Value investment project in firms with growth

What is the best way to value investment projects undertaken by firms with significant priced-in growth, whose projected cash flows may not necessarily reflect this growth? To be more specific, say your company is, for whatever reason, using a discount rate of 5% and your investment department shows you projected FCFs with and without the investment project. You look up your company’s current market cap, and it comes up significantly higher than the one implied by a DCF on the projected FCFs without the project, using the discount rate of 5%. How do you value the investment project if this happens? Should you change the discount rate so that the current market cap is equal to the one implied by the DCF on the projected FCFs without the project first, and use this new discount rate to value the project? Or should you restate both sets of FCFs to better align with the current market cap and the 5% discount rate, perhaps by scaling them up proportionally? I suppose the answer ultimately depends on how the market would view the incremental cash flows of the project, and, in particular, whether it would associate them with a similar embedded growth as it does with the firm’s current cash flows without the project.