The Cost-Volume Relationship

Another cause of variability lies in the way management views the cost-volume relationship. There are many misconceptions among managers of companies about the behavior of unit costs with changes in volume. One company president, whose background happened to be financial, likened the factory to a radio. To get more volume, you just turn up the 

The president of an electronics manufacturer who went on to run a public company had it more correct when he observed that his operation was tuned for a set volume of business. Unit cost, including both direct and overhead components, was lowest at this volume. When production volume moved up or down, unit cost only went up The expected economies of scale were a myth. 

ironically in many cases, an upward move in sales brings higher unit costs. This is frequently due to inflexibility in the supply chain and is particularly common when there is dependence on engineered, long-lead-time components. Each company in the supply chain likely has a V-shaped cost curve with the lowest cost centered on an optimal cost. Production above or below that range results in increased cost. An obvious example is production interruptions and shortages. If any one of the supply chain links breaks and fails to deliver, then the whole chain is threatened. 

Boeing, when orders expanded rapidly in the mid-1990s, was trapped in profitless prosperity. Its supply chain couldn t expand its output and choked trying to rush product to market. Late deliveries produced penalties and added cost. 

As a response, organizations should build flexibility into their own operations and into their supply chains. This resilient operation will enable them to deal with volume variations — at least within some prescribed range, extending the range in which their supply chain can cost effectively deliver product. The importance of establishing this operating range will increase to the extent that there is mutual dependence up and down the chain. 

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Figure 28.3 illustrates two views of the cost/volume relationship. The straight line depicts the way many executives view costs — increased volume brings economies of scale. The more work there is, the more overhead is absorbed. This sometimes leads to an appeal from manufacturing to sales to raise their forecasts so the factory s labor and investment will be fully utilized. 

Figure 28.4 illustrates the broadening of the cost/volume relationship curve to target a production range in which to operate. The shape changes from a V to a U. The bottom of the U is the range of operation with the lowest costs. 

In terms of the derived general relationships (3-1) and (3-2), x, y, and h are independent variables—cost and volume, dependent variables. That is, the cost and volume become fixed with the specification of dimensions. However, corresponding to the given restriedion of the problem, relative to volume, the function g(x, y, z) =xyh becomes a constraint funedion. In place of three independent and two dependent variables the problem reduces to two independent (volume has been constrained) and two dependent as in functions (3-3) and (3-4). Further, the requirement of minimum cost reduces the problem to three dependent variables x, y, h) and no degrees of freedom, that is, freedom of independent selection. 

In a production line that has a relatively long run, the cost for equipment in relationship to producing the product including its financial amortization, usually is about 5% with probably maximum of 10% Plastic material cost could be at about 50% with as high as 80% for high volume production. The other costs include power, water, labor, overhead and taxes. With precision, short runs, costs could be equipmentwise at 20 to 30%, material 45 to 50%. Thus, as it is usually stated, do not buy equipment just because it cost less since more profit could occur with the more expensive equipment study what is to be purchased. Of course the reverse is possibly true. So, you the buyer, have to know what you want and are ordering to a specification properly determined based on the designed product requirements. 

Many factors act together to determine the optimum scale of a process. These include the demand for the product, competitors share of the market, any technical limitations on the size of operation and also economies of scale effects. There is an approximate logarithmic relationship between the unit production costs for a product and the volume of production, whereby considerable economies of scale can be achieved. If the costs of a process of one size (C ) is known then the costs of larger or smaller factories (C ) can be approximately obtained from the relationship C = Cx (or n° ), where n is the scale-up ratio, i.e. n=l for a plant that is twice as big. Alternatively, a graph of log capital costs vs. log of plant capacity gives a straight line with a slope equal to the scale-up factor (n). The power term varies from case to case, but is invariably less than one. This scale effect is one reason why unit production costs are inversely proportional to the scale of manufacture. For example, most amino acids are expensive and can only be used in... 

If it is calculated that the volume of the gas space in the test cell will decrease significantly during the test, due to liquid thermal expansion, then account needs to be taken of this. Either the test can be performed at a lower fill level (at the cost of increased thermal inertia) or some estimate of the relationship between gas space volume and temperature should be made and the following equation used to find the pad gas pressure at any temperature ... 

If there is minimal byproduct formation, then the reactor costs (volume, catalyst, heating, etc.) can be traded off against the costs of separating and recycling unconverted reagents to determine the optimal reactor conversion. More frequently, the selectivity of the most expensive feeds for the desired product is less than 100%, and byproduct costs must also be taken into account. The reactor optimization then requires a relationship between reactor conversion and selectivity, not just for the main product, but for all the byproducts that are formed in sufficient quantity to have an impact on process costs. 

Equations 13.19 and 13.20 are approximations since k and a are defined in terms of the change of the volume with a change of p or T in the limit of very small p. The complete pressure-volume-temperature relationships must be considered to provide a more accurate description of the pressure dependence of rj at elevated pressures, at the cost of increased complexity of the calculations. It was shown [7] that Equation 13.21 provides a reasonable first approximation for (K/a), so that Equation 13.20 can be rewritten in the even simpler form given by Equation 13.22 ... 

Fio. 2. Relationship between estimated market price and market volume of a number of different plant products. The upper line represents the relation between the cost-price of a product produced by means of plant cell biotechnology and yearly production, at the current state of the art. The lower line is calculated from more optimistic figures and therefore represents a future situation. Products situated between the lines might be interesting goals for plant cell biotechnology in the near future. 

The capital cost of constructing the plant is depreciated over a fixed period of say 5 years. If the plant is constructed of steel pipes and pressure vessels of a characteristic diameter D, then the capital cost C is proportional to the surface area of steel used, i.e. to Dz- On the other hand, the annual capacity Q in tonnes increases in proportion to the reactor volume, i.e. to D3. Consequently, the relationship between capital cost and capacity is... 

After applying the indirect requirements, SAMIS translated total process resource requirements into a process cost. It relied on the Cost Account Catalog for this function. The catalog contained price/volume relationships for all categories of cost — labor, material, and other factors. One could construct cost catalogs for different regions to evaluate cost factors in different areas. Model outputs included process costs by step and enterprise financial statements, including income statements and balance sheets. 

The bottom-up performance and cost model described herein provides the precise mass and volume of all required battery components necessary to meet the user-specified performance. The calculated materials requirements are then directly linked to manufacturing cost calculation that determines both the materials costs and the costs associated with the manufacturing process and overhead. T.inking performance and cost allows for a complete evaluation of the relationships that govern the cost and energy density of the batteries for HEVs, PHEVs, and EVs. 

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