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Cost-Volume-Profit (CVP) Analysis

• CVP analysis helps answer questions like how much to sell to reach a desired income, the impact of price reductions on income, or the effect of capacity expansion on profitability.

Cost-Volume-Profit Relationships

• CVP analysis helps answer questions like how much to sell to reach a desired income, the impact of price reductions on income, or the effect of capacity expansion on profitability.

Fixed Costs

• Total fixed costs remain constant as activity increases.
• Cost per call declines as activity increases.

Variable Costs

• Total variable costs increase as activity increases.
• Cost per minute is constant as activity increases.

Semivariable Costs (Mixed Costs)

• Mixed costs include both fixed and variable components, with a fixed portion incurred even when the facility is unused.
• Monthly electric utility charges are an example of mixed costs, including a fixed service fee and a variable charge per kilowatt-hour used.

CVP Relationships: A Graphical Analysis

• To graphically analyze CVP relationships, first draw the total revenue line from the origin, with a slope equal to the unit sales price.
• Next, add a horizontal line representing total fixed costs horizontally from the vertical axis
• Finally, draw the total cost line with a slope equal to the unit variable cost.

Cost Behavior Summary

• Per unit, variable costs stay the same even when activity changes, while fixed costs decrease as activity increases.
• In the aggregate, variable costs change when activity levels change, and fixed costs stay the same over a wide range of activity

Economies of Scale

• Economies of scale are more apparent for businesses with high proportion of fixed costs.
• Utility companies, oil refineries, and steel mills exemplify businesses with high fixed costs.
• For an automobile plant, fixed costs of $8,400,000 per month results in fixed cost per unit of $2,100 with 4,000 cars produced, $1,400 at 6,000 cars, and $1,200 at 7,000 cars.

Semivariable Costs

• Total semivariable costs remain constant within a narrow range of activity.
• Total semivariable costs increase to a new, higher cost for the next higher range of activity.

Curvilinear Costs

• Over a relevant range, a straight line can approximate a curvilinear variable cost line.

Computing Break-Even Point

• The break-even point is the sales level where a company neither earns a profit nor incurs a loss, expressed in units or dollars.
• Company sales revenue: $81,000 (900 units), Unit: $90
• Less: Variable costs: $32,400, Unit: $36
• Contribution margin: $48,600, Unit: $54
• Less: Fixed costs: $37,800
• Operating income: $10,800
• Contribution margin is the amount by which revenue exceeds the variable costs of producing the revenue.

How Many Units Must We Sell?

• To cover fixed costs (break-even), the SnowGlide example is $37,800 ÷ $54 per unit = 700 units.
• Break-even point in units = Fixed costs / Contribution margin per unit
• Contribution margin = unit sales price less unit variable cost
• In the SnowGlide example, ($90 – $36 = $54)

Computing Break-Even Units

• ABC Co. sells product XYZ at $5.00 per unit.
• If fixed costs: $200,000 + Variable costs: $3.00 per unit, 100,000 units must be sold to break even.
• Unit contribution: $5.00 - $3.00 = $2.00
• Fixed Costs / Unit contribution = $200,000 / $2.00 per unit = 100,000 units

How Many Dollars in Sales Must We Generate?

• The break-even formula can be expressed in sales dollars.
• Break-even point in dollars = Fixed costs / Contribution margin ratio
• Contribution margin ratio = Unit contribution margin / Unit sales price
• SnowGlide must generate $63,000 in sales to cover its fixed costs (break even) with fixed costs of $37,800 and 60% Contribution margin.

Computing Break-Even Sales

• To determine the amount of sales revenue ABC must have to break even use contribution margin ratio formula.
• Fixed costs are $200,000 = Unit sales price: $5.00 and Unit variable cost: $3.00 Calculations:
• Unit contribution = $5.00 - $3.00 = $2.00, Contribution margin ratio = $2.00 ÷ $5.00 = .40
• Break-even revenue: $200,000 ÷ .4 = $500,000

Computing Sales Needed to Achieve Target Operating Income

• Break-even formulas are adjusted to show the sales volume needed to earn any amount of operating income.
• The formula for Unit sales= Fixed costs + Target income / Contribution margin per unit
• The formula for Dollar sales= Fixed costs + Target income / Contribution margin ratio

Computing Sales Needed to Achieve Target Operating Income continued

• Using the previous SnowGlide examples
• Unit sales =Fixed costs + Target income / Contribution margin per unit= $37,800 + $5,400 / $54 = an output of 800 units per month.
• If looking to earn $5,400 monthly operating income, what sales volume (in dollars) should be earned?
• Dollar sales = Fixed costs + Target income / Contribution margin ratio = $37,800 + $5,400 / 60% = $72,000 per month

Computing Sales Needed to Achieve Target Operating Income

• ABC Co. sells product XYZ at $5.00 per unit.
• If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operatingincome of $40,000?
• Unit contribution: = $5.00 - $3.00 = $2.00
• Fixed costs + Target income / Unit contribution is $200,000 + $40,000 / $2.00 per unit = 120,000 units

What is Our Margin of Safety?

• Margin of safety is the amount sales may decline before break-even sales are reached. Formula is: Actual sales - Break-even sales Examples for snow-glide:
• $9,000 Margin of Safety = $72,000 - $63,000
• The Margin of safety estimates operating income at any level of sales
• Operating Income = Margin of safety × Contribution margin ratio

For SnowGlide, these numbers result in:

• $9,000 x 60% = $5,400 operating income.

What Change in Operating Income Do We Anticipate?

• Once break-even is reached, every additional dollar of contribution margin becomes operating income.
• Formula: Change in operating income= Change in sales volume × Contribution margin ratio
• To continue the SnowGlide example sales are expected to increase by $5,000 and has a contribution margin ratio of 60%.
• The operating income increase= $5,000 × .60 = $3,000

Business Applications of CVP

• Sales (900 boards):Total is $81,000, Per Unit: $90, Percent: 100%
• Less: variable expenses: Total is $32,400, Per Unit: $36, Percent: 40%
• Contribution margin: Total is $48,600, Per Unit: $54, Percent: 60%
• Less: fixed expenses: $37,800
• Operating income: $10,800

Business Applications of CVP

• Using these figures:
• Should SnowGlide spend $1,500 on advertising to increase sales by 500 boards?
• Sales (1,400 boards): Total is $126,000, Per Unit: $90, Percent: 100%
• Less: variable expenses: Total is $50,400, Per Unit: $36, Percent: 40%
• Contribution margin: Total is $75,600, Per Unit: $54, Percent: 60% Less: fixed expenses: 39,300, Operating income $36,300

Business Applications of CVP

• Using these figures:
• Overtime work will increase direct labor costs: $1.80 per unit
• Sales volume in units required to achieve advertising director's projected monthly income figure:
• New Unit Contribution Margin= Selling Price - Unit Variable Cost = $90.00 - ($36.00 + $1.80) = $52.20
• Projected Unit Sales= (Fixed Costs + Target Operating Income) / Unit contribution Margin = ($39,300 + $36,300) / $52.20 = output of 1,448 units/month

Business Applications of CVP

• The sales VP thinks a conservative goal is 350 increase units per month:
• What selling prices achieve a target monthly income figure of $36,300?
• Projected Unit Sales =Fixed Costs + Target Op. Income/ Contribution Margin Per unit Calculations:
• 1,250 units = $39,300 + $36,300 / Contribution Margin per unit
• Contribution Margin per Unit: $60.48
• Unit Contribution Margin= Unit Selling Price - Unit Variable Cost
• $60.48 = Unit Selling Price - $37.80, Unit Selling Price = $98.28

Complying with the assumptions of CVP analysis:

• Different products with different contribution margins.
• Determining semivariable cost elements.
• Complying with the assumptions of CVP analysis

CVP Analysis When a Company Sells Many Products

• Sales mix refers to the relative combination in which a company's different products are sold.
• Each product different selling prices, costs, and contribution margins.
• If SnowGlide sells snowboards and goggles, it greatly effects the break-even analysis.

CVP Analysis When a Company Sells Many Products

• SnowGlide Product information: Product| Product CM Ratio | X | % of Sales
• --|---|---|---| Snowboards | 60% | X| 90% Goggles| 80% | X | 10% Average Contribution Margin Ratio = 62%

Improving the Quality of the Sales Mix

• Increasing focus on goggles because they have a higher contribution margin ratio than snowboards.
• A business can improve its average contribution ratio and profitability, by increasing products with high contribution margin ratios.

Determining Semivariable Cost Elements: The High-Low Method

• SnowGlide Data: production activity and maintenance costs for two months.
• High activity level| Units 950 | Cost $25,280
• Low activity level |Units 850 | Cost $25,040
• Change | Units 100 | Cost $240 Calculations:
• The variable cost per unit, total fixed cost and total cost formula needs to be calculated.

Determining Semivariable Cost Elements: The High-Low Method

• Using the Snow-glide data: (1) Unit variable cost- $240 ÷ 100 units= $2.40 per unit (2) Fixed cost= Total cost − Total variable cost Fixed cost: $25,280 - ($2.40 × 950 units) (3) Fixed cost: $25,280 – $2,280 = $23,000, Total cost= $23,000 + $2.40 per unit

The High-Low Method

• Example information
• Sales commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold
• Calculate the variable portion of sales commission per unit sold.
• Unit sales:
• High level 120,000: $ 14,000
• Low level 80,000: $ 10,000, Change 40,000: $ 4,000 Calculations: $4,000 ÷ 40,000 units = $0.10 per unit

The High-Low Method - continued

• Calculate the fixed portion of the sales commission?, with commission calculated here
• Unit sales:
• High level 120,000: $ 14,000
• Low level 80,000: $ 10,000, Change 40,000: $ 4,000
• Total cost= Total fixed cost + Total variable cost for High commissions Calculations: Formula:
• $14,000 =Total fixed cost + ($.10 x 120,000 units) Total fixed cost ( $14,000 -$12,000 = $2,000

Assumptions Underlying CVP Analysis

• A limited range of activity in relevant range
• Unit selling price is consistent
• Sales Mix stays the same
• Production = Sales

Ethics, Fraud, and Corporate Governance

• Some industries, like the airline industry high fixed costs tied to investments in equipment.
• The Sarbanes-Oxley Act requires public disclosure of material changes in fixed costs occurs.