Target Profit Analysis - Managerial Accounting

1. Zeta Inc. has the following cost structure: fixed costs $180,000, variable cost per unit $12, selling price per unit $30. The company wants to achieve an after-tax ROI of 18% on assets of $600,000, with a tax rate of 25%. If variable costs are expected to increase by 25%, what selling price per unit is required to maintain the same unit sales volume of 12,000 units?
   Answer: $42.00 Target after-tax profit = $600,000 × 18% = $108,000. Pre-tax profit needed = $108,000 ÷ (1 - 0.25) = $144,000. New variable cost = $12 × 1.25 = $15. Total contribution margin needed = $180,000 + $144,000 = $324,000. Contribution margin per unit needed = $324,000 ÷ 12,000 = $27. Required selling price = $15 + $27 = $42. Choice A adds the full profit requirement to the price. Choice B uses the original variable cost. Choice D ignores the variable cost increase.
2. A company is planning its operations for the upcoming year. The CEO has set a target for operating income to be $180,000. Management receives a bonus equal to 10% of operating income before the bonus is deducted. The company's product has a contribution margin of $40 per unit, and annual fixed costs are $200,000 (excluding any bonus). How many units must be sold to achieve the target operating income of $180,000 after the bonus has been paid?
   Answer: 10,000 units This problem involves a bonus that is dependent on profit, which requires calculating a pre-bonus profit target. 1. Define the relationship between pre-bonus and after-bonus profit: Let P_before be the operating income before the bonus, and P_after be the operating income after the bonus. The target P_after is $180,000. * P_after = P_before - Bonus * Bonus = 0.10 × P_before * P_after = P_before - (0.10 × P_before) = 0.90 × P_before 2. Calculate the required pre-bonus operating income (P_before): This becomes the target profit for the standard CVP calculation. * $180,000 = 0.90 × P_before * P_before = $180,000 / 0.90 = $200,000. 3. Calculate required sales units: Use the pre-bonus profit target in the formula. * Required Units = (Fixed Costs + P_before) / Contribution Margin per Unit * Required Units = ($200,000 + $200,000) / $40 = $400,000 / $40 = 10,000 units.
3. A company projects the following contribution format income statement data for the upcoming period: Sales (20,000 units): $1,000,000 Variable expenses: $600,000 Fixed expenses: $320,000 The company is subject to a 30% income tax rate. How many additional units must be sold to achieve an after-tax profit of $84,000?
   Answer: 2,000 units This question requires calculating the total units for a target profit and comparing it to the current level. 1. Extract CVP parameters from the provided data: * Selling Price per Unit = $1,000,000 / 20,000 units = $50. * Variable Cost per Unit = $600,000 / 20,000 units = $30. * Contribution Margin per Unit = $50 - $30 = $20. * Fixed Costs = $320,000. 2. Calculate the Target Operating Income (Pre-tax): * Target Operating Income = Target Net Income / (1 - Tax Rate) = $84,000 / (1 - 0.30) = $120,000. 3. Calculate Total Units Required for Target Profit: * Total Units = (Fixed Costs + Target Operating Income) / CM per Unit * Total Units = ($320,000 + $120,000) / $20 = $440,000 / $20 = 22,000 units. 4. Calculate Additional Units Needed: * Additional Units = Total Required Units - Current Units = 22,000 - 20,000 = 2,000 units.
4. A company manufactures a single product that sells for $150 per unit. Variable costs are $90 per unit, and annual fixed costs total $480,000. The company is subject to a 25% income tax rate. How many units must the company sell to achieve an after-tax net income of $180,000?
   Answer: 12,000 units To solve for the required sales in units for a target after-tax profit, we must first convert the target net income into a pre-tax operating income. The formula is: Target Operating Income = Target Net Income / (1 - Tax Rate). 1. Calculate Target Operating Income: Target Operating Income = $180,000 / (1 - 0.25) = $180,000 / 0.75 = $240,000. 2. Calculate Contribution Margin per Unit: Contribution Margin per Unit = Selling Price per Unit - Variable Cost per Unit = $150 - $90 = $60. 3. Calculate Required Sales in Units: Units = (Fixed Costs + Target Operating Income) / Contribution Margin per Unit = ($480,000 + $240,000) / $60 = $720,000 / $60 = 12,000 units.
5. Given the data in the passage, how many Gizmos must be sold for the company to achieve a target monthly operating profit of $84,000?
   Answer: 6,300 units This problem requires calculating the weighted-average contribution margin for a 'bundle' of products to determine the number of bundles needed, and then finding the units of a specific product. 1. Calculate Contribution Margin per Unit for each product: * Gizmo: $80 - $50 = $30 * Widget: $120 - $60 = $60 2. Calculate the Contribution Margin of a sales bundle: The sales mix is 3 Gizmos to 2 Widgets. * Bundle CM = (3 units × $30/Gizmo) + (2 units × $60/Widget) = $90 + $120 = $210. 3. Calculate the number of bundles needed: The total contribution margin required is Fixed Costs + Target Profit = $336,000 + $84,000 = $420,000. * Number of Bundles = Total Required CM / Bundle CM = $420,000 / $210 = 2,000 bundles. 4. Calculate the number of Gizmos: Each bundle contains 3 Gizmos. * Required Gizmos = 2,000 bundles × 3 Gizmos/bundle = 6,300 units.
6. Based on the information in the passage, what level of sales revenue is required for the company to achieve a target operating profit of $100,000?
   Answer: $1,300,000 This problem requires using the margin of safety information to determine the company's fixed costs before calculating the sales needed for the new target profit. 1. Calculate Breakeven Sales: Breakeven Sales = Current Sales - Margin of Safety = $1,200,000 - $300,000 = $900,000. 2. Calculate Fixed Costs: At the breakeven point, the total contribution margin equals fixed costs. * Fixed Costs = Breakeven Sales × Contribution Margin Ratio = $900,000 × 0.25 = $225,000. 3. Calculate Required Sales for Target Profit: Use the target profit formula. * Required Sales = (Fixed Costs + Target Profit) / Contribution Margin Ratio * Required Sales = ($225,000 + $100,000) / 0.25 = $325,000 / 0.25 = $1,300,000.
7. A company sells its product for $75 per unit. Variable costs are $45 per unit, and fixed costs are $240,000. In addition to these costs, the sales team earns a commission of 10% of sales revenue. How many units must the company sell to achieve a target operating profit of $90,000?
   Answer: 14,667 units The sales commission is a variable cost that is a percentage of the selling price. It must be included in the total variable cost per unit when calculating the contribution margin. 1. Calculate the total variable cost per unit: * Standard Variable Cost = $45.00 * Sales Commission per Unit = 10% of Selling Price = 0.10 × $75 = $7.50 * Total Variable Cost per Unit = $45.00 + $7.50 = $52.50 2. Calculate the contribution margin per unit: * Contribution Margin per Unit = Selling Price - Total Variable Cost per Unit = $75.00 - $52.50 = $22.50 3. Calculate the required sales in units: * Required Units = (Fixed Costs + Target Profit) / Contribution Margin per Unit * Required Units = ($240,000 + $90,000) / $22.50 = $330,000 / $22.50 = 14,666.67 units, which rounds to 14,667 units.
8. How would the total number of units required to achieve a target profit of $110,000 change if the new marketing strategy is adopted?
   Answer: Decrease by 2,300 units This is a two-scenario comparison problem involving a change in sales mix and fixed costs. 1. Analyze the Original Scenario: * Contribution Margins: Lux = $100 - $40 = $60; Basic = $50 - $30 = $20. * Original Bundle (1 Lux, 4 Basic) CM = (1 × $60) + (4 × $20) = $60 + $80 = $140. * Required Bundles = (Fixed Costs + Target Profit) / Bundle CM = ($450,000 + $110,000) / $140 = $560,000 / $140 = 4,000 bundles. * Original Total Units = 4,000 bundles × 5 units/bundle = 20,000 units. 2. Analyze the New Scenario: * New Fixed Costs = $450,000 + $30,000 = $480,000. * New Bundle (1 Lux, 2 Basic) CM = (1 × $60) + (2 × $20) = $60 + $40 = $100. * Required Bundles = ($480,000 + $110,000) / $100 = $590,000 / $100 = 5,900 bundles. * New Total Units = 5,900 bundles × 3 units/bundle = 17,700 units. 3. Calculate the Change: Change = New Total Units - Original Total Units = 17,700 - 20,000 = -2,300 units. This is a decrease of 2,300 units.
9. To achieve the company's overall profit target of $350,000, what amount of sales revenue must the Retail division generate?
   Answer: $1,350,000 This problem requires calculating a required sales level for one division given the company's overall profit target and the performance of the other division. 1. Calculate the projected segment margin for the Commercial division: * Commercial CM Ratio = 1 - 0.70 = 0.30. * Commercial Contribution Margin = $1,200,000 × 0.30 = $360,000. * Commercial Segment Margin = CM - Traceable Fixed Costs = $360,000 - $150,000 = $210,000. 2. Determine the required segment margin for the Retail division: * Company Profit = (Retail Segment Margin + Commercial Segment Margin) - Common Fixed Costs * $350,000 = (Retail Segment Margin + $210,000) - $220,000 * $350,000 = Retail Segment Margin - $10,000 * Retail Segment Margin = $360,000. 3. Calculate the required sales revenue for the Retail division: * Retail Segment Margin = (Retail Sales × Retail CM Ratio) - Retail Traceable Fixed Costs * Retail CM Ratio = 1 - 0.60 = 0.40. * $360,000 = (Retail Sales × 0.40) - $180,000 * $540,000 = Retail Sales × 0.40 * Retail Sales = $540,000 / 0.40 = $1,350,000.
10. If the firm adopts the new system, how many units must it sell to achieve a target operating profit of $300,000?
    Answer: 30,000 units The question asks for the required sales volume under a new proposed cost structure to meet a specific profit target. 1. Identify the new cost structure parameters: * New Fixed Costs = $750,000 * New Variable Cost per Unit = $15 * Selling Price remains $50 per unit. 2. Calculate the new Contribution Margin per Unit: * New CM per Unit = $50 - $15 = $35. 3. Calculate the required sales in units for the target profit: * Target Profit = $300,000. * Required Units = (New Fixed Costs + Target Profit) / New CM per Unit * Required Units = ($750,000 + $300,000) / $35 = $1,050,000 / $35 = 30,000 units.
11. Beta Industries produces two products: X and Y. Product X has a contribution margin ratio of 40% and Product Y has a contribution margin ratio of 60%. If the sales mix is 3:2 (X:Y) and total fixed costs are $150,000, what total sales revenue is needed to achieve a target profit of $75,000?
    Answer: $468,750 When you encounter multi-product break-even problems, you need to calculate a weighted average contribution margin ratio based on the sales mix before determining required sales revenue. First, calculate the weighted average contribution margin ratio. With a 3:2 sales mix (X:Y), Product X represents 60% of sales (3÷5) and Product Y represents 40% (2÷5). The weighted average is: $(0.60 × 40\%) + (0.40 × 60\%) = 24\% + 24\% = 48\%$ Next, determine total required contribution margin. You need $150,000 for fixed costs plus $75,000 target profit, totaling $225,000 in contribution margin. Finally, calculate required sales revenue: $\text{Required Sales} = \frac{\text{Required Contribution Margin}}{\text{Weighted CM Ratio}} = \frac{\$225,000}{0.48} = \$468,750$ This confirms answer D is correct. A) $425,000 likely results from incorrectly using 53% as the weighted average (simple average of 40% and 60% without considering the sales mix). B) $450,000 suggests using 50% as the weighted average, which ignores the actual 3:2 sales mix proportions. C) $500,000 appears to use 45% as the weighted average, possibly from miscalculating the sales mix weights. Strategy tip: Always convert sales mix ratios to percentages first (3:2 becomes 60%:40%), then weight each product's contribution margin ratio by its percentage of total sales. Many students forget this weighting step and simply average the ratios, leading to incorrect answers.
12. A company plans to sell 15,000 units of its product to generate a target operating profit of $70,000. The variable cost per unit is $30, and total fixed costs are $200,000. To achieve this profit goal, what selling price must the company set for its product?
    Answer: $48.00 This question requires rearranging the target profit formula to solve for the selling price. 1. Determine the total contribution margin required: The total contribution margin must cover both fixed costs and the target profit. * Total Required CM = Fixed Costs + Target Profit = $200,000 + $70,000 = $270,000. 2. Calculate the required contribution margin per unit: This is the total required CM spread over the planned sales volume. * Required CM per Unit = Total Required CM / Number of Units = $270,000 / 15,000 units = $18 per unit. 3. Calculate the required selling price: The selling price must cover both the variable cost and the required contribution margin. * Selling Price = Variable Cost per Unit + Required CM per Unit = $30 + $18 = $48.
13. Based on the passage, what is the minimum hourly billing rate the firm must charge its clients to meet its profit target?
    Answer: $113.75 This problem applies target profit analysis to a service firm context, requiring a calculation of the required 'selling price' (billing rate). 1. Calculate Total Billable Hours (Volume): Total Hours = Number of Consultants × Hours per Consultant = 40 × 1,600 = 64,000 hours. 2. Determine Total Contribution Margin Required: This must cover both fixed costs and the target profit. Total Required CM = $1,500,000 (Fixed Costs) + $980,000 (Target Profit) = $2,480,000. 3. Calculate Required Contribution Margin per Hour: Required CM per Hour = Total Required CM / Total Hours = $2,480,000 / 64,000 hours = $38.75 per hour. 4. Calculate Minimum Billing Rate: Billing Rate = Variable Cost per Hour + Required CM per Hour = $75.00 + $38.75 = $113.75.
14. A company's product sells for $200 per unit, with variable costs of $120 per unit. Fixed costs are $400,000 per year within a relevant range of 0 to 6,000 units. If the company produces and sells more than 6,000 units, fixed costs will increase by $80,000. What is the required sales volume in units to achieve a target operating profit of $160,000?
    Answer: 8,000 units This problem involves a step-fixed cost, requiring a two-step analysis. 1. Initial Calculation: First, calculate the required units using the initial fixed cost level. * Contribution Margin per Unit = $200 - $120 = $80. * Required Units = (Fixed Costs + Target Profit) / CM per Unit = ($400,000 + $160,000) / $80 = $560,000 / $80 = 7,000 units. 2. Check Relevant Range: The calculated volume of 7,000 units is outside the relevant range of 0 to 6,000 units for the $400,000 fixed cost level. 3. Recalculate with New Fixed Costs: Since the required volume exceeds 6,000 units, the higher fixed cost of $400,000 + $80,000 = $480,000 must be used. * Required Units = ($480,000 + $160,000) / $80 = $640,000 / $80 = 8,000 units. This new volume of 8,000 units is within the new relevant range (above 6,000 units), so it is the correct answer.
15. A manufacturing company has a contribution margin ratio of 40%. The company wants to achieve a target operating profit that is 25% of its total contribution margin. If the company's fixed costs are $240,000, what is the required level of sales revenue?
    Answer: $800,000 This problem defines target profit relative to contribution margin, requiring an algebraic approach. 1. Set up the CVP relationships: Let S = Sales Revenue and CM = Contribution Margin. * CM = Fixed Costs + Operating Profit CM = 0.40 S Operating Profit = 0.25 CM 2. Substitute the profit definition into the first equation: CM = Fixed Costs + (0.25 CM) 3. Solve for the required total Contribution Margin: CM - 0.25 CM = Fixed Costs 0.75 CM = $240,000 * CM = $240,000 / 0.75 = $320,000. 4. Calculate the required Sales Revenue: Since CM = 0.40 * S: $320,000 = 0.40 S * S = $320,000 / 0.40 = $800,000.
16. Theta Corp currently operates at 80% of capacity, selling 16,000 units at $35 per unit. Variable costs are $21 per unit and fixed costs are $168,000. If the company wants to achieve a target profit of $70,000 while operating at full capacity, what should be the new selling price per unit?
    Answer: $32.90 Full capacity = 16,000 ÷ 0.80 = 20,000 units. Total contribution margin needed = $168,000 + $70,000 = $238,000. Contribution margin per unit needed = $238,000 ÷ 20,000 = $11.90. New selling price = $21 + $11.90 = $32.90. Choice B uses the current contribution margin ratio incorrectly. Choice C assumes fixed costs will decrease proportionally. Choice D uses the original selling price calculation method.
17. Zenith Manufacturing has fixed costs of $120,000, variable cost per unit of $8, and a selling price of $20 per unit. If the company wants to achieve an after-tax profit of $60,000 and has a tax rate of 25%, what is the required sales volume in units?
    Answer: 17,000 units First, calculate the required pre-tax profit: $60,000 ÷ (1 - 0.25) = $80,000. Then use the CVP formula: Required units = (Fixed costs + Target pre-tax profit) ÷ Contribution margin per unit = ($120,000 + $80,000) ÷ ($20 - $8) = $200,000 ÷ $12 = 16,667 units, which rounds to 17,000 units. Choice A uses after-tax profit directly without adjusting for taxes. Choice B incorrectly calculates pre-tax profit as $60,000 × 1.25. Choice D uses only the after-tax target profit in the numerator.
18. Epsilon Corp sells products for $40 each with variable costs of $24 per unit. Fixed costs are $96,000. If the company wants to earn a target profit that provides a 15% return on invested assets of $800,000, how many units must be sold?
    Answer: 13,500 units This is a Cost-Volume-Profit (CVP) analysis problem that combines target profit planning with return on investment calculations. When you see questions asking for units to achieve a specific return percentage, you need to first convert that percentage into a dollar profit target. Start by calculating the required profit: 15% return on $800,000 in assets equals $0.15 × \$800,000 = \$120,000$ target profit. Next, find the contribution margin per unit: $\$40 - \$24 = \$16$ per unit. Now you can determine the required sales volume using the CVP formula: Units needed = (Fixed costs + Target profit) ÷ Contribution margin per unit = $(\$96,000 + \$120,000) ÷ \$16 = \$216,000 ÷ \$16 = 13,500$ units. Answer A (12,000 units) represents the break-even point calculation that ignores the target profit entirely: $96,000 ÷ $16 = 6,000 units to break even, but this doesn't account for the required return. Answer C (10,500 units) likely results from incorrectly using the selling price instead of contribution margin in the denominator. Answer D (9,000 units) appears to stem from miscalculating either the target profit amount or making an error in the contribution margin calculation. Remember that target profit problems always require two steps: convert the business goal (like ROI percentage) into a specific dollar amount, then use standard CVP analysis. Don't skip the profit calculation step—many incorrect answers trap students who jump straight to break-even formulas.
19. A company needs to generate $800,000 of sales revenue to achieve a target after-tax profit of $63,000. Total fixed costs are $210,000, and the company's income tax rate is 30%. What is the company's variable cost ratio?
    Answer: 62.5% This question requires working backward from target sales revenue and after-tax profit to find the variable cost ratio. 1. Calculate Target Operating Income (Pre-tax Profit): Target Operating Income = Target Net Income / (1 - Tax Rate) = $63,000 / (1 - 0.30) = $63,000 / 0.70 = $90,000. 2. Calculate the required Contribution Margin Ratio (CM Ratio): The formula for target sales is Sales = (Fixed Costs + Target Operating Income) / CM Ratio. Rearranging gives: CM Ratio = (Fixed Costs + Target Operating Income) / Sales Revenue. * CM Ratio = ($210,000 + $90,000) / $800,000 = $300,000 / $800,000 = 0.375 or 37.5%. 3. Calculate the Variable Cost Ratio (VC Ratio): The VC Ratio is 1 minus the CM Ratio. * VC Ratio = 1 - CM Ratio = 1 - 0.375 = 0.625 or 62.5%.
20. Company A has fixed costs of $200,000 and a contribution margin of $20 per unit. Company B has fixed costs of $320,000 and a contribution margin of $25 per unit. Both companies want to achieve a target operating profit of $80,000. How many more units must Company B sell than Company A to achieve the target profit?
    Answer: 2,000 units This question requires calculating the required sales volume for two different companies and then finding the difference. 1. Calculate Required Units for Company A: * Units_A = (Fixed Costs_A + Target Profit) / CM per Unit_A * Units_A = ($200,000 + $80,000) / $20 = $280,000 / $20 = 14,000 units. 2. Calculate Required Units for Company B: * Units_B = (Fixed Costs_B + Target Profit) / CM per Unit_B * Units_B = ($320,000 + $80,000) / $25 = $400,000 / $25 = 16,000 units. 3. Find the Difference: * Difference = Units_B - Units_A = 16,000 - 14,000 = 2,000 units.

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