Setting Up Multi-Step Problems - Managerial Accounting

1. Which expression represents the correct setup for calculating the annual after-tax net cash inflow generated by the machine?
   Answer: ($80,000 − $45,000) × (1 − 0.25) + (($120,000 / 5) × 0.25) 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).
2. Which of the following expressions correctly isolates the components needed to calculate the direct labor rate variance?
   Answer: Actual Hours × (Actual Rate − Standard Rate) 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.
3. Which equation correctly sets up the calculation for the net financial advantage (disadvantage) of buying the component instead of making it?
   Answer: Advantage(Buy) = [10,000 × ($12 + $8 + $5 + $4)] - (10,000 × $28) + $30,000 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), Direct Labor ($8), Variable Overhead ($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.
4. What is the correct setup for calculating the net present value (NPV) of this bus investment project?
   Answer: NPV = -$2,400,000 + Σ[(450,000 - 80,000 - 20,000(t-1)) × PV factor for year t] + $240,000 × PV factor for year 8, where t = 1 to 8 When evaluating capital investment projects, you need to carefully track the timing and progression of cash flows, especially when costs change over time. Net present value calculations require precise alignment between cash flow amounts and their corresponding years. The correct setup is option B because it properly handles the increasing maintenance costs. The formula uses $(t-1)$ in the maintenance cost calculation, which means: Year 1: $80,000 + $20,000(1-1) = $80,000; Year 2: $80,000 + $20,000(2-1) = $100,000; Year 3: $80,000 + $20,000(3-1) = $120,000, and so on. This correctly reflects that maintenance starts at $80,000 in year 1 and increases by $20,000 each subsequent year. The formula also properly includes the salvage value discounted to present value. Option A is incorrect because it uses $20,000t instead of $20,000(t-1)$, making year 1 maintenance costs $100,000 instead of the stated $80,000. Option C attempts to use annuity factors, but the gradient factor approach becomes complex and doesn't clearly handle the specific cash flow pattern described. Option D is wrong because it shows an initial investment of only $2,160,000 instead of $2,400,000, and it omits the salvage value entirely. Remember that when cash flows change by a constant amount each period, pay close attention to the base year amount and whether the indexing starts at zero or one. Always verify your formula produces the correct cash flows for years 1 and 2 before proceeding with the full calculation.
5. Which expression correctly sets up the calculation for the equivalent units of production for conversion costs for the period?
   Answer: (28,000 × 100%) + (7,000 × 60%) 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%).
6. 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?
   Answer: Q = ($200,000 + [$70,000 / (1 − 0.30)]) / ($50 − $30) 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). This value is then added to fixed costs, and the sum is divided by the contribution margin per unit ($50 - $30).
7. Which of the following setups correctly calculates the total budgeted cash collections for March?
   Answer: (0.60 × $150,000) + (0.30 × $120,000) + (0.08 × $100,000) 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.
8. Which of the following shows the correct structure for calculating the Cost of Goods Manufactured (COGM)?
   Answer: $20,000 + $80,000 + $60,000 + $90,000 − $25,000 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.
9. Which of the following describes the correct setup to evaluate and compare the two projects using the Net Present Value (NPV) method?
   Answer: Calculate NPVx = ($75,000 × PVIFA(12%, 4)) − $200,000 and NPVy = [($40k×PVIF(12%,1)) + ($60k×PVIF(12%,2)) + ($90k×PVIF(12%,3)) + ($100k×PVIF(12%,4))] − $200,000; choose the higher NPV. 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.
10. To set up the constraint equations for this linear programming problem, which system of inequalities correctly represents the resource limitations?
    Answer: $3A + 2B ≤ 1,200$ and $2A + 4B ≤ 1,600$ The correct setup matches each resource constraint with its availability. Alpha uses 3 machine hours and Beta uses 2 machine hours, so the machine constraint is 3A + 2B ≤ 1,200. Alpha uses 2 labor hours and Beta uses 4 labor hours, so the labor constraint is 2A + 4B ≤ 1,600. Choice B reverses the machine time coefficients. Choice C switches the resource limits. Choice D reverses both the machine coefficients and the resource limits.
11. Which expression correctly sets up the calculation for the flexible budget variance for total costs?
    Answer: $96,000 − [($4 × 11,000) + $50,000] 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. 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 - [($4 × 11,000) + $50,000].
12. Which sequence correctly demonstrates the cause-and-effect relationships in a balanced scorecard framework, moving from leading indicators to lagging financial outcomes?
    Answer: Learning & Growth: Employee training hours → Internal Process: Defect rates → Customer: Customer satisfaction scores → Financial: Return on investment The balanced scorecard framework relies on cause-and-effect relationships that flow logically from foundational improvements to ultimate financial results. When analyzing these linkages, you should trace how investments in people and processes eventually drive customer outcomes and financial performance. Option B correctly demonstrates this logical flow. It starts with Learning & Growth (employee training hours), which represents the foundation - investing in people's capabilities. This enhanced capability leads to improved Internal Processes (reduced defect rates), as better-trained employees make fewer mistakes. Lower defect rates then improve Customer outcomes (higher satisfaction scores), since customers receive higher-quality products. Finally, satisfied customers drive Financial results (better return on investment) through repeat purchases and referrals. Option A reverses the cause-and-effect by placing internal process improvements before employee development, which doesn't reflect how improvements actually occur. Option C starts with customer complaints (a lagging indicator) rather than the foundational investments that prevent problems, making it backwards. Option D begins with financial outcomes and moves toward learning and growth, which completely inverts the balanced scorecard logic - you can't start with cost reduction and expect it to automatically create innovation. Remember that balanced scorecard relationships should flow from "learning" to "doing" to "satisfying customers" to "financial results." Leading indicators (like training hours) predict future performance, while lagging indicators (like ROI) measure results after the fact. Always look for sequences that start with foundational investments in people or capabilities and end with financial outcomes.
13. 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?
    Answer: U = $120,000 / [ (0.60 × $10) + (0.40 × $15) ] 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.
14. Which of the following expressions correctly sets up the calculation for the sales price variance?
    Answer: ($11 − $12) × 11,000 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.
15. Which equation correctly sets up the calculation for the incremental income (or loss) from accepting the special order?
    Answer: (4,000 × $35) − (4,000 × $30) − [2,000 × ($50 − $30)] 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 (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.
16. 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?
    Answer: −$500,000 + $300,000 + (0.70 × $150,000) 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). 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).
17. 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)?
    Answer: Total Overhead = $26,000 + $4.50 × MH 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 $4.50 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.
18. Which of the following setups correctly calculates the total budgeted cost of raw material purchases for the quarter?
    Answer: [(40,000 × 2) + 15,000 − 10,000] × $5 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.
19. Which of the following expressions correctly structures the Net Present Value (NPV) calculation for this project?
    Answer: [($150,000 × PVIFA(10%, 5)) + (($50,000 + $30,000) × PVIF(10%, 5))] − ($500,000 + $30,000) The NPV calculation must account for all cash flows at their present values. The initial outlay is the equipment cost ($500,000) plus the working capital investment ($30,000). The annual cash inflows ($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].
20. Which cost elements should be included in the incremental analysis to determine the maximum price the company should pay per unit to an external supplier?
    Answer: Direct materials $12 + Direct labor $8 + Variable overhead $5 + Opportunity cost $3 = $28 per unit The relevant costs include all avoidable costs plus opportunity cost. Avoidable costs are direct materials ($12), direct labor ($8), and variable overhead ($5). The opportunity cost is $30,000 ÷ 10,000 units = $3 per unit. Fixed overhead is not relevant since it continues regardless. Total maximum price = $28 per unit. Choice B incorrectly includes unavoidable fixed overhead. Choice C omits the opportunity cost. Choice D omits direct materials and incorrectly includes fixed overhead.

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