Session: 09-01-02: Curriculum Innovations, Pedagogy and Learning Methodologies

Paper Number: 96205

96205 - Inclusion of Continuous Annuities in Engineering Economics Instruction 

Practicing engineers are often required to conduct financial analyses of engineering projects and related business ventures.  The financial impacts of engineering work often involve repeated payments spread out over time rather than simple single transactions.  Usually these payments occur monthly, quarterly, biannually, or annually.  However, with advances in transactional and computational capability, systems with increasingly frequent payment structures are becoming more common.  The greater efficiencies gained with these more frequent payment structures have led to the possibility of using continuous payment streams where the payment amount and time between payments goes to zero.  

Traditional annuities are generally defined as a series of discrete, regularly spaced payments usually beginning at the end of the first period.  These discrete annuities are regularly used to represent ongoing costs and revenues from projects and ongoing operations.  They are also the most common type of payment structures for large debts such as interest-only loans and self-amortizing mortgages.  Rental agreements also tend to rely on regular payments during the period of use.  The computation of the present and future values of these payment streams is a well-developed area of engineering economics.  However, this disjointed payment structure arguably relies primarily upon an archaic transactional view of financial exchange which may be improved upon.

Continuous annuities are similar in concept to discrete annuities but use an entirely different approach.  By taking the limit as the payment interval and payment amount simultaneously approach zero, the continuous annuity effectively becomes a derivative or rate of payment rather than a series of payments.  This type of monetary flow can more efficiently respond to rapid levels of growth and high levels of inflation than is possible with discrete payment systems.  In addition, by eliminating the delays and accumulations of funds found with periodic payments, continuous annuities provide for greater levels of financial efficiency than traditional transactional approaches are capable of.  Finally, the analysis of these payment structures can actually be simpler for students to conceptually understand and quantifiably calculate for people with strong analytical backgrounds such as undergraduate students than discrete annuities.

Engineering students will often find a high level of familiarity with continuous annuities in that they bear a strong similarity with many of their other engineering-related classes.  Continuous payment rates use a different set of mathematical skills than the series-based approaches used with discrete annuities.  These methods are in many ways much closer to the mathematical applications found in other types of engineering applications.  They use many common engineering mathematical methods such as limits, derivatives, integrals, and differential equations.  Various types of growth and decay models can also be adapted to these basic flow rates to provide second and third derivative elements to the analysis.  

In addition, continuous annuities offer close analogies to other types of engineering.  Their calculation is very similar to the mathematics electrical engineers use to determine charge and discharge times of resistor-capacitor circuits.  The structure of continuous payment flows also bear a strong similarity to hydraulic and even plumbing systems as revenues are directly routed to expenses just as fluids would flow under pressure.  These approaches can bring additional value of instruction in an engineering economics context.  

Despite these advantages, currently available engineering economic curriculums tend not to include coverage of continuous payment systems.  Surprisingly little research has occurred in this area and no references to its instruction at this undergraduate level can be easily found.  This paper makes the case for the inclusion of this material in undergraduate engineering economics courses and presents an introduction to the topic and suggested methodology for how it can be integrated and presented in such a curriculum.  The ultimate intention for the inclusion of this material in these courses is to improve the effectiveness of engineering economic analysis of current transactional systems as well as to potentially advance the use of continuous annuities in professional engineering-related commerce.

Presenting Author: Aaron Armstrong Milwaukee School of Engineering

Presenting Author Biography: Dr. Aaron Armstrong is an Associate Professor of Mechanical Engineering in the Industrial Engineering program at the Milwaukee School of Engineering. Aaron’s research and consulting activity focuses primarily on process improvement and product development with focuses on innovation and technology development, mass customization, value engineering project management, entrepreneurship, and supply-chain coordination. Aaron previously worked for John Deere as a supplier development engineer, supervisor, manager, and senior engineer. During this time, Aaron and his staff of engineers worked with hundreds of companies around the world in helping them become more flexible and cost effective. In addition, Aaron’s previous work experience includes setting up and running a second-tier automotive supplier, design engineering, light-metals fabrication, chemical research and development, and aerospace production. Aaron has a doctorate in Industrial Engineering and Master’s degrees in Business and in Manufacturing Systems Engineering as well as a Bachelor’s degree in Chemical Engineering, all from the University of Wisconsin in Madison.

Authors:

Aaron Armstrong Milwaukee School of Engineering