Investment cost equation

Textbooks on investment present a simple model where the net present value (NPV) of an investment equals annual future revenues [R) summed and discounted at the rate r, minus the initial investment cost, I. Using t as a time subscript to denote different years, the equation is... 

Table 9E-9 lists unit operations in the polystyrene plant. The highest temperature is 400°F, in the extruder. From this and Figure 9-5, a temperature factor of 0.04 is obtained. There are no high pressures except in the extruder, and its value is unknown. The pressure factor will be assumed to be zero. Stainless steel is used, so the material factor is 0.2. From Equation 2 a complexity factor of 3.48 can be calculated. A direct process investment cost of 350,000 per functional unit is obtained from Figure 9-7. This means that the cost of constructing the plant when the Engineering News Record Construction Index (ENRCI) is 300 would be 3,150,000. This will be updated to 1960 when the ENRCI was 350, and then the CEPI will be used to obtain the cost in 1974. The resultant cost in 1974 is... 

It is obvious from Fig. 6.6-5 that the investment costs for a specific type of plant can be determined accurately enough from the following equation ... 

Based on the flow equation some essential economic aspects can be derived. First, the investment cost of a pipeline is obviously linked to the diameter of the pipeline. The larger the diameter, the more steel is needed, and the more weight the pipeline will have. This implies that investment costs increase with increasing diameter as costs for pipeline material and installation will increase. As we can see from the equation however, the output (flow) will increase in the power of 2.5 for every unit of diameter invested. This economic fact is often referred to as economy of scale. 

Profits at the site level are calculated in equation (3.84) by subtracting all costs incurred at the site from the revenues realized at the site from finished and intermediate products as calculated by equation (3.85). In addition to the cost items already contained in the basic model formulation, the costs of intermediates received from other sites have to be allocated to the receiving site for tax purposes and the depreciation costs have to be subtracted instead of investment expenditures. Equation (3.86) defines that depreciation costs are calculated by adding to the depreciation plan of old assets (which has to be determined outside the model) depreciation incurred from new investments. Based on the assumption of straight-line depreciation and a depreciation period that exceeds the planning horizon these costs can be calculated as a fixed percentage of the total investments incurred at a site. 

A cost equation may be written to include all the costs, which are expressed in terms of the capacity of the flow-scheme components. The selection of equipment sizes that minimize capital investment is (1) complicated by interrelations between pieces of equipment, (2) limited by the discontinuity in size of standard equipment, (3) fixed by the availability of idle or used equipment, and (4) restricted by the higher cost of custom-made equipment. Writing one equation for a complete plant is a complex task. It is more likely that it may be done for small sections of the plant which can be operated as interrelated trains. 

The cost equations thus written are discontinuous functions of the size of the units which compose the trains. A mathematical minimization of any of these equations may not lead to a practical minimum. It may indicate only the domain where less-expensive solutions may exist. The practical alternative is to draw flow schemes which are equivalent to the process under investigation. The economic analysis of these schemes terminates with the selection of one which requires the minimum capital investment and operating costs. 

According to the equations developed for an ordinary annuity in Chap. 7 (Interest and Investment Costs),... 

Substituting the above equation into Eq. (5.81) and the latter into Eq. (5.82), a relationship between the operating and investment costs is obtained... 

To make an electrodialyzer compact, which decreases investment cost, it is necessary to increase the limiting current or i im for operation of the electrodialyzer at a higher current density. Many studies have been made to analyze the relationship of z )im to the degree of agitation of the solution in an electrodialyzer.13 Many equations have been proposed linking zlim and the spacer in the electrodialyzer. When the solution flows in the electrodialyzer with lamellar flow, the following equation is proposed as an example,14... 

Because of the numerous possibilities, optimization of the separation sequence with regard to investment costs and energy requirement is a difficult task that has still not been satisfactorily solved. For the simplest arrangement of columns, in which only a overhead and a bottom fraction is obtained from each column, for separaration into an increasing number of fractions Ug-,ctions, a strongly increasing number of column circuits WajcuiB results (Equation 2.3.2-36) ... 

This relationship has been foimd to give reasonable results for individual pieces of equipment and for entire plants. Although, as shown by Williams (1947a,b), the exponent, m, may vary from 0.48 to 0.87 for equipment and from 0.38 to 0.90 for plants, the average value is close to 0.60. Accordingly, Eq. (16.3) is referred to as the six-tenths rule. Thus, if the capacity is doubled, the 0.6 exponent gives only a 52% increase in cost. Equation (16.3) is used in conjunction with Eq. (16.2) to take cost data from an earlier year at a certain capacity and estimate the current cost at a different capacity. As an example, suppose the total depreciable capital investment for a plant to produce 1,250 tonnes/day (1 tonne = 1,000 kg) of ammonia... 

Key plants with all the above mentioned processes are offered by special engineering companies. The investment cost for a typical recovery plant with hot gas regeneration can be estimated by the following equation ... 

Now the formulas for the variance of the fiimre flood damage in the cost-benefit models by Van Dantzig and Eijgenraam mm out to be very valuable, since we can use them to calculate the optimal strategy for different values of the risk inversion index k. Of course, Equation 24 contains the variance of the total costs, but one should notice that this equals the variance of the future flood damage, since (within these models) the investment costs are not imcertain. 

According to the equation above, the quantities feToGav, which are related to irreversible dissipation and TKpt should be equal in any transfer unit. Generally, operating costs are linearly related to dissipation, while investment costs are linearly related to the size of equipment. The optimum size distribution of the transfer units is obtained when amortization cost is equal to the cost of lost energy due to irreversibility. The cost parameters A and B may be different from one transfer unit to another when a = b, Oav/Vopt is a constant, and the optimal size distribution reduces to equipartition of the local rate of entropy production. The optimal size of a transfer unit can be obtained from Eqn (e)... 

It will be evident from the discussions in this chapter that the mechanisms involved in intensification may involve an additional energy input. In building up the case for support the project manager will, of course, include the additional energy inputs in the cost equations, hi most instances the extra cost of the energy input will be much less significant than the financial rewards gained by investment in the intensified process and/or plant. 

Probably the main disadvantages are associated with capital cost when considering a PLC for a relatively simple application. Safety PLCs are much more expensive than standard PLCs and the cost of the sofWare package and any special training must be added in. If the application is to be repeated many times the cost equation will become more favorable as the software investment is recovered. For a simple application the modular products we have seen will be a cheaper solution until the safety function becomes complex. For example there are a munber of packaged PLC solutions on the market for the complete safety functions for mechanical and hydraulic power presses. The scope of these solutions as a contribution to increased safety as well as higher productivity may well justify their capital cost. 

In addition, payback period (PP) is calculated to determine the length of time required to recover the total investment cost. PP is expressed as the total cost of investment over GP and it is shown in the following equation ... 

A fourth method of computing depreciation (now seldom used) is the sinking-fund method. In this method, the annual depreciation A is the same for each year of the life of the equipment or plant. The series of equal amounts of depreciation Aq, invested at a fractional interest rate i and made at the end of each year over the life of the equipment or plant of s years, is used to build up a future sum of money equal to (Cpc S). This last is the fixed-capital cost of the equipment or plant minus its salvage or scrap value and is the total amount of depreciation during its useful life. The equation relating i Fc S) and Ao is simply the annual cost or payment equation, written either as... 

In considering either multiple payments or cash into and out of a company, the present values are additive. For example, at 6 percent interest, the present value of receiving both 1,000 in one year and 1,000 in three years would be 943.40 + 839.62 = 1,783.06. Similarly, if one were to receive 1,000 in one year, and pay 1,000 in 3 years the present value would be 943.40 - 839.62 = 103.78. It is common practice to compare investment options based on the present-value equation shown above. We may also apply one or all of the following four factors when comparing investment options Payback Period Internal Rale of Return Benefit-to-cost Ratio and Present Value of Net Benefit. But as we will see later, it is rate of return that is usually the most enlightening when considering an investment. 

It is eommon praetice to eompare investment options based on the present-value equation shown above. We may also apply one or all of the following four factors when comparing investment options Paybaek period Internal rate of return Benefit-to-cost ratio and Present value of net benefit. 

The aim of life cycle cost calculations is to ensure that investment decisions are not made solely on the basis of a low purchase price, but that the life cycle operating costs are considered in the equation. 

Life cycle cost calculations are an application of investment calculations. Typically, the present value of total costs (investment and operation) are calculated. In this case, the equation is ... 

In the above equation, r can indicate the internal rate of return on an investment. Suppose that an investment in an energy-saving technology cost 100 and reduces energy costs by 20 per year indefinitely. The reduction in costs is comparable to net revenues received. The above equation can be modified as follows I equals R/r, where the values of I and R are specified and the value of r is computed. Hence 100 equals 20/r, and r equals 0.20, or 20 percent. The internal rate of return on the 100 investment is 20 percent per year. An investment is generally profitable when its internal rate of return exceeds the (interest rate) cost of obtaining credit. The investment is attractive when its internal rate of return exceeds the investor s hurdle rate, which may vary depending on the riskiness of the investment, and on the rate that can be earned from alternative uses of the investment funds. 

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