Payback Period PBP

C = annual production cost D = annual depreciation S = annual sales revenues Cta = total capital investment Cjdc total depreciable capital. 

Startup period, the plant is assumed to operate each year at full capacity (or at some percentage of full capacity) for the same number of days per year. As was stated earlier, many definitions of ROI have been suggested and used. Here, the most common definition is applied 

The calculation of ROI is readily made and the concept is easy to understand. However, as stated above, the definition of ROI involves many assumptions. Furthermore, ROI does not consider the size of the venture. Would a large company favor many small projects over a few large projects, when the small projects have just slightly more favorable values of ROI  

The payback period is the time required for the annual earnings to equal the original investment. Payback period is also called payout time, payout period, payoff period, and cash recovery period. Because it is simple and even more understandable than ROI, PBP is widely used in early evaluations to compare alternatives. Like ROI, the payback period in years has several definitions, but the following is used here. This definition is not consistent with the definition of ROI in Eq. (17.7), because only the depreciable capital is used and the annual depreciation, D, is added back to the net earnings because that depreciation is retained by file company. 

High-risk ventures should have payback periods of less than 2 yr. In these times of rapid progress in technology, most companies will not consider a project with a PBP of more than 4 yr. PBP is especially useful for simple equipment replacement problems. For example, should an old, inefficient pump be replaced with a new, energy-efficient model. This decision is clear if the PBP is less than 1 yr. PBP should never be used for final decisions on large projects because it gives no consideration to the period of plant operation after the payback period. 

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Figure 9-13 is a plot of Eq. (9-61) in the form of the number of years n required to reach a certain discounted-cash-flow rate of return (DCFRR) for a given payback period (PBP). The figure is a modification of plots previously published by A. G. Bates [Hydrocarbon Process., 45, 181-186 (March 1966)], C. Estrup [Br Chem. Eng., 16, 171 (February-March 1971)], and F. A. Holland and F. A. Watson [Process Eng. Eeon., 1, 293-299 (December 1976)]. 

Inflation (DCFRR) and Payback Period More insight into the effect of inflation on (DCFRR) calculations can be gained dv considering the payback period (PBP), which is defined as the elapsed time necessary for the positive aftertax cash flows from the project to... 

Equation (9-244) shows that, to have a low payback period (PBP), Cpc W and y should be small and y, (COP), and Cj large. Clearly as the unit cost of input energy Cj increases, the economics of heat pumps becomes more favorable. 

Economic analysis can determine the discounted profitability criteria in terms of payback period (PBP), net present value (NPV), and rate of return (ROR) from discounted cash flow diagram, in which each of the annual cash flow is discounted to time zero for the LHS system. PBP is the time required, after the construction, to recover the fixed capital investment. NPV shows the cumulative discounted cash value at the end of useful life. Positive values of NPV and shorter PBP are preferred. ROR is the interest rate at which all the cash flows must be discounted to obtain zero NPV. If ROR is greater than the internal discount rate, then the LHS system is considered feasible (Turton et al., 2003). 

Payback period (PBP)—how long a project must operate to break even ignores the time value of money. 

Payback period (PBP) Net present value (NPV) Internal rate of return (IRR)... 

Payback period (PBP) the cost of an investment divided by the cash flow per period. 

Investment decisions are often based upon several criteria, such as annual return on investment (ROI), payback period (PBP), net present value (NPV), the average rate of return (ARR), present value ratio (PVR), or the internal rate of return (IRR). Discounted cash flow rate on return (DCFRR) is another popular means of evaluating the economic viability of a proposed project. Horwitz [1] recommended the DCFRR as the best means to determine the return on investment, because it accounts for the time value of money. The internal rate of return as an investment criterion gives the possibility that given cash flows may result in more than one internal rate of return. Cannaday et al. [2] developed a method for determining the relevance of an internal rate of return. They inferred that an internal rate of return is relevant, if its derivative with respect to each of the cash flows is positive. 

Fig. 1.1 Optimal results of Williams-Otto process for minimizing payback period, PBP and maximizing net present worth, NPW (a) PBP versus NPW, (b) reactor temperature, T, versus NPW and (c) reactor volume, V, versus NPW.

Multi-objective optimization (MOO) has attracted considerable attention from researchers in chemical engineering, particularly in the past decade. Reported MOO studies have mainly used criteria such as selectivity, yield, productivity and/or energy consumed see Chapter 2 for the chemical engineering applications studied since 2000 and the objectives used in them. However, profit, an important criterion in any commercial operation, was not used in many of these studies. Apart from the simple profit, several economic criteria such as payback period (PBP), net present worth or value (NPW or NPV) and internal rate of return (IRR) are popular for evaluating projects in industrial practice. Edgar et al. (2001) compared the pros and cons of these three profitability criteria. Studies by Huskies (1997) and Pintaric and Kravanja (2006), show that optimal solutions of chemical processes are dependent on the economic objective selected. This indicates the conflicting nature of some, if not all, economic objectives, which means MOO is probably required even if one is interested in only the profitability criteria. 

Be able to compute approximate profitability measures, such as return on investment (ROI), payback period (PBP), venture profit (VP), and annualized cost (C ). These measures provide a snapshot view of the economic goodness, usually in the third year of operation. They do not include the time value of money, that is, compound interest. 

The ideas discussed in Chapter 9 are extended to evaluate the profitability of chemical processes. Profitability criteria using nondiscounted and discounted bases are presented and include net present value (NPV), discounted cash flow rate of return (DCFROR), and payback period (PBP). A discussion of evaluating equipment alternatives using equivalent annual operating costs (EAOC) and other methods is presented. Finally, the concept of evaluating risk is covered and an introduction to the Monte Carlo method is presented. 

Time Criterion. The term used for this criterion is the payback period (PBP), also known by a variety of other names, such as payout period, payoff period, and cash recovery period. The payback period is defined as follows ... 

The method of evaluation for each of the criteria is given on Figure ElO.l and in Table ElO.l. Payback Period (PBP) = 3.85 years Cumulative Cash Position (CCP) = 170.5 x 10 ... 

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