June 14, 2009
June 14, 2009
June 17, 2009
14.1008.1 - 14.1008.10
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. https://peer.asee.org/4987
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