It's very likely that your first estimates of costs and benefits for a given solution or project will change as you discover additional information about the requirements and solution. It's important to keep the organizational leaders' expectations realistic, since they'll expect to see a return in solid benefits. Tools such as
Cost Benefit Analysis
give you a consistent way to capture project cost/benefit information and keep the stakeholders updated with current and historical data.
Most likely, the project manager and business analyst will work together to identify the costs of the project; but the task of analyzing the benefits generally falls to the business analyst. As the requirements change and the business needs evolve, and as the solution moves ever closer to completion, be sure to keep the cost benefit analysis documentation updated. If the anticipated costs suddenly increase due to an unexpected requirement, immediately add the costs to the cost/benefit analysis. And if the anticipated benefits change, perhaps due to a repositioning of the business need, immediately adjust the benefits.
Publish these updates as soon as they occur. Make sure to inform your project team of the changes, and ask the project manager and/or sponsor to help you communicate the updates outside the project team, for example to the project portfolio leadership, steering committee, or project governance groups.