- A company has 4,000 machine hours available. Product A: CM $18/unit, 2 hours/unit, max demand 1,500 units. Product B: CM $12/unit, 1 hour/unit, max demand 3,000 units. What product mix maximizes total contribution margin?
Answer: 500 units of A and 3,000 units of B; total CM $45,000
CM per machine hour: Product A = $18/2 = $9/hr; Product B = $12/1 = $12/hr. Product B is more efficient per constrained resource hour, so maximize B first. B: 3,000 units x 1 hr = 3,000 hrs; CM = $36,000. Remaining hours = 1,000; A: 1,000/2 = 500 units; CM = $9,000. Total CM = $45,000. Option A does not optimize the resource constraint. Option B fills all hours with A first, ignoring B's higher contribution per hour. Option C uses 4,000 hours (1,000 x 2 + 2,000 x 1 = 4,000) but does not rank by CM per hour.
- A company's fixed costs are $480,000 and variable cost ratio is 65% on a $40 selling price ($26 variable cost). The company wants to earn a target operating profit of $140,000. How many units must be sold?
Answer: 44,286 units
CM per unit = $40 - $26 = $14. Units for target profit = (Fixed costs + Target profit) / CM per unit = ($480,000 + $140,000) / $14 = $620,000 / $14 = 44,286 units. Option A is the break-even volume ($480,000 / $14), which covers fixed costs but produces zero profit. Option B uses an incorrect denominator. Option C uses an incorrect calculation.
- When using relevant cost analysis for a make-vs.-buy recommendation, which costs should be included?
Answer: Only incremental costs: variable manufacturing costs, avoidable fixed costs, and any opportunity costs from capacity freed by outsourcing
Relevant costs are future costs that differ between alternatives. For a make-vs.-buy analysis, relevant costs include: all variable manufacturing costs (which are avoided if outsourced), fixed costs that can actually be eliminated or redeployed if production stops, and any opportunity costs from capacity that would become available. Unavoidable fixed costs are irrelevant because they occur regardless of the decision. Option A includes irrelevant unavoidable fixed costs. Option C includes allocated overhead that may be unavoidable. Option D understates relevant costs by excluding overhead components that may vary or be avoidable.
- A company's in-house logistics cost is $1,800,000 annually ($1,200,000 variable, $600,000 fixed of which $400,000 is avoidable). An outsourcer offers to provide the service for $1,400,000. What is the recommended decision?
Answer: Outsource; the avoidable in-house cost of $1,600,000 exceeds the outsourcing cost by $200,000
Relevant in-house cost = Variable ($1,200,000) + Avoidable fixed ($400,000) = $1,600,000. Outsourcing cost = $1,400,000. Net savings from outsourcing = $200,000. The $200,000 of unavoidable fixed costs will be incurred regardless, so they are irrelevant to the comparison. Option A uses total cost, which overstates the in-house cost by including unavoidable fixed costs. Option B introduces non-financial factors without a data basis. Option D incorrectly assumes all $600,000 of fixed costs are avoidable.
- Analysis shows 30% of SKUs generate 85% of revenue and 90% of gross profit, while 70% of SKUs generate 15% of revenue and 10% of gross profit but consume 60% of operational overhead. Which recommendation is best supported by this data?
Answer: Conduct strategic SKU rationalization: identify which low-performing SKUs serve critical customer needs, retire those that do not, and redirect freed resources toward growing the high-performing group
The data shows severe resource inefficiency: 70% of SKUs consume 60% of operational overhead while generating only 10% of gross profit. This is a compelling case for SKU rationalization. However, immediate elimination (Option B) could harm customer relationships if some low-revenue SKUs are strategically important to key customers. A structured rationalization - analytically identifying which SKUs to retire versus retain based on customer necessity and strategic fit - captures the resource efficiency opportunity while managing the risk. Options A and D ignore the operational burden the tail SKUs create.
- An acquisition target has $20,000,000 revenue and $2,000,000 EBITDA. The proposed price is $18,000,000 (9x EBITDA). Estimated synergies are $1,000,000 annually. Post-acquisition annual debt service is $1,600,000. Which assessment is most analytically sound?
Answer: Even with synergies, EBITDA coverage of debt service is only 1.875x; this thin margin leaves limited buffer for integration risk or synergy shortfalls, and the financing structure warrants stress testing before committing to the transaction
Post-synergy EBITDA = $2,000,000 + $1,000,000 = $3,000,000. Debt service coverage = $3,000,000 / $1,600,000 = 1.875x. While above 1.0x, this coverage ratio is thin for an acquisition that requires successful integration and synergy realization. If synergies are delayed or partially achieved, coverage could fall below 1.5x - a level that would concern most lenders and create refinancing risk. A stress test at 50% synergy achievement ($2,500,000 EBITDA / $1,600,000 = 1.56x) and at base EBITDA with no synergies ($2,000,000 / $1,600,000 = 1.25x) reveals real downside vulnerability. Options A, B, and C focus on positive scenarios without addressing risk.
- Customer analysis shows the top 20% of customers generate 85% of gross profit while the bottom 40% generate only 2% of gross profit but consume 35% of resources. Which data-driven recommendation is most appropriate?
Answer: Conduct a tiered customer profitability initiative: grow wallet share with the top 20%, reduce service costs or reprice the bottom 40%, and evaluate whether unprofitable relationships can be improved or should be exited
The data reveals a classic Pareto pattern - a small group generates most value while a large group consumes disproportionate resources for minimal return. The optimal response is a segmented strategy: invest in growing relationships with the high-value 20%, improve the economics of the bottom 40% through pricing or service model changes, and selectively exit relationships that cannot be made profitable. This is more analytically sound than Option C (immediate exit, which may disrupt relationships and ignore fixed cost recovery) or Option A (equal treatment, which ignores the data entirely).
- Current pricing: $60 per unit, variable cost $36, total CM $1,200,000 at 50,000 units. Analysis: a 15% price increase to $69 reduces volume 25% to 37,500 units (new CM $1,237,500); a 10% price decrease to $54 increases volume 30% to 65,000 units (new CM $1,170,000). Which pricing recommendation is best supported by the data?
Answer: Increase price 15%; CM improves by $37,500 over current while the price decrease reduces CM by $30,000
Comparison of all three scenarios on total CM: Current $1,200,000; Price increase to $69: 37,500 x ($69-$36) = 37,500 x $33 = $1,237,500 (up $37,500); Price decrease to $54: 65,000 x ($54-$36) = 65,000 x $18 = $1,170,000 (down $30,000). The 15% price increase is the only scenario that improves CM, by $37,500. Option A selects the worst CM outcome. Option C is incorrect; the price increase outperforms the current price by $37,500. Option D uses revenue as the objective rather than profitability.
- A company can accept a contract paying $42,000 with $18,000 variable costs, but must redirect 500 machine hours currently used for Product X (CM $35 per machine hour). What is the recommended decision?
Answer: Accept; the contract generates positive incremental profit
Contract direct CM = $42,000 - $18,000 = $24,000. Opportunity cost = 500 hours x $35 = $17,500. Net benefit of accepting = $24,000 - $17,500 = $6,500. Despite the opportunity cost, the contract still generates $6,500 of net incremental value and should be accepted. Option B reaches the wrong conclusion about revenue adequacy. Option C reaches the correct accept conclusion but relies only on the gross margin without netting the opportunity cost. Option D reaches the wrong conclusion; the direct profit ($24,000) exceeds the opportunity cost ($17,500).
- Customer profitability analysis shows: Customer A ($2,000,000 revenue, $200,000 profit), Customer B ($500,000 revenue, $180,000 profit), Customer C ($1,200,000 revenue, -$60,000 loss) with 18 months remaining on contract. Which recommendation is most appropriate?
Answer: Investigate the root causes of Customer C's negative profitability, negotiate for better terms within the contract, and plan not to renew under current pricing; separately, explore growing Customer B whose profit-to-revenue ratio is highest
The recommendation must account for contractual obligations (Customer C cannot be immediately dropped) and should be data-driven across all three relationships. Customer B's profit-to-revenue ratio of 36% far exceeds Customer A's 10%, making it the most efficient relationship to grow. Customer C requires a structured remediation plan: understand the cost-to-serve drivers, seek contract improvements, and definitively exit at contract end if economics cannot improve. Option A ignores the contractual constraint. Option B prioritizes absolute revenue over return. Option D treats all customers as equivalent despite dramatically different economics.
- A product costs $42/unit at 80% capacity and $34/unit at 95% capacity due to fixed cost spreading. It sells for $48. A 12% price reduction to $42.24 is expected to drive volume to 95% capacity. What recommendation is best supported by this data?
Answer: Accept if the volume increase is achievable; at the reduced price and 95% capacity unit cost, operating income per unit ($8.24) exceeds the current $6.00, and total operating income increases due to both higher per-unit margin and more units
At current 80% capacity: operating income = $48 - $42 = $6/unit. At 95% capacity with reduced price: operating income = $42.24 - $34 = $8.24/unit. If volume increases to 95% capacity as projected, both per-unit and total operating income improve. The analytical condition is whether the volume increase is realistically achievable - if it is, the data supports the price reduction. Option A focuses on price per unit rather than total profit. Option B is overly simplistic. Option D dismisses a well-quantified analysis on grounds of uncertainty that are inherent in all forward-looking decisions.
- A company can lease a machine for $40,000 per year (6 years) or purchase it for $180,000. Tax rate 25%, cost of capital 10%, PV annuity factor 6 years at 10% = 4.355. After-tax lease cost and net PV of purchase (after depreciation tax shield) are compared. Which option is recommended?
Answer: Lease; PV of after-tax lease payments ($130,650) is lower than net PV cost of purchase ($147,337)
Lease: After-tax payment = $40,000 x 0.75 = $30,000/yr. PV = $30,000 x 4.355 = $130,650. Purchase: Straight-line depreciation = $180,000/6 = $30,000/yr. Annual tax shield = $30,000 x 0.25 = $7,500. PV of tax shield = $7,500 x 4.355 = $32,663. Net PV cost = $180,000 - $32,663 = $147,337. Leasing is $16,687 cheaper on a PV basis. Option A identifies the purchase cost correctly but recommends the more expensive option. Option B introduces a non-quantitative factor that does not override the financial analysis. Option C is incorrect; a $16,687 difference exists.
- A company produces 10,000 units at a total cost of $450,000 ($320,000 variable, $130,000 fixed). An outside supplier offers to provide the units at $38 each. The fixed costs are unavoidable. What is the data-supported recommendation?
Answer: Make; the relevant in-house variable cost of $32 per unit is lower than the $38 buy price, saving $60,000
Since fixed costs are unavoidable, only variable costs are relevant for the make-vs.-buy comparison. Variable cost to make = $320,000 / 10,000 = $32 per unit. Buy price = $38 per unit. Making saves $6 per unit x 10,000 units = $60,000. Option A reaches the wrong conclusion. Option C uses total cost ($45 per unit) which incorrectly includes unavoidable fixed costs, making the buy option appear cheaper than it actually is on a relevant-cost basis. Option D reaches the correct conclusion but uses total cost, which is the wrong analytical framework.
- A company's highest-revenue product line has seen gross margins decline from 48% to 31% over 3 years. A smaller line holds stable 52% gross margins. The strategy team recommends doubling marketing for the declining-margin line to drive volume. Which recommendation is most analytically sound?
Answer: Before increasing investment in the declining-margin line, investigate why margins are falling; if driven by competitive pricing pressure or rising input costs, more volume at lower margins may not improve profit, and resources may generate more return redirected toward the high-margin line
A 17-percentage-point gross margin decline is a serious signal that warrants root cause analysis before committing more capital to that business. If margins are declining because of competitive pricing pressure, more volume at lower prices will accelerate the problem. If input costs are rising faster than pricing power, volume alone will not restore margins. The analytically sound approach is to diagnose the cause of margin decline and redirect resources where returns are higher - a recommendation supported by the data showing the smaller line's superior margin stability. Option B uses revenue as the investment criterion rather than return on investment. Options C and D make unsupported assumptions about operational leverage and self-correction.
- A company has 2,000 units of excess capacity and receives a special order for 5,000 units at $25 (regular price $38, variable cost $20). Accepting the full order would displace 3,000 units of regular production. What recommendation is best supported by the analysis?
Answer: Reject the full order; filling it requires displacing 3,000 units of regular production, creating a $29,000 net loss; offer to supply 2,000 units at $25 using available excess capacity only
Full order analysis: Incremental CM = 5,000 x ($25-$20) = $25,000. Opportunity cost of displacing 3,000 regular units = 3,000 x ($38-$20) = $54,000. Net impact = $25,000 - $54,000 = -$29,000 (loss). However, the excess capacity portion (2,000 units) produces CM of $10,000 with no opportunity cost. The optimal recommendation is a partial acceptance at 2,000 units. Option A ignores the opportunity cost of displacing regular production. Option C introduces a relationship rationale that does not override the quantitative loss. Option D overcorrects with an absolute rule that ignores the valid partial-acceptance opportunity.
- Segment data: North (revenue $15M, EBIT margin 18%, capital $8M, ROCE 33.75%), South (revenue $8M, EBIT margin 12%, capital $6M, ROCE 16%), West (revenue $4M, EBIT margin 22%, capital $2M, ROCE 44%). Management proposes investing $3,000,000 of additional capital in the South. Which recommendation is most data-supported?
Answer: West has the highest ROCE at 44% and North has the second-highest at 33.75%; additional capital would likely generate higher returns in either region than in South at 16% ROCE, and South's lower efficiency should be understood before committing resources there
ROCE measures how efficiently capital generates earnings - it is the correct metric for evaluating incremental capital allocation. Investing in the region with the lowest ROCE (South at 16%) is unlikely to generate returns comparable to investing in the highest-ROCE regions (West at 44%, North at 33.75%). Before directing additional capital to South, management should understand whether its low ROCE reflects a fixable problem, structural market limitations, or simply a business in a less attractive competitive position. Options A and B focus on absolute metrics (EBIT dollars) that do not account for the capital required to generate them. Option C makes an unsupported generalization.
- In a data-driven recommendation, 'relevant data' is best defined as:
Answer: Information specific to the decision, differing between alternatives, and likely to affect the outcome
Relevant data meets three tests: it is future-oriented (specific to the decision at hand), it differs between alternatives (data that is the same regardless of choice is irrelevant), and it affects the outcome (it changes the financial or operational result of the decision). Presenting non-relevant data adds complexity and noise without improving the recommendation. Option B defines relevant too broadly - not all quantifiable financial data is relevant to every decision. Option C confuses data quality (accuracy) with relevance. Option D is a procedural definition that has nothing to do with the analytical concept of relevance.
- A company's current price is $50, variable cost $30/unit, CM ratio 40%, annual volume 10,000 units, total CM $200,000. A proposed 10% price decrease to $45 is expected to increase volume 20% to 12,000 units. What is the recommended pricing decision?
Answer: Maintain price; the proposed decrease reduces total CM from $200,000 to $180,000
At the new price of $45 and volume of 12,000: CM per unit = $45 - $30 = $15. Total CM = 12,000 x $15 = $180,000, which is $20,000 less than the current $200,000. Although revenue increases and volume grows, total contribution margin declines because the margin per unit falls from $20 to $15 and the volume increase is insufficient to offset the per-unit reduction. Option A focuses on revenue rather than the relevant profit metric. Option C reaches the wrong conclusion from the data. Option D identifies a valid threshold but recommends a policy rather than a recommendation based on the actual data.
- DSO has increased from 35 to 58 days on $10,000,000 revenue, locking up approximately $630,000 in excess receivables. A 2% early-payment discount program is estimated to cost $200,000 annually if all customers participate. Should the discount program be recommended?
Answer: Yes; the cash freed from receivables reduction ($630,000) exceeds the annual discount cost ($200,000) even at full participation, suggesting a net positive outcome
The one-time cash benefit from receivables reduction ($630,000) combined with the ongoing acceleration of collections must be weighed against the ongoing discount cost ($200,000 per year). Even in the worst-case scenario where all customers take the discount, the first-year impact is positive: $630,000 freed minus $200,000 discount cost = $430,000 net benefit. In subsequent years the ongoing benefit depends on whether the discount actually accelerates collections versus simply reducing revenue for customers who would have paid on time anyway. Options B and D make categorical claims contradicted by the data. Option C introduces an arbitrary participation threshold.
- Data shows each additional $1 of R&D historically generates $4.20 of revenue over 5 years. The CFO proposes cutting the R&D budget 40% to improve short-term earnings. Which assessment is most analytically sound?
Answer: The historical 4.2x revenue return suggests R&D is a high-ROI investment; a 40% cut may improve short-term earnings while destroying substantially more long-term value, and the recommendation should model the estimated revenue impact before approving the cut
The data provides a quantifiable return on R&D investment. Before accepting a trade-off between short-term earnings improvement and long-term revenue generation, the analysis should model the expected revenue impact of a 40% R&D reduction over 5 years and compare it to the near-term EPS benefit. A cut that improves this year's earnings by X while reducing future revenues by 4.2X is likely destroying net value. Option A makes a categorical claim unsupported by data. Option B dismisses a 5-year return horizon that is standard for R&D investments. Option C incorrectly treats quantified historical data as insufficiently reliable.
