Continuous Evaluation of an Ongoing Project?

I'm accustomed to using Discounted Cash Flow (DCF) analysis to determine if a new project is worth pursuing (viability analysis).

However, what is the correct approach for this analysis when a project has been underway for a few years? Specifically, how do we handle the 'Base Date concept in this ongoing evaluation?

When performing the initial viability analysis, the project is only in the pipeline, and the projection is entirely estimated into the future, with the Base Date set at T_0 (today).

Now, consider a project that was approved and is a 5-year contract, but it has already completed 2 years and has 3 years remaining.

 * The New DCF Base Date: Since the project is now ongoing, how do I calculate its present value or DCF?

The initial viability analysis had a Base Date of T_0 and a 5-year projection. The current analysis should be from T_{+2} (2 years after T_0) with a remaining 3-year projection.

 What should be done with the actual (realized) cash flows from the first two years (from T_0 to T_{+2})?

   * If I use the original Base Date (T_0), the remaining 3 years of projected cash flows must be discounted back to T_0, resulting in a very low present value.

   * If I use the new Data Date (T_{+2}), the analysis effectively starts now (T_{+2} becomes the new T_0), and I only have a 3-year projection. Do I include the actual cash flows from the past 2 years (T_0 to T_{+2}) in the current DCF calculation, and if so, how do I treat them?

If this DCF approach for continuous evaluation doesn't make sense, what method is generally considered the most appropriate for the ongoing economic-financial evaluation of an active project, especially when comparing Budgeted vs. Actuals?