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

  • [latex]CM[/latex] = contribution margin
  • [latex]CR[/latex] = contribution rate
  • [latex]NI[/latex] = net income
  • [latex]S[/latex] = selling price per unit
  • [latex]FC[/latex] = fixed costs
  • [latex]TC[/latex] = total cost
  • [latex]TR[/latex] = total revenue
  • [latex]TVC[/latex] = total variable cost
  • [latex]VC[/latex] = variable cost per unit
  • [latex]x[/latex] = number of units

• Formulas Used

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

Attribution

“Chapter 5 Summary” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.