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This is (Fixed Manufacturing Cost Per Unit of $5 × Number of units of change in inventory of 5,000) + Underapplied Fixed Manufacturing Overhead of $65,000. The underapplied fixed manufacturing overhead is not relevant to the calculation of the difference in operating income between absorption costing and variable costing, because it is handled the same way under both methods. The $65,000 underapplied fixed manufacturing cost is charged to expense under absorption costing because the problem says that underapplied or overapplied manufacturing overhead is closed out to cost of goods sold. It is also charged to expense under variable costing, because under variable costing, all fixed costs incurred are expensed as period costs as incurred. Since the amount of underapplied fixed manufacturing overhead under absorption costing is handled the same way under both methods, it is not relevant to a calculation of the difference in operating income between them.
This is not the correct answer. This answer results from including fixed administrative expenses along with fixed manufacturing overhead in calculating the fixed cost that would be included in ending inventory under absorption costing but not included under variable costing. Fixed administrative costs (along with fixed selling costs) are expensed in both methods, so the fixed administrative costs do not contribute to the difference between operating income under absorption costing and under variable costing.
This problem does not specify whether Valyn is using a standard cost system (in which standard, or planned, costs are used to account for production) or an actual cost system (in which actual costs are used). However, it does say that Valyn uses a predetermined manufacturing overhead rate for applying manufacturing overhead to its product. And since the actual, incurred per unit costs for direct materials, direct labor and variable manufacturing overhead are exactly the same as the planned per unit costs for those items, we do not need to know whether standard costing or actual costing is being used in order to answer this question. The difference between the two methods is the treatment of fixed factory overheads. Under the absorption method fixed manufacturing overheads are applied to the units produced at the predetermined rate, whereas under the variable method, they are expensed. The fixed factory overhead cost per unit is $5 and we can determine the difference between these two methods by multiplying this $5 per unit difference by the number of units that were added to inventory during the period. Inventory increased by 5,000 units and 5,000 × $5 gives us a $25,000 difference in income between the two methods. The difference in operating income can be calculated in this way because 1. The beginning finished goods inventory is valued at the same per unit manufacturing cost as the current year's planned per unit manufacturing cost (which implies that the fixed manufacturing cost in beginning inventory was the same as the current year's predetermined application rate per unit for fixed manufacturing overhead); 2. Over- or under-applied manufacturing overhead is closed to the cost of goods sold account at the end of the period; and 3. There is no beginning work-in-process inventory.
This is the amount of underapplied fixed manufacturing overhead. It is not the difference in operating income between the absorption costing and the variable costing methods.