Here's an explanation of Cost-Volume-Profit (CVP) Analysis: Step 1: Cost-Volume-Profit (CVP) Analysis CVP analysis is a management accounting tool that examines the relationships between costs, sales volume, and profit. It helps businesses understand how changes in these three factors impact profitability and aids in decision-making regarding pricing, production levels, and cost structures. Step 2: Break-even Point (BEP) The Break-even Point (BEP) is the level of sales (in units or revenue) at which total revenues equal total costs, resulting in zero net profit or loss. It's a critical metric for businesses to determine the minimum sales required to cover all expenses. To calculate the Break-even Point in units: $$ \text{BEP (units)} = \frac{\text{Fixed Costs}}{\text{Contribution Margin per Unit}} $$ Where: $$ \text{Contribution Margin per Unit} = \text{Selling Price per Unit} - \text{Variable Cost per Unit} $$ Step 3: Margin of Safety The Margin of Safety is the difference between actual or expected sales and the break-even sales. It indicates how much sales can decline before the company starts incurring a loss, providing a measure of risk. A higher margin of safety suggests a lower risk of not breaking even. To calculate the Margin of Safety: $$ \text{Margin of Safety} = \text{Actual Sales} - \text{Break-even Sales} $$ This can be expressed in units, sales revenue, or as a percentage. Step 4: Example to determine units for a particular Profit / Sale Let's assume a company has the following data: Fixed Costs = $\$10,000$ Selling Price per Unit = $\$50$ Variable Cost per Unit = $\$30$ Target Profit = $\$5,000$ First, calculate the Contribution Margin per Unit: $$ \text{Contribution Margin per Unit} = \$50 - \$30 = \$20 $$ Next, use the formula to find the number of units needed to achieve the target profit: $$ \text{Units for Target Profit} = \frac{\text{Fixed Costs} + \text{Target Profit}}{\text{Contribution Margin per Unit}} $$ Substitute the values: $$ \text{Units for Target Profit} = \frac{\$10,000 + \$5,000}{\$20} $$ $$ \text{Units for Target Profit} = \frac{\$15,000}{\$20} $$ $$ \text{Units for Target Profit} = 750 \text{ units} $$ To achieve a target profit of $\$5,000$, the company needs to sell $\boxed{\text{750 units}}$.