Pronghorn, a coffee$-$mug producer, generally conducts over half of its business in the last month of the calendar year due to holiday sales. By the end of December, its fiscal year$-$end, Pronghorn had accumulated Cost of Goods Sold in the amount of $$255,000.$ Pronghorn's business model is to maintain minimal WIP Inventory and FG Inventory, so these two accounts had balances of just $$20,000$ and $$26,000,$ respectively, on December $31.$ Pronghorn does hold a fair amount of RM Inventory, however, so it will be able to quickly fulfill its orders. As a result, its December $31$ RM Inventory $($all direct materials$)$ is $$90,000.$

Pronghorn utilizes a normal costing system, in its effort to have timely applied MOH information for each custom job, and its budgeted MOH rate is $$2\mathrm{.}25/$direct labor hour. Budgeted MOH at the beginning of the year was $$160,000$; actual MOH costs incurred by the end of the year were $$170,000.$ Actual direct labor hours used were $71,000.$

$($a$)$

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Was Pronghorn's MOH cost for the year under$-$ or overapplied? By how much?

MOH cost was underapplied by $ $10,250$