Other Formulas Needed Outside Of The Reading Material
Other Formulas Needed Outside Of The Reading Materialsales Variable
Other formulas needed outside of the reading material: Sales = Variable expenses + Fixed expenses + Profit
Sales = Quantity * Units
Profit = (Sales – CM ratio) – Fixed Cost
Review Problems : Contribution margin and ratio
Problem 1: (10 points)
Sales per unit = $250
Variable Cost per unit = $150
Units = 350
a) Calculate Contribution Margin Per Unit (2 points)
b) Calculate Contribution Margin (CM) Ratio Per Unit (3 points)
c) Calculate Total Contribution Margin (CM) Dollars (5 points)
Problem 2: (5 points)
Sales = $5,000,000
CM Ratio = 0.40
Fixed cost = $1,600,000
Calculate Profit.
Problem 3: (5 points)
A company has budgeted sales of $200,000, a profit of $60,000, and fixed expenses of $40,000.
Calculate contribution margin ratio.
Review Problem : Break-even point
Problem 4: (15 points)
Voltar Company manufactures and sells a telephone answering machine. The company's contribution format income statement for the most recent year is given below:
Total | Per unit | Pct. of sales (Ratios)
Sales | $1,200,000 | $60 | 100%
Less variable expenses | $900,000 | $45 | ?%
Contribution margin | $300,000 | $15 | ?%
Less fixed expenses | $240,000 | — | —
Net operating income | $60,000 | — | —
a) What is the Contribution Margin (CM) Ratio (or percent of sales)? (5 points)
b) Calculate break-even point both in total units and total sales dollars. (10 points)
Problem 5: (15 points)
Management is anxious to improve the company's profit performance.
Assume that next year management wants the company to earn a minimum profit of $90,000. How many units will have to be sold to meet the target profit figure?
Paper For Above instruction
The objective of this paper is to analyze various financial formulas and ratios related to contribution margin, break-even analysis, and profit planning, based on the provided review and practice problems. These fundamental financial metrics are essential for managerial decision-making and maintaining the financial health of a business. This discussion will include detailed calculations and interpretations for each of the specified problems, emphasizing the application of contribution margin concepts, break-even points, and profit target attainment.
Contribution Margin and Ratios
Contribution margin (CM) represents the amount remaining from sales revenue after variable expenses are deducted. It contributes towards covering fixed expenses and generating profit. The contribution margin per unit is calculated as:
\[ \text{CM per unit} = \text{Sales price per unit} - \text{Variable cost per unit} \]
Given the data in Problem 1, the sales per unit are $250, and the variable cost per unit are $150. Therefore:
\[ \text{CM per unit} = 250 - 150 = 100 \]
The contribution margin ratio (CM ratio) reflects the portion of sales that contributes to covering fixed costs and profits, and it is calculated as:
\[ \text{CM Ratio} = \frac{\text{Contribution Margin per unit}}{\text{Sales per unit}} \]
Using the figures:
\[ \text{CM Ratio} = \frac{100}{250} = 0.40 \text{ or } 40\% \]
Total contribution margin in dollars is the product of total sales and CM ratio:
\[ \text{Total CM} = \text{Sales} \times \text{CM Ratio} \]
Since the units sold are 350:
\[ \text{Sales} = 350 \times 250 = 87,500 \]
\[ \text{Total CM} = 87,500 \times 0.40 = 35,000 \]
Alternatively, directly calculating from contribution margin per unit:
\[ \text{Total CM} = 350 \times 100 = 35,000 \]
Profit Calculations
For Problem 2, with sales of $5,000,000 and a CM ratio of 0.40:
\[ \text{Total CM} = 5,000,000 \times 0.40 = 2,000,000 \]
Subtracting fixed costs:
\[ \text{Profit} = \text{Total CM} - \text{Fixed Costs} = 2,000,000 - 1,600,000 = 400,000 \]
In Problem 3, given sales of $200,000, profit of $60,000, and fixed expenses of $40,000, the contribution margin ratio is calculated as:
\[ \text{CM Ratio} = \frac{\text{Sales} - \text{Fixed expenses} - \text{Profit}}{\text{Sales}} \]
However, more straightforwardly, since:
\[ \text{Profit} = \text{Total CM} - \text{Fixed Expenses} \]
and
\[ \text{Total CM} = \text{Sales} \times \text{CM Ratio} \]
rearranged as:
\[ \text{CM Ratio} = \frac{\text{Total CM}}{\text{Sales}} \]
But since we know profit:
\[ \text{Total CM} = \text{Profit} + \text{Fixed Expenses} = 60,000 + 40,000 = 100,000 \]
Thus:
\[ \text{CM Ratio} = \frac{100,000}{200,000} = 0.50 \text{ or } 50\% \]
Break-Even Analysis
The break-even point is the level of sales where total contribution margin equals fixed expenses, resulting in zero profit. Using the data from Problem 4, the total contribution margin is $300,000, and fixed expenses are $240,000.
a) Contribution Margin Ratio:
\[ \text{CM Ratio} = \frac{\text{Contribution Margin}}{\text{Sales}} = \frac{300,000}{1,200,000} = 0.25 \text{ or } 25\% \]
b) Break-even sales in units:
\[ \text{Sales per unit} = \$60 \]
\[ \text{Total fixed expenses} = \$240,000 \]
\[ \text{Units needed} = \frac{\text{Fixed expenses}}{\text{Contribution margin per unit}} = \frac{240,000}{15} = 16,000 \text{ units} \]
Break-even sales in dollars:
\[ 16,000 \text{ units} \times 60 = \$960,000 \]
or directly:
\[ \text{Sales dollars} = \frac{\text{Fixed expenses}}{\text{CM ratio}} = \frac{240,000}{0.25} = \$960,000 \]
Profit Target Computation
For Problem 5, to achieve a target profit of $90,000, the company must determine the sales volume in units necessary. Using the contribution margin per unit of $15 and the CM ratio 0.25:
\[ \text{Required contribution margin} = \text{Fixed expenses} + \text{Target profit} \]
\[ \text{Fixed expenses} = \text{Total fixed costs} \]
Assuming fixed costs are consistent with earlier data ($240,000), the total contribution margin needed:
\[ 240,000 + 90,000 = 330,000 \]
In units:
\[ \text{Units} = \frac{330,000}{15} = 22,000 \text{ units} \]
Alternatively, sales dollars:
\[ \text{Sales} = \frac{\text{Total contribution margin needed}}{\text{CM ratio}} = \frac{330,000}{0.25} = \$1,320,000 \]
This sales level in units ensures the company attains the target profit.
Conclusion
Mastering these contribution margin formulas, break-even points, and profit analysis enables managers to make strategic decisions regarding pricing, production, and sales targets. Accurate calculations and interpretations ensure continuous financial health and profitability in competitive markets.
References
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