Final answer:
The overhead is overapplied by $10,000, and the cost of goods manufactured for the year is $984,500. This conclusion is derived by calculating the difference between the applied overhead costs and the actual overhead costs as well as compiling costs to calculate the cost of goods manufactured.
Step-by-step explanation:
To calculate the underapplied or overapplied overhead cost for the year, we would first determine the total overhead cost applied to jobs, which is obtained by multiplying the predetermined overhead rate ($25 per machine-hour) by the total machine-hours used (21,300 hours). Therefore, the total applied overhead would be $25 * 21,300 = $532,500. The actual overhead costs incurred amount to $522,500. The difference between the applied overhead and the actual overhead costs gives us the amount of overapplied or underapplied overhead, which in this case is applied overhead ($532,500) - actual overhead ($522,500) = $10,000. Since the applied overhead is more than the actual overhead costs, overhead is overapplied by $10,000.
Next, let's prepare the schedule of cost of goods manufactured for the year. We start with the direct materials used, which is the beginning raw materials inventory plus purchases minus the ending raw materials inventory: $21,600 + $416,000 - $31,600 = $406,000. Then, add the direct labor cost of $76,000 and the applied manufacturing overhead of $532,500 to get the total manufacturing costs. Adding the beginning work in process and subtracting the ending work in process gives us: $406,000 (raw materials) + $76,000 (direct labor) + $532,500 (applied overhead) + $41,600 (beginning work in process) - $71,600 (ending work in process) = $984,500. This is the total cost of goods manufactured for the year.