Contribution Margin - Cost Accounting

1. Based on the company's budget, what is the contribution margin ratio?
   Answer: 46.0% The contribution margin ratio is calculated as (Sales - Variable Costs) / Sales. 1. First, determine the total variable costs. Total Costs = Fixed Costs + Variable Costs. Therefore, Variable Costs = Total Costs - Fixed Costs. Variable Costs = $420,000 - $150,000 = $270,000. 2. Next, calculate the total contribution margin. Contribution Margin = Sales - Variable Costs. Contribution Margin = $500,000 - $270,000 = $230,000. 3. Finally, calculate the contribution margin ratio. Contribution Margin Ratio = $230,000 / $500,000 = 0.46, or 46.0%.
2. What is the total contribution margin at the current sales level of $750,000?
   Answer: $300,000 This is a two-step problem. First, find the contribution margin ratio using the break-even data, then apply it to the current sales level. 1. Calculate the contribution margin ratio (CMR). At the break-even point, Total Contribution Margin = Total Fixed Costs. The formula for break-even sales is Fixed Costs / CMR. CMR = Fixed Costs / Break-even Sales = $240,000 / $600,000 = 0.40 or 40%. 2. Use the CMR to calculate the total contribution margin at the current sales level. Total Contribution Margin = Current Sales CMR = $750,000 0.40 = $300,000.
3. What is the company's total contribution margin?
   Answer: $570,000 Contribution margin is Sales minus all variable costs. The costs must be reclassified from the traditional format. 1. Calculate variable Cost of Goods Sold (COGS): Variable COGS = $750,000 (1 - 0.40) = $750,000 0.60 = $450,000. 2. Calculate variable Selling & Administrative (S&A) Expenses: Variable S&A = $300,000 * 0.60 = $180,000. 3. Calculate total variable costs: Total Variable Costs = Variable COGS + Variable S&A = $450,000 + $180,000 = $630,000. 4. Calculate total contribution margin: Total Contribution Margin = Sales - Total Variable Costs = $1,200,000 - $630,000 = $570,000.
4. What is the unit contribution margin for the product?
   Answer: $35 The unit contribution margin is the selling price per unit minus all variable costs per unit (both manufacturing and selling). 1. Sum the variable costs per unit: - Direct materials: $25 - Direct labor: $18 - Variable manufacturing overhead: $7 - Variable selling expenses: $5 Total Variable Cost per Unit = $25 + $18 + $7 + $5 = $55. 2. Calculate the unit contribution margin (UCM): UCM = Selling Price per Unit - Total Variable Cost per Unit = $90 - $55 = $35. Fixed costs are not used in the calculation of contribution margin.
5. What would be the effect on the company's total contribution margin if the special order is accepted?
   Answer: An increase of $20,000 The effect on total contribution margin is determined by the contribution margin generated by the special order. The $5,000 tool cost is a fixed cost that affects profit but not contribution margin. Variable selling expenses are typically avoided on special orders as they don't go through normal sales channels. 1. Identify relevant variable costs per unit for the order: Direct Materials ($15) + Direct Labor ($10) + Variable Manufacturing Overhead ($5) = $30. 2. Calculate the unit contribution margin for the special order: Special Price ($40) - Relevant Variable Costs ($30) = $10. 3. Calculate the total increase in contribution margin: UCM ($10) × Units (2,000) = $20,000.
6. Delta Enterprises operates with a contribution margin ratio of 35% and monthly fixed costs of $140,000. If the company achieves its target net income of $28,000 for the month, and then decides to increase advertising spending by $15,000 while maintaining the same net income level, what total contribution margin will be required?
   Answer: $183,000 to cover increased fixed costs while maintaining target net income levels Original required contribution margin = Fixed costs + Target net income = $140,000 + $28,000 = $168,000. With the additional $15,000 advertising expense (increasing fixed costs to $155,000), the new required contribution margin = $155,000 + $28,000 = $183,000. The contribution margin must increase by exactly the amount of the additional fixed cost to maintain the same net income.
7. If the new compensation plan is adopted and sales volume remains unchanged, what would be the company's total contribution margin?
   Answer: $1,300,000 The new commission is a variable cost that reduces the contribution margin per unit. 1. First, calculate the new variable commission cost per unit. The sales price is $50. Commission per unit = $50 * 8% = $4. 2. Next, calculate the new total variable cost per unit. New Total VC per unit = Variable Manufacturing Cost + Commission = $20 + $4 = $24. 3. Calculate the new unit contribution margin (UCM). New UCM = Selling Price - New Total VC per unit = $50 - $24 = $26. 4. Finally, calculate the new total contribution margin for the 50,000 units sold. New Total CM = New UCM Units Sold = $26 50,000 = $1,300,000.
8. A product sells for $150 per unit and has a contribution margin ratio of 30%. If the selling price is increased by $15 per unit, and the variable cost per unit and total units sold remain unchanged, what will be the new unit contribution margin?
   Answer: $60.00 An increase in selling price, with no change in variable cost per unit, directly increases the unit contribution margin by the same amount. 1. Calculate the original unit contribution margin (UCM). Original UCM = Selling Price CMR = $150 0.30 = $45. 2. Alternatively, one could calculate the original variable cost per unit. Variable Cost = Selling Price (1 - CMR) = $150 0.70 = $105. Original UCM = $150 - $105 = $45. 3. Calculate the new unit contribution margin. The new selling price is $150 + $15 = $165. The variable cost per unit is still $105. New UCM = New Selling Price - Variable Cost per Unit = $165 - $105 = $60.
9. If the company had made this investment at the beginning of last year and sales volume had remained at 25,000 units, what would the total contribution margin have been?
   Answer: $525,000 The change in contribution margin is driven solely by the change in variable costs. The increase in fixed costs does not affect the contribution margin. 1. The reduction in variable cost per unit directly increases the unit contribution margin by the same amount ($5 per unit). 2. Calculate the total increase in contribution margin for the given sales volume. Total Increase in CM = Increase in UCM Units Sold = $5/unit 25,000 units = $125,000. 3. Add this increase to the original total contribution margin to find the new total. New Total CM = Original Total CM + Total Increase in CM = $400,000 + $125,000 = $525,000.
10. What is the total contribution margin for the company for the period?
    Answer: $320,000 The total contribution margin is the sum of the contribution margins from all products. 1. Calculate the contribution margin for Product Alpha: - Unit Contribution Margin (UCM) Alpha = $100 - $65 = $35. - Total CM Alpha = $35/unit * 4,000 units = $140,000. 2. Calculate the contribution margin for Product Beta: - UCM Beta = $120 - $90 = $30. - Total CM Beta = $30/unit * 6,000 units = $180,000. 3. Sum the total contribution margins for both products: - Total Company CM = Total CM Alpha + Total CM Beta = $140,000 + $180,000 = $320,000.
11. What is the division's total contribution margin?
    Answer: $320,000 The degree of operating leverage (DOL) is the ratio of contribution margin to net operating income. 1. Recall the formula for DOL: DOL = Contribution Margin / Net Operating Income. 2. Rearrange the formula to solve for Contribution Margin: Contribution Margin = DOL * Net Operating Income. 3. Substitute the given values into the formula: Contribution Margin = 4.0 * $80,000 = $320,000.
12. What is the company's total contribution margin at the target sales level?
    Answer: $400,000 The total contribution margin must cover both fixed costs and the pre-tax target profit. 1. First, convert the after-tax net income target to a pre-tax income target. Pre-tax Income = After-Tax Income / (1 - Tax Rate). Pre-tax Income = $105,000 / (1 - 0.30) = $105,000 / 0.70 = $150,000. 2. Next, use the profit formula: Total Contribution Margin = Fixed Costs + Pre-tax Profit. Total Contribution Margin = $250,000 + $150,000 = $400,000.
13. If the advertising campaign is implemented, what is the expected total contribution margin?
    Answer: $176,000 The change in fixed costs affects net income but not the contribution margin ratio. The new total contribution margin will be based on the new sales level. 1. First, calculate the current contribution margin ratio (CMR). Current Total CM = $400,000 - $240,000 = $160,000. CMR = $160,000 / $400,000 = 0.40 or 40%. 2. Next, calculate the new expected sales level. New Sales = $400,000 * (1 + 0.10) = $440,000. 3. Calculate the new total contribution margin by applying the stable CMR to the new sales level. New Total CM = New Sales CMR = $440,000 0.40 = $176,000.
14. Assuming the cost structure remains unchanged, what is the expected increase in total contribution margin for next month compared to the most recent month?
    Answer: $15,000 The question asks for the increase in total contribution margin, not the new total. 1. First, calculate the unit contribution margin (UCM). UCM = Total Contribution Margin / Units Sold. UCM = $150,000 / 5,000 units = $30 per unit. 2. Next, determine the increase in sales volume. Increase in units = 5,500 units - 5,000 units = 500 units. 3. Calculate the total increase in contribution margin by multiplying the increase in units by the UCM. Increase in Total CM = 500 units * $30/unit = $15,000.
15. A company achieved a contribution margin of $500,000 on sales of $1,250,000. If sales increase by $200,000 and the cost structure does not change, by how much will net operating income increase?
    Answer: $80,000 With a stable cost structure, fixed costs do not change with an increase in sales. Therefore, the increase in net operating income will be equal to the increase in the total contribution margin. 1. First, calculate the contribution margin ratio (CMR) from the given data. CMR = Total Contribution Margin / Total Sales = $500,000 / $1,250,000 = 0.40 or 40%. 2. Next, calculate the increase in total contribution margin resulting from the increase in sales. Increase in CM = Increase in Sales CMR = $200,000 0.40 = $80,000. 3. Since fixed costs are constant, the increase in net operating income is equal to the increase in contribution margin, which is $80,000.
16. What amount of total contribution margin must be generated to achieve the target profit?
    Answer: $500,000 This problem can be solved by setting up the CVP formula algebraically. 1. Define the relationships: - Contribution Margin Ratio (CMR) = 1 - Variable Cost Ratio = 1 - 0.75 = 0.25. - Total Contribution Margin (TCM) = Sales CMR = Sales 0.25. - Target Profit = Sales * 0.10. - Sales = Fixed Costs + Target Profit + Variable Costs, OR TCM = Fixed Costs + Target Profit. 2. Substitute the expressions into the last formula: Sales 0.25 = $300,000 + (Sales 0.10). 3. Solve for Sales: (Sales 0.25) - (Sales 0.10) = $300,000. Sales * 0.15 = $300,000. Sales = $300,000 / 0.15 = $2,000,000. 4. The question asks for the total contribution margin, not the sales. Calculate the total contribution margin at this sales level: Total Contribution Margin = Sales CMR = $2,000,000 0.25 = $500,000.
17. Alpha Manufacturing produces widgets with a selling price of $45 per unit. Variable costs are $28 per unit, and monthly fixed costs are $85,000. If the company currently sells 6,000 units per month but plans to increase advertising expenses by $12,000 monthly (which will increase fixed costs), what will be the new contribution margin ratio after this change?
    Answer: 37.78% since the contribution margin ratio remains unchanged by fixed cost increases The contribution margin ratio is calculated as (Selling Price - Variable Cost per Unit) ÷ Selling Price = ($45 - $28) ÷ $45 = $17 ÷ $45 = 37.78%. The contribution margin ratio is unaffected by changes in fixed costs because it only considers the relationship between selling price and variable costs per unit. The $12,000 increase in advertising is a fixed cost change and does not alter the per-unit contribution margin or ratio.
18. Using the information in the passage above, Kappa's regular product sells for $2,400 per unit with variable costs of $1,680 per unit. A special order for 500 units offers $2,100 per unit, but requires $45,000 in additional setup costs (fixed for this order) and $125 per unit in extra variable costs. If Kappa has excess capacity, what is the total contribution margin from this special order?
    Answer: $147,500 calculated by properly considering only variable costs in contribution margin For the special order: Revenue per unit = $2,100. Variable costs per unit = $1,680 + $125 = $1,805. Unit contribution margin = $2,100 - $1,805 = $295. Total contribution margin = 500 units × $295 = $147,500. The $45,000 setup cost is a fixed cost for this order and does not affect the contribution margin calculation, though it would be considered separately in determining the overall profitability of accepting the order.
19. Based on the data in the passage above, if Epsilon wants to achieve a target contribution margin ratio of 45% while keeping the same sales volume, and variable costs cannot be reduced, what new selling price per unit would be required?
    Answer: $163.64 calculated by applying the target ratio to current variable costs per unit Current variable cost per unit = $720,000 ÷ 8,000 = $90. If the contribution margin ratio should be 45%, then variable costs represent 55% of the selling price. Therefore: $90 ÷ 0.55 = $163.64 per unit. This can be verified: contribution margin = $163.64 - $90 = $73.64, and ratio = $73.64 ÷ $163.64 = 45%.
20. What is the company's contribution margin ratio?
    Answer: 40.0% When fixed costs are constant, the change in net operating income is equal to the change in contribution margin. The contribution margin ratio can be calculated by dividing the change in contribution margin by the change in sales. 1. Calculate the change in sales: Change in Sales = $1,500,000 * 20% = $300,000. 2. Calculate the change in net operating income (which equals the change in contribution margin): Change in Contribution Margin = $240,000 - $120,000 = $120,000. 3. Calculate the contribution margin ratio (CMR): CMR = Change in Contribution Margin / Change in Sales = $120,000 / $300,000 = 0.40 or 40%.

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