Chemical Engineering Plant Design 1my.fit.edu/~akurdi2012/Plant Design 1/Cost Project/Costing...

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Chemical Engineering Plant Design 1 Costing of Ethylene Oxide Plant CHE 4181 By: Abdullah Kurdi Khalid Almansoori Nasser Almakhmari Report Submitted: 12/2/2015 Instructor: Dr. Jonathan Whitlow

Transcript of Chemical Engineering Plant Design 1my.fit.edu/~akurdi2012/Plant Design 1/Cost Project/Costing...

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Chemical Engineering Plant Design 1

Costing of Ethylene Oxide Plant

CHE 4181

By: Abdullah Kurdi

Khalid Almansoori

Nasser Almakhmari

Report Submitted: 12/2/2015

Instructor: Dr. Jonathan Whitlow

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Table of Content

Summery 2

Capital Cost 3

I. Methodology 4

II. Results 7

Manufacturing Cost 8

I. Methodology 9

II. Results 10

Profitability

I. Methodology 14

II. Results 15

References 16

Appendix A: Detailed Capital Cost Information 17

Appendix B: Manufacturing Cost Detailed Calculations 18

Appendix C: Electricity Price Extrapolation 22

Appendix D: Profitability Detailed Calculations 23

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Summery

The following report shows and discusses the methodology for the costing of a chemical

plant. The plant discussed specifically in this report is an Ethylene Oxide Production Plant (1).

The costing of a chemical plant has three main section: the capital cost, the manufacturing cost,

and the profitability. Each of the three sections is described on its own, and all results are shown.

Sample calculations and specific results are available in the Appendix section of this report for

demonstration and clarification. A supporting electronic spreadsheet, showing all the calculations

and graphs, is uploaded on the Canvas.fit.edu website.

In summary, the cost of an ethylene oxide production plant has been estimated; it has a

capacity of producing 130,318 metric tons annually. The plant needs a total capital cost of $

1,077,715,000 and has an estimated $577,785,000 for manufacturing cost. The land cost is

projected to be 5 million, and it is expected that the construction period will take two years; and

operation will start on the third year. If the plant doubles the production rate of ethylene oxide,

from the current specified one (1), the breakeven point is estimated to be between the fifth and

sixth year of operation.

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Capital Cost

The following section discusses the capital cost of the production plant of Ethylene Oxide

using the methodology discussed in appendix A of the Analysis, Synthesis and Design of

Chemical Processes, by Turton(1); the appendix consists of several sources and helpful

parameters in estimating the cost of process equipment. The capital cost is basically the sum

of the costs of all process units. It is important to note that the data used in the calculations

are based on a survey of equipment manufacturers that were taken in the year of 2001(2); the

average Chemical Engineering capital Cost Index (CEPCI) in 2001 was 397, and it must be

used to account for inflation (2). The CEPCI for the year 2016 was given by Dr. Whitlow as

604 and was used to update the total capital cost to the year 2016. There were some

assumptions made in the design, all of which are mentioned in the following Table 1.

Table 1: Assumptions Made in Calculating the Cost of certain Equipment

Unit Assumptions

Over Design Factor A safety over design factor of 10 %

Heat Exchangers

The pressures in the in the tube side

were the same as the inlet pressure of

the process multiplied by 10%

The pressures in the shell side were

chosen to be 35 psi because it was

assumed to be cooling water and

multiplied by 10 %

Some heat exchangers found to have

capacity not within the range. The

capacity was forced to be within the

range by dividing by lowest possible

number of exchangers. The final cost

was multiplied also by the number of

exchangers.

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Table 1 (Cont.): Assumptions Made in Calculating the Cost of certain Equipment

Unit Assumptions

Reactors

Reactors are modeled as Heat

Exchangers – Floating Head

Effective diameter is the diameter of

the reactor using the volume and height

Vessels

Some of Towers were modeled as

Process Vessels (vertical).

The assumptions were made to find

𝐹𝑃,𝑉𝑒𝑠𝑠𝑒𝑙, FM, B1, and B2. B1 and B2

were found in Ethylene oxide table(1)

Costing Correction to the year 2016 Linear extrapolation between 2001 and

2010, then using the line equation to

get the 2016 index number

I. Capital Methodology

Purchased Equipment Cost

The following equation was used for calculating the purchased cost of the equipment,

assuming ambient operating pressure and using carbon steel construction (2):

𝑙𝑜𝑔10𝐶𝑝𝑜 = 𝐾1 + 𝐾2 𝑙𝑜𝑔10(𝐴) + 𝐾3 [𝑙𝑜𝑔10(𝐴)]2

𝐶𝑝𝑜: Purchased cost

A: Capacity or size parameter for the equipment

K1, K2, and K3: given constants in Turton (2)

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Purchased Equipment Cost (for capacities out of the range)

The following correction was used to accommodate the capacity values that were out of

the range of specifications mentioned in Turton (2):

𝐶𝑎 = 𝐶𝑏 (𝐴𝑎

𝐴𝑏)

2

Where Ca is the cost of the equipment with the out of range capacity, Cb is the cost of the

equipment at the maximum capacity, Aa is the out of range capacity value, and Ab is the

maximum capacity value.

Pressure Factors for Process Vessels

𝐹𝑃,𝑉𝑒𝑠𝑠𝑒𝑙

(𝑃 + 1) ∗ 𝐷2[850 − 0.6(𝑃 + 1)]

+ 0.00315

0.0063

The previous equation was used to determine the pressure factors for Vessels and

Towers. P is the pressers in barg, and D is the diameter in meter. There are three Towers and

one Vessel; two of the towers are the same, and the third one has a different operating

pressure and diameter. The values of 𝐹𝑃,𝑉𝑒𝑠𝑠𝑒𝑙𝑠 were found to effects the cost due to the high

pressure factors value (2).

Pressure Factor for other Process Equipment

The pressure factor, FP, for other equipment such as Pumps, Heat Exchangers,

Compressors, and Reactors in the plant was found using the following equation:

𝑙𝑜𝑔10𝐹𝑝 = 𝐶1 + 𝐶2 𝑙𝑜𝑔10(𝑃) + 𝐶3 [𝑙𝑜𝑔10(𝑃)]2

P: Design pressure in barg

C1, C2, and C3: given constants in Table A.2 in Turton (2)

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Material Factors for Heat Exchangers, Process Vessels, and Pumps

The values of the material factors, FM, for heat exchangers, process vessels and pumps

are obtained from figure A.18 in Turton (2) and the identification numbers are also listed in

Table A.3 in Turton (2)

Bare Module Factor for Heat Exchangers, Process Vessels, and Pumps

𝐶𝐵𝑀 = 𝐶𝑝𝑜𝐹𝐵𝑀 = 𝐶𝑝

𝑜(𝐵1 + 𝐵2𝐹𝑀𝐹𝑝)

CPo: Purchased Cost

FBM: Bare module factor

B1 and B2; Given constants in Table A.4 in Turton (2)

FM: Material Factor

Fp: Pressure Factor

Bare Module and Material Factors for the Remaining Process Equipment

The values of the Bare Module and Material Factors, FBM and FM for the remaining

equipment can be found using Figure A.19 and Table A.6 in Turton (2).

Bare Module Cost for Sieve Trays

In the case of Sieve trays, the bare Module cost is calculated differently; the value of CBM

is obtained using the following equation:

𝐶𝐵𝑀 = 𝐶𝑝𝑜𝑁𝐹𝐵𝑀𝐹𝑞

CPo: Purchased Cost

N: number of trays

FBM: Bare module factor

Fq: Quantity factor for trays

The quantity factor for trays, Fq, for N ≥ 20: Fq = 1

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Costing Correction to 2016

𝐶𝑎 = 𝐶𝑏 (𝐴𝑎

𝐴𝑏)

2

Where Ca is the cost of the equipment in 2016, Cb is the cost of the equipment in 2001,

Aa is the CEPCI in 2016 given by Dr. Whitlow to be 605, as a fixed assumption, and Ab is

the CEPCI in 2001.

II. Capital Results

The following Table 2 shows the total costs of the equipment used in the plant.

Table 2: Total Cost of Equipment

Equipment Total Cost (2016) Percentage of

Capital Cost

Pump $51,000 0.005%

Vessel (horizontal) $264,000 0.024%

Heat Exchangers $906,300,000 84.095%

Compressors $260,000 0.024%

Towers $166,000,000 15.403%

Sieve Trays $4,640,000 0.431%

Reactors $200,000 0.019%

The total capital cost is $ 1,077,715,000. From Table 2, it can be noticed that the Heat

Exchangers govern the majority of the capital cost with 84.095 %, and the second large cost is

for the Towers, occupying 15.403 % of the total capital cost.

A more detailed costing for each unit is presented in Appendix A of this report.

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Manufacturing Cost

After calculating the capital investment needed to build the Ethylene Oxide plant, the

operational investment is to be determined. There are three types of manufacturing costs to

take into account: Direct Manufacturing costs, Fixed manufacturing costs, and General

Expenses.

Direct Costs are dependent on production rate, and it includes raw materials, utilities,

labor, waste treatment, supplies, maintenance, lab charges, and patents & royalties. Fixed

costs are independent of production rate, and it includes taxes & insurance and plant

overhead. Finally general expenses costs are loosely tied to the production rate, and it

includes sales and marketing, research & development and administrative costs.

The following report shows the manufacturing cost for the ethylene oxide plant, using the

methodology stated in Turton(2).

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I. Manufacturing Methodology

Utility Cost:

In this section, the expenses associated with electricity, cooling water, process steam and

many other utilities are accounted for. It is important to note that the cost of utilities are

dependent on both inflation and energy cost. The main utilities needed in the plant are

electricity, cooling water, high pressure steam and boiling feed water; these utilities are used

in the plant in the heat exchangers, reactors and compressors. Table 3 shows the total amount

of each utility needed in the plant annually, and the price and annual cost of each utility. For

the cost of electricity, the cost was linearly extrapolated using the data found in the U.S.

Energy Information Administration (3) to find the estimated price in 2016. All the calculation

that are involved in the manufacturing cost of ethylene oxide plant are presented in Appendix

B. For cooling water, high pressure steam and boiling feed water. The cooling water cost was

based on the total annual increase in the cost of electricity between 2006 and 2015. The high

pressure steam and the boiler feed water are based on the total annual increase between 2009

and 2015 for natural gas. The data presented in Appendix C shows the linear extrapolation

that was used the electricity cost.

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II. Manufacturing Results

The following Table 3 shows a summary of the costs included in the manufacturing of

the plant.

Table 3: Summary of the Costs included in the Manufacturing Cost

Direct Manufacturing Costs $401,419,00

Direct Supervisory and Clerical Labor $193,000

Maintenance and Repairs $64,654,000

Fixed Manufacturing Cost $74,033,000

Local taxes and Insurance $34,483,000

Plant Overhead costs $39,551,000

Raw Materials $21,732,000

Utilities $286,330,000

Operating Labor $1,071,000

Waste treatment $250,000

Lab Charges $161,000

Patents and Royalties $17,334,000

Fixed Capital Investment $1,077,564,000

Cost of Manufacturing $577,785,000

General Expenses $102,334,000

Administration Costs $9,925,000

Distribution and Selling Costs $63,557,000

Research and Development $28,890,000

Form Table 3, the total manufacturing cost of the plant is $577,785,000 while the fix

capital investment is $1,077,564,000. The direct manufacturing cost is $401,419,000; the fixed

manufacturing cost is $74,033,000 and the general expenses have a total of $102,334,000.

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Figure 1: Direct Costs Distribution

Figure 1 above shows the distribution of the direct costs between its elements; it can be

noticed that utilities take a large part of the pie chart with a 73.13% of the total direct cost. The

second largest cost is for the maintenance and repairs of the plant which occupies 16.51% of the

pie chart. The third largest segment in the pie chart is for raw materials occupying 5.55% of the

direct costs. Patents and royalties occupy 4.43%, while operating labor, waste treatment, and lab

charges occupy 0.27%, 0.06% and 0.04% respectively.

16.51%

5.55%

73.13%

0.27%

0.06%0.04%

4.43%

Direct Costs

Maintenance and Repairs

Raw Materials

Utilities

Operating Labor

Waste treatment

Lab Charges

Patents and Royalties

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The following Table 4 shows the utility cost of each utility needed in the plant annually.

Table 4: Price, Total Amount, and Cost Annually Needed for Utilities

Cost (2016 $) Total Amount Needed Cost ($/yr) in 2016

Electricity ($/kW-hr) 0.0718 3,100,000,000 $225,000,000

Cooling water ($/kg) 0.0000175 116,600,000,000 $2,000,000

High Pressure Steam ($/kg) 0.01459 4,000,000,000 $140,000,000

Boiler Feed Water ($/kg) 0.00119 205,600,000 $600,000

The total utility cost, from Table 3, is $286,330,000. It can be noticed from Table 4 that

the cost of electricity occupies a large part of the total with 78.58 % of the cost. The next

largest utility is high pressure steam with a total cost of $140,000,000, which is 20.63% of

the total utility cost.

Figure 2: Fixed Manufacturing Cost Distribution

From Table 3, the total fixed manufacturing cost is $74,033,000; Figure 2 shows the

distribution of the cost between the local taxes and insurance and the plant overhead costs, which

occupy 53% and 47% respectively.

47%53%

Fixed Manufacturing Costs

Local taxes and

Insurance

Plant Overhead costs

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Figure 3: General Expenses Distribution

From Table 3, the general expenses in the plant have a total of $102,334,000; this total is

divided by the administration costs, 10%, research and development, 28%, and the distribution

and selling cost, 62% of the total expenses.

10%

62%

28%

General Expenses

Administration Costs

Distribution and Selling Costs

Research and Development

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Profitability

I. Profitability Methodology:

Profitability of the ethylene oxide plant was determined through several steps. The

product annual flow rate and the cost of the product were calculated in order to find the

revenue. Some assumptions were made in the profitability calculation; details are shown in

Appendix D. The land cost was assumed to be equal to 5 million dollars. In addition, the

annual interest rate was assumed to be 6 %. The revenue was assumed to increases by 5 %

annually, and the operation cost by 2 % annually. The tax rate was assumed to be 25%; while

the working capital was assumed to be 15% of the fixed capital investment. The construction

period was assumed to be two years, with an expected plant life time of ten years.

It was noticed that there is no breakeven point when the product flow rate is as given. An

assumption was made in order to find a breakeven point which was doubling the annual

production of the product, ethylene oxide. The total cost of doubling the ethylene oxide was

found to be $1.120 billion. The cost of ethylene oxide was found using linear extrapolation

from the costing data found for the years 2009-2011 and assuming a fixed annual increase of

15.64% (6).

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II. Profitability Results:

Figure 4: Cumulative Future vs. Time

Based on Figure 4 above, it can be concluded that the breakeven point is going to be

between the fifth and sixth year of operation. The revenue in the sixth year will be $

671,100,000.

It is important to note that this prediction assumes the doubling of the production of

ethylene oxide, i.e. twice the output flow rate specified.

The discounted cash flow rate of return (DCFROR) was found to be at a 27.31% annually

interest rate.

-$3,000,000,000

-$2,000,000,000

-$1,000,000,000

$0

$1,000,000,000

$2,000,000,000

$3,000,000,000

$4,000,000,000

$5,000,000,000

$6,000,000,000

0 1 2 3 4 5 6 7 8 9 10 11 12

Cash

Flo

w

Time (years)

Discrete Cash Flow

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References

1) Analysis, Synthesis and Design of Chemical Processes, by Turton, Baillie, Whiting,

Shaeiwitz & Bhattacharyya 4th Edition, Prentice Hall, 2012, Ethylene Oxide Production,

Unit 700.

2) Analysis, Synthesis and Design of Chemical Processes, by Turton, Baillie, Whiting,

Shaeiwitz & Bhattacharyya 4th Edition, Prentice Hall, 2012

3) U.S. Energy Information Administration, Electric Power Monthly, August 2015, Table

5.3. Average Price of Electricity to Ultimate Customers

4) 51-9011 Chemical Equipment Operators and Tenders." U.S. Bureau of Labor Statistics.

U.S. Bureau of Labor Statistics. Web. 2 Dec. 2015.

5) "Ethylene | Prices, News & Market Analysis | ICIS.com." Ethylene | Prices, News &

Market Analysis | ICIS.com. Web. 2 Dec. 2015.

6) Nigam, Shirish. "Impact of Crude Oil Price Trends on Feed Additives' Prices." Engormix.

Animal Feed, 26 May 2011. Web. 1 Dec. 2015.

7) "CHE_4181_Economics_Profitability_2015.pptx." 16 Nov. 2015. Lecture.

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Appendix A: Detailed Capital Cost Information

Table 5: Cost of Each Piece of Equipment

Equipment Unit # Cost (2016 $)

Pump P-701 A/B $50,623

Vessel (horizontal) V-701 $264,033

Heat Exchangers

E-701 $5,176,300

E-702 $86,965,925

E-703 $171,762,029

E-704 $202,704,703

E-705 $201,336,855

E-706 $207,954,249

E-707 $18,322,587

E-708 $10,368,570

E-709 $1,675,570

Compressors

C-701 A/B $66,018

C-702 A/B $81,291

C-703 A/B $75,561

C-704 A/B $15,808

C-705 A/B $15,808

Towers T-701 $10,640,056

T-702 $10,640,056

T-703 $144,608,451

Sieve Trays T-701 $793,233

T-702 $793,233

T-703 $3,053,945

Reactors R-701 $99,514

R-702 $99,514

Table 6: Total Capital Cost

Total Module Cost (2001) Total Module Cost (2016)

$664,274,660 $1,077,563,932

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Appendix B: Manufacturing Cost Detailed Calculations

Operating labor Cost:

As shown in Table (1), there are 52 weeks in one year, 3 weeks for vacation, 8 hours in

each shift, and 5 shift per week. To calculate the total hours per year, the number of week should

be 49 by subtracting 52 from 3. Calculating Total hour is by Multiplying 8 × 5 × 49 = 1960

and total hour/year is 24 × 365 = 8760. To obtain the number of operator hired for each

operators is by using this equation (Total hours of operation / Total hour/year) which gives

8760

1960=4.5 and this number should be rounded to 5.

𝑁𝑂𝐿 = √6.29 + 31.7𝑃2 + 0.23𝑁𝑛𝑝 (1)

This Equation (1) represent the number of operators per shift. P is the number of steps

involving particulate solids handling. Nnp is the number of steps not involving particulate solids

handling. P will be zero because there are no solids that need handling such as no transportation

or Particulate removal. Nnp is the number of none particulate process includes reactors, towers,

compressor, and heat exchanger, Pump and Vessel are not included (2). Nnp will be 19. Putting P

and Nnp in the equation of 𝑁𝑂𝐿 will give 3.265 and this number should be rounded to 4.

Labor Wages and Total number of operators are needed to calculate the COL . Annual

Labor wages were found to be 52500$ in 2014(2). The Annual labor wages in 2016 is $53550 by

assuming 2 percent increasing from 2014. To calculate the total number of operators is by using

this equation 𝑁𝑂𝐿 × # 𝑜𝑓 𝑜𝑝𝑒𝑟𝑎𝑡𝑜𝑟 ℎ𝑖𝑟𝑒𝑑 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑜𝑝𝑒𝑟𝑎𝑡𝑜𝑟 = 5 × 4 = 20.

COL = The Annual labor wages × Total number of operators = 1,071,000 $

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Table 7: Operating labor cost variable

Number of week in year 52

Number of weeks for vacation 3

Number of shift per week 5

Hours each shift 8

Total hours /year 1960

Total hours of operation 8760

Number of operator hired for each operator 4.5

NOL 4

Annual mean Wages in 2016 53,550

Total number of operators 20

COL $1,071,000

Cost of Raw Materials:

The raw materials in the Ethylene Oxide production are Ethylene, air, and process water.

The mass flowrate of ethylene was given in the process description. Moreover, the price of

ethylene was found to be 39 $/tonne therefore the mass flowrate was converted in tonne / year in

order to find the final cost in unit of $/year. The cost of the process water and air were calculated

using the same methodology. Since air does not affect the reaction of producing ethylene oxide,

the source of air was considered to be from the atmosphere.

Ethylene: The price of ethylene was found to be equal to 39 $/tonne.

Air: the price of air was assumed to be equal to zero

Process water: it was assumed to be hot water. The price of process water found to be equal to

29.97 $/tonne

Cost of Waste treatment

Waste water: the only waste of the process is water. Using the given mass flow rate. The price

found to be equal to 0.041$/tonne.

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Direct Manufacturing Costs:

The direct manufacturing cost was calculated by summing the following:

CRM + CWT + CUT + 1.33 COL + 0.03 COM + 0.069 FCL

Where

CRM is the cost of raw materials

CWT is the cost of waste treatment

CUT is the cost of utilities

COL is the cost of operating labor

FCL is the fixed capital cost

COM is cost of manufacturing

Using the correlation above, the direct manufacturing cost found to be $ 489,242,558.

Direct Supervisory and Clerical Labor:

The Direct Supervisory and Clerical Labor was calculated using the formula below.

Direct Supervisory and Clerical Labor = 0.18 (Operating Labor)

Using the correlation above, the Direct Supervisory and Clerical Labor cost found to be $

192,780.

Maintenance and Repairs:

Maintenance and Repairs was calculated using the formula below.

Maintenance and Repairs = 0.06 (Fixed Capital Investment)

Using the correlation above, the Maintenance and Repairs cost found to be $ 65,870,122.

Fixed Manufacturing:

Fixed Manufacturing Cost = 0.708 (Operating Labor) + 0.068 (Fixed Capital Investment)

Using the correlation above, the Fixed Manufacturing cost found to be $ 78,411,073.

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Local taxes and Insurance:

Local taxes and Insurance = 0.032 (Fixed Capital Investment)

Using the correlation above, Local taxes and Insurance cost found to be $ 35,130,732.

Plant Overhead costs:

Plant Overhead costs = 0.708 (Operating Labor) + 0.036 (Fixed Capital Investment)

Using the correlation above, the Plant Overhead costs cost found to be $ 40,280,314.

Lab Charges:

Lab Charges = 0.15 (Operating Labor)

Using the correlation above, the Lab Charges costs cost found to be $ 160,650.

Patents and Royalties:

Patents and Royalties = 0.03 (Cost of Manufacturing)

Using the correlation above, the Patents and Royalties costs cost found to be $

20,525,847.

Cost of Manufacturing :

COM = (1/0.81) (Raw Materials+ Waste treatment+ Utilities) + 2.215(Operating Labor) +…

…0.146FCI

Where FCI is Fixed Capital Investment

Using the correlation above, the Cost of Manufacturing found to be $ 684,194,901.

General Expenses:

General Expenses = 0.177 (Operating Labor) + 0.009((Fixed Capital Investment) + 0.16 (COM)

Using the correlation above, the Cost of Manufacturing found to be $ 119,541,270.

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Administration Costs:

Administration Costs = 1.177 (Direct Supervisory and Clerical Labor) + 0.009 ( FCI)

Using the correlation above, the Administration Costs found to be $ 10,107,420.

Distribution and Selling Costs:

Distribution and Selling Costs = 0.11 (Raw Materials)

Using the correlation above, the Distribution and Selling Costs found to be $ 75,261,439.

Research and Development:

Research and Development = 0.05 (COM)

Using the correlation above, the Distribution and Selling Costs found to be $ 34,209,745.

Appendix C: Electricity Price Extrapolation

year cent/kW-

h

2005 5.73

2006 6.16

2007 6.39

2008 6.96

2009 6.83

2010 6.77

2011 6.82

2012 6.67

2013 6.89

2014 7.01

2015 6.89

2016 7.18

The data in the table was used to plot the correlation in the figure above and extrapolate linearly

to find the cost of electricity in 2016.

y = 0.0919x - 178.09

R² = 0.5915

5.0

5.5

6.0

6.5

7.0

7.5

2004 2006 2008 2010 2012 2014 2016

Pri

ce in

Cen

ts/k

W-h

r

Year

Price of Electricity

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23

Appendix D: Profitability Detailed Calculations

1. Revenue Calculation:

To get the revenue calculation, we need to get the product price ($/MT) and also the

amount annually that the plant will produce (MT/year) to get the total price.

Total Price = Amount Annually × Price = 260635.2 MT

Year × 4298.23

$

MT

= 1,120,272,081 $

year

2. Taxes:

Taxes = (Revenue − Operating Cost − Depreciation) × Tax rate

= (1,120,272,081 − 577,784,528 − 107,576,393) × 0.25 = $108,682,790

3. After tax (Net Profit) :

Taxes = (Revenue − Operating Cost − Depreciation − Taxes)

= (1,120,272,081 − 577,784,528 − 107,576,393 − 108,682,790) = $108,682,790

4. Present Worth Discrete Cash Flow (P):

P = A [(1 + i)n − 1

i(1 + i)n] = −22,449,249 $ × [

(1 + 0.005)12 − 1

0.005(1 + 0.005)12] = −$260,836,294

Where A is the monthly distributed cash flow and 𝑖 is the Annual or monthly interest rate and

n is the annual or monthly period.

5. Future Worth Discrete Cash Flow (F):

F = P[(1 + i)n] = −$260,836,294 × (1 + 0.005)144 = −$534,910,243