The sponsor is asking for the Estimate at Completion (EAC), which represents the " expected total costs based on its progress. " This is a core component of Earned Value Management (EVM) as described in the PMBOK® Guide.

Forecasting with EAC: The Estimate at Completion (EAC) is the forecasted total cost of the project at its conclusion. When the sponsor asks for this " based on progress, " they are assuming that the project ' s past performance (represented by the CPI) will continue into the future.

The Formula ($EAC = BAC / CPI$ ): This is the most common formula used to determine the total expected cost if the current cost performance is expected to persist for the remainder of the project.

BAC (Budget at Completion): The original total budget.

CPI (Cost Performance Index): A measure of cost efficiency ($EV / AC$).

Alternative Assumptions: If the remaining work is expected to be performed at the budgeted rate (regardless of past performance), the formula would be $EAC = AC + (BAC - EV)$. However, the question specifically mentions " based on its progress, " which points toward using the performance index (CPI).

Analysis of Other Options:

A. Earned value (EV) / actual cost (AC): This is the formula for the Cost Performance Index (CPI). While it measures progress/efficiency, it is a ratio, not the " expected total cost. "

B. Estimate at completion (EAC) - AC: This formula results in the Estimate to Complete (ETC), which represents the expected cost of the remaining work, not the total cost.

D. EV - planned value (PV): This is the formula for Schedule Variance (SV), which measures schedule performance in currency units, not expected costs.