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

## TL;DR

This paper models a firm's decision-making process regarding investment and exit in declining profit scenarios using stochastic analysis, revealing threshold-based policies and the impact of volatility on investment strategies.

## Contribution

It introduces a threshold-based optimal policy framework for investment and exit decisions under stochastic profit streams with a profit-boost option.

## Key findings

- Optimal policy characterized by three thresholds.
- Investment threshold decreases with volatility when profit boost is large.
- Thresholds depend on drift and volatility of profit stream.

## Abstract

Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order 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 which 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.