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Reconciling Variable & Absorption Costing - Managerial Accounting

  1. What was the company's operating income under variable costing for the month?
    Answer: $135,000 To reconcile the incomes, we must determine the amount of fixed manufacturing overhead (FMOH) released from inventory. 1. Calculate the change in inventory in units: Change=Ending Inventory−Beginning Inventory=1,500−3,000=−1,500 units \text{Change} = \text{Ending Inventory} - \text{Beginning Inventory} = 1,500 - 3,000 = -1,500 \text{ units} . The inventory level decreased. 2. Calculate the FMOH released from inventory: Released FMOH=Decrease in Inventory×FMOH Rate=1,500 units×$10/unit=$15,000 \text{Released FMOH} = \text{Decrease in Inventory} \times \text{FMOH Rate} = 1,500 \text{ units} \times \text{\$10/unit} = \text{\$15,000} . 3. Reconcile the operating incomes: When inventory decreases, absorption costing expenses the current period's FMOH plus the FMOH from beginning inventory. This results in a lower income compared to variable costing. Therefore, variable costing income is higher. Variable OI=Absorption OI+Released FMOH=$120,000+$15,000=$135,000 \text{Variable OI} = \text{Absorption OI} + \text{Released FMOH} = \text{\$120,000} + \text{\$15,000} = \text{\$135,000} .
  2. Based on this information, what is the difference between the company's absorption costing and variable costing operating income for the year?
    Answer: Absorption income is $100,000 higher. This question requires separating the fixed and variable components of the inventory value change. 1. Determine the total absorption cost per unit: Absorption Cost/Unit = Variable Mfg. Cost + Fixed MOH Rate = $10 + $5 = $15. 2. Calculate the change in inventory in units: Change in Units = Increase in Inventory Value / Absorption Cost/Unit = $300,000 / $15/unit = 20,000 units. 3. Calculate the income difference: The difference in operating income is the change in inventory units multiplied by only the fixed manufacturing overhead rate. Difference = Change in Units × FMOH Rate = 20,000 units × $5/unit = $100,000. As inventory increased, absorption income is higher by $100,000.
  3. Which of the following scenarios will result in variable costing operating income being greater than absorption costing operating income for a given period?
    Answer: A company sells more units than it produces by drawing down inventory from a previous period. Variable costing operating income is greater than absorption costing operating income when the number of units sold exceeds the number of units produced. In this situation, inventory levels decrease. Under absorption costing, the cost of goods sold includes not only all of the fixed manufacturing overhead (FMOH) from the current period's production (which is now attached to fewer units) but also the FMOH that was capitalized in the beginning inventory that was sold. This release of previously deferred FMOH results in higher expenses and lower operating income for absorption costing compared to variable costing.
  4. By how much will absorption costing income differ from variable costing income in Year 2?
    Answer: Variable costing income will be $60,000 higher. The difference in income in Year 2 is determined by the fixed manufacturing overhead (FMOH) released from beginning inventory. 1. Determine the source of units sold in Year 2: The company sold 33,000 units but only produced 30,000. The 3,000 unit shortfall must have come from beginning inventory. 2. Determine the cost of beginning inventory: The beginning inventory for Year 2 is the ending inventory from Year 1. These units were produced in Year 1 when the FMOH rate was $20 per unit. 3. Calculate FMOH released: The total FMOH released from inventory is 3,000 units×$20/unit=$60,0003,000 \text{ units} \times \text{\$20/unit} = \text{\$60,000}. 4. Determine the income relationship: Since inventory decreased, more fixed costs (current period's plus the amount from inventory) are expensed under absorption costing than under variable costing. Therefore, variable costing income will be higher by the amount of FMOH released, which is $60,000.
  5. What was the company's fixed manufacturing overhead rate per unit?
    Answer: $7.00 per unit We can work backwards from the difference in operating incomes to find the fixed manufacturing overhead (FMOH) rate. 1. Calculate the difference in operating income: Difference=Absorption OI−Variable OI=$280,000−$315,000=−$35,000 \text{Difference} = \text{Absorption OI} - \text{Variable OI} = \text{\$280,000} - \text{\$315,000} = -\text{\$35,000} . The negative sign indicates that variable costing income was higher, which is consistent with sales exceeding production. 2. Calculate the change in inventory in units: Change=Units Produced−Units Sold=50,000−55,000=−5,000 units \text{Change} = \text{Units Produced} - \text{Units Sold} = 50,000 - 55,000 = -5,000 \text{ units} . Inventory decreased by 5,000 units. 3. Calculate the FMOH rate: The difference in income is the result of the FMOH released from inventory. FMOH Rate=Difference in OIChange in Inventory=−$35,000−5,000 units=$7.00 per unit \text{FMOH Rate} = \frac{\text{Difference in OI}}{\text{Change in Inventory}} = \frac{-\text{\$35,000}}{-5,000 \text{ units}} = \text{\$7.00} \text{ per unit} .
  6. What is the expected difference between the company's annual operating income calculated under absorption costing versus variable costing?
    Answer: $0 The difference between absorption costing and variable costing operating income is solely due to the change in the amount of fixed manufacturing overhead capitalized in inventory. If a company maintains zero ending inventory, and presumably starts with zero beginning inventory, then the number of units produced must equal the number of units sold. When production equals sales, there is no change in inventory levels. Consequently, no fixed manufacturing overhead is deferred in or released from inventory, and the operating incomes under both methods will be identical. The amounts of the fixed costs are irrelevant to the difference.
  7. Based on the information provided, what was the company's operating income under absorption costing?
    Answer: $218,000 The reconciliation of variable costing and absorption costing income is based on the treatment of fixed manufacturing overhead (FMOH). The difference is the amount of FMOH deferred in, or released from, inventory. 1. Calculate the predetermined FMOH rate per unit: Rate=Total FMOHUnits Produced=$90,00015,000 units=$6 per unit \text{Rate} = \frac{\text{Total FMOH}}{\text{Units Produced}} = \frac{\text{\$90,000}}{15,000 \text{ units}} = \text{\$6} \text{ per unit} . 2. Calculate the change in inventory in units: Change=Units Produced−Units Sold=15,000−12,000=3,000 units \text{Change} = \text{Units Produced} - \text{Units Sold} = 15,000 - 12,000 = 3,000 \text{ units} . Since production exceeds sales, inventory increased. 3. Calculate the amount of FMOH deferred in ending inventory: Deferred FMOH=Change in Inventory×FMOH Rate=3,000 units×$6/unit=$18,000 \text{Deferred FMOH} = \text{Change in Inventory} \times \text{FMOH Rate} = 3,000 \text{ units} \times \text{\$6/unit} = \text{\$18,000} . 4. Reconcile the operating incomes: When inventory increases, absorption costing income is higher than variable costing income. Absorption OI=Variable OI+Deferred FMOH=$200,000+$18,000=$218,000 \text{Absorption OI} = \text{Variable OI} + \text{Deferred FMOH} = \text{\$200,000} + \text{\$18,000} = \text{\$218,000} .
  8. What is the company's operating income under absorption costing?
    Answer: $174,000 The reconciliation requires calculating the fixed manufacturing overhead (FMOH) deferred in inventory. 1. Calculate the change in inventory in units: Change=Units Produced−Units Sold=20,000−18,000=2,000 units \text{Change} = \text{Units Produced} - \text{Units Sold} = 20,000 - 18,000 = 2,000 \text{ units} . Inventory increased by 2,000 units. 2. Calculate the amount of FMOH deferred in inventory: Deferred FMOH=Increase in Inventory×FMOH Rate=2,000 units×$12/unit=$24,000 \text{Deferred FMOH} = \text{Increase in Inventory} \times \text{FMOH Rate} = 2,000 \text{ units} \times \text{\$12/unit} = \text{\$24,000} . 3. Reconcile the operating incomes: When inventory increases, absorption costing income is higher than variable costing income because a portion of fixed overhead is deferred to the balance sheet. Absorption OI=Variable OI+Deferred FMOH=$150,000+$24,000=$174,000 \text{Absorption OI} = \text{Variable OI} + \text{Deferred FMOH} = \text{\$150,000} + \text{\$24,000} = \text{\$174,000} .
  9. What is the expected relationship between the cumulative operating income reported under absorption costing and variable costing?
    Answer: The cumulative operating incomes will be equal. The difference between absorption and variable costing is one of timing. Absorption costing defers the recognition of fixed manufacturing overhead (FMOH) costs by capitalizing them into inventory, while variable costing expenses them as incurred. Over the entire life of a company, all units produced are ultimately sold. Therefore, all FMOH that was ever capitalized into inventory under absorption costing is eventually charged to Cost of Goods Sold. In the long run, the total amount of FMOH expensed is identical under both methods, leading to equal cumulative operating incomes.
  10. Polaris Corp uses both variable and absorption costing for different purposes. The company's financial data shows: Fixed manufacturing overhead incurred $720,000, fixed overhead in beginning inventory $96,000, fixed overhead in ending inventory $144,000, and variable costing operating loss $(75,000). The company's tax advisor needs the absorption costing operating income to calculate tax obligations. What amount should be reported?
    Answer: $(27,000) loss The difference between absorption and variable costing equals the change in fixed overhead in inventory. Change in fixed overhead = $144,000 (ending) - $96,000 (beginning) = $48,000 increase. When fixed overhead in inventory increases, absorption costing shows higher operating income (or lower loss) than variable costing. Absorption costing result = $(75,000) + $48,000 = $(27,000) loss. The $48,000 represents fixed overhead costs that are deferred under absorption costing but expensed immediately under variable costing. Choice B incorrectly subtracts the difference, making the loss larger. Choices C and D incorrectly show positive income when the base variable costing amount was already a significant loss.
  11. Assuming the company had no beginning inventory, how many units were sold during the year?
    Answer: 15,000 units The difference in operating income between the two methods can be used to determine the change in inventory units, which then allows for the calculation of units sold. 1. Calculate the difference in operating income: Difference=Absorption OI−Variable OI=$75,000−$63,000=$12,000 \text{Difference} = \text{Absorption OI} - \text{Variable OI} = \text{\$75,000} - \text{\$63,000} = \text{\$12,000} . Since absorption costing income is higher, production must have exceeded sales. 2. Calculate the predetermined FMOH rate per unit: Rate=Total FMOHUnits Produced=$48,00020,000 units=$2.40 per unit \text{Rate} = \frac{\text{Total FMOH}}{\text{Units Produced}} = \frac{\text{\$48,000}}{20,000 \text{ units}} = \text{\$2.40} \text{ per unit} . 3. Calculate the change in inventory in units: Change in Inventory=Difference in OIFMOH Rate=$12,000$2.40/unit=5,000 units \text{Change in Inventory} = \frac{\text{Difference in OI}}{\text{FMOH Rate}} = \frac{\text{\$12,000}}{\text{\$2.40/unit}} = 5,000 \text{ units} . This represents the increase in inventory. 4. Calculate units sold: Units Sold=Units Produced−Increase in Inventory=20,000−5,000=15,000 units \text{Units Sold} = \text{Units Produced} - \text{Increase in Inventory} = 20,000 - 5,000 = 15,000 \text{ units} .
  12. What was the company's operating income under absorption costing?
    Answer: $220,000 This question requires calculating the fixed manufacturing overhead (FMOH) rate before reconciling the income figures. 1. Calculate units produced: Units Produced = Units Sold + Ending Inventory - Beginning Inventory = 22,000 + 8,000 - 5,000 = 25,000 units. 2. Calculate the FMOH rate per unit: Rate = Total FMOH / Units Produced = $250,000 / 25,000 units = $10 per unit. 3. Calculate the change in inventory in units: Change = Ending Inventory - Beginning Inventory = 8,000 - 5,000 = 3,000 units (increase). 4. Calculate deferred FMOH: Deferred FMOH = 3,000 units × $10/unit = $30,000. 5. Reconcile incomes: As inventory increased, absorption income is higher. Absorption OI = Variable OI + Deferred FMOH = $190,000 + $30,000 = $220,000.
  13. By how much does the variable costing operating income differ from the absorption costing operating income?
    Answer: Variable costing income is $28,000 higher. The difference between the two costing methods is entirely due to the treatment of fixed manufacturing overhead (FMOH) and the change in inventory levels. Fixed selling and administrative expenses are treated as period costs under both methods and do not contribute to the difference. 1. Identify the change in inventory: Inventory decreased by 4,000 units. 2. Calculate the FMOH released from inventory: Released FMOH=Decrease in Inventory×FMOH Rate=4,000 units×$7/unit=$28,000 \text{Released FMOH} = \text{Decrease in Inventory} \times \text{FMOH Rate} = 4,000 \text{ units} \times \text{\$7/unit} = \text{\$28,000} . 3. Determine the income relationship: When inventory decreases, absorption costing recognizes all of the current period's FMOH plus the FMOH carried in the inventory that was sold. This leads to higher expenses and lower income compared to variable costing. Thus, variable costing income is higher by $28,000.
  14. What is the total value of ending inventory under absorption costing?
    Answer: $75,000 The value of ending inventory under absorption costing includes all manufacturing costs: direct materials, direct labor, variable overhead, and fixed overhead. 1. Calculate ending inventory in units: Ending Inventory=Beginning Inventory+Production−Sales=0+25,000−20,000=5,000 units \text{Ending Inventory} = \text{Beginning Inventory} + \text{Production} - \text{Sales} = 0 + 25,000 - 20,000 = 5,000 \text{ units} . 2. Calculate the fixed manufacturing overhead rate per unit: Rate=Total FMOHUnits Produced=$125,00025,000 units=$5 per unit \text{Rate} = \frac{\text{Total FMOH}}{\text{Units Produced}} = \frac{\text{\$125,000}}{25,000 \text{ units}} = \text{\$5} \text{ per unit} . 3. Calculate the full absorption cost per unit: Unit Cost=Variable Mfg. Cost+Fixed MOH Rate=$10+$5=$15 per unit \text{Unit Cost} = \text{Variable Mfg. Cost} + \text{Fixed MOH Rate} = \text{\$10} + \text{\$5} = \text{\$15} \text{ per unit} . 4. Calculate the value of ending inventory: Value=Ending Inventory Units×Unit Cost=5,000 units×$15/unit=$75,000 \text{Value} = \text{Ending Inventory Units} \times \text{Unit Cost} = 5,000 \text{ units} \times \text{\$15/unit} = \text{\$75,000} .
  15. Which of the following best describes the immediate impact of the manager's decision?
    Answer: Absorption costing income will increase, while variable costing income will remain unaffected. The core difference between the methods is the treatment of fixed manufacturing overhead (FMOH). Under absorption costing, FMOH is a product cost. By increasing production without a corresponding increase in sales, more of the period's FMOH is attached to the unsold units and deferred in ending inventory, rather than being expensed in the current period. This lowers the Cost of Goods Sold and increases absorption costing income. Under variable costing, all FMOH is treated as a period cost and is expensed in the quarter it is incurred, regardless of the production level. Therefore, increasing production has no effect on variable costing income.
  16. Stellar Manufacturing produces specialty widgets. For the year ended December 31, the company produced 50,000 units and sold 45,000 units. Variable manufacturing costs were $15 per unit, and fixed manufacturing overhead was $400,000. There were no beginning inventories. Under absorption costing, operating income was $180,000. What was the operating income under variable costing?
    Answer: $140,000 The difference between absorption and variable costing operating income equals the fixed overhead in ending inventory. Ending inventory = 50,000 - 45,000 = 5,000 units. Fixed overhead per unit = $400,000 ÷ 50,000 = $8. Fixed overhead in ending inventory = 5,000 × $8 = $40,000. Since absorption costing includes this fixed overhead in inventory (higher operating income), variable costing operating income = $180,000 - $40,000 = $140,000. Choice B incorrectly uses half the difference. Choice C adds instead of subtracts. Choice D incorrectly calculates the per-unit fixed overhead.
  17. What is the relationship between absorption costing operating income (AC OI) and variable costing operating income (VC OI) for Year 2?
    Answer: AC OI is $10,000 less than VC OI. The difference between absorption and variable costing income is determined by the change in inventory levels during the period. 1. Analyze Year 2 inventory change: In Year 2, the company sold 12,000 units but only produced 10,000 units. This means inventory decreased by 2,000 units (10,000−12,000=−2,00010,000 - 12,000 = -2,000). 2. Calculate the FMOH released from inventory: When inventory decreases, fixed manufacturing overhead costs from a prior period (which were stored in beginning inventory) are released and expensed through COGS under absorption costing. The amount released is 2,000 units×$5/unit=$10,0002,000 \text{ units} \times \text{\$5/unit} = \text{\$10,000}. 3. Determine the income relationship: Because an additional $10,000 of fixed overhead from a prior period is expensed under absorption costing in Year 2, its operating income will be $10,000 less than variable costing operating income. Under variable costing, all fixed overhead from Year 2 was already expensed in Year 2, and the costs from Year 1 were expensed in Year 1.
  18. Based on the information provided, what is the difference between operating income under absorption costing and variable costing, and what causes this difference?
    Answer: Absorption costing income is $50,000 higher due to fixed overhead in ending inventory of 3,000 units Fixed overhead per unit = $600,000 ÷ 36,000 units = $16.67 per unit. Ending inventory = 36,000 produced - 33,000 sold = 3,000 units. Under absorption costing, ending inventory includes fixed overhead of 3,000 units × $16.67 = $50,000 (rounded) that is deferred to future periods. Under variable costing, all $600,000 of fixed overhead is expensed in the current period. Therefore, absorption costing shows $50,000 higher operating income due to this deferral. Choice B uses an incorrect amount. Choices C and D incorrectly state that variable costing income is higher, when inventory increases always make absorption costing income higher.
  19. Which additional piece of information is required to determine the exact change in inventory units for the period?
    Answer: The number of units produced. The formula to reconcile the two income figures is: Difference in OI=(Units Produced−Units Sold)×FMOH rate per unit \text{Difference in OI} = (\text{Units Produced} - \text{Units Sold}) \times \text{FMOH rate per unit} . We know the difference in OI ($40,000) and the total FMOH ($320,000), but we need to find the change in inventory units (Units Produced−Units Sold\text{Units Produced} - \text{Units Sold}). To do this, we must first find the FMOH rate per unit. The rate is calculated as Total FMOHDenominator Level Units \frac{\text{Total FMOH}}{\text{Denominator Level Units}} . In this case, the denominator level is the number of units produced. Therefore, knowing the number of units produced is essential to calculate the rate, which can then be used to find the change in inventory units.
  20. What was the beginning inventory in units?
    Answer: 4,000 units This problem requires working backward from the income difference to find the change in inventory, and then using that to find the beginning inventory. 1. Calculate the difference in operating income: Difference=Absorption OI−Variable OI=$400,000−$370,000=$30,000 \text{Difference} = \text{Absorption OI} - \text{Variable OI} = \text{\$400,000} - \text{\$370,000} = \text{\$30,000} . 2. Calculate the change in inventory in units: Since absorption income is higher, inventory increased. Change in Inventory=Difference in OIFMOH Rate=$30,000$5/unit=6,000 units \text{Change in Inventory} = \frac{\text{Difference in OI}}{\text{FMOH Rate}} = \frac{\text{\$30,000}}{\text{\$5/unit}} = 6,000 \text{ units} . This is the net increase in inventory. 3. Calculate beginning inventory: We know that Ending Inventory=Beginning Inventory+Change in Inventory \text{Ending Inventory} = \text{Beginning Inventory} + \text{Change in Inventory} . Rearranging the formula gives Beginning Inventory=Ending Inventory−Change in Inventory=10,000 units−6,000 units=4,000 units \text{Beginning Inventory} = \text{Ending Inventory} - \text{Change in Inventory} = 10,000 \text{ units} - 6,000 \text{ units} = 4,000 \text{ units} .

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