# Cost-Volume-Profit (CVP) Analysis

Some things we know:

The objective of every business is to make money (profit) for the owners

Profit = Revenues – Expenses

Revenues = Sales = Quantity sold x price per unit

Expenses = the costs related to:

the specific revenue (COGS)

or the specific accounting period

Matching Principle

Role of Management is:

Planning, control and performance measurement, and decision-making

Decision-making relates to future events and involves risk

Full costing (full-absorption costing) is a good historical tool but may not

Be the best indicator of future activity because it is based on past events.

Cost Behavior

Variable Costs – total dollars change with volume, Cost per unit is constant

Fixed Costs – total dollars are constant, cost per unit changes with volume

Mixed Costs – include some variable costs and some fixed costs

Total Cost = Fixed Costs + Volume(variable cost per unit)

Fixed Component Variable Component

Purely Fixed $25,000$ 0

Purely Variable 0 5.00 per unit

Mixed Costs 10,000 2.00 per unit

Total Costs $35,000$7.00 per unit

Graphing Total Costs

X axis (horizontal/across) = volume

Y axis (vertical/up & down) = dollars

Estimating the Composition of Mixed Costs

Account Analysis

Scattergraph – Visual inspection of plotted points

High-Low Estimation

Theory: The change in total costs between the high volume point and

The low volume point, must be purely variable costs

Linear Regression (computer assisted scattergraph)

Contribution Margin Income Statement

Ignores the function of the expenses

Focus is on cost behavior (fixed and variable)

Used extensively in forecasting future potential outcomes (planning & decision making)

Because

Profit = Revenue – Expenses(Costs)

Where:

Revenue = Volume x price per unit

AndTotal Costs = Fixed Cost + (Volume x Variable cost per unit)

Therefore:

Volume x price per unit

Less Volume x variable cost per unit

Less Fixed costs

Profit

Revenue

Less Variable Costs

CONTRIBUTION MARGIN

Less Fixed Costs

Pretax Profit

KNOW THIS FORMULA FRONTWARDS AND BACKWARDS

Margin of Safety = the difference between the expected level of volume and the break-even point (normally using sales dollars but could also use units sold).

When comparing two or more alternatives it may be helpful to look at the Margin of Safety as a percentage of sales.

Contribution Margin Ratio = CM per unit / Selling Price per unit

OrContribution Margin / Sales

Operating Leverage = Fixed Costs / Contribution Margin

Or

Contribution Margin/Pretax Profit

Cost-Volume-Profit (CVP) Analysis

Break-Even Point = the point at which profit = zero (i.e. we break even)

= The point at which Contribution Margin = Fixed Costs

Once we know the break-even point, we can begin to plan for target profit

Target Pre Tax Profit versus Target After Tax Profit

Pretax Profit$100

Less Tax Expense 40

After Tax or Net Profit$ 60

Effective Tax Rate = Tax Expense / Pretax Profit(40% above)

Tax Expense = Pretax Profit x Effective Tax Rate

Net Income = Pretax Profit x (1- effective tax rate)

Pretax Profit = Net Profit / (1- effective tax rate)

Multiple Product CVP Analysis

Weighted-Average Contribution Margin (also referred to as blended average)

PRODUCT MIX IS CRITICAL

Product 1Product 2Total

Units Sold10020

Selling Price$10.00$50.00

Variable Costs 5.00$30.00

Sales$1,000$1,000$2,000

Contribution Margin 500$ 400 900

CM Ratio 50% 40% 45%

SO LONG AS THE PRODUCT MIX REMAINS AT 5:1 THE PROJECTED

CM RATIO WILL STAY AT 45%. Therefore if sales are expected to be $20,000, AND WE SELL 5 of Product 1 for every 1 unit of Product 2, Contribution...

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