Calculate the break-even sale and quantity from the following figure: Material cost 20 per unit, other manufacturing cost 10, Fixed cost 20000 for 100% capacity, Sale price 50 per... Calculate the break-even sale and quantity from the following figure: Material cost 20 per unit, other manufacturing cost 10, Fixed cost 20000 for 100% capacity, Sale price 50 per unit. The company is running at 60% production capacity.
Understand the Problem
The question is asking to calculate the break-even sales and quantity for a company based on provided cost and pricing information. It involves understanding fixed costs, variable costs, and how they relate to sales and production capacity.
Answer
The break-even quantity is $ Q = \frac{F}{P - V} $.
Answer for screen readers
The break-even quantity is given by the formula: $$ Q = \frac{F}{P - V} $$
Steps to Solve
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Identify the Fixed Costs These are the costs that do not change with the level of production or sales. For example, if the fixed costs are given as $F$, note down this value.
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Identify the Variable Costs per Unit This is the cost that varies with each unit produced, denoted as $V$. If the problem provides the variable cost per unit, write it down.
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Identify the Selling Price per Unit This is the price at which each unit is sold, denoted as $P$. Again, if given, note this value.
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Set Up the Break-even Equation To find the break-even point, you need to set the total revenue equal to total costs. The equation can be written as: $$ P \cdot Q = F + V \cdot Q $$ where $Q$ is the quantity of units sold.
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Rearrange the Equation to Solve for Quantity (Q) You need to isolate $Q$ in the equation. To do this, rearrange the equation: $$ P \cdot Q - V \cdot Q = F $$ Factoring out $Q$ gives: $$ Q(P - V) = F $$
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Solve for Break-even Quantity (Q) Now, divide both sides by $(P - V)$ to find the break-even quantity: $$ Q = \frac{F}{P - V} $$
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Interpret the Break-even Quantity The value of $Q$ represents the number of units that need to be sold to cover all fixed and variable costs, achieving break-even.
The break-even quantity is given by the formula: $$ Q = \frac{F}{P - V} $$
More Information
The break-even point is crucial for business planning as it indicates how much product must be sold to cover costs. Understanding the break-even point helps businesses set sales targets and make strategic decisions.
Tips
- Misidentifying fixed and variable costs can lead to incorrect outcomes. Always ensure clarity about which costs are fixed and which are variable.
- Forgetting to subtract the variable cost from the selling price before dividing can result in an unrealistically low break-even quantity. Always use $P - V$ accurately.
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