# 2.6 Chapter Summary

## Key Concepts

• 2.1 Cost-Volume-Profit Terminology
• The different types of costs.
• How to determine the unit variable cost.
• Explanation of break-even analysis.
• 2.2 Revenue and Cost Functions
• Calculating the net income using the revenue and cost functions.
• Calculating the break-even point using the revenue and cost functions.
• 2.3 Contribution Margin
• Calculating the contribution margin.
• Calculating the net income using the contribution margin.
• Calculating the break-even point using the contribution margin.
• 2.4 Contribution Rate
• Calculating the contribution rate.
• Calculating the net income using the contribution rate.
• Calculating the break-even revenue using the contribution rate.

## Glossary of Terms

• Break-Even Analysis.  An analysis of the relationship between costs, revenues, and net income with the sole purpose of determining the point at which total revenue equals total cost.
• Break-Even Point. A quantity that represents the level of output (in units or dollars) at which all costs are paid but no profits are earned, resulting in a net income equal to zero.
• Contribution Margin. The amount each unit sold adds to the net income of the business.
• Contribution Rate. A contribution margin expressed as a percentage of the selling price.
• Cost. An outlay of money required to produce, acquire, or maintain a product, which includes both physical goods and services.
• Economies of Scale. The principle that, as production levels rise, per-unit variable costs tend to become lower as efficiencies are achieved.
• Fixed Cost.  A cost that does not change with the level of production or sales.
• Net Income. The amount of money left over after all costs are deducted from all revenues.
• Selling Price. The amount the business charges its customers to purchase one unit of an item produced.
• Total Cost. The sum of all costs for the company, including both the total fixed costs and total variable costs.
• Total Fixed Cost.  The sum of all fixed costs that a business incurs.
• Total Revenue. The entire amount of money received by a company for selling its product, calculated by multiplying the quantity sold by the selling price.
• Total Variable Cost. The sum of all variable costs that a business incurs at a particular level of output.
• Unit Variable Cost. The assignment of total variable costs on a per-unit basis.
• Variable Cost.  A cost that changes with the level of production or sales.

## Formulas

• ### Symbols Used

• $CM$ = contribution margin
• $CR$ = contribution rate
• $NI$ = net income
• $S$ = selling price per unit
• $FC$ = fixed costs
• $TC$ = total cost
• $TR$ = total revenue
• $TVC$ = total variable cost
• $VC$ = variable cost per unit
• $x$ = number of units
• ### Formulas Used

• Unit Variable Cost: $\displaystyle{VC=\frac{TVC}{x}}$
• Total Costs: $\displaystyle{TC=FC+VC \times x}$
• Total Revenue: $\displaystyle{TR=S \times x}$
• Net Income:  $\displaystyle{NI=S\times x-(FC+VC \times x)}$
• Contribution Margin:  $\displaystyle{CM=S-VC}$
• Net Income:  $\displaystyle{NI=CM \times x-FC}$
• Number of Units Sold:  $\displaystyle{\mbox{Number of Units Sold}=\frac{FC+NI}{CM}}$
• Break-Even Point:  $\displaystyle{\mbox{Break-Even Point}=\frac{FC}{CM}}$
• Contribution Rate:  $\displaystyle{CR=\frac{CM}{S} \times 100\%}$
• Contribution Rate:  $\displaystyle{CR=\frac{TR-TVC}{TR} \times 100\%}$
• Total Revenue: $\displaystyle{TR=\frac{FC+NI}{CR}}$
• Break-Even Revenue:  $\displaystyle{\mbox{Break-Even Revenue}=\frac{FC}{CR}}$