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

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Document pages: 32 pages

Abstract: Even in the face of deteriorating and highly volatile demand, firms ofteninvest in, rather than discard, aging technologies. In order to study thisphenomenon, we model the firm s profit stream as a Brownian motion withnegative drift. At each point in time, the firm can continue operations, or itcan stop and exit the project. In addition, there is a one-time option to makean investment which boosts the project s profit rate. Using stochasticanalysis, we show that the optimal policy always exists and that it ischaracterized by three thresholds. There are investment and exit thresholdsbefore investment, and there is a threshold for exit after investment. We alsoeffect a comparative statics analysis of the thresholds with respect to thedrift and the volatility of the Brownian motion. When the profit boost uponinvestment is sufficiently large, we find a novel result: the investmentthreshold decreases in volatility.

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