A cost–volume–profit (CVP) graph is a useful technique for showing relationships between costs, volume, and profits in an organization.
(a) Identify the numbered components in the accompanying CVP graph.
No.DescriptionNo.Description16273849510
(b) Using the typical CVP relationship shown, fill in the missing amounts in each of the following four situations (each case is independent of the others):
Contribution VariableMargin perFixedNet IncomeCase Units SoldSalesExpensesUnitExpenses(Loss)A9,000$270,000$162,000 $ 90,000 B $350,000 $15$170,000$ 40,000C20,000 $280,000$ 6 $ 35,000D5,000$100,000 $ 82,000($12,000)
The Correct Answer and Explanation is :
To properly analyze the problem, let’s break it into two parts:
(a) Identifying the numbered components in the CVP graph
A typical Cost-Volume-Profit (CVP) graph consists of the following components:
- Total Revenue Line – This line shows how total revenue increases with the number of units sold. It starts at the origin (zero units and zero revenue) and increases linearly as sales increase.
- Total Cost Line – This line shows the total costs, which consist of fixed and variable costs. The line starts at the level of fixed costs (which remain constant) and increases as more units are sold, reflecting the variable costs.
- Break-even Point – The point at which total revenue equals total costs. At this point, there is no profit or loss.
- Profit Region – The area above the break-even point where the company is making a profit.
- Loss Region – The area below the break-even point where the company is incurring a loss.
Without access to the actual graph link, the numbered components typically represent these key areas.
(b) Filling in the missing amounts for each case:
We can calculate the missing figures using the relationship between sales, variable costs, fixed costs, contribution margin, and net income.
Formulae:
- Contribution Margin (CM) = Sales – Variable Costs
- Net Income (or Loss) = Contribution Margin – Fixed Costs
- Contribution Margin per Unit = (Sales – Variable Costs) / Units Sold
- Variable Costs per Unit = Variable Expenses / Units Sold
Case A:
- Units Sold: 9,000
- Sales: $270,000
- Variable Expenses: $162,000
- Fixed Expenses: $90,000
- Contribution Margin (CM) = $270,000 – $162,000 = $108,000
- Contribution Margin per Unit = $108,000 / 9,000 = $12 per unit
- Net Income = $108,000 – $90,000 = $18,000
Case B:
- Sales: $350,000
- Variable Margin per Unit: $15
- Fixed Expenses: $170,000
- Net Income: $40,000
- Contribution Margin (CM) = (Sales – Variable Expenses)
- Variable Expenses = (Sales – Contribution Margin)
- Using the given Contribution Margin per unit, calculate the number of units:
[
\text{Units Sold} = \frac{350,000}{15} = 23,333 \, \text{units}
] - Variable Expenses = $15 * 23,333 = $350,000
- Net Income = $350,000 – $170,000 = $40,000 (confirming correctness)
Case C:
- Units Sold: 20,000
- Sales: $280,000
- Variable Costs per Unit: $6
- Fixed Expenses: We are given net income of $35,000.
- Total Variable Costs = $6 * 20,000 = $120,000
- Contribution Margin (CM) = $280,000 – $120,000 = $160,000
- Fixed Expenses = Contribution Margin – Net Income = $160,000 – $35,000 = $125,000
Case D:
- Units Sold: 5,000
- Sales: $100,000
- Variable Costs: $82,000
- Net Loss: $12,000
- Contribution Margin (CM) = $100,000 – $82,000 = $18,000
- Fixed Expenses = Contribution Margin – Net Loss = $18,000 – (-$12,000) = $30,000
Explanation:
The CVP analysis involves understanding the relationship between costs, volume, and profit. The key concept is the contribution margin (sales minus variable costs), which represents the portion of sales that contributes to covering fixed costs and generating profit. By manipulating these relationships, you can determine how changes in sales volume, pricing, or costs impact profitability.
In the cases, the contribution margin helps to calculate net income (or loss), by subtracting fixed expenses. This shows how well the business is performing and if it is at risk of making a loss or achieving profit at different sales volumes. Understanding this helps businesses in decision-making, such as adjusting sales prices, reducing variable costs, or changing fixed costs to optimize profits.