In accordance with the PMBOK® Guide (Project Cost Management), specifically within the Control Costs process, Earned Value Management (EVM) is used to forecast the final project cost using the Estimate at Completion (EAC).

There are several formulas for calculating EAC depending on the assumptions made about future performance. Given the options provided, the formula used assumes that the remaining work will be performed at the budgeted rate (i.e., the original plan is still valid for the remaining work).

The formula is:

$$EAC = AC + (BAC - EV)$$

Where:

BAC (Budget at Completion) = $\$100$

AC (Actual Cost) = $\$50$

EV (Earned Value) = $\$25$

Calculation Steps:

Determine the value of the remaining work (Estimate to Complete at the budgeted rate):

$$BAC - EV = \$100 - \$25 = \$75$$

Add the Actual Cost already incurred to the remaining work value:

$$EAC = \$50 + \$75 = \$125$$

Analysis of Distractors:

A. $50: This is only the Actual Cost (AC) and does not account for the work remaining.

B. $100: This is the original Budget at Completion (BAC). Since the project is currently over budget ($CV = EV - AC = -\$25$), the final cost will be higher than the original budget.

D. $175: This value does not correlate with standard EVM forecasting formulas given the provided data. (Note: If the current cost performance was expected to continue, the calculation would be $BAC / CPI = 100 / 0.5 = 200$, which is also not an option).

Therefore, based on the provided options and standard PMP calculation logic for when future work returns to the planned rate, $125 is the correct answer.