In the fourth chapter of their book, Newnan, Eschenbach, and Lavelle build on the ideas presented in chapter three – the basic principles of economic engineering analysis. The chapter introduces the reader to complex problems in economic analysis and presents formulas to work with uniform series cash flows and arithmetic/geometric gradient cash flows. The first portion of the chapter is the “Student solar power” case devoted to engineering students in Indiana who analyze the feasibility of their emergency lighting system using sunlight energy (Newnan et al., 2018, p. 110). After getting acquainted with the case, the readers are supposed to reflect on five questions concerning calculations, the nature of costs, and other practical problems.
The next portions of the text are devoted to practical solutions helping to evaluate decisions and the long-term financial outcomes of their implementation. Thus, in the section titled “Uniform series compound interest formulas,” the researchers provide formulas to estimate the expected benefits and costs if there is a uniform series of payments (Newnan et al., 2018, p. 112). Different ways to represent data graphically, including tables for assumptions, are specified and discussed. Step by step, the researchers explain the notion of the uniform series compound amount factor, which allows calculating a future single sum. They also provide practical tips for those using Microsoft Excel for calculations. Thus, the basic Excel functions helping to calculate annuities are listed in a well-organized way. To continue, the section “Cash flows that do not match basic patterns” explains mismatches between different diagrams and ways to avoid this problem (Newnan et al., 2018, p. 120). In particular, some approaches to presenting cash flow diagrams in a standard form are presented and explained with examples.
Then, in the section “Economic equivalence viewed as a moment diagram,” the authors use similarities between cash flow diagrams and force diagrams to further illustrate the concept of economic equivalence (Newnan et al., 2018, p. 125). On such diagrams, positive and negative cash flows represent positive and negative forces. This approach to teaching the topic of economic equivalence was developed by Matson and Elizandro more than ten years ago. In the next subsection, “Relationships between compound interest factors,” the authors summarize relationships between compound amount/present worth factors in individual payments (Newnan et al., 2018, p. 127). For the uniform series of payments, relationships between capital recovery and present worth factors and between compound amount and sinking fund factors are established.
The following parts of the chapter present new aspects of economic analysis by introducing the notions of arithmetic and geometric gradients. The authors decompose cash flows and graphically depict two of its components – constant amounts and changes between periods. They use a series of growing cash flows to demonstrate how the arithmetic gradient factors are derived. This information is then applied to solve problems and calculate costs given gradually increasing maintenance expenses.
The part titled “Geometric gradient” discusses a different situation, in which the amount of change between periods is unstable, whereas the rate of growth is fixed (Newnan et al., 2018, p. 135). The way to derive the geometric series present worth factor and use it to solve tasks with the uniform rate of growth is demonstrated with the help of examples and sample problems. In the section named “Spreadsheets for economic analysis,” the authors discuss spreadsheets as the tool for engineers (Newnan et al., 2018, p. 139). In particular, attention is paid to cash flows illustrated with the help of tables, annuity functions in Excel, graphs for data presentation, and the basics of what-if analysis. In the next section, the approach to calculating costs given that payment and compounding periods are dissimilar is discussed. Finally, the chapter ends with a full list of formulas and notations with definitions.
Reference
Newnan, D. G., Eschenbach, T. G., & Lavelle, G. P. (2018). Engineering economic analysis (13th ed.). New York, NY: Oxford University Press.