# Cost Volume Profit

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 Margin should be \$9,000 (\$20,000 x 45%)

However if sales of Product 1 are only \$1,000 and the remaining \$19,000 are sales of Product 2 the Contribution margin is only \$8,100 and the CM Ratio drops to 40.5%.

\$ 1,000 x 50% = \$ 500
plus\$19,000 x 40% = \$7,600
\$20,000 \$8,100 = 40.5% of sales

or (1/20 x .50) + (19/20 x .40)
.025 + .38 = 40.5%

When computing the Weighted-Average Contribution Margin USE SALES DOLLARS as the weighing factor (NOT UNITS).

Constraint = a limitation of resources

To maximize profits given a limited resource, produce the product that generates the highest contribution margin per limited resource. This may not be the product with the highest contribution margin ratio.

Illustration: A company manufactured two types of beer, premium and regular. Both types of beer are brewed in the same kettles. A regular batch brews for 15 days and yields 12,000 bottles. A premium batch brews for 30 days and yields 12,000 bottles. Regular beer sells for \$1.00 per bottle and has variable costs of \$0.40 per bottle. The premium sell for \$1.50 per bottle and has variable costs of \$0.50 per bottle. Assuming unlimited demand of both products, which product should the company brew?

Per Batch:
Sales\$15,000\$12,000
CM\$12,000\$ 7,200
CM % 66.67% 60.00%

CM per Limited Resource (Days)
CM\$12,000\$ 7,200
Divided by days 30 15
CM per day of limited
Resource use \$400 \$480

Regular beer has a higher CM per limited resource.
Therefore, given unlimited demand of both types, produce only regular.

Proof: In 30 days we can make one batch of premium, which will yield \$12,000 in CM. In the same 30 days we can make 2 batches of regular, which will yield \$14,400 in CM.

We are in business to make money for the owners, not percentages. You can’t deposit percentages in the bank!