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Real Options And The Use Of Discrete And Continuous Interest Rates

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2009 Annual Conference & Exposition


Austin, Texas

Publication Date

June 14, 2009

Start Date

June 14, 2009

End Date

June 17, 2009



Conference Session

Frontiers in Engineering Economy

Tagged Division

Engineering Economy

Page Count


Page Numbers

14.1008.1 - 14.1008.10



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Paper Authors


Neal Lewis University of Bridgeport

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Dr. Neal Lewis received his Ph.D. in engineering management in 2004 and B.S. in chemical engineering in 1974 from the University of Missouri – Rolla, and his MBA in 2000 from the University of New Haven. He is an associate professor in the School of Engineering at the University of Bridgeport. He has over 25 years of industrial experience, having worked at Procter & Gamble and Bayer. Prior to UB, he has taught at UMR, UNH, and Marshall University.

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Ted Eschenbach TGE Consulting

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Dr. Ted Eschenbach, P.E. received the MCE degree in 1998 from the University of Alaska Anchorage. His masters in operations research and his doctorate in industrial engineering are from Stanford University. He is the principal of TGE Consulting, an emeritus professor of engineering management at UAA, and the founding editor emeritus of the Engineering Management Journal. He is the author or co-author of engineering economy texts currently published by Oxford University Press.

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Joseph Hartman University of Florida

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Dr. Joseph C. Hartman, P.E. received his Ph.D. in 1996 and M.S. in 1994 in industrial engineering from the Georgia Institute of Technology and his B.S. in general engineering from the University of Illinois at Urbana-Champaign in 1992. He is a professor in the Department of Industrial and Systems Engineering at the University of Florida and serves as department chair.. His research interests are in economic decisions analysis and dynamic programming. He is an active member of ASEE, IIE, and INFORMS and currently serves as editor of The Engineering Economist.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Real Options and the Use of Discrete and Continuous Interest Rates Abstract

Traditional engineering economics computes the net present value with a single interest rate. This is not the case in real options analysis. In options analysis, the present value of the benefits and the costs are needed in order to calculate the option value. In the last few years, the literature has had several examples where authors use multiple interest rates and different compounding assumptions for calculating present values. For example, “first” costs are almost always discounted using a continuous risk-free interest rate while later cash flows are often discounted using discrete market interest rates.

This paper focuses on the compounding assumptions. Two approaches are used: (1) Real option articles in Harvard Business Review, Journal of Finance, and The Engineering Economist are surveyed over matching periods to determine typical practices; and (2) A realistic delay option example is analyzed. The goal is to determine whether compounding assumptions are practically important or not. We conclude with a discussion of what should be taught in undergraduate and graduate engineering economy courses.


Real options analysis differs from traditional engineering economics in that it attempts to provide a value for managerial flexibility. This value is called the option value, which is based on the mathematics used to determine the value of a financial option. The Black-Scholes equation is widely used to determine the value of financial options,2 and has been adapted for use in real options. Binomial lattices can also be used to determine the value of either a financial or a real option, and some authors strongly advocate their use. Binomial lattices use discrete time steps to substitute for the Black-Scholes equation which uses continuous compounding. It has been demonstrated 12 that as the number of time steps increases, the binomial lattice method approaches the same answer as provided by Black-Scholes.

The Black-Scholes equation determines the value of a European call option, and is defined as:

C = S0η (d1 ) - Xe-rT η (d 2 ) (1)

ln   + r+ σ 2 T ∗ + S0   X 2 where d1 =  d 2 = d1 - σ T (2) σ T

The variables are defined as follows: C value of a call option S0 value of the stock at the current time ф(dx) cumulative standard normal distribution of the variable dx X strike price r risk-free interest rate T time to option expiration

Lewis, N., & Eschenbach, T., & Hartman, J. (2009, June), Real Options And The Use Of Discrete And Continuous Interest Rates Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--4987

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