Break-even production rate

If we consider the situation, as above, where sales of 2-ethylhexanol show a net sales income of 690/tonne and the variable cost is 382/tonne, then there will be some level of production in the plants at which the sales income will cover all the costs (variable plus fixed including depreciation) but show no profit margin. This is the break-even production rate. Table 6.5 shows the build up of sales income and costs for the two plants and the figures are plotted in Fig. 6.2. 

From the table and Fig. 6.2 it can be seen that the break-even production level, under the assumed conditions, for the 50 kilotonnes/year plant is 29 kilotonnes/year (58% of plant capacity) whereas the 100 kilotonnes/year plant must have sales of 45 kilotonnes/year (45% capacity) to break-even as a result of the higher fixed costs incurred by the larger plant. 

Examination of the figures shows that, as capacity is increased, the reduction in cost plus return for the next increment of capacity is diminished. Looking at the incremental reduction in cost plus return against the incremental fixed capital used to produce it, it can be seen that the additional capital has less effect as the scale is increased. This is to be expected since, with increase in production scale and reduction in fixed costs per tonne of product, the scale-independent variable cost will dominate the cost plus return. Thus from Table 6.3 for the 50 kilotonnes/year plant the variable cost represents 53% of the cost plus return, and fixed costs (including depreciation and return) the balance of 47%. For the 100 kilotonnes/year plant the relationship of 

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Figure 6.2 Break-even production rates for 2-ethylhexanol plants.

There is good reason not to use AWP in country U. Suppose that drug firms in some country are able to earn above-normal rates of return on new products, year in and year out. If monopoly rents are built into AWP there, they should surely be backed out if the analysis is to be done from a true societal perspective. The argument in Gold et al. (1996) that prices must be at least high enough for firms to break even does not preclude the possibility that most ventures do much better than just break even. 

Figure 8.3-5 shows the discounted cumulative cash-flow as a function of elapsed years. With the assumptions contained in this qualitative discussion, we found that the discounted break-even period is 4 years when the product can be sold at 220 EUR/kg, it is 9 years when the price is 150 EUR/kg, but it is more than 20 years if the price falls to 120 EUR/kg. These results are obtained assuming an inflation rate of 3% per year. 

Selling price may change depending on the production level P due to market circumstances. Figure 3 shows a plot of the sales revenue, which, for illustration, is linear with P. It also shows the total product cost plotted at various production levels, which nearly depends on the 0.6 power of P. At high production levels, total production costs lay below the possible sales revenue the difference between the two costs indicates the total profit at that production level. At low production levels total production costs are larger than the possible sales revenue, and plant operation yields losses. The production level at which total costs equal the possible revenues is the break-even point. Plant production and sales must run at higher rates for the operation to be competitive. 

Figure 6-3 gives a graphical analysis of the effect on costs and profits when the rate of production varies. As indicated in this figure, the fixed costs remain constant and the total product cost increases as the rate of production increases. The point where the total product cost equals the total income is known as the break-even point. Under the conditions shown in Fig. 6-3, an ideal production rate for this chemical processing plant would be approximately 450,000 kg/month, because this represents the point of maximum net earnings. 

A process plant making 2000 tons per year of a product selling for 0.80 per lb has annual direct production costs of 2 million at 100 percent capacity and other fixed costs of 700,000. What is the fixed cost per pound at the break-even 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 34 percent of gross earnings ... 

The future reduction in PEM fuel cell prices is indicated in Fig. 6.1 in terms of two curves corresponding to learning rates of 10-20% corresponding to the limiting cases of photovoltaic modules and wind turbines over the recent decade. Even with the lower curve, break-even with current vehicles would not be reached until the cumulated production reached about 500 GW. However, difficulties with the market for oil products (peaking production, instability of major supplier countries) may make PEM fuel cell vehicles competitive at higher prices than the currently seen break-even price. 

The answer obtained in either case is DCFROR = 7.85%. This is the maximum interest rate at which this proj ect can be financed to break even in 15 years of production. 

Because of the ozone depletion that occurs by photolysis, the NO, break-even concentration at which net O, production occurs is somewhat larger than the value based just on the ratio of the rate constants of reactions 5.47 and 5.25. The approximate crossover point for NO, between O destruction and production is usually considered to be at about 30 ppt. Ozone mixing ratios in the planetary boundary layer over the remote Pacific Ocean are only about 5 to 6 ppb NO, levels are about 10 ppt. Thus, this region of the atmosphere is probably below the crossover point. 

Any comparison between different materials, regarding their suitability for an application, must be related to the processes involved and thence to the optimum levels of production. For something as large and complex as a car body, the analysis of the break even points is absolutely crucial. Factors such as model lifetime, production levels, tool costs, material prices and production rates must be taken into account, as well as less predictable market forces. 

Hiring unqualified personnel at lower pay rates expecting that training would get them qualified, only to find out that the time and effort is not worth it. Unqualified personnel reduce productivity and break-even takes longer. 

The principal characteristic of induced reactions of this type which have not been stressed so far, is that the extent of the induced change greatly decreases and in most cases reaction even ceases in the presence of chain-breaking substances. The induced reaction can be suppressed by any substances reacting with chain carriers at a higher rate than does the acceptor, and the product of the reaction of the suppressor can easily react with the inductor. Since the concentration of the chain carriers is generally low, the supressors of induced chain reactions exert considerable effect even in small quantity. The effect is particularly pronounced when the suppressor reacts reversibly. 

Therefore, the rate at which chemical bonds break increases with elastic shear stressing of the material. The rupture of chemical bonds, hence fracture of material, leads to its fragmentation into particles. This reduces the average particle size in powder as fractured particles multiply into even smaller particles. Equation (1.24) points to the importance of elastic shear strains in mechanical activation of chemical bonds for particle size refinement and production of nanoparticles. 

In reality, the reaction could not be persuaded to go exactly as shown in Scheme 21.1, because the Cl—C3 bond would certainly break at very nearly the same rate as Cl—C2. In the experiments actually conducted by Baldwin et al., this problem was resolved by deuterium labeling both C2 and C3—creahng diastereomericaUy pure, but achiral molecules. Even then, there remained a large number of technical difficulties, which in the end the researchers were able to overcome. Their results indicated that the four stereochemical courses for the reaction run at 300 °C were sr 23%, si 40%, ar 13%, and ai 24%. These numbers do not ht the expectations from either mechanism. Clearly, the Woodward-Hoffmann forbidden and allowed products are formed in nearly equal amounts ([sr] + [ai] =47% [si] + [ar] = 53%)— hardly what one would expect for a pericyclic reaction. On the other hand, the stereochemical paths do not show the pairwise equalities expected from the stepwise mechanism. 

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