costs.
Investment
Expense
C
Expense.
Any non-depreciable investment other than working capital. Relative E is expressed as a percentage of capital. Charts are based on an E outlay in the fist year of venture life. Reference cases assume E = 0.
E
57 Operating
Cost
All periodic, non-depreciable expenditures such as production or manufacturing costs, selling and delivery expense, and corporate charges. Operating cost is the sum of variable, semivariable, and fixed costs expressed in $/year.
Pammete
One of the process and economic
price
Equals selling price. In a multi-product case, a major product is used for expressing volume and its price is adjusted to account for the other products. Charts assume constant price over the venture life.
Production
Rate
variables that determines
_
DCF-RR. P
See Volume.
Reference
Reference case is a selected DCF-RR of 10,20, “I 30%.
Relative
DCF-RR
DCF-RR divided by its reference
Relative
Parameter
Parameter investment
combination
of parameter
values
to yield
a reference
value.
divided by its Base Case value, except for the relative depletion allowance, expense, and salvage which are defined in a different way (see these terms).
Sales
Annual gross sales revenue, i.e., before subtracting any periodic expense, such as selling cost. Charts assume G =PQ and treat all reimbursements as sales except for salvage.
Sales Volume
See Volume.
Salvage (Value)
Portion of capital cost that is recovered in a later year of venture life. Relative 2 is expressed as a percentage of capital. Charts are based on depreciating capital to zero and treating Z as a cash inflow in the last year. Reference cases assume Z = 0.
Semivariable
Operating cost component that can be assumed proportional to capital, such items as maintenance cost, property taxes and insurance, depreciation,
Cost
cxprcsscd
as a perccntagc
Annual federal, state, and local income income. Reference cases assume T = 50%.
Variable Cost
Operating cost component that can be assumed proportional a sum of such items as raw materials, selling and distribution,
Venture
Includes the entire period of time during which expenditures and reimbursements associated with the process occur, such as R&D, investment and operating costs, sales revenues and satvagc value. Charts are based on using the first year of venture life solely for capital, working capital, and investment expense outlays. Reference cases assume L = 21 years.
of taxable
to production rate, i.e., and some utilities costs.
VOlU*e
Annual sales volume expressed in terms of a major product (see Price). Charts assume that volume does not change over the venture life and equals production rate. Differences between volume and production rate are included in working capital variations.
Working Capital
Charts assume that working capital can be expressed as a sum of items, each proportional to either sales, capital, or an operating cost item. It is laid out in the fist year of venture life and adjusted, if necessary, to reflect variations in sales, capital, and operating cost in the later years. Definitions and basis of working capital items, and values of proportionality factors used in reference caxs, are shown below:
WorkinK Capital Structure Item
Basis
Factor**
Inventories: Raw materials Work in process Finished goods Materials & Supplies
Raw material cost per day Operating cost per day* Total operating cost per day Depreciable capital
30 3 30 0.03
Accounts: Receivable Payable (negative)
Sales per day Operating cost per day*
30 30
Operating
Fixed cost per day
30
cash
(Item) = (Factor)
*Excluding depreciation. **Value of factor on which the charts are based.
(Basis)
G
i.e., a sum of etc.
Tax Rate
Life
taxes
Lower Case Letter
Q
W
The generalized sensitivity charts are plots of relative DCF-RR versus a relative parameter. Two types of charts were developed as follows: l The one-parameter charts comprise a family of seven curves, representing process categories; l On the two-parameter charts, the family of curves represents the second parameter. Assumptions underlying the charts are summarized in Table 2. The relative DCF-RRS are based on three arbitrary reference values of 10, 20, and 30 percent. Accordingly, there should be 3 X 13 = 39 one-parameter charts because of the 13 selected parameters involved. With seven process categories, the corresponding number of two-parameter charts would be excessive. Rather, the number was limited to the categories and parameters which have the greatest effect on profitability. This effect was determined in a separate study [I]. The resulting TABLE Index
selection and 4. TABLE
of charts is summarized
in Tables 3
3
Index of one-parameter
charts
Parameter
Table Number
Selling Price Sales Volume Depreciable Capital Tax Rate Variable Cost Fixed Cost Capital Factor* Depreciation Life Working Capital Venture Life Depletion Allowance Investment Expense Salvage Value
for Reference
DCF-RR
10%
20%
30%
Ala A2a A3a A4a A5a A6a A7a A8a _
Alb A2b A3b A4b A5b A6b A7b A8b A9 Al0 Allb A12b Al3
Ale A2c A3c A4c A5c A6c A7c A8c _
Al la A12a _
Allc A12c _
*Capital factor equals all capital charges against operating cost excluding depreciation. It is expressed as a percentage of capital cost.
4 of two-parameter
Parameter Combination
charts Table Number
for
Category 1, Reference DCF-RR
Price Volume Price Capital Price Variable Cost Price Fixed Cost Price Capital Factor Volume Variable Cost Volume Fixed Cost Volume Capital Factor Volume Capital
Category 2, Reference DCF-RR
Category 3, Reference DCF-RR
Category 4, Reference DCF-RR
10%
20%
30%
10%
20%
30%
10%
20%
30%
10%
20%
30%
Bla
Blb
Blc
Cla
Clb
Clc
Dla
Dlb
Dlc
Ela
Elb
Elc
B2a
B2b
B2c
C2a
C2b
c2c
D2a
D2b
D2c
E2a
E2b
E2c
B3a
B3b
B3c
D3a
D3b
D3c
B4a
B4b
B4c
E3a
E3b
E3c
BSa
B5b
B5c
B6a
B6b
B6c
B7a
B7b
B7c
E4a
E4b
E4c
B8a
B8b
B8c
C4a
C4b
c4c
B9a
B9b
B9c
C5a
C5b
c5c
E5a
E5b
E5c
C3a
C3b
c3c
D4a
D5a
D4b
D5b
D4c
D5c
59 Table 4 (continued) Capital -
Variable Cost Capital Fixed Cost Capital Capital Factor Variable -
, Fixed Cost Variable ~~ Capital Factor Fixed Cost -
Capital Factor Price Tax Rate Price Depreciation Life Price Venture Life Volume -
Depreciation Life Volume Venture Life Variable Cost -
Depreciation Life Variable Cost Venture Life Fixed Cost -
Depreciation Life Fixed Cost Venture Life olpital Factor -
Depreciation Life Capital Factor Venture Life Tax -
Fixed Cost Tax Variable Cost Tax Capital Tax Volume Tax Capital Factor Tax Depreciation Life Tax Venture Life Depreciation
Life -
Capital Venture Life -
Capital Venture Life ~~ Depreciation Life
BlOa
Blob
Bloc
Blla
Bllb
Bllc
B12a
B12b
B12c
B13a
B13b
B13c
B14a
B14b
B14c
BlSa
BlSb
BlSc
B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30 B31 B32 B33 834 B35 B36
D6a
D6b
D6c E6a
C6a
C6b
C6c
E6b
E6c
60 TABLE 5 Chart usage step NO.
Example
Step Description
Sales volume, Depreciable capital, Operating cost items: raw material, selling & distribution, utilities, operating labor, supervision & services, capital factor, Tax depreciation life, DCF rate of return,
= lS$/ib = 3$/lb = 2$/lb = $lZMM/yr =40%1 k =9%C D =13yrs R = 14.9%
Establish parameter variations
(a) Increased productivity, (b) Decreased capital,
p’ = 140 MM lbs/yr C” = $77 MM lbs/yr
Calculate variable cost
V=(m+d+u)Q = (0.15 + 0.13 + 0.02) 100
= $20 MM/y1
Calculate fixed cost
F = (l.o+s) I = (1.4) 12
= $16.8 MM/yr
Calculate semivariable cost
S=(K+l/D)C =(0.09+
Determine
Category
Calculate relative parameters
(a) Relative increased productivity q = Q’/Q = 140/100 = 1.4 (b) Relative decreased capital c = c-/c = 17/l 10 = 0.7
Determine relative DCF Rate of Return (DCI:-RR)
For a reference DCl‘-RR of 20%, the relative DC&RR, denoted as r, is: (a) r’ = 1.6 for q = 1.4 from Chart A2b (b) I” = 1.4 for c = 0.7 from Chart A3b More accurate r’ err” values may be obtained by interpolating between Charts A2b and A3b and the corresponding 10% reference DCF-RR charts
Calculate DCI:-RR sensitivity to parameter variations
(a) For increased productivity, R’ = r’R = 1.6 (14.9) = 23.8% (b) For decreased capital, R” = r”R = 1.4 (14.9) = 20.9% The actual values calculated by computer
Establish reference ca.se
l/13)
Q = 100 MM lbs/yr C =$llOMM m d u I
110
= $18.36 MMlyr
No. 1 because V, S and F are approximately
The charts are used in the following way. First, the user establishes the reference values of all parameters, determines the process the reference computes category, and DCF-RR. Second, he selects the parameter and/or pairs of parameters to be investigated in the sensitivity analysis. For the parameters involved, he computes one or more relative values within the investigated range. Third, for each relative parameter value, or pair of he determines the relative such values, DCF-RR by interpolating between curves and he computes the correcharts. Finally, sponding DCF-RRs by dividing each relative -
equal
are R’ = 24.6,
R” = 21.8
value by the reference value. An illustrative example is shown in Table 5. REFERENCES 1
2
3
Agarwal, J.C., and Klumpar, I.V., 1975. Generalized Profitability and Sensitivity Analysis, Trans. AACE 1975 paper, C-l. Agarwal, J.C., and Klumpar, I.V., 1975. Profitability sensitivity and risk analysis for project economics. Chem. Eng., 82(20): 66. Klumpar, I.V., 1980. Sensitivity analysis charts. Proceedings, 6th Int. Cost. Eng. Congress, Mexico City, Oct. 1980, paper Dl.
(Received
March 25,
1983; accepted
November
21,
19831
61 CHART Alb
-
PRlCE
AT
*o?& REFERENCE
“CF
RR
/I
3.0
2.5
E
2
/
2.0
Y 5 i Lt
1.5
-
1.0
0.5
0
0.5
I
I
1.0 RELATlVE
I
I
I
1.5
2.0
25
PRICE
I
30
2.3.7
A6 I 1.0
2.0
I 3.0
I 4.0
3
CHART
A2b
-
SALES
VOLUME
AT
20% REFERENCE
CHART
DCF-RR
A2c - SALES
VOLUME
CATEGORY
AT 30% REFERENCE
DCF RR
NO.
3.0 -
2.5 -
2.0 -
1.5 -
1.0 -
RELATIVE
VOLUME
0.5 -
RELATIVE
CHART
A&
-
DEPREClABLE
CAPlTAL
AT
IO?6 REFERtNCE
CHART
DCFRR
A3b
-
DEPREClASLE
CAPlTAL
VOLUME
AT
20% REFERENCE
DCFRR
-
-
-
\ <
I 0.25
I 0.5
!
I 0 75
RELATIVE
-
-Y I
1.0
1.25 CAPITAL
1.5 COST
1
-_-L i
2.0
I 2.25
0.25
I 0.5
I 0.75
I 1.0
RELATIVE
I
I
I
I
1.25
1.5
1.75
2.0
CAPITAL
COST
CHART
A3c
-
DEPRECIABLE
CAPITAL
AT
5.0-
30%
l-
REFERENCE
I
I
CHART
DCFRR
A4a
-
TAX
RATE
AT
10% REFERENCE
OCF RR
I
!
I I
I
0’
1 0.75
0.5
0.25
I
I
,
I
1.0
1.25
1.5
1.75
RELATIVE
CHART
A4b
TAX
RATE
AT
CAPITAL
20%
RELATIVE
COST
REFERENCE
DCF-RR
y
1.0
F
4 g
0.8
0.6
0.4
2.0
I .8 RELATIVE
I 1.2 TAX
I 1.6 RATE
RATE
I 2.0
CHART
I .4
TAX
\I 2.0
I
A4c
-
TAX
RATE
AT
30%
REFERENCE
\
DCF-RR
‘t
-
\
-
L
OO
0.2 I
\
I 3.4
I 0.4
I 0.6
I 0.8
I 1.0
I
I
1.2
1.4
I 1.6
I I 1.8
6
64 CHART
Ma
-
VARIABLE
CHART
COST AT 10% REFERENCE DCF-RR
A5b
-
“AHIABLE
COST AT 20%
DCF-RR
REFERENCE
2.5
0
5
\ J CHART
3.0-
A!%
oz 8 ?
2.0
COST
AT
30%
REFERENCE
ASa -
FlXED
COST
AT 10%
2.5
COST
REFERENCE
DCF-RR
DCF-RR
I
3
-
\
C/
~
? r 4 %
CHART VARIABLE
VARIABLE
__
6
2.5--
-
20
15
1.0 RELATIVE
--
l.!i-
& to--2.5
2.5
-
p .5-
OO
-
f
I
1.0 REI_AT,“E
I 1.5 VARIABLE
I
2.0 COST
I
2.5
2.5 RELAT,“E
FIXED
COST
65 CHART
A&
-
FIXED
COST
AT
30%
REFERENCE
DCF-RR
I-
,-
I-
\
CHART 1.4
1.2
f
1.0
B y
0.6
I=
4 E
0.6 0.4 0.2 0
\,
I 20
1.6
,-
A7b
-
CAPITAL
FACTOR
AT
20%
REFERENCE
DCF-RR
66 CHART
0
A7c
-
CAPITAL
1I
01
FACTOR
AT
2I
30%
REFERENCE
3I
OCF-RR
4I
I
CHART
A&
-
DEPRECIATION
LIFE
AT
10% REFERENCE
DCF-RR
(
5 RELATIVE
CAPITAL
FACTOR
RELATIVE
CHART
1.20
A86
-
I
DEPRECIATION
I
I
LIFE
AT
20% REFERENCE
I
’ CATEGORY NO.
0.9
J 0
, 0.4
I 0.8
1 1.2 RELATIVE
I 1.6 DEPRECIATION
LIFE
DCF-RR
I
/
(
/
1 2.0
, 2.4
LIFE
DEPREclATloN
CHART
A&
-
DEPRECIATION
RELATIVE
LIFE
AT
DEPRECIATION
30%
REFERENCE
LIFE
DCF-RR
CHART
A9
-
WORKING
CAPlTAL
AT
20%
REFERENCE
CHART
DCF RR
A10
VENTURE
LIFE
AT
20%
REFERENCE
z=-
T
DCFRR
1.2.
x7
/ ITEGC
NC
-
-
-
0.2 -
OO I
1I
2I
RELATIVE
31
WORKlNG
41
CAPITAL
I
I
I
05
RELATIVE
CHART
Alla
-
DEPLETION
ALLOWANCE
AT
10% REFERENCE
DCFRR
CHART
Allb
-
DEPLETION
I 0.9
I 0.8
0.7
0.6
VENTURE
ALLOWANCE
AT
I
I 1.1
1.0
LIFE
20%
REFERENCE
F
-
6
-
Ik -
1
3.4
3.46
-.-
-
’
1
~ /
5
10 DEPLETION
15 ALLOWANCE;
20 % SALES
25
5
2
10
DEPLETION
15 ALLOWANCE,
20 % SALES
25
DCFRR
CHART
A12a
-
INVESTMENT
EXPENSE.
CHART
A,%
-
,N”ESTMENT
EXPENSE
AT
2096 RELATIVE
DCF-RR
CHART
0 0 EXPENSE,
% DEPRECfABLE
CAPITAL
A,%
1 20
-
I EXPENSE,
AT
sb DEPRECIABLE
INVESTMENT
40
EXPENSE
EXPENSE
1 60 % DEPREClABLE
10% RELATIVE
DCF.RR
CAPITAL
AT
30% RELATIVE
I
I
60
100 CAPlTAL
DCF-RR
I 120
I
69 CHART
A13
-
SALVAGE
VALUE
AT
2096 REFERENCE
CHART Bla- PRICE - VOLUME
DCF-RR
Far
01
I
I 40
1
0
20
SALVAGE.
% DEPRECIABLE
CHART For
Bib
Category
-
PRICE
I
I
60
80
Category
1 a, 10% Reference
DCF-RR
CAPITAL
-
CHART
VOLUM@
1 at 20% Reference
For
DCF RR
Blc
Category
-
PRiCE
-
VOLUME
1 at 30% Reference
DCF-RR
4.5
RELATIVE
4.0
PRICE = 2.0
-
3.6
1.1 ? L
0 RELATIVE
VOLUME
-
.6
hi
.8
I
I
I
1.0
1.2
1.4
RELATfVE
“OL
70 CHART For
E2a -
Category
PRICE
-
CAPITAL
1 at 10% Reference
DCF RR
CHART For
Bzb
Cafesw
-
PRICE
-
1 at 20%
CAPITAL
Reference
DCF-RR
5.0
4.5 -
4.0 -
-- t
3.5
t
3.0 1 -
-
RELATlYE PRICE = 2.0
I.7 ):
,i+?.IQ 1.4 -
-i-
1’
RELATIVE
CAPITAL
RELATIVE CHART
B3a -
FOr CafegorY
CHART Far
f32c -
Catwon/
PRICE 1 at 30%
RELATIVE
-
PRICE 1 at
-
VARIABLE
10% Reference
CAPITAL Reference
DCF.RR
CAPITAL RELATIVE
VARIABLE
CWST
COST DCF-RR
CNfTA
71 CHART Far
B3b -
I
PRICE
-
VARIABLE
1 at 20% Reference
categor”
I
COST
CHART
OCF-RR
I
I
For
I
B3c -
Category
PRICE
-
1 at 3%
VARIABLE
COST
Reference DCF-RR
I
3.6
3.0
2.5
2.0
1.5
RELATIVE
VARIABLE
COST
1.0
5
0
1.0
.5
CHART
B‘la
Far Catagar”
1.5
-
PRICE
-
2.0 RELATIVE FlXED
2.6 VARIABLE COST
COST
1 ax 10%‘ Reference DCF-RR CHA@T
B4b -
For Category
I
I
PRICE 1 af 20%
-
FIXED
COST
Reference DCF-RR
I
I
I
1.0
1.5
2.0 RELATIVE
I
3.5 -
0 RELATIVE
FIXED
COST
.5
2.5 FIXED COST
72 CHART For
B4c -
CBtegory
PRICE
-
1 at 30%
RELATIVE
FIXED Reference
FIXED
CHART
COST
For
DCF-RR
For
I
I
B5b
Catego,”
I
-
PRICE
1 at 20%
PRICE 1 ilt
-
lo?6
CAPITAL Reference
FACTOR DCF.RR
COST
.B CHART
B5a -
category
-
CAPITAL
Reference
.8
1.0
FACTOR
1.2 RELATIVE
1.4 CAPITAL
1.6 FACTOR
DCF-RR
I
I
I
CHART For
RELATWE
CAPITAL
FACTOR
B5c
Categwy
-
PRICE
-
CAPITAL
1 at 30%Reference
RELATIVE
CAPITAL
FACTOR DCF-RR
FACTOR
1.8
2.0
CHART
BSa -
“DLVME
-
VARIABLE
COST CHART
For Catesarv
66b
-
VOLUME
-
VARIABLE --
1 at 10% Reference DCF-RR
0
1.0
.5
1.6
2.0 RELATIVE
RELATIVE
VARIABLE
COS’,
CHART For
CHART S6c For
OL .s
Carqjorv
VOLUME f at 30%
-
VARIABLE
Category
VOLUME
-
FIXED
2.5 VARIABLE
COST
COST
1 at 10% Reference DCF-RR
COST
Reference DCF-RR
I
I
I
.8
I
I
I
1.0
1.2
1.4
1.6
1.8
RELATIVE
B7a -
COST
VARIABLE
COST
I 2.0
1.0 RELATIVE
1.5 FlXED
COST
2.0
74 CHART CHART
67b
For categor”
0
-
VOLUME
FIXED
1 at 2G% Referenae
COST
For
B7c -
Catergary
VOLUME
-
FIXED
1 at 30% Reference
RELATIVE
2.5 FIXED COST CHART FM
BBb -
Caewry
FIXED
VOLUME
-
COST
CAPITAL
1 at 20% Reference
Fo,
S8a -
Category
VOLUME 1 at lC%
-
CAPITAL
Reterence
FACTOR
DCF-RR I
I CHART
COST DCF RR
DCF.RR
2.0 RELATIVE
1.5
1.0
.5
-
FACTOR -
DCF-RR 3.5
3.0
2.5
4 i z
2.0
I! P ‘).
,.
) RELATWE
CAPITA‘
FACTOR
.5
1.0
2.5
2.0
1.5 RELATIVE
CAPITAL
FACTOR
75 CHART For
BBC -
Catewry
VOLUME I at 30%
RELATIVE
CHART For
Wb
Category
.._
-
-
CAPITAL
Reference
CAPITAL
CAPITAL
1at 20%
CHART
FACTOR
DCF.RR
For
Wa
-
Catepxv
FACTOR
-
CAPITAL
-
VOLUME
1 at 10% Reference
RELATIVE
DCF-RR
VOLUME
VOLUME
Reference
I
PCF-RR
I
I
CHART For
Wc
Category
-
CAPITAL 1 at 30%
-
VOLUME
Reference
DCF-RR
2.5
2 8 s j
1.5
I
0’ .5
1.0
1.5
2.0 RELATIVE
VOLUME
0.5
0.75
I
I
1
1.25 RELATIVE
VOLUME
I
1.5
I
1.75
I 2
76 CHART BlOa - VARIABLE For
Categor”
COST
1 at 10% Reference
-
CAPITAL
CHART For
DCF-RR
BlOb
-
VARIABLE
category 1 at
20%
COST
Reference
I
I
I
.5
1.0
1.5
2.5
-
CAPITAL
OCF-RR
I
I
-I
3.I 20
3.c 1.5 x g i a
2.5 1.0 z
L
B ;
2.0
.5 4 z 1.5 0 .6
.B
1.2
1.0
1.4
RELATIVE
1.6
1.8
2.0
CAPITAL I.0
.5
0 0
CHART For 1.8,
I
BlOc
-
caregary1 I
VARIABLE 30%
a2
I
COST
Reference
I
-
CAPITAL
OCF-RR
I
I
I CHART For
RELATIVE
CAPITAL
2.0 RELATIVE
Bl,a
Category
-
FIXED
1 at lwb
-
CAPITAL
Reference
COST
DCF.RR
2.5 CAPITAL
77 CHART
Bllb
-
For Category
FIXED
COST
-
CHART
CAPITAL
Bllc
-
For Category
1 at 20% Reference DCF-RR
I 1.0
I
.2
.a
.6
FIXED
1.0
1.5
2.0 RELATIVE
Rl2b
-
For Category I
B12a
For Categov
-
CAPITAL
FACTOR
-
CAPlTAL
1 at 10% Reference DCF.RR
RELATIVE
CAPlTAL
CAPITAL
I
I
I
I
1.4
1.6
1.8
2.0
CAPITAL
2.5 CAPITAL CHART
CHART
-
Reference DCF-RR
1.2 RELATIVE
s
COST
1 at 30%
1
CAPITAL
FACTOR
-
CAPITAL
1 at 20% Reference DCF-RR I
I
I
I
78 CHART
812~
-
For Category 2
I
CAPITAL
1 at 30%
FACTOR
-
CHART
CAPITAL
B13a -
VARIABLE
COST
-
FIXED
I
I
I
I
I
I
I
I
-.
1.5 I--_
f ri
X z 4: w’ c
1
0.5 I-.
I
a
0.5
COST
Reference DCF-RR
0.75
I 1
I
I 1.5
1.25 RELATIVE
I 1.75 RELATIVE
CAPITAL
CHART
B13b
-
VARIABLE
For Category
COST
-
FIXED
COST
1 af 20% Reference DCF-RR
RELATIVE
FIXED
COST
FIXED
COST
79
CHART 813C _ “AR,ABLE For Categw+
0 0.5
I
0.75
COST
--
FIXED
CHART 814-
COST
For
category
VARIABLE
COST
-
CAPITAL
1 at 10% Reference DCF-RR
, at 30% Reference DCF-RR
I
1 RELATIVE
I
I
I
1
1.25
1.5
1.75
2
FIXED
COST
RELATIVE
CHART
B,Q,,
-
VARIABLE
For Csfegory
I af 2wb
RELATIVE
COST
-
CAPITAL
~e‘erense
CAPITAL
DCF-RR
FACTOR
FACTOR
CAPITAL
FACTOR
FACTOR
80 CHART Far 1.2,
.51 .6
8%
-
Category I
I
.a
VARIABLE
COST
-
CAPITAL
FACTOR
1 at 30%
Reference
DCF-RR
t
I
I
r
I
I
I
I
1.2
1.4
1.6
1.8
I 1.0 RELATIVE
CAPITAL
CHART
61%
-
FIXED
COST
-
CAPITAL
FACTOR -
f
1
2.0
FACTOR
.6
.6
1.0 RELATIVE
CHART
B,Sb For
-
FIXED
Categon/
COST
-
CAPITAL
1 at 26% Reference
RELATIVE
CAPfTAL
FACTOR
DCF-RR
FACTOR
1.2
1.4 CARTAL
1.6 FWTOR
1.8
2.0
81 CHART
B1E.c -
For Category
.5 .d
FlXED
1 at 30%
COST
-
CAPITAL
FACTOR
CHART
Reference DCF-RR
For
I
I
I
I
I
I
.8
1.0
1.2
1.4
1.6
1.8
RELATIVE
CAPITAL
816
Category
-
PRICE
-
TAX
RATE
1 at 2096 Reference DCF-RR
2.0
FACTDH
RELATWE CHART
817
For Category
-
PRICE
-
DEPRECIATION
UFE -
CHART
1 af 20% Reference DCF.RR
818
-
For Categow
PRICE
-
“ENTVRE
TAX
RATE
LiFE
1 at 20% Reference DCF-RR
3.5
3.0
2.5
$ x 2.0 g I5 z x5
l.0
.5
0
I 3
I 1.0
I 1.5 RELATlVE
I
J
I
2.0 2.5 OEPREClATlDN
a
I/ .25
UFE
I
I
.5
.75
I 1.0 RELATWE
I 1.25 VENTURE UFE
1
CHART
019
For Category
-
VOLUME
-
DEPRECIATION
CHART
LIFE
1 at 20% Reference DCF-RR
820
For Category
-
VOLUME
-
“ENTVRE
1 at 20% Re‘xence
LlFE
DCF-RR
4.0
.5 -
3.5
.O -
3.0
RELATIVE
VOLUME = 2.5 -
-
/-
.5 -
.O -
.5 -
.Q -
.5 -
Q0 RELATIVE
CHART
821
-
VARIABLE
Far Category
COST
-
DEPRECIATION
1 at 20% Reference DCF-RR
2& i i
RELATIVE
DEPREClATlON
LIFE
LIFE
VENTURE
LIFE
0.0
0.0
0.5 RELATIVE
For Category
1.0 DEPRECIATION
1.5
1 af 20% Reference
LIFE
DCF-RR
2.0
For
2.5
VENTURE
LIFE
1 at 20% Reference DCF-RR
RELATIVE
Cmg~ry
0.2
0.4
For
CHART
-
0.5
Category
824
RELATIVE
VENTURE
0.8 UFE
LIFE
1.0
DCF-RR
VENTURE Reference
COST 1 at 20%
FIXED
1.2
84 CHART
0.4 0.0
825
-
CAPITAL
FACTOR
-
DEPRECIATION
LIFE
I
I
I
I
0.5
1.0
1.5
2.0
RELATIVE
CHART
826
-
CAPITAL
RELATIVE
DEPRECIATION
FACTOR
-
“ENTVRE
LlFE
VENTURE
LIFE
LIFE
I 2.5
85 CHART For
I
827 -
Category
I
TAX
-
1 at 20%
FlXED Reference
I
CHART
COST
For
DCF-RR
1
828
-
Category
TAX
-. VARIABLE
COST
1 at 2046 Reference DCF-RR
l-
1.75
-
-
i ::
Y F
5
z
I
I
I
.5
3.0
1.5
I 2.0 RELATIVE
L 2.5 FI, (ED
0
.5
1.0
1.5
COST
CHART
830
-
TAX
2.0 RELATIVE
, 2.5 VARlABLE COST
-- VOLUME
RELATIVE
VOL”,,
86 CHART For
831
Category
-
TAX
-
CAPITAL
FACTOR
1 at ZG% Reference
OCF-RR
+.!+ 1.7
,.li 0.0
OS
1.5
1.0 RELATIVE
CHART For
0.0
0.5
832
-
CafegDry
TAX
CAPITAL
-
2.0
OEPRECIATION
LfFE
1 a120% Rsference
OCF-RR
1.0
1.5
RELATWE
2.5
FACTOR
D.wI)EC,AT,DN
2.0 UFE
2.6
87 CHART
2
0.4
833
-
TAX
0.6
834
For Category
VENTURE
LIFE
1.0
0.8 RELATIVE
CHART _.
-
-
VENTURE
DEPRECIATION
1.2
LIFE
LIFE
-- CAPlTAL
1 at 20% Reference DCF-RR
RELATIVE
DEPRECIABLE
CAPITAL
88 CHART
835
-
For Cafegory I
I
I
VENTURE
LIFE
1 at 2056 Referents
-
CAPITAL DCF-RR
I
I
I
2.5
$
x
2.a
z 2 2 1.5
1.0
.5
0 0
1.5 RELATIVE
CHART
836
-
VENTURE
For Category
1
0.5
t
-
0
DEPRECIATION
LlFE
at 20% Reference DCF-RR
1.0 RELATIVE
1.5 DEPRECIATION
2.0 LIFE
89 CHART For
0.25
0.5
Cla
Category
0.75
3.5
3
g
2.5
B 5 F
2
Is :
1.5
1
0.5
0
VOLUME 2 at
10%
1 RELATIVE
4
-
-
PRICE
Reference
1.25 PRICE
DCF-ROR
1.5
1.75
*
90 CHART
ClC
For Categ~y
VOLUME
-
2 at 30%
RELATIVE
CHART
C2a -
For Category 1.5
4
3.0
3
_
PRICE
-
Reference DCF-ROR
CAPITAL
PRICE
-
PRICE
2 a, 10% Reference DCF-ROR
91 WART
C2b -
For Categcn,
0.75
CAPITAL
2 at Zwb
-
CZc -
For category
0.25
0.6
0.76
DCF-ROR
1
1.5
REALTIVE
CHART
PRICE
Referam
CAPITAL
1.15
PRICE
-
PRICE
2 at 3G?4 Reference DCF-ROR
1 RELATIVE
1.25 PRICE
1.5
1.75
z
92
3
2.5
2
x 5
1.5
9 z 1
0.5
0 0.25
0.5
0.75
1 RELATIVE
CHART
C3b -
For Catqpry
0.25
0.5
0.75
CAPITAL
1.25
1.5
1.75
PRICE
FACTOR
-
PRICE
2 .w 20% Reference DCF-ROR
1 RELATIVE
1.25 PRICE
1.5
1.75
2
93 CHART
C3c -
For Category
CAPITAL
I 0.2%
0.5
I
il.75
1 RELATIVE
CHART
C&
For Cafegory
FACTOR
-
PRICE
2 at 30% Reference DCF-ROR
-
CAPITAL
I
I
1.5
1.25 PRICE
FACTOR
-
VOLUME
2 at 10% Reference DCF-ROR
RELATIVE
“OLVME
I 1.75
2
94 CHART
C4b -
For Category
CAPITAL
FACTOR
-
VOLUME
2 at 2c% Reference DCF-ROR
I
0.25
0.5
0.75
1
RELATIVE
CHART
C4E -
For Category
0.25
0.5
0.75
CAPITAL
1
1.75
2
VOLVME
FACTOR
2 at 30% reference
RELATIVE
1.5
1.25
1.25 VOLVME
-
VOLUME
DcF.ROR
1.5
1.75
2
95 CHART -
C5a -
CAPITAL
RELATIVE
CHART
C5b -
For Category
CAPITAL
2 at 2m
-
VOLUME
VOLUME
-
VOLUME
Reference CJCF-ROA
4.6
3.5
1
0 0.25
0.5
0.75
1
RELATIVE
1.25
VOLUME
I.5
1.75
2
96 CHART
C5c -
For Category 3.5
CAPITAL
-
VOLUME
_
2 a, 30% Reference DCF-ROR
-I-
3
1
0.5
0 0.25
0.5
0.75
1
1.25
RELATIVE
CHART For
C5a -
Category
CAPITAL 2 al
1.5
1.75
2
1.75
*
VOLUME
FACTOR
-
CAPITAL
10% Reference DCF.RDR
2.5
.
2
0.5
0 0.25
0.5
0.75
1 RELATIVE
1.25 CAPITAL
1.5
97 CHART
C6b -
For Category
CAPITAL 2 at 20%
FACTOR
-
CAPITAL
Reference DCF-ROR
2 CAPITAL FACTOR = 0.6
1.6
E L
1.2
8 ;
9 &
0.8
0.4
0. 0.25
0.5
U.75
1 RELATIVE
CHART
C6c -
For Categor”
0 0.25
0.5
0.75
CAPITAL 2 at 30%
1 RELATIVE
1.m
1.5
1.75
2
1.75
2
CAPITAL
FACTOR
-
CAPITAL
Reference DCF ROR
1.25 CAPITAL
1.5
98 CHART For
D,a
-
VOLUME
-
category3 at 10%
PRICE
Reference
DCF-ROR
4 3
0 0.25
0.5
1
0.75
RELATIVE
CHART
Dlb
-
VOLUME
1.25
1.75
2
I
I
I
1.5
1.75
2
1.5
PRlCE
-
PRICE
For Category 3 at 20% Reference DCF-ROR 9,
0.25
I
I
0.5
0.75
I
1 RELATIVE
I
1.25 PRlCE
99 CHART For
0.25
0.5
Dlc
Category
0.75
-
VOLUME
-
1
1.25
RELATIVE
CHART For
D2a -
PRICE
3 at 3D% Reference DCF-ROA
CAPITAL
1.5
PRICE
-
PRlCE
Category 3 ax 10% Reference
DCF-ROR
1.75
2
100 CHART
D2b -
CAPITAL
-
PRICE
For Category 3 at 20% Reference DCF-ROR
0
7
0
5
4
3
2
1
0 0.25
0.5
1
0.75
1.25
RELATWE
CHART
D2c -
For Categary
CAPITAL
3 a, 30%
RELATIVE
1.5
PRICE
-
PRICE
Reference DCF.ROR
PRICE
1.75
2
101
0.25
0.5
1
0.75
CHART
0%
-
1.5
1.25
RELATIVE
2
1.75
PRICE
VARIABLE
COST
-
PRKE
0 0.25
0.5
0.75
1 RELATIVE
1.25 PRICE
1.5
1.75
2
102 CHART
D3c -
For Category
-0.25
OS
COST -
VARIABLE
3 at 30%
0.75
1
1.25
RELATIVE
CHART
D4a -
For Category
PRICE
Reference DCF-ROR
1.5
1.75
2
PRICE
VARIABLE
COST
-
VOLUME
3 at 10% Reference DCF-ROR
10
9 REMTIVE
8
VARIABLE
.
COST = a*,
2
0.25
0.5
0.75
I RELATIVE
1.25 VOLUME
1.5
1.75
2
CHART for
D4b
Cegory
-
“ARlABLE
RELATIVE
C,,Am FM
COST
-
VOLUME
3 at Xl?& Reference DCF-ROR
Dk
-
VOLUME
VARIABLE
Caregoni ‘3 at 3%
COST
-
VOLUME
Refereny? RCF-RDR
4.6
00.25
I 0.5
0.75
t RELATWE
1.25 VOLUME
1.5
1.75
2
104 CHART
D5a -
For Category
0.25
0.5
CAPITAL
3 ar 10%
0.75
1.5
D5b -
For Categary
0.25
0.5
0.75
VOLUME
1 RELATWE
CHART
-
Reference DCF-ROR
1.75
VOLUME
CAPITAL
-
VOLUME
3 a, 2C% Reference DCF-ROR
1 REALTWE
1.25 VOLUME
1.5
1.75
2
105 CHART
D5c -
For Category
0.5
CAP,TAL
3 at 3wb
0.75
-
1
1.25
RELATIVE
CHART
0.25
0.5
0.75
D6a -
VOLUME
Reference DCF-ROR
VARIABLE
1 RELATIVE
1.5
1.75
2
VOLUME
COST
1.25 CAPITAL
-
CAPITAL
1.5
1.75
2
106 CHART
D6b -
VARIABLE
COST
-
CAPITAL
For Cafeg~ry 3 sf 10% Reference DCF.ROR
4
2
1
O0.25
0.5
0.75
1 RELATIVE
CHART
D&
For Category
-
1.25
1.5
1.75
2
CAPITAL
VARIABLE
COST
-
CAPITAL
3 at 30% Reference DCF-ROR
1.5
1
.
0.5
0.25
0.5
0.75
1 RELATIVE
1.25 CAPITAL
1.5
1.75
2
107 CHART
Ela
-
For Category
VOLUME
-
PRICE
4 at 10% Reference DCF-ROR
18
RELATWE
CHART
Elb
For Category
-
PRICE
VCWJME
4 at 20%
-
PRICE
Reference DCF.ROR
10
8
RELATIVE “OLUME
= f” I
’
1.5
1.75
1.8
8
__
0.25
0.5
0.75
1
RELATIVE
1.25
PRICE
2
108 CHART
0.25
0.5
Elc
-
VOLUME
0.75
1 RELATIVE
CHART For
0.25
0.5
0.75
-
E2a -
CAPITAL
PRICE
1.5
1.25
1.75
2
PRICE
-
PRICE
Category 4 at 10% Reference DCF-ROR
1 RELATWE
._
1.25 PRICE
1.5
1.75
2
109 CHART For
CHART For
E2b -
Categor”
E2C -
Category
CAPITAL
-- PRICE
4 at 20% Reference
CAPITAL 4 at 30% I
-
OCF-ROR
PRKE
Reference
DCF-ROR I
110 CHART
E3a -
For Categarv
15
-
14
.
12
-
10
-
FIXED
COST
-
PR,CE
4 at 10% Reference DCF~ROR
8
6
-
4
-
2
-
0.25
0.5
0.75
1
1.25
RELATIVE
CHART
E2b
For Category
-
FIXED
1.5
1.75
2
PRKE
COST
-
PR,CE
4 at 2D% Reference DCF-ROR
9
8
7
5-’ 5
4
3
2
1
0 0.25
a5
0.75
1 RELATWE
1.25 PRfCE
1.5
1.75
2
111 CHART
E3.z -
For Category
FIXED 4 at 30%
COST
-
PRICE
Reference DCF-ROR
7
6
5
I
3
2
1
0 0.25
0.5
0.75
1
1.25
RELATIVE
CHART
E4a -
For Category
0.25
0.5
0.75
1.5
-
VOLUME
4 at 10% Relative
FIXED
DCF-ROR
1 RELATIVE
1.75
2
PRlCE
COST
1.25 VOLVME
1.5
1.75
2
112 CHART Far
0.25
0.6
0.75
E4b -
Category
FIXED
COST
-
4 at 10%
Reference
1
1.25
RELATIVE
VOLUME
VOLUME DCF-RCIR
1.5
1.75
2
113 CHART
E5a -
For Category
CAPITAL
-
VOLUME
P at 10% Reference
DCF-ROR
14
12
10
c %
8
5
3 E
5
4
2
0 0.25
0.5
0.75
3 RELATIVE
CHART
0.5
0.75
1.5
1.75
2
E5b -
For Category
0.25
1.25 VOLUME
CAPlTAL - VOLUME 4 at 20% Reference DCF-ROR
1 RELATWE
1.25 VOLUME
1.5
1.75
2
114 CHART
E5c -
CAPITAL
-
VOLUME
For Category 4 at 30% Reference DCF-ROR
0.25
0.5
0.75
1.25
1 RELATIVE
CHART
EBa -
FIXED
1.5
1.75
2
VOLUME
COST
-
CAPITAL
For Category 4 at 10% Reference DCF-ROR 9
5
7
6
5
4
3
2
1
0 0.25
0.5
0.75
1 RELATIVE
1.25 CAPITAL
1.5
1.75
2
115 CHART
mb
-
For Category
FIXED
CDST
4 at 20%
1
-
CAPITAL
Reference DCF.RDR
I
I
I
-7% /
I
10
I
I
0.25
a.5
0.75
1
RELATIVE
CHART
E6c -
For Category
FIXED 4 at 30%
/
1.25
1.5
I 1.75
2
CAPITAL
COST
-
CAPITAL
Reference DCF RDR
3
1.5
0 0.25
0.5
0.75
1 RELATIVE
1.25 CAPITAL
1.5
1.75
2
Costs and Production
Elsevier Science
Publishers
Ecor&omics,
B.V., Amsterdam
8 (1984)
55 - 115
- Printed
in The Netherlands
GENERALISED SENSITIVITY CHARTS Ivan V. Klumpar * Massachusetts
Institute
of Technology,
One of the most important parts of the economic evaluation of industrial processes is sensitivity analysis. It assesses the effect on the process economics of various engineering and economic parameters. A widely used method of sensitivity analysis starts with defining a base or reference case and determining its economics in terms of a criterion, such as cost or profitability. Subsequently, one parameter at a time is varied over a range of values, and the corresponding changes in the selected criterion are estimated. In some cases, the investigator varies two related parameters at the same time. Assume, for example, that it is desired to investigate the effect on profitability of plant capacity, with all other independent variables unchanged. A higher capacity implies the increase in two parameters, capital cost and production, as opposed to the increase in production at constant capital, which can be denoted as attaining higher plant productivity. Capital and production are two distinct parameters. The former, an economic variable, affects cash flow primarily during the construction period; while production, an engineering variable, may have a major impact only after start-up. Rarely are more than two selected parameters varied at the same time in sensitivity analysis. The purpose of this analytical tool would be defeated, as the individual effects would become blurred. The variation of a *Currently
with
0167-188X/84/$10.00
Sturtevant,
Inc.,
Boston,
MA
1984 Elsevier Science
(U.S.A.).
Publishers
Cambridge,
MA (U.S.A.1
parameter (e.g., production) changes, of course, a certain number of other parameters (e.g., raw material consumption), but this change can be considered secondary. The remaining parameters (e.g., raw material cost per pound) are not affected. Mathematically, the latter can be considered independent variables together with the varied parameter (production); while the other parameters, subject to secondary change (raw material consumption), are dependent variables. In using sensitivity analysis, it should be kept in mind that this mathematical model is a convenient simplification of the real life. In most sensitivity analysis applications, the preferable economic criterion is profitability because it allows the measurement, with one yardstick, of the effects of both capital and operating costs. Profitability analysis has been lately done almost exclusively using yardsticks based on discounted cash flow, such as net present value, discounted cash flow rate of return (DCF-RR), etc. However, for back-of-the-envelope calculations, return on investment (ROD is still widely used. In a typical sensitivity analysis, a number of independent parameters is investigated, the profitability being calculated for several values of each. Accordingly, sensitivity analysis exceeds profitability analysis in the volume of computations by one or two orders of magnitude. To speed up routine sensitivity analyses, a set of generalized charts was developed that allows the determination of the B.V.
56 approximate DCF-RR sensitivity of any industrial process to 13 selected engineering and economic parameters. Upon classifying industrial processes into seven categories, it was found that the’ DCF-RR of any process within a category approximately conforms to a general correlation of a selected set of independent parameters if both the DCF-RR and each parameter are expressed as ratios to their relative variables. A set of reference parameter values is defined as a selected set of values that constitute a reference case with a reference DCF-RR value. The approach is discussed in detail elsewhere [ l-31. Process categories are defined, based on the concept of the variable, semivariable, and fixed components of operating cost. The variable component is proportional to plant capacity and includes such items as raw materials. The fixed component, such as overhead, is a constant, independent of capacity within the range of sensitivity analysis. The semivariable component varies directly with
capital cost, but is affected less by capacity changes. Accordingly, it is expressed as a capital factor. If the capital is $100 million and the capital factor lo%, the semivariable cost is $10 million per year. A typical semivariable item is maintenance cost. The process categories are defined according to the extent to which the components control operating cost (see Table 1). TABLE 1 Process Category
Number
1 2 3 4 5 6 I
categories
Name of controlling component(s)
All three Semivariable Variable Fixed Semivariable and fixed Variable and fixed Variable and semivariable
Component expressed as Percent Operating Cost Variable
Semivariable
Fixed
33.3 4 92 4 4
33.3 92 4 4 48
33.3 4 4 92 48
48
4
48
48
48
4
TABLE 2 Definitions
and assumptions
Term
Text
Base Case
A combination of parameters selected by the user of the charts as a basis for the sensitivity analysis. The Base Case DCI: rate of return must be known to the user.
Capital (Cost)
Equals depreciable life.
Capital Factor
Represents all capital charges against operating cost excluding a percentage of C. Reference cases assume K = 10%.
Category
Used to classify processes according to whether variable, or two of them, or all control operating cost. See Table 1.
Depletion
Allowance
Depreciable
Capital
Depreciation
Life
DCF Rate of Return
Symbol
capital (cost). Charts assume capital outlay in the first year of venture depreciation. semivariable
Expressed or fiied
as
costs,
Amount by which taxable income may be decreased by law for certain processes. Relative A is expressed as a percentage of sales. Reference cases assume A = 0. See Capital (Cost). Period of time during which capital may be written off for tax purposes by law. Charts are based on straight line depreciation and reference cases assume D = 12 years. Discounted-cash-flow DC&RR” of 10,20,
rate of return and 30%.
or DW-RR.
Reference
cases assume a “reference
Expense
See Investment
Fixed Cost
Operating cost component that can be assumed independent of capital and production rate within a limited range, as long as the number of trains doesn’t change. Fixed cost is a sum of such items as supervision, most operating labor, and some overhead costs.
Investment
Expense
C
Expense.
Any non-depreciable investment other than working capital. Relative E is expressed as a percentage of capital. Charts are based on an E outlay in the fist year of venture life. Reference cases assume E = 0.
E
57 Operating
Cost
All periodic, non-depreciable expenditures such as production or manufacturing costs, selling and delivery expense, and corporate charges. Operating cost is the sum of variable, semivariable, and fixed costs expressed in $/year.
Pammete
One of the process and economic
price
Equals selling price. In a multi-product case, a major product is used for expressing volume and its price is adjusted to account for the other products. Charts assume constant price over the venture life.
Production
Rate
variables that determines
_
DCF-RR. P
See Volume.
Reference
Reference case is a selected DCF-RR of 10,20, “I 30%.
Relative
DCF-RR
DCF-RR divided by its reference
Relative
Parameter
Parameter investment
combination
of parameter
values
to yield
a reference
value.
divided by its Base Case value, except for the relative depletion allowance, expense, and salvage which are defined in a different way (see these terms).
Sales
Annual gross sales revenue, i.e., before subtracting any periodic expense, such as selling cost. Charts assume G =PQ and treat all reimbursements as sales except for salvage.
Sales Volume
See Volume.
Salvage (Value)
Portion of capital cost that is recovered in a later year of venture life. Relative 2 is expressed as a percentage of capital. Charts are based on depreciating capital to zero and treating Z as a cash inflow in the last year. Reference cases assume Z = 0.
Semivariable
Operating cost component that can be assumed proportional to capital, such items as maintenance cost, property taxes and insurance, depreciation,
Cost
cxprcsscd
as a perccntagc
Annual federal, state, and local income income. Reference cases assume T = 50%.
Variable Cost
Operating cost component that can be assumed proportional a sum of such items as raw materials, selling and distribution,
Venture
Includes the entire period of time during which expenditures and reimbursements associated with the process occur, such as R&D, investment and operating costs, sales revenues and satvagc value. Charts are based on using the first year of venture life solely for capital, working capital, and investment expense outlays. Reference cases assume L = 21 years.
of taxable
to production rate, i.e., and some utilities costs.
VOlU*e
Annual sales volume expressed in terms of a major product (see Price). Charts assume that volume does not change over the venture life and equals production rate. Differences between volume and production rate are included in working capital variations.
Working Capital
Charts assume that working capital can be expressed as a sum of items, each proportional to either sales, capital, or an operating cost item. It is laid out in the fist year of venture life and adjusted, if necessary, to reflect variations in sales, capital, and operating cost in the later years. Definitions and basis of working capital items, and values of proportionality factors used in reference caxs, are shown below:
WorkinK Capital Structure Item
Basis
Factor**
Inventories: Raw materials Work in process Finished goods Materials & Supplies
Raw material cost per day Operating cost per day* Total operating cost per day Depreciable capital
30 3 30 0.03
Accounts: Receivable Payable (negative)
Sales per day Operating cost per day*
30 30
Operating
Fixed cost per day
30
cash
(Item) = (Factor)
*Excluding depreciation. **Value of factor on which the charts are based.
(Basis)
G
i.e., a sum of etc.
Tax Rate
Life
taxes
Lower Case Letter
Q
W
The generalized sensitivity charts are plots of relative DCF-RR versus a relative parameter. Two types of charts were developed as follows: l The one-parameter charts comprise a family of seven curves, representing process categories; l On the two-parameter charts, the family of curves represents the second parameter. Assumptions underlying the charts are summarized in Table 2. The relative DCF-RRS are based on three arbitrary reference values of 10, 20, and 30 percent. Accordingly, there should be 3 X 13 = 39 one-parameter charts because of the 13 selected parameters involved. With seven process categories, the corresponding number of two-parameter charts would be excessive. Rather, the number was limited to the categories and parameters which have the greatest effect on profitability. This effect was determined in a separate study [I]. The resulting TABLE Index
selection and 4. TABLE
of charts is summarized
in Tables 3
3
Index of one-parameter
charts
Parameter
Table Number
Selling Price Sales Volume Depreciable Capital Tax Rate Variable Cost Fixed Cost Capital Factor* Depreciation Life Working Capital Venture Life Depletion Allowance Investment Expense Salvage Value
for Reference
DCF-RR
10%
20%
30%
Ala A2a A3a A4a A5a A6a A7a A8a _
Alb A2b A3b A4b A5b A6b A7b A8b A9 Al0 Allb A12b Al3
Ale A2c A3c A4c A5c A6c A7c A8c _
Al la A12a _
Allc A12c _
*Capital factor equals all capital charges against operating cost excluding depreciation. It is expressed as a percentage of capital cost.
4 of two-parameter
Parameter Combination
charts Table Number
for
Category 1, Reference DCF-RR
Price Volume Price Capital Price Variable Cost Price Fixed Cost Price Capital Factor Volume Variable Cost Volume Fixed Cost Volume Capital Factor Volume Capital
Category 2, Reference DCF-RR
Category 3, Reference DCF-RR
Category 4, Reference DCF-RR
10%
20%
30%
10%
20%
30%
10%
20%
30%
10%
20%
30%
Bla
Blb
Blc
Cla
Clb
Clc
Dla
Dlb
Dlc
Ela
Elb
Elc
B2a
B2b
B2c
C2a
C2b
c2c
D2a
D2b
D2c
E2a
E2b
E2c
B3a
B3b
B3c
D3a
D3b
D3c
B4a
B4b
B4c
E3a
E3b
E3c
BSa
B5b
B5c
B6a
B6b
B6c
B7a
B7b
B7c
E4a
E4b
E4c
B8a
B8b
B8c
C4a
C4b
c4c
B9a
B9b
B9c
C5a
C5b
c5c
E5a
E5b
E5c
C3a
C3b
c3c
D4a
D5a
D4b
D5b
D4c
D5c
59 Table 4 (continued) Capital -
Variable Cost Capital Fixed Cost Capital Capital Factor Variable -
, Fixed Cost Variable ~~ Capital Factor Fixed Cost -
Capital Factor Price Tax Rate Price Depreciation Life Price Venture Life Volume -
Depreciation Life Volume Venture Life Variable Cost -
Depreciation Life Variable Cost Venture Life Fixed Cost -
Depreciation Life Fixed Cost Venture Life olpital Factor -
Depreciation Life Capital Factor Venture Life Tax -
Fixed Cost Tax Variable Cost Tax Capital Tax Volume Tax Capital Factor Tax Depreciation Life Tax Venture Life Depreciation
Life -
Capital Venture Life -
Capital Venture Life ~~ Depreciation Life
BlOa
Blob
Bloc
Blla
Bllb
Bllc
B12a
B12b
B12c
B13a
B13b
B13c
B14a
B14b
B14c
BlSa
BlSb
BlSc
B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30 B31 B32 B33 834 B35 B36
D6a
D6b
D6c E6a
C6a
C6b
C6c
E6b
E6c
60 TABLE 5 Chart usage step NO.
Example
Step Description
Sales volume, Depreciable capital, Operating cost items: raw material, selling & distribution, utilities, operating labor, supervision & services, capital factor, Tax depreciation life, DCF rate of return,
= lS$/ib = 3$/lb = 2$/lb = $lZMM/yr =40%1 k =9%C D =13yrs R = 14.9%
Establish parameter variations
(a) Increased productivity, (b) Decreased capital,
p’ = 140 MM lbs/yr C” = $77 MM lbs/yr
Calculate variable cost
V=(m+d+u)Q = (0.15 + 0.13 + 0.02) 100
= $20 MM/y1
Calculate fixed cost
F = (l.o+s) I = (1.4) 12
= $16.8 MM/yr
Calculate semivariable cost
S=(K+l/D)C =(0.09+
Determine
Category
Calculate relative parameters
(a) Relative increased productivity q = Q’/Q = 140/100 = 1.4 (b) Relative decreased capital c = c-/c = 17/l 10 = 0.7
Determine relative DCF Rate of Return (DCI:-RR)
For a reference DCl‘-RR of 20%, the relative DC&RR, denoted as r, is: (a) r’ = 1.6 for q = 1.4 from Chart A2b (b) I” = 1.4 for c = 0.7 from Chart A3b More accurate r’ err” values may be obtained by interpolating between Charts A2b and A3b and the corresponding 10% reference DCF-RR charts
Calculate DCI:-RR sensitivity to parameter variations
(a) For increased productivity, R’ = r’R = 1.6 (14.9) = 23.8% (b) For decreased capital, R” = r”R = 1.4 (14.9) = 20.9% The actual values calculated by computer
Establish reference ca.se
l/13)
Q = 100 MM lbs/yr C =$llOMM m d u I
110
= $18.36 MMlyr
No. 1 because V, S and F are approximately
The charts are used in the following way. First, the user establishes the reference values of all parameters, determines the process the reference computes category, and DCF-RR. Second, he selects the parameter and/or pairs of parameters to be investigated in the sensitivity analysis. For the parameters involved, he computes one or more relative values within the investigated range. Third, for each relative parameter value, or pair of he determines the relative such values, DCF-RR by interpolating between curves and he computes the correcharts. Finally, sponding DCF-RRs by dividing each relative -
equal
are R’ = 24.6,
R” = 21.8
value by the reference value. An illustrative example is shown in Table 5. REFERENCES 1
2
3
Agarwal, J.C., and Klumpar, I.V., 1975. Generalized Profitability and Sensitivity Analysis, Trans. AACE 1975 paper, C-l. Agarwal, J.C., and Klumpar, I.V., 1975. Profitability sensitivity and risk analysis for project economics. Chem. Eng., 82(20): 66. Klumpar, I.V., 1980. Sensitivity analysis charts. Proceedings, 6th Int. Cost. Eng. Congress, Mexico City, Oct. 1980, paper Dl.
(Received
March 25,
1983; accepted
November
21,
19831
61 CHART Alb
-
PRlCE
AT
*o?& REFERENCE
“CF
RR
/I
3.0
2.5
E
2
/
2.0
Y 5 i Lt
1.5
-
1.0
0.5
0
0.5
I
I
1.0 RELATlVE
I
I
I
1.5
2.0
25
PRICE
I
30
2.3.7
A6 I 1.0
2.0
I 3.0
I 4.0
3
CHART
A2b
-
SALES
VOLUME
AT
20% REFERENCE
CHART
DCF-RR
A2c - SALES
VOLUME
CATEGORY
AT 30% REFERENCE
DCF RR
NO.
3.0 -
2.5 -
2.0 -
1.5 -
1.0 -
RELATIVE
VOLUME
0.5 -
RELATIVE
CHART
A&
-
DEPREClABLE
CAPlTAL
AT
IO?6 REFERtNCE
CHART
DCFRR
A3b
-
DEPREClASLE
CAPlTAL
VOLUME
AT
20% REFERENCE
DCFRR
-
-
-
\ <
I 0.25
I 0.5
!
I 0 75
RELATIVE
-
-Y I
1.0
1.25 CAPITAL
1.5 COST
1
-_-L i
2.0
I 2.25
0.25
I 0.5
I 0.75
I 1.0
RELATIVE
I
I
I
I
1.25
1.5
1.75
2.0
CAPITAL
COST
CHART
A3c
-
DEPRECIABLE
CAPITAL
AT
5.0-
30%
l-
REFERENCE
I
I
CHART
DCFRR
A4a
-
TAX
RATE
AT
10% REFERENCE
OCF RR
I
!
I I
I
0’
1 0.75
0.5
0.25
I
I
,
I
1.0
1.25
1.5
1.75
RELATIVE
CHART
A4b
TAX
RATE
AT
CAPITAL
20%
RELATIVE
COST
REFERENCE
DCF-RR
y
1.0
F
4 g
0.8
0.6
0.4
2.0
I .8 RELATIVE
I 1.2 TAX
I 1.6 RATE
RATE
I 2.0
CHART
I .4
TAX
\I 2.0
I
A4c
-
TAX
RATE
AT
30%
REFERENCE
\
DCF-RR
‘t
-
\
-
L
OO
0.2 I
\
I 3.4
I 0.4
I 0.6
I 0.8
I 1.0
I
I
1.2
1.4
I 1.6
I I 1.8
6
64 CHART
Ma
-
VARIABLE
CHART
COST AT 10% REFERENCE DCF-RR
A5b
-
“AHIABLE
COST AT 20%
DCF-RR
REFERENCE
2.5
0
5
\ J CHART
3.0-
A!%
oz 8 ?
2.0
COST
AT
30%
REFERENCE
ASa -
FlXED
COST
AT 10%
2.5
COST
REFERENCE
DCF-RR
DCF-RR
I
3
-
\
C/
~
? r 4 %
CHART VARIABLE
VARIABLE
__
6
2.5--
-
20
15
1.0 RELATIVE
--
l.!i-
& to--2.5
2.5
-
p .5-
OO
-
f
I
1.0 REI_AT,“E
I 1.5 VARIABLE
I
2.0 COST
I
2.5
2.5 RELAT,“E
FIXED
COST
65 CHART
A&
-
FIXED
COST
AT
30%
REFERENCE
DCF-RR
I-
,-
I-
\
CHART 1.4
1.2
f
1.0
B y
0.6
I=
4 E
0.6 0.4 0.2 0
\,
I 20
1.6
,-
A7b
-
CAPITAL
FACTOR
AT
20%
REFERENCE
DCF-RR
66 CHART
0
A7c
-
CAPITAL
1I
01
FACTOR
AT
2I
30%
REFERENCE
3I
OCF-RR
4I
I
CHART
A&
-
DEPRECIATION
LIFE
AT
10% REFERENCE
DCF-RR
(
5 RELATIVE
CAPITAL
FACTOR
RELATIVE
CHART
1.20
A86
-
I
DEPRECIATION
I
I
LIFE
AT
20% REFERENCE
I
’ CATEGORY NO.
0.9
J 0
, 0.4
I 0.8
1 1.2 RELATIVE
I 1.6 DEPRECIATION
LIFE
DCF-RR
I
/
(
/
1 2.0
, 2.4
LIFE
DEPREclATloN
CHART
A&
-
DEPRECIATION
RELATIVE
LIFE
AT
DEPRECIATION
30%
REFERENCE
LIFE
DCF-RR
CHART
A9
-
WORKING
CAPlTAL
AT
20%
REFERENCE
CHART
DCF RR
A10
VENTURE
LIFE
AT
20%
REFERENCE
z=-
T
DCFRR
1.2.
x7
/ ITEGC
NC
-
-
-
0.2 -
OO I
1I
2I
RELATIVE
31
WORKlNG
41
CAPITAL
I
I
I
05
RELATIVE
CHART
Alla
-
DEPLETION
ALLOWANCE
AT
10% REFERENCE
DCFRR
CHART
Allb
-
DEPLETION
I 0.9
I 0.8
0.7
0.6
VENTURE
ALLOWANCE
AT
I
I 1.1
1.0
LIFE
20%
REFERENCE
F
-
6
-
Ik -
1
3.4
3.46
-.-
-
’
1
~ /
5
10 DEPLETION
15 ALLOWANCE;
20 % SALES
25
5
2
10
DEPLETION
15 ALLOWANCE,
20 % SALES
25
DCFRR
CHART
A12a
-
INVESTMENT
EXPENSE.
CHART
A,%
-
,N”ESTMENT
EXPENSE
AT
2096 RELATIVE
DCF-RR
CHART
0 0 EXPENSE,
% DEPRECfABLE
CAPITAL
A,%
1 20
-
I EXPENSE,
AT
sb DEPRECIABLE
INVESTMENT
40
EXPENSE
EXPENSE
1 60 % DEPREClABLE
10% RELATIVE
DCF.RR
CAPITAL
AT
30% RELATIVE
I
I
60
100 CAPlTAL
DCF-RR
I 120
I
69 CHART
A13
-
SALVAGE
VALUE
AT
2096 REFERENCE
CHART Bla- PRICE - VOLUME
DCF-RR
Far
01
I
I 40
1
0
20
SALVAGE.
% DEPRECIABLE
CHART For
Bib
Category
-
PRICE
I
I
60
80
Category
1 a, 10% Reference
DCF-RR
CAPITAL
-
CHART
VOLUM@
1 at 20% Reference
For
DCF RR
Blc
Category
-
PRiCE
-
VOLUME
1 at 30% Reference
DCF-RR
4.5
RELATIVE
4.0
PRICE = 2.0
-
3.6
1.1 ? L
0 RELATIVE
VOLUME
-
.6
hi
.8
I
I
I
1.0
1.2
1.4
RELATfVE
“OL
70 CHART For
E2a -
Category
PRICE
-
CAPITAL
1 at 10% Reference
DCF RR
CHART For
Bzb
Cafesw
-
PRICE
-
1 at 20%
CAPITAL
Reference
DCF-RR
5.0
4.5 -
4.0 -
-- t
3.5
t
3.0 1 -
-
RELATlYE PRICE = 2.0
I.7 ):
,i+?.IQ 1.4 -
-i-
1’
RELATIVE
CAPITAL
RELATIVE CHART
B3a -
FOr CafegorY
CHART Far
f32c -
Catwon/
PRICE 1 at 30%
RELATIVE
-
PRICE 1 at
-
VARIABLE
10% Reference
CAPITAL Reference
DCF.RR
CAPITAL RELATIVE
VARIABLE
CWST
COST DCF-RR
CNfTA
71 CHART Far
B3b -
I
PRICE
-
VARIABLE
1 at 20% Reference
categor”
I
COST
CHART
OCF-RR
I
I
For
I
B3c -
Category
PRICE
-
1 at 3%
VARIABLE
COST
Reference DCF-RR
I
3.6
3.0
2.5
2.0
1.5
RELATIVE
VARIABLE
COST
1.0
5
0
1.0
.5
CHART
B‘la
Far Catagar”
1.5
-
PRICE
-
2.0 RELATIVE FlXED
2.6 VARIABLE COST
COST
1 ax 10%‘ Reference DCF-RR CHA@T
B4b -
For Category
I
I
PRICE 1 af 20%
-
FIXED
COST
Reference DCF-RR
I
I
I
1.0
1.5
2.0 RELATIVE
I
3.5 -
0 RELATIVE
FIXED
COST
.5
2.5 FIXED COST
72 CHART For
B4c -
CBtegory
PRICE
-
1 at 30%
RELATIVE
FIXED Reference
FIXED
CHART
COST
For
DCF-RR
For
I
I
B5b
Catego,”
I
-
PRICE
1 at 20%
PRICE 1 ilt
-
lo?6
CAPITAL Reference
FACTOR DCF.RR
COST
.B CHART
B5a -
category
-
CAPITAL
Reference
.8
1.0
FACTOR
1.2 RELATIVE
1.4 CAPITAL
1.6 FACTOR
DCF-RR
I
I
I
CHART For
RELATWE
CAPITAL
FACTOR
B5c
Categwy
-
PRICE
-
CAPITAL
1 at 30%Reference
RELATIVE
CAPITAL
FACTOR DCF-RR
FACTOR
1.8
2.0
CHART
BSa -
“DLVME
-
VARIABLE
COST CHART
For Catesarv
66b
-
VOLUME
-
VARIABLE --
1 at 10% Reference DCF-RR
0
1.0
.5
1.6
2.0 RELATIVE
RELATIVE
VARIABLE
COS’,
CHART For
CHART S6c For
OL .s
Carqjorv
VOLUME f at 30%
-
VARIABLE
Category
VOLUME
-
FIXED
2.5 VARIABLE
COST
COST
1 at 10% Reference DCF-RR
COST
Reference DCF-RR
I
I
I
.8
I
I
I
1.0
1.2
1.4
1.6
1.8
RELATIVE
B7a -
COST
VARIABLE
COST
I 2.0
1.0 RELATIVE
1.5 FlXED
COST
2.0
74 CHART CHART
67b
For categor”
0
-
VOLUME
FIXED
1 at 2G% Referenae
COST
For
B7c -
Catergary
VOLUME
-
FIXED
1 at 30% Reference
RELATIVE
2.5 FIXED COST CHART FM
BBb -
Caewry
FIXED
VOLUME
-
COST
CAPITAL
1 at 20% Reference
Fo,
S8a -
Category
VOLUME 1 at lC%
-
CAPITAL
Reterence
FACTOR
DCF-RR I
I CHART
COST DCF RR
DCF.RR
2.0 RELATIVE
1.5
1.0
.5
-
FACTOR -
DCF-RR 3.5
3.0
2.5
4 i z
2.0
I! P ‘).
,.
) RELATWE
CAPITA‘
FACTOR
.5
1.0
2.5
2.0
1.5 RELATIVE
CAPITAL
FACTOR
75 CHART For
BBC -
Catewry
VOLUME I at 30%
RELATIVE
CHART For
Wb
Category
.._
-
-
CAPITAL
Reference
CAPITAL
CAPITAL
1at 20%
CHART
FACTOR
DCF.RR
For
Wa
-
Catepxv
FACTOR
-
CAPITAL
-
VOLUME
1 at 10% Reference
RELATIVE
DCF-RR
VOLUME
VOLUME
Reference
I
PCF-RR
I
I
CHART For
Wc
Category
-
CAPITAL 1 at 30%
-
VOLUME
Reference
DCF-RR
2.5
2 8 s j
1.5
I
0’ .5
1.0
1.5
2.0 RELATIVE
VOLUME
0.5
0.75
I
I
1
1.25 RELATIVE
VOLUME
I
1.5
I
1.75
I 2
76 CHART BlOa - VARIABLE For
Categor”
COST
1 at 10% Reference
-
CAPITAL
CHART For
DCF-RR
BlOb
-
VARIABLE
category 1 at
20%
COST
Reference
I
I
I
.5
1.0
1.5
2.5
-
CAPITAL
OCF-RR
I
I
-I
3.I 20
3.c 1.5 x g i a
2.5 1.0 z
L
B ;
2.0
.5 4 z 1.5 0 .6
.B
1.2
1.0
1.4
RELATIVE
1.6
1.8
2.0
CAPITAL I.0
.5
0 0
CHART For 1.8,
I
BlOc
-
caregary1 I
VARIABLE 30%
a2
I
COST
Reference
I
-
CAPITAL
OCF-RR
I
I
I CHART For
RELATIVE
CAPITAL
2.0 RELATIVE
Bl,a
Category
-
FIXED
1 at lwb
-
CAPITAL
Reference
COST
DCF.RR
2.5 CAPITAL
77 CHART
Bllb
-
For Category
FIXED
COST
-
CHART
CAPITAL
Bllc
-
For Category
1 at 20% Reference DCF-RR
I 1.0
I
.2
.a
.6
FIXED
1.0
1.5
2.0 RELATIVE
Rl2b
-
For Category I
B12a
For Categov
-
CAPITAL
FACTOR
-
CAPlTAL
1 at 10% Reference DCF.RR
RELATIVE
CAPlTAL
CAPITAL
I
I
I
I
1.4
1.6
1.8
2.0
CAPITAL
2.5 CAPITAL CHART
CHART
-
Reference DCF-RR
1.2 RELATIVE
s
COST
1 at 30%
1
CAPITAL
FACTOR
-
CAPITAL
1 at 20% Reference DCF-RR I
I
I
I
78 CHART
812~
-
For Category 2
I
CAPITAL
1 at 30%
FACTOR
-
CHART
CAPITAL
B13a -
VARIABLE
COST
-
FIXED
I
I
I
I
I
I
I
I
-.
1.5 I--_
f ri
X z 4: w’ c
1
0.5 I-.
I
a
0.5
COST
Reference DCF-RR
0.75
I 1
I
I 1.5
1.25 RELATIVE
I 1.75 RELATIVE
CAPITAL
CHART
B13b
-
VARIABLE
For Category
COST
-
FIXED
COST
1 af 20% Reference DCF-RR
RELATIVE
FIXED
COST
FIXED
COST
79
CHART 813C _ “AR,ABLE For Categw+
0 0.5
I
0.75
COST
--
FIXED
CHART 814-
COST
For
category
VARIABLE
COST
-
CAPITAL
1 at 10% Reference DCF-RR
, at 30% Reference DCF-RR
I
1 RELATIVE
I
I
I
1
1.25
1.5
1.75
2
FIXED
COST
RELATIVE
CHART
B,Q,,
-
VARIABLE
For Csfegory
I af 2wb
RELATIVE
COST
-
CAPITAL
~e‘erense
CAPITAL
DCF-RR
FACTOR
FACTOR
CAPITAL
FACTOR
FACTOR
80 CHART Far 1.2,
.51 .6
8%
-
Category I
I
.a
VARIABLE
COST
-
CAPITAL
FACTOR
1 at 30%
Reference
DCF-RR
t
I
I
r
I
I
I
I
1.2
1.4
1.6
1.8
I 1.0 RELATIVE
CAPITAL
CHART
61%
-
FIXED
COST
-
CAPITAL
FACTOR -
f
1
2.0
FACTOR
.6
.6
1.0 RELATIVE
CHART
B,Sb For
-
FIXED
Categon/
COST
-
CAPITAL
1 at 26% Reference
RELATIVE
CAPfTAL
FACTOR
DCF-RR
FACTOR
1.2
1.4 CARTAL
1.6 FWTOR
1.8
2.0
81 CHART
B1E.c -
For Category
.5 .d
FlXED
1 at 30%
COST
-
CAPITAL
FACTOR
CHART
Reference DCF-RR
For
I
I
I
I
I
I
.8
1.0
1.2
1.4
1.6
1.8
RELATIVE
CAPITAL
816
Category
-
PRICE
-
TAX
RATE
1 at 2096 Reference DCF-RR
2.0
FACTDH
RELATWE CHART
817
For Category
-
PRICE
-
DEPRECIATION
UFE -
CHART
1 af 20% Reference DCF.RR
818
-
For Categow
PRICE
-
“ENTVRE
TAX
RATE
LiFE
1 at 20% Reference DCF-RR
3.5
3.0
2.5
$ x 2.0 g I5 z x5
l.0
.5
0
I 3
I 1.0
I 1.5 RELATlVE
I
J
I
2.0 2.5 OEPREClATlDN
a
I/ .25
UFE
I
I
.5
.75
I 1.0 RELATWE
I 1.25 VENTURE UFE
1
CHART
019
For Category
-
VOLUME
-
DEPRECIATION
CHART
LIFE
1 at 20% Reference DCF-RR
820
For Category
-
VOLUME
-
“ENTVRE
1 at 20% Re‘xence
LlFE
DCF-RR
4.0
.5 -
3.5
.O -
3.0
RELATIVE
VOLUME = 2.5 -
-
/-
.5 -
.O -
.5 -
.Q -
.5 -
Q0 RELATIVE
CHART
821
-
VARIABLE
Far Category
COST
-
DEPRECIATION
1 at 20% Reference DCF-RR
2& i i
RELATIVE
DEPREClATlON
LIFE
LIFE
VENTURE
LIFE
0.0
0.0
0.5 RELATIVE
For Category
1.0 DEPRECIATION
1.5
1 af 20% Reference
LIFE
DCF-RR
2.0
For
2.5
VENTURE
LIFE
1 at 20% Reference DCF-RR
RELATIVE
Cmg~ry
0.2
0.4
For
CHART
-
0.5
Category
824
RELATIVE
VENTURE
0.8 UFE
LIFE
1.0
DCF-RR
VENTURE Reference
COST 1 at 20%
FIXED
1.2
84 CHART
0.4 0.0
825
-
CAPITAL
FACTOR
-
DEPRECIATION
LIFE
I
I
I
I
0.5
1.0
1.5
2.0
RELATIVE
CHART
826
-
CAPITAL
RELATIVE
DEPRECIATION
FACTOR
-
“ENTVRE
LlFE
VENTURE
LIFE
LIFE
I 2.5
85 CHART For
I
827 -
Category
I
TAX
-
1 at 20%
FlXED Reference
I
CHART
COST
For
DCF-RR
1
828
-
Category
TAX
-. VARIABLE
COST
1 at 2046 Reference DCF-RR
l-
1.75
-
-
i ::
Y F
5
z
I
I
I
.5
3.0
1.5
I 2.0 RELATIVE
L 2.5 FI, (ED
0
.5
1.0
1.5
COST
CHART
830
-
TAX
2.0 RELATIVE
, 2.5 VARlABLE COST
-- VOLUME
RELATIVE
VOL”,,
86 CHART For
831
Category
-
TAX
-
CAPITAL
FACTOR
1 at ZG% Reference
OCF-RR
+.!+ 1.7
,.li 0.0
OS
1.5
1.0 RELATIVE
CHART For
0.0
0.5
832
-
CafegDry
TAX
CAPITAL
-
2.0
OEPRECIATION
LfFE
1 a120% Rsference
OCF-RR
1.0
1.5
RELATWE
2.5
FACTOR
D.wI)EC,AT,DN
2.0 UFE
2.6
87 CHART
2
0.4
833
-
TAX
0.6
834
For Category
VENTURE
LIFE
1.0
0.8 RELATIVE
CHART _.
-
-
VENTURE
DEPRECIATION
1.2
LIFE
LIFE
-- CAPlTAL
1 at 20% Reference DCF-RR
RELATIVE
DEPRECIABLE
CAPITAL
88 CHART
835
-
For Cafegory I
I
I
VENTURE
LIFE
1 at 2056 Referents
-
CAPITAL DCF-RR
I
I
I
2.5
$
x
2.a
z 2 2 1.5
1.0
.5
0 0
1.5 RELATIVE
CHART
836
-
VENTURE
For Category
1
0.5
t
-
0
DEPRECIATION
LlFE
at 20% Reference DCF-RR
1.0 RELATIVE
1.5 DEPRECIATION
2.0 LIFE
89 CHART For
0.25
0.5
Cla
Category
0.75
3.5
3
g
2.5
B 5 F
2
Is :
1.5
1
0.5
0
VOLUME 2 at
10%
1 RELATIVE
4
-
-
PRICE
Reference
1.25 PRICE
DCF-ROR
1.5
1.75
*
90 CHART
ClC
For Categ~y
VOLUME
-
2 at 30%
RELATIVE
CHART
C2a -
For Category 1.5
4
3.0
3
_
PRICE
-
Reference DCF-ROR
CAPITAL
PRICE
-
PRICE
2 a, 10% Reference DCF-ROR
91 WART
C2b -
For Categcn,
0.75
CAPITAL
2 at Zwb
-
CZc -
For category
0.25
0.6
0.76
DCF-ROR
1
1.5
REALTIVE
CHART
PRICE
Referam
CAPITAL
1.15
PRICE
-
PRICE
2 at 3G?4 Reference DCF-ROR
1 RELATIVE
1.25 PRICE
1.5
1.75
z
92
3
2.5
2
x 5
1.5
9 z 1
0.5
0 0.25
0.5
0.75
1 RELATIVE
CHART
C3b -
For Catqpry
0.25
0.5
0.75
CAPITAL
1.25
1.5
1.75
PRICE
FACTOR
-
PRICE
2 .w 20% Reference DCF-ROR
1 RELATIVE
1.25 PRICE
1.5
1.75
2
93 CHART
C3c -
For Category
CAPITAL
I 0.2%
0.5
I
il.75
1 RELATIVE
CHART
C&
For Cafegory
FACTOR
-
PRICE
2 at 30% Reference DCF-ROR
-
CAPITAL
I
I
1.5
1.25 PRICE
FACTOR
-
VOLUME
2 at 10% Reference DCF-ROR
RELATIVE
“OLVME
I 1.75
2
94 CHART
C4b -
For Category
CAPITAL
FACTOR
-
VOLUME
2 at 2c% Reference DCF-ROR
I
0.25
0.5
0.75
1
RELATIVE
CHART
C4E -
For Category
0.25
0.5
0.75
CAPITAL
1
1.75
2
VOLVME
FACTOR
2 at 30% reference
RELATIVE
1.5
1.25
1.25 VOLVME
-
VOLUME
DcF.ROR
1.5
1.75
2
95 CHART -
C5a -
CAPITAL
RELATIVE
CHART
C5b -
For Category
CAPITAL
2 at 2m
-
VOLUME
VOLUME
-
VOLUME
Reference CJCF-ROA
4.6
3.5
1
0 0.25
0.5
0.75
1
RELATIVE
1.25
VOLUME
I.5
1.75
2
96 CHART
C5c -
For Category 3.5
CAPITAL
-
VOLUME
_
2 a, 30% Reference DCF-ROR
-I-
3
1
0.5
0 0.25
0.5
0.75
1
1.25
RELATIVE
CHART For
C5a -
Category
CAPITAL 2 al
1.5
1.75
2
1.75
*
VOLUME
FACTOR
-
CAPITAL
10% Reference DCF.RDR
2.5
.
2
0.5
0 0.25
0.5
0.75
1 RELATIVE
1.25 CAPITAL
1.5
97 CHART
C6b -
For Category
CAPITAL 2 at 20%
FACTOR
-
CAPITAL
Reference DCF-ROR
2 CAPITAL FACTOR = 0.6
1.6
E L
1.2
8 ;
9 &
0.8
0.4
0. 0.25
0.5
U.75
1 RELATIVE
CHART
C6c -
For Categor”
0 0.25
0.5
0.75
CAPITAL 2 at 30%
1 RELATIVE
1.m
1.5
1.75
2
1.75
2
CAPITAL
FACTOR
-
CAPITAL
Reference DCF ROR
1.25 CAPITAL
1.5
98 CHART For
D,a
-
VOLUME
-
category3 at 10%
PRICE
Reference
DCF-ROR
4 3
0 0.25
0.5
1
0.75
RELATIVE
CHART
Dlb
-
VOLUME
1.25
1.75
2
I
I
I
1.5
1.75
2
1.5
PRlCE
-
PRICE
For Category 3 at 20% Reference DCF-ROR 9,
0.25
I
I
0.5
0.75
I
1 RELATIVE
I
1.25 PRlCE
99 CHART For
0.25
0.5
Dlc
Category
0.75
-
VOLUME
-
1
1.25
RELATIVE
CHART For
D2a -
PRICE
3 at 3D% Reference DCF-ROA
CAPITAL
1.5
PRICE
-
PRlCE
Category 3 ax 10% Reference
DCF-ROR
1.75
2
100 CHART
D2b -
CAPITAL
-
PRICE
For Category 3 at 20% Reference DCF-ROR
0
7
0
5
4
3
2
1
0 0.25
0.5
1
0.75
1.25
RELATWE
CHART
D2c -
For Categary
CAPITAL
3 a, 30%
RELATIVE
1.5
PRICE
-
PRICE
Reference DCF.ROR
PRICE
1.75
2
101
0.25
0.5
1
0.75
CHART
0%
-
1.5
1.25
RELATIVE
2
1.75
PRICE
VARIABLE
COST
-
PRKE
0 0.25
0.5
0.75
1 RELATIVE
1.25 PRICE
1.5
1.75
2
102 CHART
D3c -
For Category
-0.25
OS
COST -
VARIABLE
3 at 30%
0.75
1
1.25
RELATIVE
CHART
D4a -
For Category
PRICE
Reference DCF-ROR
1.5
1.75
2
PRICE
VARIABLE
COST
-
VOLUME
3 at 10% Reference DCF-ROR
10
9 REMTIVE
8
VARIABLE
.
COST = a*,
2
0.25
0.5
0.75
I RELATIVE
1.25 VOLUME
1.5
1.75
2
CHART for
D4b
Cegory
-
“ARlABLE
RELATIVE
C,,Am FM
COST
-
VOLUME
3 at Xl?& Reference DCF-ROR
Dk
-
VOLUME
VARIABLE
Caregoni ‘3 at 3%
COST
-
VOLUME
Refereny? RCF-RDR
4.6
00.25
I 0.5
0.75
t RELATWE
1.25 VOLUME
1.5
1.75
2
104 CHART
D5a -
For Category
0.25
0.5
CAPITAL
3 ar 10%
0.75
1.5
D5b -
For Categary
0.25
0.5
0.75
VOLUME
1 RELATWE
CHART
-
Reference DCF-ROR
1.75
VOLUME
CAPITAL
-
VOLUME
3 a, 2C% Reference DCF-ROR
1 REALTWE
1.25 VOLUME
1.5
1.75
2
105 CHART
D5c -
For Category
0.5
CAP,TAL
3 at 3wb
0.75
-
1
1.25
RELATIVE
CHART
0.25
0.5
0.75
D6a -
VOLUME
Reference DCF-ROR
VARIABLE
1 RELATIVE
1.5
1.75
2
VOLUME
COST
1.25 CAPITAL
-
CAPITAL
1.5
1.75
2
106 CHART
D6b -
VARIABLE
COST
-
CAPITAL
For Cafeg~ry 3 sf 10% Reference DCF.ROR
4
2
1
O0.25
0.5
0.75
1 RELATIVE
CHART
D&
For Category
-
1.25
1.5
1.75
2
CAPITAL
VARIABLE
COST
-
CAPITAL
3 at 30% Reference DCF-ROR
1.5
1
.
0.5
0.25
0.5
0.75
1 RELATIVE
1.25 CAPITAL
1.5
1.75
2
107 CHART
Ela
-
For Category
VOLUME
-
PRICE
4 at 10% Reference DCF-ROR
18
RELATWE
CHART
Elb
For Category
-
PRICE
VCWJME
4 at 20%
-
PRICE
Reference DCF.ROR
10
8
RELATIVE “OLUME
= f” I
’
1.5
1.75
1.8
8
__
0.25
0.5
0.75
1
RELATIVE
1.25
PRICE
2
108 CHART
0.25
0.5
Elc
-
VOLUME
0.75
1 RELATIVE
CHART For
0.25
0.5
0.75
-
E2a -
CAPITAL
PRICE
1.5
1.25
1.75
2
PRICE
-
PRICE
Category 4 at 10% Reference DCF-ROR
1 RELATWE
._
1.25 PRICE
1.5
1.75
2
109 CHART For
CHART For
E2b -
Categor”
E2C -
Category
CAPITAL
-- PRICE
4 at 20% Reference
CAPITAL 4 at 30% I
-
OCF-ROR
PRKE
Reference
DCF-ROR I
110 CHART
E3a -
For Categarv
15
-
14
.
12
-
10
-
FIXED
COST
-
PR,CE
4 at 10% Reference DCF~ROR
8
6
-
4
-
2
-
0.25
0.5
0.75
1
1.25
RELATIVE
CHART
E2b
For Category
-
FIXED
1.5
1.75
2
PRKE
COST
-
PR,CE
4 at 2D% Reference DCF-ROR
9
8
7
5-’ 5
4
3
2
1
0 0.25
a5
0.75
1 RELATWE
1.25 PRfCE
1.5
1.75
2
111 CHART
E3.z -
For Category
FIXED 4 at 30%
COST
-
PRICE
Reference DCF-ROR
7
6
5
I
3
2
1
0 0.25
0.5
0.75
1
1.25
RELATIVE
CHART
E4a -
For Category
0.25
0.5
0.75
1.5
-
VOLUME
4 at 10% Relative
FIXED
DCF-ROR
1 RELATIVE
1.75
2
PRlCE
COST
1.25 VOLVME
1.5
1.75
2
112 CHART Far
0.25
0.6
0.75
E4b -
Category
FIXED
COST
-
4 at 10%
Reference
1
1.25
RELATIVE
VOLUME
VOLUME DCF-RCIR
1.5
1.75
2
113 CHART
E5a -
For Category
CAPITAL
-
VOLUME
P at 10% Reference
DCF-ROR
14
12
10
c %
8
5
3 E
5
4
2
0 0.25
0.5
0.75
3 RELATIVE
CHART
0.5
0.75
1.5
1.75
2
E5b -
For Category
0.25
1.25 VOLUME
CAPlTAL - VOLUME 4 at 20% Reference DCF-ROR
1 RELATWE
1.25 VOLUME
1.5
1.75
2
114 CHART
E5c -
CAPITAL
-
VOLUME
For Category 4 at 30% Reference DCF-ROR
0.25
0.5
0.75
1.25
1 RELATIVE
CHART
EBa -
FIXED
1.5
1.75
2
VOLUME
COST
-
CAPITAL
For Category 4 at 10% Reference DCF-ROR 9
5
7
6
5
4
3
2
1
0 0.25
0.5
0.75
1 RELATIVE
1.25 CAPITAL
1.5
1.75
2
115 CHART
mb
-
For Category
FIXED
CDST
4 at 20%
1
-
CAPITAL
Reference DCF.RDR
I
I
I
-7% /
I
10
I
I
0.25
a.5
0.75
1
RELATIVE
CHART
E6c -
For Category
FIXED 4 at 30%
/
1.25
1.5
I 1.75
2
CAPITAL
COST
-
CAPITAL
Reference DCF RDR
3
1.5
0 0.25
0.5
0.75
1 RELATIVE
1.25 CAPITAL
1.5
1.75
2