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The concept of contribution margin is central to understanding break-even analysis and profitability. It refers to the amount by which the selling price of a product exceeds its total variable cost. In simple terms, it's the profit that contributes towards covering a company's fixed costs and eventually enables the realization of net income. For Brooke Motors, the selling price of a car is \(27,000, and the variable costs (purchase cost and commission) sum up to \)23,600.Thus, the contribution margin per car is calculated as:\[\text{Contribution Margin} = \\(27,000 - (\\)23,000 + \\(600) = \\)3,400\]This $3,400 is crucial because it helps to cover the fixed expenses and move towards profitability after achieving the break-even point. Understanding this margin helps Brooke Motors, and businesses alike, plan their sales targets and pricing strategies efficiently.

Fixed costs are expenses that don't vary with production or sales levels. Understanding and calculating these costs are vital as they lay the groundwork for determining a company’s break-even point. Unlike variable costs, fixed costs remain constant regardless of how many units are produced or sold.For Brooke Motors, the fixed costs include:

• Rent and utilities: \(48,200
• Salaries: \)68,000
• Advertisements: \(13,000

By adding these costs, the total fixed monthly costs are computed as:\[\text{Total Fixed Costs} = \\)48,200 + \\(68,000 + \\)13,000 = \$129,200\]Comprehending fixed costs helps Brooke Motors focus on covering these expenses through contribution margin from car sales before they can reach break-even or profitability.

Setting a target net income is an essential goal for many businesses, as it ultimately reflects the company's profitability aspirations. Before achieving the target net income, a business must first focus on generating enough operating income to cover taxes and all other expenses.In the case of Brooke Motors, their target monthly net income is \(51,000. To understand how this translates into operating income, we use the formula:\[\text{Operating Income} = \frac{\text{Net Income}}{1 - \text{Tax Rate}}\]Given Brooke's tax rate of 40%, the calculation is:\[\text{Operating Income} = \frac{\\)51,000}{1 - 0.40} = \\(85,000\]This means that before applying taxes, Brooke Motors needs to achieve an operating income of \)85,000. Knowing this helps in planning sales volume and managing expenses effectively.

Operating income is a measure of company profitability from its core business activities. It is calculated before interest and tax expenses, providing insight into how well a company is performing based on its day-to-day operations.For Brooke Motors, understanding the required operating income is crucial to meet their desired net income target. The target operating income is \(85,000, as calculated earlier. This value must be achieved after covering all fixed costs to then satisfy the company’s profit goals reflected in the net income.To determine how many cars need to be sold to reach this operating income, Brooke Motors uses the formula:\[\text{Cars for Target Income} = \frac{\text{Operating Income} + \text{Total Fixed Costs}}{\text{Contribution Margin}}\]Calculating gives:\[\frac{\\)85,000 + \\(129,200}{\\)3,400} \approx 63 \text{ cars}\]Thus, selling 63 cars a month will meet both the operating and net income targets, illustrating how operating income directly impacts sales strategy.