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### Cost-Volume-Profit Analysis

Chapter 19

Types of Costs

- The effect of volume of activity on costs
- Variable costs
- Increase or decrease in total in direct proportion to changes in the volume of activity
- Fixed costs
- Do not change over wide ranges of volume
- Mixed costs
- Have both variable and fixed components

Variable Costs

- Total variable costs change in direct proportion to changes in the volume of activity
- If activity increases, so does the cost
- Unit variable cost remains constant
- Volume can be measured in many different ways:
- Number of units sold
- Number of units produced
- Number of miles driven by a delivery vehicle
- Number of phone calls placed

Fixed Costs

- Tend to remain the same in amount, regardless of variations in level of activity
- Examples:
- Straight-line depreciation
- Salaries
- Total fixed costs do not change, but the fixed cost per event depends on the number of events
- The more activity, the less the fixed cost per unit

Mixed Costs

- Have both a fixed and variable component
- Example:
- Utilities that charge a set fee per month, plus a charge for usage
- Your cell phoneprovider

High-Low Method

- Method to separate mixed costs into variable and fixed components
- Identify the highest and lowest levels of activity over a period of time
- STEP 1: Calculate variable cost per unit
- STEP 2: Calculate total fixed cost
- STEP 3: Create and use equation to show the behavior of a mixed cost

Variable cost per unit = Change in total cost ÷ Change in activity volume

Total fixed cost = Total mixed cost – Total variable cost

Total mixed cost = (Variable cost per unit X number of units) + Total fixed costs

High-Low Method: Steps 1 and 2

- Data
- Step 1
- Step 2

Step 3

($2 x 400 event-playing hours) + $1,000 = $1,800

Now check your formula against the original data

($2 x 480 + $1000 = $1960) or($2 x 240 + $1,000 = $1480)

Relevant Range

- Range of volume:
- Where total fixed costs remain constant and variable cost per unit remains constant
- Outside the relevant range, costs can differ

S19-1: Variable, fixed, and mixed costs

- Philadelphia Acoustics builds innovative speakers for music and home theater systems. Consider the following costs. Identify the costs as variable (V), fixed (F), or mixed (M).

V

V

F

M

V

S19-1: Variable, fixed, and mixed costs

- Philadelphia Acoustics builds innovative speakers for music and home theater systems. Consider the following costs. Identify the costs as variable (V), fixed (F), or mixed (M).

F

V

M

V

F

S19-3: Mixed costs—high-low method

Martin owns a machine shop. In reviewing his utility bill for the last 12 months, he found that his highest bill of $2,800 occurred in August when his machines worked 1,400 machine hours. His lowest utility bill of $2,600 occurred in December when his machines worked 900 machine hours.

- Calculate (a) the variable rate per machine hour and (b) Martin’s total fixed utility cost.

Variable cost per unit = Change in total cost ÷ Change in activity volume

a. Variable cost per unit = ($2,800 - $2,600) ÷ (1,400 – 900)

Variable cost per unit = $200 ÷ 500 = 0.40 per machine hour

b. Total fixed cost = Total mixed cost – Total variable cost

Total fixed cost = $2,800 – (0.40 X 1,400)

Total fixed cost = $2,800 - $560

Total fixed cost = $2,240

S19-3: Mixed costs—high-low method

Martin owns a machine shop. In reviewing his utility bill for the last 12 months, he found that his highest bill of $2,800 occurred in August when his machines worked 1,400 machine hours. His lowest utility bill of $2,600 occurred in December when his machines worked 900 machine hours.

2. Show the equation for determining the total utility cost for Martin’s.

$ 0.40 per machine hour + $2,240

3. If Martin’s anticipates using 1,200 machine hours in January, predict his total utility bill using the equation from Requirement 2.

($ 0.40 per machine hour x 1,200 machine hours) + $2,240

$480 +$2,240 = $2,720

Basic CVP Analysis

- Expresses the relationships among costs, volume, and profit or loss
- Answers:
- How many products or services must the company sell to break even?
- What will profits be if sales double?
- How will changes in selling price, variable costs, or fixed costs affect profits?

Basic CVP Analysis

- Assumptions:
- Managers can classify each cost as either variable or fixed
- Only factor that affects total costs is change in volume, which increases variable and mixed costs
- Fixed costs do not change

Breakeven Point

- Sales level at which operating income is zero:
- Total revenues equal total costs (expenses)
- Sales above breakeven result in a profit
- Sales below breakeven result in a loss

Breakeven Point

- Two methods to compute breakeven point:
- Income statement approach
- Sales revenue − Total costs = Operating income
- Contribution margin approach
- Sales revenue – Variable costs = Contribution margin – Fixed costs = Operating income

Break Even Example Data

- Unit sale price
- Unit variable cost
- Fixed costs
- Unit contribution margin

- $200
- $80
- $12,000
- $120 ($200 - $80)

Income Statement Approach

- Express income in equation form and then break it down into its components:

Contribution Margin Approach

- Shortcut method
- The contribution margin is sales revenue minus variable costs (expenses)
- Called contribution margin because the excess of sales revenue over variable costs contributes to covering fixed costs

- Rearrange the income statement—use the contribution margin to develop a shortcut method
- Shortcut equation:

Contribution Margin Approach

- Given fixed costs total $12,000. The contribution margin per event is $120 ($200 sale price – $80 variable cost)
- Check your answer

Contribution Margin Ratio

- Ratio of contribution margin to sales revenue
- Used to compute the breakeven point in terms of sales dollars
- Contribution margin is equal to:
- Sales price – variable cost
- Contribution margin divided by sales revenue yields a percentage
- Percentage of each dollar of sales revenue that contributes toward fixed costs and profit

Contribution Margin Ratio

- Formula:
- Example:
- Yields the same breakeven as the contribution margin approach earlier

Unit CM $120Unit Sale Price $200

S19-4: Computing breakeven point in sales units

Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month.

1. Compute the number of tickets Story must sell to break even. Perform a numerical proof to show that your answer is correct.

Units sold = ($240,000 + 0) ÷ ($50 - $10)

Units sold = $240,000 ÷ $40

= 6,000 units to breakeven

S19-4: Computing breakeven point in sales units

Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month.

1. Compute the number of tickets Story must sell to break even. Perform a numerical proof to show that your answer is correct.

- Total sales revenue $300,000 (6,000 x 50)
- Variable cost 60,000 (6,000 x 10)
- Contribution margin $240,000
- - Fixed cost 240,000
- Operating income $ 0

S19-5: Computing breakeven point in sales dollars

Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month.

1. Compute Story Park’s contribution margin ratio. Carry your computation to two decimal places.

$50 - $10 = $40

$40 ÷ $50 = 0.80 or 80%

2. Use the contribution margin ratio CVP formula to determine the sales revenue Story Park needs to break even.

$240,000 ÷ 0.80 = $300,000

Use CVP analysis for profit planning, and graph the CVP relations

Using CVP to Plan Profits

- Managers more interested in:
- Sales level needed to earn a target profit
- Profits they can expect to earn
- How many products or service events must be sold to earn a specific operating profit
- Use either method (equation or CM)
- Set operating profit equal to desired profit

Graphing Cost-Volume-Profit Relations

- Graph provides a picture that shows how changes in the levels of sales will affect profits
- Four steps:
- Choose a sales volume and plot the point for total sales revenue at that volume
- Draw the fixed cost line
- Draw the total cost line (total costs are the sum of variable costs plus fixed costs)
- Identify the breakeven point and the areas of operating income and loss

S19-6: Computing contribution margin, breakeven point, and units to achieve operating income

Consider the following facts:

S19-6: Computing contribution margin, breakeven point, and units to achieve operating income

Consider the following facts:

$72,000/$60

($72,000 + $180,000)/$60

Sensitivity Analysis

- Predict how changes in sale prices, cost, or volume affect profits
- “What-if?” analysis
- Allows managers to see how various business strategies affect profits
- Changing selling price
- Changing variable Costs
- Changing fixed Costs

Sensitivity Analysis: Example

- How will the lower sale price affect the breakeven point?
- Lower price yields higher unit sales to breakeven
- Higher prices yields lower unit sales to breakeven

Sensitivity Analysis: Example

- How will increased costs affect the breakeven point?
- Higher cost yields higher unit sales to breakeven
- Lower cost yields lower unit sales to breakeven

Sensitivity Analysis: Example

- How will the increased fixed costs affect the breakeven point?
- Higher fixed costs yields higher unit sales to breakeven
- Lower fixed costs yields lower unit sales to breakeven

Sensitivity Analysis Summary

- Exhibit 19-6

Margin of Safety

- Excess of expected sales over breakeven sales
- Cushion, drop in sales, a company can absorb without incurring a loss
- Margin of safety in units
- Margin of safety in dollars

S19-7: Sensitivity analysis of changing sale price and variable costs on breakeven pointStory Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month.

1. Suppose Story Park cuts its ticket price from $50 to $40 to increase the number of tickets sold. Compute the new breakeven point in tickets and in sales dollars.

Units sold = ($240,000 + 0) ÷ ($40 - $10)

Units sold = $240,000 ÷ $30

= 8,000 units to breakeven

$320,000 sales dollars to breakeven

Old Breakeven 6,000 units, $300,000

S19-7: Sensitivity analysis of changing sale price and variable costs on breakeven pointStory Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month.

2. Ignore the information in Requirement 1. Instead, assume that Story Park increases the variable cost from $10 to $20 per ticket. Compute the new breakeven point in tickets and in sales dollars.

Units sold = ($240,000 + 0) ÷ ($50 - $20)

Units sold = $240,000 ÷ $30

= 8,000 units to breakeven

= $400,000 in sales dollars

S19-9: Computing margin of safetyStory Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month.

1. If Story Park expects to sell 6,200 tickets, compute the margin of safety in tickets and in sales dollars.

Expected sales - Breakeven sales = Margin of safety in units

6,200 – 6,000 = 200 in units

Margin of safety in units x Sales price = Margin of safety in dollars

200 units x $50 = $10,000

Breakeven Point Multiple Product Lines

- Selling prices and variable costs differ for each product
- Different contribution to profits
- Weighted-average contribution margin computed
- Sales mix provides weights to make up total product sales
- Weights equal 100% of total product sales

Steps for Computing Breakeven Point with Multiple Product Lines

- To compute breakeven sales in units for multiple products, complete the following three steps:
- STEP 1: Calculate the weighted-average contribution margin per unit
- STEP 2: Calculate the breakeven point in units for the “package” of products
- STEP 3: Calculate the breakeven point in units for each product and then multiply the “package” breakeven point in units by each product’s proportion of the sales mix

Step 1

- Calculate the weighted-average contribution margin per unit:

Step 2

- Calculate the breakeven point in units for the “package” of products:

Step 3

- Calculate the breakeven point in units for each product. Multiply the “package” breakeven point in units by each product’s proportion of the sales mix:

Proof

- Prove this breakeven point by preparing a contribution margin income statement:

S19-10: Calculating weighted-average contribution margin

Wet Weekend Swim Park sells individual and family tickets, which include a meal, three beverages, and unlimited use of the swimming pools. Wet Weekend has the following ticket prices and variable costs for 2012:

Wet Weekend expects to sell two individual tickets for every four family tickets. Wet Weekend’s total fixed costs are $75,000.

1. Compute the weighted-average contribution margin per ticket.

2. Calculate the total number of tickets Wet Weekend must sell to break even.

3. Calculate the number of individual tickets and the number of family tickets the company must sell to break even.

S19-10: Calculating weighted-average contribution margin

Wet Weekend expects to sell two individual tickets for every four family tickets. Wet Weekend’s total fixed costs are $75,000.

1. Compute the weighted-average contribution margin per ticket.

S19-10: Calculating weighted-average contribution margin

2. Calculate the total number of tickets Wet Weekend must sell to break even.

3. Calculate the number of individual tickets and the number of family tickets the company must sell to break even.

$75,000 ÷ $25 = 3,000 total tickets

3,000 total tickets x 2/6 = 1,000 individual tickets

3,000 total tickets x 4/6 = 2,000 family tickets

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