Annualization of Capital Cost

P = present worth of estimated capital cost F = future worth of estimated capital cost i = fractional interest rate per year n = number of years 

After the first year, the future worth F of the capital cost present value P is given by  

Take the capital cost and spread it as a series of equal annual payments A made at the end of each year, over n years. The first payment gains interest over (n—1) years, and its future value after (n—1) years is  

The future worth of the second annual payment after (n — 2) years is  

Holland FA, Watson FA and Wilkinson, JK (1983) Introduction to Process Economics, 2nd Edition, Wiley, New York. 

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In this case, the lives of the machines are unequal, and the comparison is conveniently made on the basis of capitalized cost. This puts lives on the same basis, which is an infinite number of years. The net annual cash flows generated by each machine are equal. 

The annual depreciation of a fixed capital investment is referred to as annualized fixed cost. It allows the company to set aside an annual portion of profit and use it for purposes of capital-cost recovery and tax deduction. 

For ROPE applications to tar sand mining, economic projections were published for capital costs and operating costs. Total capital costs were estimated at 53,336,000 and annual operating costs were estimated at 9,683,000. For the estimation of capital costs, direct field cost was estimated at 35,558,000. Other capital costs were based on percentages of that estimate. These cost estimates were based on mid-1989 dollars (D13089C, pp. 242-243). 

The scope of the economic evaluation includes estimation of capital cost figures for a nitric add plant producing 280 tonnes/day of a 60% product. Following this capital cost estimation the total annual operating costs are estimated, both variable and fixed components being considered. Also considered is the cost of providing finance for the initial capital outlay at 25% interest per annum. 

The capital cost of STPs is one quarter to a half of that of PV power plant (Table 1). The LEC is defined by the total cost, [(capital cost)x(fixed charge rate) + O M + fuel cost], per annual net electricity production in kWh. It varies depending on the plant scale and solar share. The LEC ranges between 0.05kWh and 0.12/kWh for the STP, and attains 0.4/kWh- l/kWh for PV electricity. Thus, the solar H2 production cost by PV and STP electricity is not comparable in terms of capital cost and LEC. However, the cost of STP electricity is still not competitive with that of a conventional coal-fired power plant. To close the price gap, the solar thermal parabohc trough power plant industry has introduced integrated solar combined cycle systems (ISCCS) which are able to offer a competitive base-load electricity cost of 0.05-0.07/kWh at solar shares of 15-25% [7] (Fig.l). 

Conservation Measure Energy Saved and Type of Fuel Capital Cost of Unit (1975) Specific Capital Cost of Conservation Measure ( /Annual Quad) Capital Cost of Comparable New Supply... 

Basfd on bOOO hours per year, annual electricity cost is 1.34U kW/hp X 0.03 x y0i0itJi> = 3 2l.bP. CApiLal and annual costs, assuminjft fixed charges are 30 1 of capital cost, arei... 

The FCR typically falls between 0.11 and 0.17 and represents the percentage of capital costs that must be recovered each year. For example, for a 1 million capital investment and an FCR of 0.15, the annual capital cost for that investment is 150 000. 

An annual capital charge of 25% of capital cost was specified for any new process plant taken up in the calculation. All costs were calculated in terms of 1976 U.S. dollars. 

Please submit a report on the two designs and cost estimates (flxed capital and utility operating costs only). For the capital cost of each of the two alternative sequences, sum the purchase costs of the distillation columns, heat exchangers, and any vacuum equipment. Multiply that cost by the appropriate Lang factor. To annualize the capital cost, multiply by 0.333. Add to this annualized cost the annual utility cost for steam and cooling water. Call this the total annualized cost for the alternative. 

The second item is maintenance supplies (spare parts, oils, greSses and other lubricants, etc.) estimated at 1% of the annual amortized capital costs or... 

The annual cost of maintenance and depredation is 10% of capital costs. 

Bast d on 8000 houru par cost ii 1,340 kW/hp X 0 CapiLal and annual costs are 30 of capital cost. year, annual ale Ctrlciiy 03 X aOiOiOl = -3 2l.bP.. assumirja fixed charges aiei ... 

Increasing the chosen value of process energy consumption also increases all temperature differences available for heat recovery and hence decreases the necessary heat exchanger surface area (see Fig. 6.6). The network area can be distributed over the targeted number of units or shells to obtain a capital cost using Eq. (7.21). This capital cost can be annualized as detailed in App. A. The annualized capital cost can be traded off against the annual utility cost as shown in Fig. 6.6. The total cost shows a minimum at the optimal energy consumption. 

EP = value of products - raw materials costs - annualized capital cost - energy cost... 

There can be an element of maintenance costs that is fixed and an element which is variable. Fixed maintenance costs cover routine maintenance such as regular maintenance on safety valves which must be carried out irrespective of the rate of production. There also can be an element of maintenance costs which is variable. This arises from the fact that certain items of equipment can need more maintenance as the production rate increases. Also, royalties which cover the cost of purchasing another company s process technology may have different bases. Royalties may be a variable cost, since they can sometimes be paid in proportion to the rate of production. Alternatively, the royalty might be a single-sum payment at the beginning of the project. In this case, the single-sum payment will become part of the project s capital investment. As such, it will be included in the annual capital repayment, and this becomes part of the fixed cost. 

The cost of the capital depends on its source. The source of the capital often will not be known during the early stages of a project, and yet there is a need to select between process options and carry out preliminary optimization on the basis of both capital and operating costs. This is difficult to do unless both capital and operating costs can be expressed on a common basis. Capital costs can be expressed on an annual basis if it is assumed that the capital has been borrowed over a fixed period (usually 5 to 10 years) at a fixed rate of interest, in which case the capital costs can be annualized according to... 

As stated previously, the source of capital is often not known, and hence it is not known whether or not Eq. (A. 10) is appropiiate to represent the cost of capital. Equation (A. 10) is, strictly speaking, only appropriate if the money for capital expenditure is to be borrowed over a fixed period at a fixed rate of interest. Moreover, if Eq. (A. 10) is accepted, then the number of years over which the capital is to be annualized is unknown, as is the rate of interest. However, the most important thing is that even if the source of capital is not known, etc., and uncertain assumptions are necessary, Eq. (A. 10) provides a common basis for the comparison of competing projects. 

When using annualized capital cost to carry out optimization, the designer should not lose sight of the uncertainties involved in the capital annualization. In particular, changing the annualization period can lead to very different results when, for example, carrying... 

In the above example, the discount rate used was the annual compound interest rate offered by the bank. In business investment opportunities the appropriate discount rate is the cost of capital to the company. This may be calculated in different ways, but should always reflect how much it costs the oil company to borrow the money which it uses to invest in its projects. This may be a weighted average of the cost of the share capital and loan capital of a company. 

A low temperature of approach for the network reduces utihties but raises heat-transfer area requirements. Research has shown that for most of the pubhshed problems, utility costs are normally more important than annualized capital costs. For this reason, AI is chosen eady in the network design as part of the first tier of the solution. The temperature of approach, AI, for the network is not necessarily the same as the minimum temperature of approach, AT that should be used for individual exchangers. This difference is significant for industrial problems in which multiple shells may be necessary to exchange the heat requited for a given match (5). The economic choice for AT depends on whether the process environment is heater- or refrigeration-dependent and on the shape of the composite curves, ie, whether approximately parallel or severely pinched. In cmde-oil units, the range of AI is usually 10—20°C. By definition, AT A AT. The best relative value of these temperature differences depends on the particular problem under study. 

Annual iadirect costs are estimated as percentages of the direct labor and fixed capital costs. Typical direct labor percentage ranges are 25—30% for payroll overhead, 15—20% for stores and suppHes, 10—20% for control laboratory, 10—20% for security, 10% for yard, and 10—15% for process improvements. That is, total iadirect costs are usually 80—115% of the direct labor cost (1). 

If money is borrowed, interest must be paid over the time period if money is loaned out, interest income is expected to accumulate. In other words, there is a time value associated with the money. Before money flows from different years can be combined, a compound interest factor must be employed to translate all of the flows to a common present time. The present is arbitrarily assumed often it is either the beginning of the venture or start of production. If future flows are translated backward toward the present, the discount factor is of the form (1 + i) , where i is the annual discount rate in decimal form (10% = 0.10) and n is the number of years involved in the translation. If past flows are translated in a forward direction, a factor of the same form is used, except that the exponent is positive. Discounting of the cash flows gives equivalent flows at a common time point and provides for the cost of capital. 

The total annual return rate on investment is the sum of both the capital cost rate, ie, discount rate, and the net return rate (NRR). Any given numerical value can represent a low capital cost rate and a high net return rate, or a high capital cost rate and a low net return rate. The IRR, as the discounting rate that gives a vanishing net return, cannot be related to the total return rate at appropriate discount rates because of the nonlinear nature of the discounting step. 

Various i Interest rate per period, usually annual, often tbe cost of capital Dimensionless... 

On the basis of sum-of-years-digits depreciation, the annual amount of depreciation for a specified number of years s for a plant of fixed-capital cost Cpc, scrap v ue S, and service life s is given by... 

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... 

Net annual cash income after tax A ci = 25,500 in each of 10 years Fixed-capital cost Cpc = 120,000... 

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