<p>Carbon Capture, Utilization and Storage (CCUS) has provided a viable pathway toward the green transformation of coal-fired power plants (CFPPs). The investment return of CCUS projects must be accurately and effectively assessed to support the investment decision of CFPPs, which is necessary for their advancement and intensive development. However, the existing assessment methodology ignores sudden climate risk shocks, resulting in a discrepancy between the value assessment of CCUS projects and reality. This paper introduces the geometric Brownian motion containing the Poisson jump process to sketch the jumping fluctuation characteristics of carbon price by taking the high temperature risk as an example. Then, we develop a novel investment return assessment model for the CCUS projects with the real options theory. Employing the novel model, the optimal investment strategy for CCUS projects is explored, as well as the incentive effect and applicability of different financial subsidy methods for CFPPs. The findings indicate that carbon prices should undergo a Poisson jump process as a way to reduce the bias in assessing investment advantages for CCUS projects caused by climate change. CCUS investments for CFPPs can be encouraged by subsidies that target initial investment, CO₂ storage technology, and electricity tariff. Policies that prioritize subsidies for carbon storage technology and electricity tariff are found to be more beneficial than those that don't. This paper offers helpful suggestions finally.</p>