Real investment decision under CRRA utility: The flow payoff case

This paper explores how payoff volatility (idiosyncratic volatility), time preference and investment-wealth ratio affect an entrepreneur's real investment decision in a constant relative risk aversion (CRRA) framework, when the investment project generates a flow payoff. We find that time preference has an important effect on the optimal investment threshold, which comes from wealth effects on the implied project value and the implied option value. Particularly, we discover that the optimal investment threshold is convex in time discount rate. At most cases, a larger payoff volatility increases the optimal investment threshold and makes the entrepreneur invest later. However, if the entrepreneur has lower risk aversion and more sufficient patience, a larger payoff volatility may decrease the optimal investment threshold and makes the entrepreneur invest earlier. Moreover, a higher investment-wealth ratio makes the entrepreneur invest later.