Using a Real-Options Analysis Tutorial in Teaching Undergraduate Students

An undergraduate tutorial on real-options analysis used in teaching an advanced engineering economy course is presented. The tutorial includes the binomial option pricing model and the Black-Scholes model. Reasons for using real-options analysis are included, as well as examples of calculations of the values of financial options and real options for a variety of investment scenarios. Implications of real-options analysis on the way engineering economy is taught are also treated. Specifically, the need to incorporate multiple discount rates, continuous compounding, and terminal value analysis in economic justifications is addressed. Lessons learned are shared from using the tutorial in 2015 and 2016. Introduction After many years of teaching engineering economy (EngEcon), an opportunity was presented in 2014 for me to teach advanced engineering economy (AdvEngEcon). AdvEngEcon is a 3-credit-hour course offered during spring semester; it is a technical elective for industrial engineering majors and is occasionally taken by graduate students. The prerequisite for AdvEngEcon is EngEcon. As such, several students are juniors, but the majority are seniors. As taught for many years, AdvEngEcon typically began with a review of material covered in EngEcon: annual worth, future worth, present worth, and rate of return methods of comparing mutually exclusive investment alternatives, after-tax comparison of investment alternatives under inflationary conditions; and replacement analysis. Additional material in AdvEngEcon included: cost estimation; capital planning and budgeting; break-even, sensitivity, and risk analysis; decision analysis; analytic hierarchy process; and real options. The textbook adopted for the course was Capital Investment Analysis for Engineering and Management, 3 edition, by Canada, Sullivan, rd White, and Kulonda. After teaching AdvEngEcon in 2014, I decided to provide an enhanced treatment of real options in 2015. Toward that end, I developed a tutorial, targeting undergraduate students enrolled in AdvEngEcon. The tutorial has been revised numerous times in an attempt to increase its value to students taking the course. A copy of the tutorial for the 2016 spring semester is provided in the Appendix. My purposes in preparing this paper are twofold: 1) encourage engineering economy educators to incorporate real-options analysis in their engineering economy courses and 2) share lessons learned in teaching the subject of real-options analysis to undergraduate students. The paper is organized as follows: challenges for students are addressed; sample homework and test problems and solutions are provided; and lessons learned regarding teaching engineering economy are shared. Challenges Among the challenges for undergraduate students when real-options analysis is taught are the following: 1) when and why real-options analyses should be performed; 2) how to recognize opportunities for real-options analysis; 3) understanding the assumptions and mathematics underlying the various methods used to calculate option values; and 4) how to incorporate elements of real-options analysis in present worth comparisons of investment alternatives. When and why real-options analyses should be performed: As to when real-options analyses should be performed, Eschenbach, et al pointed out, “Real options have their application only in those projects where the NPV is close to zero, where there is uncertainty, and where management has the ability to exercise [its] managerial options.” [2, p. 401] When deciding if an individual investment should be pursued in the future, students have no difficulty accepting the decision rule: pursue if the present worth is positive-valued; otherwise, do not pursue the investment. However, they do not readily accept a decision to pursue a future investment having a negative-valued present worth because of the intrinsic value of the flexibility to pursue (or not pursue). Realizing such decisions are not binary (pursue, don’t pursue), but include a “wait and see before deciding” option takes time for students to understand and accept. No doubt, some of the difficulty students face is due to their engineering economy course being taught as though we live in a deterministic world. And, when uncertainty is discussed, we usually discuss it in negative terms. Realizing uncertainty about future events produces economic value does not come easily to students (or some professors, for that matter!) As Canada, et al stated, the “... option to postpone all or part of a capital investment has intrinsic value that is generally not recognized in traditional investment decision studies of project profitability.” [1, p. 495] In addition, as Eschenbach, et al noted, “Real options analysis is a tool intended to place a monetary value on the managerial flexibility in future choices.” [2, p. 401] Why should real-options analyses be performed? We posit two reasons: it forces you to consider strategic options embedded in the investment and it can help you avoid making a Type I error. Strategic options embedded in the investment might include staging the investment over time. Too often, we think of an investment as all or none, rather than employing the strategy of “eating the elephant one bite at a time.” Real-options analysis forces you to identify options. Drawing on a knowledge of hypothesis testing from an engineering statistics course, a Type I error occurs when something that should be accepted is rejected; a Type II error occurs when something that should be rejected is accepted. For economic justifications, a Type I error occurs when an investment is rejected that should be pursued. Arguably, a Type I error is more expensive than a Type II error, because an investment can be abandoned once it becomes obvious a Type II error has occurred; however, we seldom know if a Type I error occurs (hindsight is not 20/20), because no investment occurs. (Because Type II errors are visible, the tendency is to avoid them. Unfortunately, attempts to decrease the probability of making one type error tend to increase the probability of making the other type error!) Real-options analyses are performed for future investments. As such, management holds the option of rejecting the investment as more information is obtained with the passage of time. Contrary to the parenthetic comment, above, the benefit of “wait and see” can reduce both the probability of making a Type I error and the probability of making a Type II error. (Of course, there can be a cost associated with waiting and it is often overlooked, as noted in [2].) How to recognize opportunities for real-options analysis: Triantis provides the following taxonomy of real options ! growth options < expanding current production capacity < developing, producing, and selling new products ! contraction options < abandoning one or more current products or plants < shrinking current production capacity ! switching option < mixed use real estate development < changing the mix of products being produced < changing the mix of input sources ! contractual options < purchase contracts with options to buy at stated future prices < guaranteed salvage values on purchased equipment [5] If an investment does not fit one of the “standard” categories of real-option investments, it can be quite challenging to see the potential for a real-options analysis. It is easier to know when an opportunity does not exist for a real-option analysis. As Eschenbach, et al pointed out, “When a project’s NPV is large, there is no need to determine an option value–do it. When the NPV is highly negative, the project should be abandoned; no option value will justify the project.” [2, p. 401] Necessary conditions for a real option to exist are time and volatility! If faced with a “go, no go” decision that must be made now, there is no reason to perform a real-options analysis, because no option exists. Likewise, in a deterministic world, there is no reason for a real-options analysis. (As the level of uncertainty approaches zero, real-options analysis approaches present-worth analysis.) As Mun noted, “It is only when uncertainty exists, and management has the flexibility to defer making midcourse corrections until uncertainty becomes resolved through time, actions, and events, that a project has option value.” [4, p. 582] Of course, even with time and volatility, a real-options analysis should not be performed if no options exist. However, we believe this is an unlikely scenario. Creativity may well be required in identifying the options, but with time and volatility, surely, options will be available for the investor. In identifying opportunities for real-options analyses, Triantis provided the following advice: avoid viewing investments as “now or never” opportunities; avoid fixating on “most likely scenarios” and allow alterations in the investment as time unfolds and circumstances warrant; invest in stages, rather than all at once; and develop a diverse set of future alternatives. Understanding the assumptions and mathematics underlying the various methods used to calculate option values: Undergraduate students who have taken a course in engineering statistics will be familiar with the binomial and normal distributions. However, they are unlikely to have been exposed to the lognormal distribution, to stochastic processes, and to stochastic differential equations. However, it is not necessary for details of the latter subjects to be understood . What is important is for them to understand what is included in the volatility measurement: the rate of change in the underlying stock price with financial options and the rate of change in the positive-valued cash flows resulting from the future investment with real options. Specifically, in the case of the BlackScholes method of pricing options, it is assumed the period-to-period changes in the stock price (positive-valued cash flow) are normally distributed; as such, t