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C H A P T E R

Analysis of Cost Estimation n acceptable plant design must represent a plant that can produce a product which will sell at a profit. Initially, sufficient capital must be committed to t construct all aspects of the facility necessary for the plant. Since ~ cprofit equals total income minus all expenses. it is essential that the chemical sngneer be aware of the various types of costs associated with each manufacturing step. Funds must be available for direct plant expenses, such as those for raw materials. ]&or, and utilities, and for indirect expenses, such as administrative salaries, product sales, and distribution costs. In this chapter, jnvestment and plant operation costs are reciswed as well as cash flow and gross and net profits.

CASH FLOW FOR INDUSTRIAL OPERATIONS Cash Flow Figure 6-1 shows a simplified representation of the flow of funds for an over& industrial operation based on a corporate treasury serving as a reservoir and source ,of capital. Inputs to the capital reservoir normally are in the form of loans, stock isswes, bond sales, and other capital sources, and the cash flow from project operations. Outputs from the capital reservoir are in the form of capital investments in projects. dividends to stockholders, repayment of debts, and other investments. Figure 6-1 illustrates capital inputs and outputs for an industrial operafiom using a tree growth analogy, depicting as the trunk the total capital investment, excludkg land cost, necessary to initia!e the particular operation. The total capital investment comprises the fixed-capital investment in the plant and equipment, including tEnc necessary investment for auxiliaries, and nonmanufacturing facilities, plus the workingcapital investment. Some of the capital investments can usually be considered Lo occur as a lump sum, such as the provision of working capital required at the start of owration

Cash Flow for Industrial Operations Net profit after taxes = (sj - c, - dj)(l Income taxes = (sj - c , - dj)@ (@ is generally 35% of gross profit) 4 Gross profit = si - c , - dj

-0 )

I d, = depreciation charge Gross profit = s; - c, (before depreciation charge) Costs for operations = c, (not including project depreciation)

S from sales = sj

11 Net cash flow from the pro,ect including deprecijtion charge = A, = (sj - c., - dj)( 1 - @) + d, = (sj - c , ) ( 1 - 0 ) + djO

&I

(total income)

Working capital

source

4

Other capital input Loans Preferred stock

Bonds Common stock

Figure 6-1

Tree diagram showing cash flow for industrial operations of the completed plant. The flow of cash for the fixed-capital investment is usually spread over the entire construction period. Because income from sales _andthe costs of operation may occur on an irregular time basis, a reservoir of working capital must be available to meet these requirements. The rectangular box near the top of Fig. 6-1 represents the operating phase for the complete project with working-capital funds maintained at a level acceptable for

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CHAPTER 6 Analys~sof Cost Est~mation

efficient operation. Cash flows into the operations box as dollars of income sj from all sales while annual costs for operation, such as for raw materials and labor, but not including depreciation, are shown as outflow costs c,j. These cash flows for intome and operating expenses can be considered as continuous and represent rates of flow at a given time using the same time basis, such as dollars per day or dollars per year; the subscript J indicates thejth tlme penod. Since, as discussed in Chap. 7. depreciation charges are in effect costs that are paid into the company capital reservotr. such charges are not included In the operation costs. The difference between the Income and operating costs 7, - c,, is the gross projt before deptec~arroncharge and is reprehenred by the vertical line rising out of the operations box. Depreciation is subtracted as a cost before income tax charges are calculared and pad, and net profits are reported to the stockholders. Consequently, removal of depreciation as a charge against profits is shown at the top of Fig. 6-1. The depreciat~on charge cl, is added to the net profit to make up the total cashflo~vfor return ro the capital reservoir. The result~ngglassprojt of s, - c,, - d, that accounts for the depreciation charge is taxable. The income tax charge is shown at the top of the diagram where , @ is the fixed income tax rate it is removed in the amount (sj - coj - d j ) ( @ )where designated as a fraction of the annual gross profits. The remainder after income taxes are paid (sj - cOj- d j ) ( l - @ )is the netprofir after taxes that is returned to the capital reservoir. When the depreciation charge d, is added to the net profit, the t o d projectgenerated cash flow returned to the capital reservoir on an annual basis is

where Aj is the cash Po)^^ from the project to the corporate capital reservo? resulting from the operation in !-earj in dollars, sj the sales rate in yearj in dollars. cojihe cost of operation (depreciation not included) in year j in dollars, dj is the depreciadon ~ h a r g e in yearj in dollars. and @ the fractional income tax rate. This cash flow is used 6or new investments, dividends. and repayment of loans, as indicated by the various branches emanating from the capital source in Fig. 6-1, as well as for retained earnings.

Cumulative Cash Position The cash flow diagram in Fig. 6-1 represents the rates of cash flow with s j , C-,>,- and dj all based on the same time increment. Figure 6-2 is for the same type of cash 60w for an industrial operation except that it depicts the situation as the cunzlllarive cash posilion over the life cycle of a project. The numerical values are only for illustntitm. In the situation depicted in Fig. 6-2, land value is included as part of the total capital investment to show clearly the conlplete sequence of steps in the full lifc cycle for an industrial project. The zero point on the time coordinate represents tf.d point at which the plant has been completely constructed and begins start-up of opentian. The total capital investment at the zero time point includes land cost, manufacrunag and nonmanufacturing fixed-capital investment, and working capital. The cash po&.ion is negative by the amount of the total capital investment at zero time. In the idrdl situation, revenues come in from the operation as soon as time is positive. Cash 3ow to the company treasury, in the form of net profits after taxes plus depreciation. searts to

Cash Flow for Industrial Operations

f

Life of project earnings Land, salvage, and working capital recovery

Cumulative cash oosition.

;

Cumulative cash position = net profit aftsr taxes + depreciation - total capital investment

Eumulative cash position over total life of project

Construction IM period

\

Start of

Fixed capital investment (depreciable)

1\

-'**

land)

..-

Land, salvage, and working capital recovery

Book value of investment (wi$ 10-year straight-line depreciation)

Y

charge (straight line) capital investment

Zera 1

Dollars (-)

Figure 6-2

Graph of cumulative cash position showing effects of cash flow over the full life cycle for an industrial operation, neglecting the time value of money accumulate and gradually repays the total capital investment. In the figure, a constant cash flow rate has been assumed from time zero until the end of operation, although in reality a constant cash flow would not be expected. For the conditions shown in Fig. 6-2, the total capital investment is repaid in 5 years, and the cumulative cash position is zero. After that time, profits accumulate on the positive side of the cumulative cash position until the end of the project life, when the plant is shut down and project operation ceases. At shutdown, the working capital and land value are recovered. The working capital is recovered by the sale of materials, supplies, and equipment. Land can be either sold or transferred to another company use. For evaluation purposes it is generally assumed that the dollar amount recovered for working capital and land is the same as that spent originally. Thus, the final cumulative cash position over the 10-year life of the project is shown in the upper right-hand bracket in Fig. 6-2. The relationships presented in Fig. 6-2 are very important for the understanding of the factors to be considered in cost estimation. To put emphasis on the basic nature of the role of cash flow, Fig. 6-2 has been simplified considerably by neglecting the time' value of money and using constant annual profit and constant annual depreciation. In the chapters to follow, more complex cases will be considered in detail.

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230'

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CHAPTER 6 Analysis of Cost Estimation

FACTORS AFFECTING INVESTMENT AND PRODUCTION COSTS

t

When a chemical engineer determines costs for any type of industrial process, these costs should be of sufficientaccuracy to provide reliable decisions. To accomplish this, the engineer must have a complete understanding of the many factors that can affect costs. For example, some companies have reciprocal arrangements with other companies whereby certain raw materials or types of equipment may be purchased at prices lower than the prevailing market prices. Therefore, if the chemical engineer bases the cost of the raw materials for the process on regular market prices, the resulr msy be that the process could appear to be unprofitable rather than profitable. Accordiilgly, the engineer must be aware of actual prices for raw materials and equipment. company policies, government regulations, and other factors affecting costs.

Sources of Equipment One of the major costs involved in any chemical process is for equipment. In many cases, standard types of tanks, reactors, or other equipment are used, and 2 scbstantial reduction in cost can be realized by employing idle equipment or by purchasing secondhand equipment. If new equipment must be bought, several independent qnotations should be obtained from different manufacturers. When specifications are 9 v z n to the manufacturers, the chances for a low-cost estimate are increased if overly s u k t limitations on the design are kept to a minimum.

Price Fluctuations In today's economic market, prices may vary widely from one period to mccher. For example, plant operators or supervisors cannot be hired today at the same wage rate as in 1985. The same statement applies to comparing prices of equipment ~urchasedat different times. The chemical engineer, therefore, must keep up to date on price and wage fluctuations. One of the most complete sources of information on elrisrring price conditions is the Morzthly Lnbor Review, published by the U.S. Bureau of Labor Statistics. This publication gives up-to-date information o n present prices ard wages for different types of industries.

Company Policies Policies of individual companies have a direct effect on costs. For examplr. s m e companies have particularly strict safety regulations, and these must be met in c \ q detail. Accounting procedures and methods for allocating corporate costs vary among companies. Company policies with reference to labor unions must be c o n s i d m h because these can affect overtimeiabor charges and the type of work that operators orcother employees can perform. Labor union policies may. for example, even dictat- dre amount of wiring and piping that can be done on a piece of equipment before it is brought into the plant and thus have a direct effect on the total cost of installed equiprnenr;.

Factors Affecting Investment and Production Costs

Operating Time and Rate of Production One of the factors that has a major effect on the profits is the fraction of time a process is in operation. If equipment stands idle for an extended period, raw materials and labor costs are usually low; however, many other costs, designated as fixed costs, for example, maintenance, protection, and depreciation, continue even though the equipment is not in active use. More importantly, anytime that a plant is not producing a product. it is also not producing revenue. Some time must be allowed periodically to perform scheduled routine maintenance; however, downtime should be kept to a necessary minimum, as it is one of the chief sources of poor profitability in process plants. Sales demand, rate of production, and operating time are closely interrelated. The ideal plant should operate under a time schedule that gives the maximum production rate consistent with market demand, safety, maintainability, and economic operating conditions. In this way, the total cost per unit of production is minimized because the variable cos s averaged over time are low. If the production capacity of the process is greater than the sales demand, the operation can be operated continuously at reduced capacity or periodically at ful!capacity. Figure 6-3 shows the effect on costs and profits.,based oqthe rate of production. As indicated in this figure, the fixed costs remain constant, and the total product cost

Rate of production, kgls Figure 6-3

Breakeven chart for chemical processing plant

CHAPTER 6 Analysis of Cost Estimation

increases as the rate of production increases. The point where the total product cost equals the total income is designated as the breokeven point. Under the conditions shown in Fig. 6-3, a desirable production rate for this chemical processing plant would be approximately 5 x lo6 kg/yr, because this represents the point of maximum gross and net profit. By considefiig sales demand along with the capacity and operating characteristics of the equipment, the engineer can recommend the producrion rate and operating schedules that will give optimal economic results.

Government Policies The national government has many laws and regulations that have a direzt effect on industrial costs. Some examples of these are import and export tariff regulaiions. depreciation rates, income tax rules, and environmental and safety regulations. Of these, income tax regulations and depreciation have the largest impact on most bosinesses. As of the writing of this text, modifications of federal corporate tar l a v ~ swere under consideration in the U.S. Congress. However, the last major changs in federal corporate income tax rates was in 1993 and in depreciation was in 1988. E e important point to remember is that tax law is subject to change at any time, and the design engineer must consult with tax experts to be sure that the most currenr tax codcs are used in economic analyses. More details on tax policies may be found in Chap. 7.

CAPITAL INVESTMENT A traditional economic definitionof capitol is "a stock of accumulated ~ ~ ~ s lInhan .'' applied sense, capital is savings that may be used as the owner decides. One use of the savings is invesrment; that is, to use the savings ". . . to promote the ~;odnctionof other goods, instead of being available solely for purposes of immediate enjoyment" with ". . . the view of obtaining an income or profit."' Before an industrial plant can be put into operation, a large sum of mcneq- must be available to purchase and install the required machinery and equipment. h d must be obtained, service facilities must be made available, and the plant must be trccxd complete with all piping, controls, and services. In addition, funds are require? w F i which to pay the expenses involved in the plant operation before sales revezue becomes available. The capital needed to supply the required manufacturing and plani f ~ i l i t i e sis called thefired-capital i?7vestment (FCI), while that necessary for the optratiton of the plant is termed the ~corkirlgcapital (WC). The sum of the fixed-capital in?-esment and (TCI). The $xed-capital the working capital is known as the total capital investr~~erzr portion may be further subdivided into nmnrrfrtctririr~gJired-capital iniwmwnt, also irlvesnnetlr. also known as known as direct cost, and ~~ortmnr~~lfncr~~ri~zgfuced-capital indirect cost. +W. A. Neilaon, ed., I.\'ebsirr:~ tVc,iv b~rerrtrttio~~al Dicrionan: 2d ed.. G. R: C. Xfsrriarn Cornpin?. Springfield, MA. 1957.

Estimation of Capital lnvestment

Fixed-Capital lnvestment Manufacturing fixed-capital investment represents the capital necessary for the installed process equipment .with all components that are needed for complete process operation. Expenses for site preparation, piping, instruments, insulation, foundations, and auxiliary facilities are typical examples of costs included in the manufacturing i fixed-capital investment. The capital required for construction overhead and for all plant components that are not directly related to the process operation is designated the norzrnan~lfncturing fixexerl-capital irzvestmeizt. These plant components include the land; processing buildings, administrative add other offices, warehouses, laboratories, transportation, shipping, and receiving facilities, utility and waste disposal facilities, shops, and other permanent parts of the plant. The corzstr~lctiorzoverhead cost includes field office and supervision expenses, home office expenses, engineering expenses, miscellaneous construction costs, contractors' fees. and contingencies. In some cases, construction overhead is proportioned between manufacturing and nonmanufacturing fixed-capital investment.

Working Capital

'ir.

The working capital for an industrial plant consists of the total amount of money invested in ( I ) raw materials and supplies carried in stock; (2) finished products in stock and semifinished products in the process of being manufactured; (3) accounts receivable; (4) cash kept on hand for monthly payment of operating expenses, such as salaries, wages, and raw material purchases; (5) accounts payable; and (6) taxes payable. The raw material inventory included in working capital usually amounts to a I-month supply of the raw materials valued at delivered prices. Finished products in stock and semifinished products have a value approximately equal to the total manufacturing cost for 1 month's production. Because credit terms extended to customers are usually based on an allowable 30-day payment perlod, the working capital requ~red because of accounts receivable ordinarily amounts to the production cost for 1 month of operation. The ratio of working capital to total capital investment varies with different companies, but most chemical plants use an initial working capital amounting to 10 to 20 percent of the total capital investment. This percentage may increase to as much as 50 percent or more for companies producing products of seasonal demand, because of the large inventories which must be maintained for appreciable periods.

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ESTIMATION OF CAPITAL INVESTMENT Most estimates of capital investment are based on the cost of the equipment required. The most significant errors in capital investment estimation are generally due to ornissions of equipment, services, or auxiliary facilities rather than to gross errors in costing. Table 6-1 provides a checklist of items for a new facility and is an invaluable aid in making a complete estimation of the fixed-capital investment.

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C H A P T E R 6 Analysis of Cost Estimation

Table 6-1 Breakdown of fixed-capital investment items for a chemical p r o c e s s

Direct costs 1. Purchased equipntent All equipment listed on a complete flowsheet Spare parts and noninstalled equipment sparesSurplus equipment, supplies, and equipment allowance Inflation cost allowance Freight charges Taxes, insurance, duties Allowance for modifications during start-up 2. Purchased-equip~ne~tr installntion Installation of all equipment listed on complete flowsheet Structural supports Equipment insulation and painting 3. Instru~~~entfltion and controls Purchase. installation, calibration, computer control with supportive software 4. Piping Process piping - . - utilizing suitable structural materials Pipe hangers, fittings, valves Insulation 5. Electrical systems Electrical equipment switches, motors. conduit, wire, fittings, feeders, grounding, instrument and conma1 wiring, lighting, panels Electrical materials and labor 6. Buildings (iizcluding seivices) Process buildings-substructures, superstructures, platforms, supports, stairways. ladders, access a-~1%.cranes, monorails, hoists, elevators Auxiliary buildings-administration and office, medical or dispensary, cafeteria. garage. product ww present can be determined by multiplying the original cost by the ratio ofthe pr:sc~index value to the index value applicable when the original cost was obtained. name;?. Present cost = original cost

index value at present index value at time original cost was o b ~ n c d

Cost indexes can be used to give a general estimate.'but no index ca? t d i e into account all factors, such as special technological advancements or local sonjitions. The common indexes permit fairly accurate estimates if the period involxd is less than 10 years. Indexes are frequently used to extrapolate costs into the near f u m e . For example, the cost estimator may project costs forward from the time a stuC~-i3 being done until the expected start-up time of a plant. Such projections are d o w by using extrapolated values of an index, or an expected inflation rate. Many different types of cost indexes are published repularly. Some can 'Ehs nsed for estimating equipment costs; others apply specifically to labor. construction. m e r i a l s , or other specialized fields. The most colnrnon of these indexes are the Mcrshull and %ee Chap. 8 for a discussion of the effects of intlntion or deflation on costs and re\.enuec in the f u r

P

Required information

Figure 6-4

Cost-estimating information guide

0

B

D

0

F

a,

e

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C H A P T E R 6 Analysis of Cost Estimation

Table 6-2 Cost indexes as annual averages

' ~ l costs l presented in this text and in the McGrau.-Hill website are based on this value for Janultr). 2002. obtained fror;. iie Chenlical Engineering index unless otherwise inqicated. The website provides the corresponding mathematicd cost relationships fm d l -ne graphical cost data oresented in the text. 'Projected. 'Calculated with revised index: see Cllen~.Errg., 109: 62 (2002).

Swift all-industry and process-indlrst~yeqttipmenr iide.res,' the Et~girzerrin: NewsRecord co~lstr~tcriort inde,r,' the 1Velso11-Fclrrarrefinery c o t ~ s t r ~ r c t iindr.:.? o ~ ~ and the Chemical E~zgineerirlgplarzt cost irldex! Table 6-2 presents a list of values for various types of indexes over the past 15 years. There are numerous other indexes presented in the literature that can k used for specialized purposes. For example, cost indexes for materials and labor for various 'Values for the Marshall and Swift equipment cost indexes are published ehch month in Chenricc E~t.ni~leerirrg. For a complete description oithese indexes. see R. W. Stevens. Chenl. Eng.. 541 1I): 124 (1947). 5c.e JI!SO Clrern. Er~g..85(13): IS9 (1978) and 92(9): 75 (1985). $The Errgb~eeringNews-Record construction cost index appears weekly in [he Errgirreerirrg rVe~?-Rri::ord.For a complete description of this index and the revised basis, see Eng. i\'e~-Record. 143(9): 398 (194:). 178(11): 87 (1967). A history is presented in the March issue each year: for example. see Errg. Newr-Recoc. 13U(ll): 54 (1988). "e Nelson-Famar refiner?. construction index is published the first week of each month in th: Oijl and Gas Ju~rrrral.For a complete descriprion of this index, see Oil Gus J.. 63(1.?): IS5 (1965). 74(18): id I O976), and 83(52): 145 (1985). "Thc Clremicol Erzgirreerinp plant cost index is published each month in Chenricul Er~girreenri..A, complete description of this indcn is found in Clrern. err^,. 70(4): 143 (1963) with recapping and updating es-nc:ally every 3 ycnrs. The index is being revised in 2002 to provide a better relarionship &tween the \wiois ci:,st factors involved in the index; see \V. hl. Vavatuk. Clrern. Eng.. 109(1): 62 (2M)Z) for derails.

Cost Components in Capital Investment

types of industries are published monthly by the U.S. Bureau of Labor Statistics in the Monthly Labor Review. These indexes can be useful for special kinds of estimates involving particular materials or unusual labor conditions. Another example of a cost index which is useful for worldwide comparison of cost charges with tifie is published periodically in the International Journal of Prod~lcrionEconomics (formerly Engineering Costs and Prodt[ctiorzEconomics). This presents cost indexes for plant costs for various countries in the world including Australia, Belgium, Canad$, Denmark, France. Germany, Italy, Netherlands, Norway, Japan, Sweden, the United Kingdom, and the United states.? All cost indexes are base4 on limited sampling of the goods and services in question; therefore, two indexes covering the same types of projects may give results that differ considerably. The most that any index can hope to do is to reflect general trends. These trends may at times have little meaning when applied to a specific case. For example, a contractor may, during a slack period, accept a construction job with little profit just to keep the construction crew together. On the other hand, if there are current local labor shortages, a project may cost considerably more than a similar project in another geographic location. The Marshall and Swift equipment cost indexes and the Chemical Engineering plant cost indexes are recommended for process equipment and %emical-plant investment estimates. These two cost indexes give very similar results, while the Eizgineeriizg News-Record construction cost index has increased with time much more rapidly than the other two because it does not include a productivity improvement factor. Similarly, the Nelson-Farrar refinery construction index has shown a very large increase with time and should be used with caution and only for refinery construction.

COST COMPONENTS IN CAPITAL INVESTMENT Capital investment is the total amount of money needed to supply the necessary plant and manufacturing facilities plus the amount of money required as working capital for operation of the facilities. Let us now consider the proportional costs of each major component of fixed-capital investment, as outlined previously in Table 6-1. The cost factors presented here are based on a careful interpretation of recent sources: with input based on fndustrial experience. Table 6-3 summarizes these typical variations in component costs as percentages of fixed-capital investment (FCI) for multiprocess grass-roots plants or large batterylimit additions. Agrass-roots plant is defined as a complete plant erected on a new site.

or methods used, see Eng. Costs Prod. Econ., 6(1): 267 (1982). 'ti. M. Guthrie, Process Plorrt Errimarirlg, Evolrmrion, arrd Conrrol. Craftsman Book Company of America, Solana Beach. CA, 1974; G. D. Ulrich, A Glrirle lo Clrer?licol E1rgineerir1.q Process Design ottd Ecurrornics, J. Wilcy, Ncw York. 1984: R. K. Sinnott, AII Irrtrodrrctiori to Clrernicol E~rgirleeringDesign. Per~amonPress, Oxford. Unitcd Kingdom. 1983; P. F. Ostw;~ld.Ah1 Cost E.stir~mtocMcGraw-Hill, New York. 1988; D. R. Woods, Prucess Desigrl rrrrd E~rgbleeri~rg Prf$20 per 50 kg f.0.b. (i.e.. the customer pays the freight charzes). The company offcs am equally

6-3

effective soap containing only 5 percent water. The water content is of no importance to the laundry, and it is willing to accept the soap containing 5 percent water if the delivered costs are equivalent. If the freight rate is $1.50 per 50 kg, how much should the company charge the laundry per 50 kg f.0.b. for-the soap containing 5 percent water? 6-13 The total capital investment for a conventional chemical plant is $1,500,000, and the plant produces 3 million kg of product annually. The selling price of the product is $0.82kg. Workiilg capital amounts to 15 percent of the total capital investment. The investmentis from company funds, and no interest is charged. Delivered raw materials costs for the product are $0.09/kg; labor, $0.08/kg; utilities, $0.05kg; and packaging, $0.008kg. Distribution costs are 5 percent of the total product cost. Estimate the following: a. Manufacturing cost per Kilogram of product b. Total product cost per year c. Profit per kilogram of product before taxes d. Profit per kilogram of product after income taxes at 35 percent of gross profit 6-14 Estimate the manufacturing cost per 100 kg of product under the following conditions: Fixed-capital investment = $4 million. Annual production output = 9 million kg of product. Raw materials cost = $0.25/kg of product.

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9 800-kPa steam = 50 kgkg of product. Purchased electric power = 0.9 kWhkg of product. Filtered and softened water = 0.083 m3/kg of product. Operating labor = 12 persons per shift at $25.00 per employee-hour. Plant operates three hundred 24-h days per year. Corrosive liquids are involved. Shipments are in bulk carload lots. A large amount of direct supervision is required. There are no patent, royalty, interest, or rent charges. Plant overhead costs amount to 50 percent of the cost for operating labor, supervision, and maintenance. 6-15 A company has direct production costs equal to 50 percent of total annual sales, and fixed charges, overhead, and general expenses equal to $200,000. If management proposes to increase present annual sales of $800,000 by 30 percent with a 20 percent increase in fixed charges, overhead, and general expenses, what annual sales amount is required to provide the same gross earnings as the present plant operation? What would be the net profit if the expanded planit were operated at full capacity with an income tax on gross earnings of 35 percent? What would be the net profit for the enlarged plant if total annual sales remained at $800,000? What would be the net profit for the enlarged plant if the total annual sales actually decreased to $700,000? 6-16 Aprocess plant making 5000 kgtday of a product selling for $1.75kg has annual variable production costs of $2 million at 100 percent capacity and fixed costs of $700,000. What is the fixed cost per kilogram at the breakeven point? If the selling price of the product is increased by 10 percent, what is the dollar increase in net profit at full capacity if the income tax rate is ..-35 percent of gross earnings? 6-17 A rough rule of thumb for the chemical industry is that $ I of annual sales requires $2 of fixedcapital investment. In a chemical processing plant where this rule applies, the total capital investment is $2,500,000, and the working capital is 20 percent of the total capital investment.

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CHAPTER 6

Analysis of Cost Estimation

The annual total product cost amounts to $1,500,000. If the income tax rates on g o s s earnings total 35 percent, determine the following: ' a. Percent of total capital investment returned annually as grosq earnings b. Percent of total capital investment returned annually as net profit 6-18 The total capital investmeiit for a proposed chemical plant. which will produce S1500,OOO worth of goods per year, is estimated to be $I million. It will be necessary to do a considerable amount of research and development (RbD)work on the project before &< tinal plant can be constructed, and management wishes to estimate the permissible researci and development costs. It has been decided that the after tax return from the plant should 'x mfficient to pay off the total capital investment plus all research and development costs in 7 years. A return after taxes of at least 12 percent of sales must be obtained. Because RbD ir an expense and the company's income tax rate is 35 percent of gross earnings, only 65 pxcenr of the funds spent on RbD must be recovered after taxes are paid. Under these condidonx what is the total amount the company can afford to pay for research and development? 6-19 A chemical processing unit has a capacity for producing 1 n~illionkg of a protuct xr year. After the unit has been put into operation, it is found that only 500.000 kg of the pmduct can be sold per year. An analysis of the existing situation shows that all fixed and cK7-r kvariant charges, which must be paid whether or not the unit is operating. amount to 35 Fercmt of the total product cost when operating at full capacity. Raw marsrial costs and o t h prfiduction ~ costs that are directly proportional to the quantity of production ii.e., constant p c W * ~ g r a m of product at any production rate) amount to 40 percent of the total product cost ar %I! capacity. The remaining 25 percent of the total product cost is for variable overhead and riiscellaneous expenses, and the analysis indicates that these costs are directly propottional to tie production rate during operation raised to the 1.5 power. What will be the percent change in tad cost per kilogram of product if the unit is switched from the original dzsign rate of 1O6kZ.~.roiproduct to a time and rate schedule which will produce 0.5xiOh kg or "half that amour:" ciproduct per year at the least total cost?