Certainty equivalent and uncertainty premium of time-to-build
研究了投资项目建设周期不确定性对投资时机和企业价值的影响，推导出确定性等价和不确定性等价，帮助企业仅用均值和方差近似最优策略。
Time-to-build of an investment project induces a difference between the timing of investment and that of revenue generation. Jeon (2024b) showed that uncertainty in the time-to-build always accelerates investment and enhances pre-investment firm value, regardless of its distribution. This study examines the extent to which the uncertainty advances the timing of investment and improves firm value. Specifically, we show that there always exists a unique certainty equivalent of an uncertain time-to-build and derive it in an analytic form. This enables us to derive the investment strategy with an uncertain time-to-build in the form of the one that would have been adopted in the absence of such uncertainty. Even without full knowledge of the uncertainty, the firm can approximate the optimal investment strategy using only the mean and variance of time-to-build. Furthermore, we show that there always exists an uncertainty equivalent of fixed time-to-build. This enables firms to evaluate the level of risk implicitly assumed by their investment strategies established without accounting for uncertainty in time-to-build. Lastly, we illustrate the practical application of our findings using some representative probability distributions and analyze the effects of the variance of time-to-build. In particular, we contrast the effects of uncertainty in demand with those of uncertainty in time-to-build, deriving the level of variance in time-to-build that offsets the negative impact of increased demand volatility on investment.