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of the costs and savings associated with the retrofit. When comparing alternative schemes, the focus of
                    attention is on the profitability of the incremental investment required. We will consider simple discrete
                    choices in this section. The problem of optimizing a continuous variable is covered in Chapter 14.


                    The initial step in an incremental analysis of competing alternatives is to identify the potential alternatives
                    to be considered and to specify the increments over which the analysis is to be performed. Our first step
                    is to rank the available alternatives by the magnitude of the capital cost. We will identify the alternatives
                    as A , A , ..., A . There are n possible alternatives. The first alternative, A , which is always available, is
                             2
                                     n
                                                                                                        1
                         1
                    the “do nothing” option. It requires no capital cost (and achieves no savings). For each of the available
                    alternatives, the project cost (capital cost), PC, and the yearly savings generated (yearly cash flow), YS,
                    must be known.


                    For larger retrofit projects, discounted profitability criteria should be used. The algorithm to compare
                    alternatives using discounted cash flows follows the same four-step method outlined in Section 10.3. For
                    small  retrofit  projects,  nondiscounted  criteria  may  often  be  sufficiently  accurate  for  comparing
                    alternatives. Both types of criteria are discussed in the next sections.


                    10.6.1 Nondiscounted Methods for Incremental Analysis





                    For nondiscounted analyses, two methods are provided below.
                          1.   Rate of Return on Incremental Investment (ROROII)






                          2.   Incremental Payback Period (IPBP)









                    Examples 10.10–10.12 illustrate the method of comparison of projects using these two criteria.

                    Example 10.10



                    A circulating heating loop for an endothermic reactor has been in operation for several years. Due to an
                    oversight  in  the  design  phase,  a  certain  portion  of  the  heating  loop  piping  was  left  uninsulated.  The
                    consequence is a significant energy loss. Two types of insulation can be used to reduce the heat loss. They
                    are  both  available  in  two  thicknesses.  The  estimated  cost  of  the  insulation  and  the  estimated  yearly
                    savings in energy costs are given below. (The ranking has been added to the alternatives and is based on
                    increasing project cost).
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