Managerial Accounting Quiz: Setting Up Multi Step Problems
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Setting Up Multi Step ProblemsQuestion 1 of 20

A company uses a standard costing system. The following data are available for labor costs in the most recent period:

  • Actual hours worked: 4,200 hours
  • Actual labor rate: $21 per hour
  • Standard hours allowed for actual output: 4,000 hours
  • Standard labor rate: $20 per hour

Which of the following expressions correctly isolates the components needed to calculate the direct labor rate variance?

Standard Rate × (Actual Hours − Standard Hours)
(Actual Hours × Actual Rate) − (Standard Hours × Standard Rate)
Actual Hours × (Actual Rate − Standard Rate)
Standard Hours × (Actual Rate − Standard Rate)
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Managerial Accounting Quiz

Managerial Accounting Quiz: Setting Up Multi Step Problems

Practice Setting Up Multi Step Problems in Managerial Accounting with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Setting Up Multi Step Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for Managerial Accounting.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

A company uses a standard costing system. The following data are available for labor costs in the most recent period:

  • Actual hours worked: 4,200 hours
  • Actual labor rate: $21 per hour
  • Standard hours allowed for actual output: 4,000 hours
  • Standard labor rate: $20 per hour

Which of the following expressions correctly isolates the components needed to calculate the direct labor rate variance?

  1. Standard Rate × (Actual Hours − Standard Hours)
  2. (Actual Hours × Actual Rate) − (Standard Hours × Standard Rate)
  3. Actual Hours × (Actual Rate − Standard Rate) (correct answer)
  4. Standard Hours × (Actual Rate − Standard Rate)
Explanation: The direct labor rate variance measures the difference between the actual price paid for labor and the standard price, multiplied by the actual quantity of labor hours used. The formula is: Labor Rate Variance = (Actual Rate - Standard Rate) × Actual Hours. This isolates the impact of paying a different rate than expected for the hours actually worked.

Question 2

A company manufactures a component with the following costs per unit: Direct Materials $12, Direct Labor $8, Variable Overhead $5, and Fixed Overhead $10. An outside supplier has offered to sell the component to the company for $28 per unit. If the component is purchased, $4 of the fixed overhead per unit would be avoided. Furthermore, the freed-up manufacturing capacity could be used to produce a new product line that would generate a total contribution margin of $30,000. The company requires 10,000 units of the component annually.

Which equation correctly sets up the calculation for the net financial advantage (disadvantage) of buying the component instead of making it?

  1. Advantage(Buy) = [10,000 × ($12 + $8 + $5 + $10)] - (10,000 × $28) + $30,000
  2. Advantage(Buy) = [10,000 × ($12 + $8 + $5 + $4)] - (10,000 × $28)
  3. Advantage(Buy) = [10,000 × ($12 + $8 + $5 + $4)] - (10,000 × $28) + $30,000 (correct answer)
  4. Advantage(Buy) = [10,000 × ($12 + $8 + $5 + $4)] - (10,000 × $28) - $30,000
Explanation: The correct setup compares the relevant costs of making versus buying and includes the opportunity cost. The relevant cost to make is the sum of all avoidable costs: Direct Materials (12),DirectLabor(12), Direct Labor (8), Variable Overhead (5),andavoidableFixedOverhead(5), and avoidable Fixed Overhead (4), for a total of $29 per unit. The cost to buy is $28 per unit. The opportunity cost of making (i.e., the benefit foregone) is the $30,000 contribution margin from the new product line, which is a benefit of buying. The total advantage of buying is the cost savings on the component plus the opportunity cost gained: [Relevant Cost to Make] - [Cost to Buy] + [Opportunity Cost] = [10,000 × $29] - [10,000 × $28] + $30,000.

Question 3

A company makes all sales on credit. The company's collection history indicates the following pattern:

  • 60% collected in the month of sale
  • 30% collected in the month following the sale
  • 8% collected in the second month following the sale
  • 2% uncollectible

Budgeted sales are: January $100,000; February $120,000; March $150,000.

Which of the following setups correctly calculates the total budgeted cash collections for March?

  1. (0.60 × $150,000) + (0.30 × $120,000) + (0.08 × $100,000) (correct answer)
  2. (0.60 × $150,000) + (0.30 × $150,000) + (0.08 × $150,000)
  3. (0.60 × $100,000) + (0.30 × $120,000) + (0.08 × $150,000)
  4. 0.98 × ($150,000 + $120,000 + $100,000)
Explanation: Total cash collections in March are the sum of collections from March sales, February sales, and January sales. According to the collection pattern, March collections will be: 60% of March sales (0.60 × $150,000), plus 30% of the prior month's (February) sales (0.30 × $120,000), plus 8% of sales from two months prior (January) (0.08 × $100,000). The uncollectible portion is irrelevant to the cash collected.

Question 4

A company manufactures a product that requires 2 pounds of raw material X per finished unit. The company is preparing its raw materials purchases budget for the upcoming quarter. Budgeted production is 40,000 units. The company's policy is to maintain an ending inventory of raw material X equal to 15,000 pounds. The beginning inventory of X is 10,000 pounds. The cost of raw material X is $5 per pound.

Which of the following setups correctly calculates the total budgeted cost of raw material purchases for the quarter?

  1. [(40,000 × 2) + 10,000 − 15,000] × $5
  2. [(40,000 × 2) + 15,000 − 10,000] × $5 (correct answer)
  3. (40,000 × 2) × $5
  4. (40,000 + 15,000 - 10,000) × 2 × $5
Explanation: The calculation starts with the raw materials needed for production (40,000 units × 2 lbs/unit = 80,000 lbs). To this, we add the desired ending inventory (15,000 lbs) to determine total needs. From the total needs, we subtract the beginning inventory (10,000 lbs) that is already on hand to find the quantity that must be purchased. Finally, this quantity is multiplied by the cost per pound ($5). The correct setup is: [(Production Needs) + Desired Ending Inv. - Beginning Inv.] × Cost per pound.

Question 5

A company is analyzing its materials variances. The standard for one unit of output is 5 pounds of material at a standard price of $4.00 per pound. During the period, the company purchased 55,000 pounds of material at an actual price of $4.20 per pound. The company used 51,000 pounds of this material to produce 10,000 units of output.

Which of the following sets of calculations correctly establishes the inputs for determining the direct materials quantity variance?

  1. Compare actual quantity used (51,000 lbs) with standard quantity allowed (10,000 units × 5 lbs/unit), and multiply the difference by the standard price ($4.00). (correct answer)
  2. Compare actual quantity purchased (55,000 lbs) with actual quantity used (51,000 lbs), and multiply the difference by the standard price ($4.00).
  3. Compare actual quantity used (51,000 lbs) with standard quantity allowed (10,000 units × 5 lbs/unit), and multiply the difference by the actual price ($4.20).
  4. Compare actual quantity purchased (55,000 lbs) with standard quantity allowed (10,000 units × 5 lbs/unit), and multiply the difference by the standard price ($4.00).
Explanation: The direct materials quantity (or usage) variance measures the efficiency of material usage. It compares the actual quantity of materials used in production with the standard quantity that should have been used for the actual output. The formula is (Actual Quantity Used - Standard Quantity Allowed) × Standard Price. Here, Actual Quantity Used is 51,000 lbs. Standard Quantity Allowed is the actual output (10,000 units) times the standard material per unit (5 lbs), or 50,000 lbs. The price used is the standard price ($4.00) to isolate the effect of quantity differences.

Question 6

A company is preparing its production budget for the third quarter. Budgeted sales are: July 50,000 units; August 60,000 units; September 75,000 units; and October 70,000 units. The company's policy is to maintain ending finished goods inventory equal to 20% of the following month's budgeted sales. The finished goods inventory on June 30 was 10,000 units.

Which of the following correctly sets up the calculation for the total required production for the third quarter (the sum of July, August, and September)?

  1. (50,000 + 60,000 + 75,000) + (0.20 × 75,000) - 10,000
  2. (50,000 + 60,000 + 75,000) + 10,000 - (0.20 × 70,000)
  3. (50,000 + 60,000 + 75,000) + (0.20 × 70,000) - (0.20 × 50,000)
  4. (50,000 + 60,000 + 75,000) + (0.20 × 70,000) - 10,000 (correct answer)
Explanation: The production budget formula for a period is: Budgeted Sales + Desired Ending Inventory - Beginning Inventory. For the entire third quarter, this is: Total Budgeted Sales (Q3) + Desired Ending Inventory (Sept 30) - Beginning Inventory (July 1). Total sales are 50,000 + 60,000 + 75,000 = 185,000. Desired ending inventory for the quarter (at Sept 30) is 20% of the next month's (October's) sales, which is 0.20 × 70,000. The beginning inventory for the quarter (at July 1, which is the same as June 30) is given as 10,000 units. Thus, the correct setup is (185,000) + (0.20 × 70,000) - 10,000.

Question 7

A company uses Activity-Based Costing (ABC) and has identified a 'Machine Setups' activity cost pool with total estimated overhead of $300,000. The company produces two products, Lux and Stan. Expected activity for the period is 500 setups for Lux and 300 setups for Stan.

Which of the following expressions represents the first two steps to determine the amount of machine setup cost to be allocated to the Lux product line?

  1. Calculate a rate by dividing $300,000 by 500 setups, then multiply the result by the total units of Lux produced.
  2. Calculate a rate by dividing $300,000 by 800 total setups, then multiply the result by 500 setups. (correct answer)
  3. Multiply $300,000 by the ratio of direct labor hours for Lux to total direct labor hours for the company.
  4. Multiply $300,000 by the ratio of 500 setups for Lux to 300 setups for Stan.
Explanation: In ABC, the first step is to calculate the activity rate for the cost pool. This is done by dividing the total cost in the pool by the total activity level for that cost driver. Here, the total activity is 500 setups (Lux) + 300 setups (Stan) = 800 setups. The rate is $300,000 / 800 setups. The second step is to allocate the cost to a specific product by multiplying this rate by the amount of the cost driver consumed by that product. For Lux, this would be the calculated rate multiplied by 500 setups.

Question 8

A company produces a single product that it sells for $50 per unit. Variable costs are $30 per unit, and annual fixed costs are $200,000. The company has a maximum capacity of 20,000 units and is currently operating at 90% capacity, selling 18,000 units. A new customer offers to buy 4,000 units in a one-time special order for $35 per unit. Fulfilling this order would require the company to forgo sales of 2,000 units to its regular customers.

Which equation correctly sets up the calculation for the incremental income (or loss) from accepting the special order?

  1. (4,000 × $35) − (4,000 × $30)
  2. (4,000 × $35) − (4,000 × 30)−[2,000×(30) − [2,000 × (50 − $30)] (correct answer)
  3. (4,000 × 35)−(4,000×(35) − (4,000 × (30 + ($200,000 / 20,000)))
  4. (4,000 × $35) − (4,000 × 30)−[4,000×(30) − [4,000 × (50 − $30)]
Explanation: The incremental income analysis should include incremental revenues, incremental costs, and any opportunity costs. The incremental revenue is 4,000 units × $35. The incremental cost is the variable cost of 4,000 units × 30(fixedcostsareirrelevantastheydonotchange).Becausethecompanyonlyhassparecapacityfor2,000units(20,000max−18,000current),acceptinga4,000−unitorderrequiresgivingup2,000unitsofregularsales.Theopportunitycostisthelostcontributionmarginfromtheseregularsales:2,000units×(30 (fixed costs are irrelevant as they do not change). Because the company only has spare capacity for 2,000 units (20,000 max - 18,000 current), accepting a 4,000-unit order requires giving up 2,000 units of regular sales. The opportunity cost is the lost contribution margin from these regular sales: 2,000 units × (50 price - $30 variable cost). This opportunity cost must be subtracted.

Question 9

A company's budget planned for sales of 10,000 units at a standard price of $12 per unit. Actual results for the period were sales of 11,000 units at an actual average price of $11 per unit.

Which of the following expressions correctly sets up the calculation for the sales price variance?

  1. (11,000 − 10,000) × $12
  2. (11,000 × $11) − (10,000 × $12)
  3. ($11 − $12) × 10,000
  4. ($11 − $12) × 11,000 (correct answer)
Explanation: The sales price variance is designed to isolate the effect of a change in the selling price from the effect of a change in sales volume. The formula is (Actual Selling Price - Standard Selling Price) × Actual Quantity of Units Sold. Using the actual quantity sold (11,000 units) ensures that the variance reflects the total impact of the price difference across all units actually sold.

Question 10

A company wants to earn an after-tax net income of $70,000. The company's product sells for $50 per unit, with variable costs of $30 per unit. Total fixed costs are $200,000. The company's income tax rate is 30%.

Let Q be the number of units to be sold. Which equation correctly solves for the number of units required to achieve the target after-tax profit?

  1. Q = ($200,000 + 70,000)/(70,000) / (50 − $30)
  2. Q = [($200,000 + 70,000)×(1−0.30)]/(70,000) × (1 − 0.30)] / (50 − $30)
  3. Q = (200,000+[200,000 + [70,000 / (1 − 0.30)]) / ($50 − $30) (correct answer)
  4. Q = ($200,000 + 70,000)/[(70,000) / [(50 − $30) × (1 − 0.30)]
Explanation: The standard CVP formula (Fixed Costs + Target Profit) / CM per unit uses a before-tax profit figure. To use an after-tax profit target, it must first be converted to its before-tax equivalent. The formula for this is: Before-Tax Profit = After-Tax Profit / (1 - Tax Rate). In this case, the target before-tax profit is 70,000/(1−0.30).Thisvalueisthenaddedtofixedcosts,andthesumisdividedbythecontributionmarginperunit(70,000 / (1 - 0.30). This value is then added to fixed costs, and the sum is divided by the contribution margin per unit (50 - $30).

Question 11

A company's static budget, based on 10,000 units of activity, includes variable costs of $40,000 and fixed costs of $50,000. During the period, the company actually produced and sold 11,000 units and incurred total actual costs of $96,000. The company's cost formula for budgeting purposes is $4 per unit plus $50,000 of fixed costs.

Which expression correctly sets up the calculation for the flexible budget variance for total costs?

  1. 96,000−(96,000 − (40,000 + $50,000)
  2. [$96,000 / 11,000] - $4
  3. 96,000−[(96,000 − [(4 × 11,000) + $50,000] (correct answer)
  4. (4×11,000)−(4 × 11,000) - (4 × 10,000)
Explanation: The flexible budget variance compares actual costs to the flexible budget amount for the actual level of activity. First, a flexible budget is created for the actual activity level of 11,000 units. Using the cost formula, this is: (11,000 units × $4/unit) + $50,000 fixed costs = 94,000.Theflexiblebudgetvarianceisthedifferencebetweentheactualcostincurred(94,000. The flexible budget variance is the difference between the actual cost incurred (96,000) and this flexible budget amount ($94,000). The expression is therefore 96,000−[(96,000 - [(4 × 11,000) + $50,000].

Question 12

A company sells two products, Alpha and Beta, in a constant sales mix of 3 units of Alpha for every 2 units of Beta. Alpha has a contribution margin of $10 per unit, and Beta has a contribution margin of $15 per unit. Total fixed costs for the company are $120,000. Which of the following equations correctly sets up the calculation for the total number of units (U) of both products needed to break even?

  1. U = $120,000 / [ (0.60 × $10) + (0.40 × $15) ] (correct answer)
  2. U = 120,000/[(120,000 / [ (10 + $15) / 2 ]
  3. U = $120,000 / [ (0.40 × $10) + (0.60 × $15) ]
  4. U = $120,000 / [ (3 × $10) + (2 × $15) ]
Explanation: To find the break-even point in total units for a multi-product company, one must first calculate the weighted-average contribution margin per unit. The sales mix is 3 Alphas for every 2 Betas, meaning for every 5 units sold, 3 (or 60%) are Alpha and 2 (or 40%) are Beta. The weighted-average contribution margin is (0.60 × $10) + (0.40 × $15) = $6 + $6 = $12. The break-even point in total units is then Total Fixed Costs divided by this weighted-average contribution margin: $120,000 / $12.

Question 13

A company is considering investing in a machine that costs $120,000 and has a 5-year useful life with no salvage value. The machine will be depreciated using the straight-line method for both tax and accounting purposes. The machine is expected to increase annual revenues by $80,000 and annual cash operating expenses by $45,000. The company's tax rate is 25%.

Which expression represents the correct setup for calculating the annual after-tax net cash inflow generated by the machine?

  1. ($80,000 − $45,000) × (1 − 0.25)
  2. ($80,000 − 45,000−(45,000 − (120,000 / 5)) × (1 − 0.25)
  3. ($80,000 − 45,000)−((45,000) − ((120,000 / 5) × 0.25)
  4. ($80,000 − 45,000)×(1−0.25)+((45,000) × (1 − 0.25) + ((120,000 / 5) × 0.25) (correct answer)
Explanation: The annual after-tax cash inflow can be calculated in two main ways. One method is to start with the after-tax net income and add back non-cash expenses like depreciation. The other, more direct method, is to take the before-tax cash flow (Revenues - Cash Expenses), tax it, and then add the depreciation tax shield. The depreciation tax shield is the tax savings from the depreciation deduction (Depreciation Expense × Tax Rate). The before-tax cash flow is $80,000 - $45,000. Annual depreciation is $120,000 / 5. The correct setup is: (Before-Tax Cash Flow × (1 - Tax Rate)) + (Depreciation × Tax Rate).

Question 14

A company is considering a 5-year project requiring an initial investment of $500,000 in equipment. The project is expected to generate annual net cash inflows of $150,000. At the end of 5 years, the equipment can be sold for a salvage value of $50,000. The project also requires an immediate investment of $30,000 in working capital, which will be fully recovered at the end of the project's life. The company's required rate of return is 10%. Let PVIFA(10%, 5) represent the present value interest factor for an annuity and PVIF(10%, 5) represent the present value interest factor for a single sum.

Which of the following expressions correctly structures the Net Present Value (NPV) calculation for this project?

  1. [(150,000×PVIFA(10150,000 × PVIFA(10%, 5)) + (50,000 × PVIF(10%, 5))] − $500,000
  2. [(150,000×PVIFA(10150,000 × PVIFA(10%, 5)) + ((50,000 + 30,000)×PVIF(1030,000) × PVIF(10%, 5))] − (500,000 + $30,000) (correct answer)
  3. [(150,000×PVIF(10150,000 × PVIF(10%, 5)) + (50,000 × PVIF(10%, 5))] − ($500,000 + $30,000)
  4. [(150,000×PVIFA(10150,000 × PVIFA(10%, 5)) + (50,000 × PVIF(10%, 5))] − ($500,000 + $30,000)
Explanation: The NPV calculation must account for all cash flows at their present values. The initial outlay is the equipment cost (500,000)plustheworkingcapitalinvestment(500,000) plus the working capital investment (30,000). The annual cash inflows (150,000)formanannuityandshouldbediscountedusingPVIFA.Thecashflowattheendofyear5isasinglesumconsistingofthesalvagevalue(150,000) form an annuity and should be discounted using PVIFA. The cash flow at the end of year 5 is a single sum consisting of the salvage value (50,000) plus the recovery of working capital ($30,000), which should be discounted using PVIF. Therefore, the correct structure is: [PV of annual inflows] + [PV of terminal year cash flow] - [Initial investment].

Question 15

A manufacturing company has the following cost and inventory data for the most recent period:

  • Direct materials used: $80,000
  • Direct labor: $60,000
  • Manufacturing overhead applied: $90,000
  • Beginning work-in-process inventory: $20,000
  • Ending work-in-process inventory: $25,000

Which of the following shows the correct structure for calculating the Cost of Goods Manufactured (COGM)?

  1. $20,000 + $80,000 + $60,000 + $90,000 − $25,000 (correct answer)
  2. $80,000 + $60,000 + $90,000 − $20,000 + $25,000
  3. $80,000 + $60,000 + $90,000
  4. $20,000 + $80,000 + $60,000 + $90,000 + $25,000
Explanation: The Cost of Goods Manufactured (COGM) represents the total cost of all goods that were completed and moved from Work-in-Process to Finished Goods during a period. The calculation begins with the Beginning WIP inventory, adds the total manufacturing costs incurred during the period (Direct Materials + Direct Labor + MOH Applied), and subtracts the Ending WIP inventory. The correct setup is: Beginning WIP + (DM + DL + MOH) - Ending WIP.

Question 16

A company is evaluating whether to drop its East division. The division's income statement shows Sales of $500,000, Variable Costs of $300,000, Traceable Fixed Costs of $150,000, and Allocated Common Fixed Costs of 80,000,resultinginaNetLossof(80,000, resulting in a Net Loss of (30,000). Further analysis reveals that 70% of the division's traceable fixed costs can be eliminated if the division is dropped. The allocated common fixed costs would remain unchanged for the company as a whole.

Which expression correctly sets up the analysis to determine the change in the company's overall net operating income if the East division is dropped?

  1. −$500,000 + $300,000 + $150,000
  2. $500,000 − $300,000 − $150,000 − $80,000
  3. −$500,000 + $300,000 + (0.70 × $150,000) (correct answer)
  4. −$500,000 + $300,000 + (0.70 × $150,000) + $80,000
Explanation: The decision to drop a segment should be based on the change in overall company profit. This is determined by comparing the lost contribution margin to the avoidable fixed costs. If the division is dropped, the company loses the contribution margin ($500,000 Sales - $300,000 Variable Costs = $200,000). The costs that will be saved are the avoidable fixed costs, which are 70% of the traceable fixed costs (0.70 × 150,000).Commoncostsareirrelevantbecausetheywillbereallocated,noteliminated.Theimpactonincomeis:(AvoidedCosts)−(LostContributionMargin),orexpressedasasumofchanges:(LostRevenue)+(AvoidedVariableCosts)+(AvoidedFixedCosts)=−150,000). Common costs are irrelevant because they will be reallocated, not eliminated. The impact on income is: (Avoided Costs) - (Lost Contribution Margin), or expressed as a sum of changes: (Lost Revenue) + (Avoided Variable Costs) + (Avoided Fixed Costs) = −500,000 + $300,000 + (0.70 × $150,000).

Question 17

A processing department uses the weighted-average method of process costing. The following data pertains to the department's activities for the month:

  • Beginning work-in-process: 5,000 units (40% complete for conversion costs)
  • Units started into production: 30,000 units
  • Units completed and transferred out: 28,000 units
  • Ending work-in-process: 7,000 units (60% complete for conversion costs)

Which expression correctly sets up the calculation for the equivalent units of production for conversion costs for the period?

  1. (28,000 × 100%) + (7,000 × 60%) (correct answer)
  2. (30,000 × 100%) + (7,000 × 60%) − (5,000 × 40%)
  3. (28,000 × 100%) + (5,000 × 40%)
  4. (5,000 × 60%) + (23,000 × 100%) + (7,000 × 60%)
Explanation: Under the weighted-average method, equivalent units are calculated as the sum of units completed and transferred out during the period plus the equivalent units in the ending work-in-process inventory. The work done on the beginning inventory in the prior period is blended in. Therefore, the setup is: (Units completed and transferred out, which are 100% complete) + (Ending WIP units × percentage of completion). This translates to (28,000 × 100%) + (7,000 × 60%).

Question 18

A company uses job-order costing and applies manufacturing overhead to jobs based on direct labor hours. At the beginning of the year, it estimated total manufacturing overhead would be $400,000 and total direct labor hours would be 20,000. For a specific job, Job #101, the actual direct labor hours worked were 500.

Which of the following setups correctly calculates the amount of manufacturing overhead to be applied to Job #101?

  1. ($400,000 / 20,000) × 500 (correct answer)
  2. ($400,000 / Actual total direct labor hours) × 500
  3. $400,000 × (500 / 20,000)
  4. Actual total overhead incurred × (500 / Actual total direct labor hours)
Explanation: Overhead is applied to jobs using a predetermined overhead rate (POHR). The POHR is calculated at the beginning of the period using estimated figures: POHR = Estimated Total MOH / Estimated Total Allocation Base. Here, POHR = 400,000 / 20,000 DLH. To apply overhead to a specific job, this rate is multiplied by the actual amount of the allocation base incurred by that job. Therefore, the applied overhead for Job #101 is (400,000 / 20,000) × 500 actual DLH.

Question 19

A company is considering two mutually exclusive projects, Project X and Project Y. Both projects have a 4-year life and require an initial investment of $200,000. Project X generates equal annual cash inflows of $75,000. Project Y generates cash inflows of $40,000 in Year 1, $60,000 in Year 2, $90,000 in Year 3, and $100,000 in Year 4. The company's cost of capital is 12%. Let PVIF(12%, n) be the present value factor for a single sum in year n, and PVIFA(12%, 4) be the present value factor for a 4-year annuity.

Which of the following describes the correct setup to evaluate and compare the two projects using the Net Present Value (NPV) method?

  1. Calculate NPVx = ($75,000 × 4) − 200,000andNPVy=(200,000 and NPVy = (40k+60k+60k+90k+$100k) − $200,000; choose the higher NPV.
  2. Calculate NPVx = ($75,000 × PVIFA(12%, 4)) − 200,000andNPVy=(200,000 and NPVy = (72,500 × PVIFA(12%, 4)) − $200,000; choose the higher NPV.
  3. Calculate NPVx = 75,000×PVIFA(1275,000 × PVIFA(12%, 4) and NPVy = (40k×PVIF(12%,1)) + (60k×PVIF(1260k×PVIF(12%,2)) + (90k×PVIF(12%,3)) + ($100k×PVIF(12%,4)); choose the higher present value.
  4. Calculate NPVx = ($75,000 × PVIFA(12%, 4)) − 200,000andNPVy=[(200,000 and NPVy = [(40k×PVIF(12%,1)) + (60k×PVIF(1260k×PVIF(12%,2)) + (90k×PVIF(12%,3)) + ($100k×PVIF(12%,4))] − $200,000; choose the higher NPV. (correct answer)
Explanation: To compare projects using NPV, the present value of all cash inflows for each project must be calculated and the initial investment subtracted. For Project X, with its equal annual inflows (an annuity), the setup is (Annual Inflow × PVIFA) - Initial Investment. For Project Y, with its uneven cash flows, the present value of each individual cash flow must be calculated using the appropriate single-sum factor (PVIF) for each year, and then these present values are summed. The initial investment is then subtracted from this total present value. Finally, the project with the higher positive NPV is chosen.

Question 20

Alpine Company is setting up a flexible budget for manufacturing overhead. The company has identified the following cost behaviors: maintenance costs are $8,000 fixed plus $2.50 per machine hour; utilities are $3,000 fixed plus $1.20 per machine hour; depreciation is $15,000 fixed; and indirect materials are purely variable at $0.80 per machine hour. How should the total overhead cost formula be structured for any level of machine hours (MH)?

  1. Total Overhead = $26,000 + $3.70 × MH
  2. Total Overhead = $23,000 + $4.50 × MH
  3. Total Overhead = $26,000 + $4.50 × MH (correct answer)
  4. Total Overhead = $23,000 + $3.70 × MH
Explanation: When you encounter flexible budgeting questions, you're working with cost formulas that separate fixed and variable components. The goal is to create a single formula: Total Cost = Fixed Costs + (Variable Rate × Activity Level). To solve this, you need to identify and sum all fixed costs, then sum all variable rates per machine hour. Let's break down Alpine Company's overhead costs: Fixed costs:
  • Maintenance: $8,000
  • Utilities: $3,000
  • Depreciation: $15,000
  • Indirect materials: $0 (purely variable)
  • Total fixed costs = $8,000 + $3,000 + $15,000 = $26,000
Variable costs per machine hour:
  • Maintenance: $2.50
  • Utilities: $1.20
  • Depreciation: $0 (purely fixed)
  • Indirect materials: $0.80
  • Total variable rate = $2.50 + $1.20 + $0.80 = $4.50
Therefore, the formula is: Total Overhead = $26,000 + $4.50 × MH. Answer A incorrectly calculates the variable rate as $3.70, likely by omitting the indirect materials cost of $0.80 per machine hour. Answer B makes two errors: understating fixed costs at $23,000 (missing $3,000 in utilities fixed costs) while correctly calculating the 4.50variablerate.AnswerDcombinesbothmistakesfromAandB—wrongfixedcosts(4.50 variable rate. Answer D combines both mistakes from A and B—wrong fixed costs (23,000) and wrong variable rate ($3.70). Study tip: Always create two separate lists when building flexible budget formulas—one for all fixed cost components and another for all variable rates. This systematic approach prevents you from missing components or double-counting mixed costs.