Final answer:
The FIFO (First-In, First-Out) costing method excludes prior-period work and costs in computing current-period unit costs, recognizing the costs of the oldest products first.
Step-by-step explanation:
The unit-costing method that excludes prior-period work and costs when computing current-period unit work and costs is the FIFO costing method (First-In, First-Out).
This method assumes that the oldest products are used or sold first, thus the costs associated with those products are also recognized first.
This is in contrast to methods like the weighted average method, which blends the costs of prior and current periods, averaging them together when calculating the cost of units.
The unit-costing method that excludes prior-period work and costs in computing current-period unit work and costs is called the Weighted average method.