Final answer:
To determine the under applied manufacturing overhead at year-end, calculate the applied manufacturing overhead by multiplying the direct labor cost by 140% and compare it to the actual manufacturing overhead incurred.
Step-by-step explanation:
To determine the under applied manufacturing overhead at year-end, we need to calculate the applied manufacturing overhead and compare it to the actual manufacturing overhead incurred.
Given that the manufacturing overhead is applied at a rate of 140% of direct labor cost, we can calculate the applied manufacturing overhead by multiplying the direct labor cost incurred during the current year by 140%.
In this case, the direct labor cost incurred during the current year is $40,000. So the applied manufacturing overhead would be 140% of $40,000, which is $56,000.
The actual manufacturing overhead incurred during the year is given as $315,000.
Therefore, the under applied manufacturing overhead at year-end would be the difference between the applied manufacturing overhead and the actual manufacturing overhead, which is $56,000 - $315,000 = -$259,000.
Since the under applied amount is significant, it means that the manufacturing overhead was under allocated and there is a shortage of overhead applied to the products.