Invest or Exit? Optimal Decisions in the Face of a Declining Profit Stream

Operations Research, Vol. 58, No. 3, pp. 638-649, May-June 2010

Posted: 4 Jan 2011  

H. Dharma Kwon

University of Illinois at Urbana-Champaign - Department of Business Administration

Date Written: April 24, 2009

Abstract

Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. To study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At each point in time, the firm can continue operations, or it can stop and exit the project. In addition, there is a one-time option to make an investment that boosts the project's profit rate. Using stochastic analysis, we show that the optimal policy always exists and that it is characterized by three thresholds. There are investment and exit thresholds before investment, and there is a threshold for exit after investment. We also effect a comparative statics analysis of the thresholds with respect to the drift and the volatility of the Brownian motion. When the profit boost upon investment is sufficiently large, we find a novel result: the investment threshold decreases in volatility.

Keywords: decision analysis, sequential, finance, investment criteria, probability, diffusion

Suggested Citation

Kwon, H. Dharma, Invest or Exit? Optimal Decisions in the Face of a Declining Profit Stream (April 24, 2009). Operations Research, Vol. 58, No. 3, pp. 638-649, May-June 2010 . Available at SSRN: https://ssrn.com/abstract=1734013

H. Dharma Kwon (Contact Author)

University of Illinois at Urbana-Champaign - Department of Business Administration ( email )

1206 South Sixth Street
Champaign, IL 61820
United States

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