Straight-line method for determining

In the straight-line method for determining depreciation, it is assumed that the value of the property decreases linearly with time. Equal amounts are charged for depreciation each year throughout the entire service life of the property. The annual depreciation cost may be expressed in equation form as follows ... 

Depreciation. Depreciation arises from two causes deterioration and outdatedness (economically). These two causes do not necessarily operate at the same rate, and the one having the faster rate determines the economic life of the project. Depreciation is an expense, and there are several permissible ways of allocating it. For engineering purposes, depreciation is usually calculated by the straight-line method for the economic life of the project. Frequently, economic lives of 10 years or less are assumed for projects of less than 250,000. 

Fixed capital investments are characterized by the fact that they have to be replaced after a number of years commonly referred to as service life or useful life period. This replacement is not necessarily due to wear and tear of equipment. Other factors include technological advances that may render the equipment obsolete. Furthermore, over the usefiil life of the equipment, the plant should plan to recover the capital cost expenditure. In this regard, the notion of depreciation is useful. Depreciation or amortization is an annual allowance which is set aside to account for the wear, tear, and obsolescence of a process such that by the end of the useful life of the process, enough fund is accumulated to replace the process. The simplest method for determining depreciation is referred to as the straight line method in which... 

The current methods for determining aimual depreciation charges are the straight-line depreciation and the Modified Accelerated Cost Recovery System (MACRS). In the straight-line method, the cost of an asset is distributed over its expected useful life such that the annual charge is... 

In Equation 8.3-1, D is depreciation, FCI is fixed-capital investment, t is the number of years over which the depreciation is accounted for, and S is the salvage value. Thus S is the value the plant could be sold for after the t years of operation. In this discussion we assume that the plant lasts for ten years, and that its salvage value is zero. With the straight-line method, annual depreciation costs are constant. Other methods, such as the sum-of-the-years-digits method, determine depreciation costs to be greater in the early years of the property than in the later years. Local regulatory laws generally define which method can be used to determine depreciation costs. 

Because of its simplicity, the straight-line method is widely used for determining depreciation costs. In general, design engineers report economic evaluations on the basis of straight-line depreciation unless there is some specific reason for using one of the other methods. 

Comparison of straight-line, multiple straight-line, sum-of-the-years-digits, and declining-balance methods for determining depreciation. 

In order to make it worthwhile to purchase a new piece of equipment, the annual depreciation costs for the equipment cannot exceed 3000 at any time. The original cost of the equipment is 30,000, and it has zero salvage and scrap value. Determine the length of service life necessary if the equipment is depreciated (a) by the sum-of-the-years-digits method, and (b) by the straight-line method. 

A proposal has been made to replace the present piece of property by one of more advanced design. The proposed equipment would cost 40,000, and the operating costs would be 15,000/year. The service life is estimated to be 10 years with a nonzero salvage value. Each piece of equipment will perform the same service, and all costs other than those for operation and depreciation will remain constant. Depreciation costs are determined by the straight-line method. The company will not make any unnecessary investments in equipment unless it can obtain an annual return on the necessary capital of at least 10 percent. 

Measurements of E are then taken for a variety of m values in very dilute solutions, yielding a set of L values. As seen from the expression on the right, a plot of the left-hand side, L, versus m should produce a straight line in that range of molalities where Eq. (4.10.6) is found to be valid. From the slope one may determine the value of C appropriate to the HCi solution under study. Extrapolation of the straight line back to m - 0 yields ° as the intercept. This provides a convenient alternative method for determining the standard emf with respect to molality in the present case f ° - 0.22234 V at 25°C. 

This equation predicts that a graph of 1/ uni against 1/[M] (or /p) will be a straight line whose intercept is 1 /ho and whose slope is 1 /k. This type of plot is called a Lindemann plot, and provides, in principle, an elementary method for determining both the high and low-pressure limiting rate coefficients and for testing the theory. Unfortunately, as discussed below, Lindemann plots are often not linear. 

Figure 16-14 A graphical method for determining activation energy, E. At each of several different temperatures, the rate constant, k, is determined by methods such as those in Sections 16-3 and 16-4. A plot of In k versus 1/T gives a straight line with negative slope. The slope of this straight line is —EJR. Use of this graphical method is often desirable, because it partially compensates for experimental errors in individual k and T values.

It so happens that, when the results for any given dye/salt ratio are plotted as log uptake against log bath concentration, the points fall along a straight line to a good approximation. This fact has been used in the statistical analysis of the results. Straight lines have been determined for each dye/salt ratio (including zero) by the method of least mean squares, and the various lines have been compared by the methods of analysis of covariance. 

If the design was for a second-order model and examination of the contour plots or canonical analysis (see below) showed that the optimum probably lay well outside the experimental domain, then the direction for exploration would no longer be a straight line, as for the steepest ascent method. In fact, the "direction of steepest ascent" changes continually and lies on a curve called the optimum path. The calculations for determining it are complex, but with a suitable computer program the principle and graphical interpretation become easy. 

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