intamational journal of

production economics

ELS EVIER Int. J. Production Economics 34 (1994) 83-89

Investment and production costs analysis in food processing plants

Maria A. Parin , I,* Aurora Zugarramurdi2

Centro de Inuestigaciones de Tecnologia Prsquera (CITEP), Marc& T. de Alwar 1168, 7600, Mar drl Plats, Argentina

(Received 19 October 1992; accepted 1 November 1993)

Abstract

An analysis of investment and production cost estimates for food plants is presented. Mathematical expressions have been generalized so that they could be used to compare different chemical and food processing plants. Different type of costs are analyzed, specially those named as semivariable costs. Short- and long-run total costs of several food plants have been correlated in order to develop a methodology to estimate total operating costs. The results hereby presented are useful for economic and feasibility estimations in food plants.

1. Introduction

A large number of papers have been published on investment and production cost estimates for chemical and petrochemical plants [l-5]. They cover a number of topics such as cost-capacity factor estimates applied to either major items of equipment [6-81, complete chemical plants [9, lo], simple relationships between cost capacity to esti- mate operating costs for plants of different sizes [ 111, and factored operating cost correlations [ 121.

For food plants it is possible to find a lot of papers focused exclusively on short- and long-run cost functions [13-151, some of them concerning

* Corresponding author. Also at:

’ (CONICET (National Council of Scientific and Technical

Research). ’ INTI (National Institute of Industrial Technology).

production costs applied to fish plants [ 16-181 and some compiling data from certain food plants [ 19-221.

The purpose of this work is to present an analysis of investment and production cost estimates for food plants as well as the development of the math- ematical expressions which have been generalized so that they could be used to compare different food plants. Semivariable cost estimations are care- fully introduced, considering short- and long-run total costs for several food plants.

2. Investment

The concept of cost-capacity factor was intro- duced by Roger Williams [23] for the purpose of investment estimation. This method has been very helpful in quick capital investment estimations and it is widely used and discussed today [l 1, 24, 251.

0925-5273/94/$07X)0 0 1994 Elsevier Science B.V. All rights reserved SSDI 0925-5273(93)E0084-9

84 M.A. Purin, A. Zuprrumurdi/Int. J. Productiort Economics 34 i 1994) X3-89

J

102 9

103

103

lo4

104

105

105

lO6

Production

IO6 (ton/year)

,07 Volume

(barrels/year:

Fig. 1. References.

Number Symbol Plant Data calculated from:

1

2

3

4

5

6

7

8

9

10

11

12

13 14

15

16 17

18

19

20

0

0 A

Fish freezing

Lemons packaging Fish canning

Fish Protein Concentrate

Peas canning Lima beans canning

Pears producing

Peas freezing

Lima beans freezing

Spinach freezing

Polyethylene

Alkylation

Acetic acid

Ammonia Methanol

Reforming

Nitric acid

Cracking

Ammonium nitrate

Polymerization

127-311

Cl51 116, 32-341

[34-361

PO1 Cl91 Cl41 PI P21 c221 c91 191 c91 c91 c9j c91 f91 191 f91 c91

Williams originally stated that the total investment (11, 12) for two plants with different capacities of production (Qr, Qz), but elaborating the same product, are linked by the 6/10 rule. Mathematically:

lz = 1, .(Qz/QJ">

x being the cost-capacity The results obtained

plants are depicted in

(1)

factor. for chemical and food Fig. 1. Chemical and

M.A. Parin, A. Zugarramurdijlnt. J. Production Economics 34 (1994) 83-89 85

petrochemical plants have an average slope value of 0.68 [23]. The most recent average factor pub- lished for chemical plants and processes is 0.67, according to Remer [25]. A value of 0.7 has been considered as the most advisable for complete chemical plants [9].

For fruit and vegetable processing plants, the average value of the exponent is 0.74, while for fish processing plants the average exponent is 0.846 which is close to the 0.85 value proposed for solid process plants [26]. All the correlations for com- plete plants and for those involving common op- erations (such as critic packing, food and vegetables freezing, etc.) are concentrated in very well-defined areas. Capacity and investment ranges are signifi- cantly different since, on average, the amount that should be invested in chemical plants is about 10 times the food plant investment for equal capacity, when the capacity is measured in mass units.

3. Microeconomic analysis of production costs in food processing plants

The analysis of economic efficiency involves two different aspects: best (or optimum) plant utiliza- tion (short run) and best (or optimum) plant size (long run).

In the short run, the firm cannot vary its fixed inputs such as major pieces of equipment, space available and so on. Output is alterable only by changing the usage of variable inputs.

In the long run, there are no fixed factors, and the company may build a plant of any size to produce at any scale.

In general, the total cost of a given output rate is the sum of total fixed cost, total variable cost and total semivariable cost:

TC = TFC + TVC + TSVC. (2)

Total fixed costs (TFC) (insurance, taxes, depre- ciation), varies according to Eq. 1.

Total variable costs (TVC) (raw material, direct labor, utilities, etc.) are directly proportional to output, which is actually true for food processing plants. Usually, in food factories, labor costs are calculated on the basis of hourly rates due to the irregularity of supply of raw material and an

intensive-labor processing. Besides, monthly payments may in fact be used in chemical and petrochemical plants, where it has been suggested that labor’ requirements vary by about 0.2-0.25 power of the capacity ratio when processing plant capacities are scaled up or down [9]. However, such information should be used with caution be- cause increasing automation tends to reduce the need for personnel. Each company usually has a particular labor policy that fixes the real number of employees according to the sophistication of the installation.

Other costs like administrative services, manage- ment, supervision, distribution costs and mainte- nance, vary in a different proportion and they will be referred as semivariable costs (TSVC).

To elaborate a model which could include all the different inputs and mainly those previously men- tioned as semivariable costs, short- and long-run total costs of several food plants have been ana- lyzed. To make possible a statistical analysis of data from different sources, plant sizes have been converted to a dimensionless parameter named by S and defined as follows:

S = KIK,,,, (3)

where K is the plant capacity and K,,, is the maximum capacity of real plants operating with acceptable efficiency, using the current technology. Then, for S = 1,

TC = TFC,,, + TVC,,, + TSVC,,,,

and for S # 1,

(4)

TC = TFC (K”) + TVC,,, S + TSVC,,, f. (5)

where TFC is a function of the plant size at the power x, according to expression (1) andf depends on the return to scale of the plant, as shown in

Eq. (6).

f= TSVC (K)/TSVC (Kmax), (6)

The cost of any product is derived from the technology and the type and cost of the inputs used to produce it. The behavior of costs is largely dependent on the character of the underlying production function which accounts for returns to scale. The most general type of production

86 M.A. Parin. A. Zugarramurdillnt. J. Production Economics 34 (1994) 83-89

function is the one where, first a range of increas- ing returns to scale is encountered, then a range of approximately constant returns to scale is encoun- tered and finally a range of decreasing returns to scale as production capacity increases. It should be noted that a cubic expression is the most generally utilized one to describe the cost function associated with this production function. Consequently, a gen- eral expression for factor f can be presented as follows:

.f = g + kS -.jS2 + mS3,

where g, k, j, and m are positive constant.

(7)

When only increasing or decreasing returns to scale is observed, Eq. (7) is reduced to a quadratic expression. Constant returns to scale corresponds to a linear expression.

The three models hereby presented are in agree- ment with data gathered from food processing plants of different economic scales.

Expression (a) correlates extended economies which call for large-scale operations with plants that can hardly be split into small units (fish, fruit and vegetable canneries, juice plants).

.f; = 0.2213 + 3.0508s - 4.86825’ + 2.6066S3,

(8.793) (6.347) (5.537)

R2 = 0.9 156, d.f. = 39, (8)

where .fa is a factor f‘ for extended economies (f-statistics in parentheses), R2 is the correlation coefficient and d.f. is the degree of freedom.

Correlation (b) is obtained for plants of modular design, where modules are added to obtain higher capacities (fish salting plants, vegetable freezing plants).

,fb = 0.0496 + 1.0332s - 1.4793S2 + 0.4887S3,

(3.263) (1.084) (0.569)

R2 = 0.9489, d.f. = 16, (9)

where fb is a factor f for early diseconomies. Expression (c) correlates plants with constant

return to scale, like in the case of agricultural pro- duction, where all costs are proportional to pro- duction (land, labor, seeds, fertilizers).

fc = 0.0407 + 0.0639s

R2 = 0.9918, d.f. = 14,

(10)

where fc is a factor ,f for constant returns to scale.

From the mathematical point of view, the long- run total cost (LRTC) curve is an “envelope” of the short-run curves that is tangent to each of the short-run total cost (SRTC) curves. Then, it follows that the results in the short run will follow the shape of the long-run curves 1371. On the basis, the use of the long-run correlations for the short run is proposed as follows.

A dimensionless relation in the short run, similar to the dimensionless parameter proposed by Eq. (3) may be defined by

S = QIK (11)

where Q is a percentage of plant utilization and K is plant design capacity.

In order to apply correlation (8)-(IO) for the short run, factorf may be defined as follows:

f‘= TSVC(Q)/TSVC(K). (12)

In Fig. 2, data of TSVC in the short run for juices, agricultural products and actual fish plants are also depicted, where it can be observed that short-run curves follow the shape of the long-run curve for extended economies. It can be seen that there is a coincidence of the values shown in Fig. 2 with some semivariable costs as the maintenance ex- penses for chemical plants in the short run found in Ref. [9].

This result implies that the behavior of the SRTC will be similar to the LRTC. For example, when a plant with extended economy is operating at 75% capacity, TSVC will be about 85% of the TSVC at 100% capacity. When operating at 50% capacity, the TSVC will be about 75% of the TSVC at 100% capacity [9]. In the same way, in the long run, plants with an output 75% of the defined maximum capacity will have TSVC of about 85% of the TSVC of the maximum capacity plant. When plant output is 50% of the defined maximum capacity, TSVC will be about 75% of the TSVC at maximum output.

M.A. Parin, A. Zugarramurdillnt. J. Production Economics 34 (1994) 83-89 87

.25

0.00 0.00 .25 .50 .75 1.00

S

Fig. 2.

3.1. Methodology to calculate TSVC

The following calculation scheme is proposed for the estimation of production costs in the long and short run. 1.

2.

3.

4.

5.

4.

Estimate TSVC for the plant of maximum size, K max, using the methods proposed in the bibli- ography (see Appendix 1). Select fa,fb orfc, according to the type of plant, and so obtain the TSVC for the chosen capacity, applying expression (6). Calculate the TFC with Eq. (1) for each capacity. Calculate the TVC directly proportional to the plant capacity. Calculate the TC as the addition of the TSVCTFC and TVC. In the short run, the scheme is similar, taking into account that: The percentage of plant utilization should be used to calculate factorf: Calculate TSVC using factorfand expression (12). The TFC value is constant and the same as the value calculated in step 3. The TVC are proportional to capacity.

Conclusions

It should be noted that the cost of maintenance increases as the equipment ages, but in these esti- mates average figures are used.

This can be important for the economic evalu- ation of the project, since in this technique the costs for the first years of operation will include a greater maintenance expenses charge.

The analysis on investment and production costs With this in mind, a different form of estimating hereby presented will be helpful for economic and maintenance costs has been suggested, using

feasibility estimates in food plants. Capacity and investment ranges are significantly

different since, on average, the amount that should be investedin chemical plants is about 10 times the food plant investment for equal capacity, when the capacity is measured in mass units.

In order to calculate TSVC for plants with differ- ent types of return to scale, a factorfis proposed for each one.

For the estimation of total production costs in the long and short run, a calculation scheme is presented.

Appendix 1

Some costs are neither fixed nor directly propor- tional to output and are known as semivariable costs (SVC), such as supervision, administrative services, management, supervision, distribution costs and maintenance.

For example, maintenance costs include the cost of materials and labor (direct and supervision) em- ployed in routine or incidental repairs and, in some cases, the overhaul of equipment and buildings. When no other data are available, it can be esti- mated as 4-6% of fixed investment. This method gives maintenance costs as a fixed cost, though not completely correct. A more realistic estimate can be made using the method proposed by Pierce (1948) if some costs and additional information are available.

K = X(a + by),

where K is the maintenance cost (us $/yr), X is the annual consumption of electricity (kWh/yr), a is the index for materials equal to the cost of material for repairs per kWh used, b is the index for labor equal to the man-hours worked in repairs per kWh used, and y is the cost of man-hour with supervision.

88 M.A. Purin, A. Zugarramurdi/Int. J. Production Economics 34 i 1994) 83-89

a parameter which is equal to the investment multi- plied by the actual age of the equipment or installa- tion.

Different approaches can be also found for esti- mating the other semivariable costs. Although, the best source of information for these type of costs are based on company records for similar or iden- tical projects within the firm.

However, for preparing preliminary evaluations, the following procedures for estimating semi- variable costs are useful when no other data are available. Maintenance costs: 2210% of fixed investment per year [4, 91; administrative services costs: 15% of labor, supervision and maintenance or 225% of total cost [4]; supervision costs: lo-25% of labor [4,9]; distribution costs: l-3% of sales [9] or 2220% of total cost [4].

Acknowledgements

Financial support from National Council of Sci- entific and Technical Research for the completion of this research is gratefully acknowledged.

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[II

121

c31

141

c51

C61

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PI

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