lecture 4 the nature of costs

The Nature of Costs

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20-8Volume in Units

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Break-evenPoint

Profit

Loss

CVP Relationships : A Graphical Analysis

Fixed Costs: The cost when there is no production.

Variable cost: The cost of producing one additional unit at any given production level.

Cost Definitions

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Price does not change with quantity. Variable cost per unit does not change with

quantity. Fixed costs are known.

Assumptions for Cost-Volume-Profit Analysis

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Total Cost = Fixed Cost + (Variable Cost * Q)

TC = FC + (VC x Q)

Cost Equation

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Contribution margin per unit equals price per unit minus variable cost per unit:

CM = (P – VC)

Total contribution margin equals total revenue minus total variable costs:

(CM * Q) = (P*Q) – (VC*Q)

C-V-P Analysis

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Breakeven point: The number of units that must be sold at price P such that total revenues (TR) equal total costs (TC).

TR = TC(P * QBE) = FC + (VC * QBE)

(P - VC) * QBE = FC

QBE = FC / (P – VC)

QBE = (FC / CM)

At breakeven, the total contribution margin equals fixed costs. CM = FC

C-V-P Analysis - Breakeven Point

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20-13

Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.

Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.

Total Unit

Sales Revenue (2,000 units) 100,000$ 50$

Less: Variable costs 60,000 30

Contribution margin 40,000$ 20$

Less: Fixed costs 30,000

Operating income 10,000$

Computing BreakComputing Break--Even PointEven Point

How much contribution margin must this company have to cover its fixed costs (break even)?

How much contribution margin must this company have to cover its fixed costs (break even)?

How much contribution margin must this company have to cover its fixed costs (break even)?

Answer: $30,000

How much contribution margin must this company have to cover its fixed costs (break even)?

Answer: $30,000

How many units must this company sell to cover its fixed costs (break even)?

How many units must this company sell to cover its fixed costs (break even)?

How many units must this company sell to cover its fixed costs (break even)?

Answer: $30,000 ÷ $20 per unit = 1,500 units

How many units must this company sell to cover its fixed costs (break even)?

Answer: $30,000 ÷ $20 per unit = 1,500 units

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20-15

The break-even formula can be expressed in sales dollars.

Unit sales price Unit variable cost

How Many Dollars in Sales at Break-even point?

Break-evenpoint in dollars

Fixed costsContribution margin ratio

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Fixed Cost/ CM = Breakeven Sales

$30,000/ 40% = $75,000

Total Revenue - Total Costs = Profit {(P * Q ) - [(VC * Q ) – FC]} = Profit {[(P - VC) * Q] - FC} = Profit

[(CM * Q) - FC] = Profit (CM * Q) = (Profit + FC)

Q = [(Profit + FC )/CM]

The number of units that must be sold to earn a target profit is equal to the target profit plus the fixed cost divided by the contribution margin.

C-V-P: Target Profit

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20-18

Unit sales = Fixed costs + Target incomeContribution margin per unit

Dollar sales = Fixed costs + Target income

Contribution margin ratio

Computing Sales Needed to Achieve Target Operating Income

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20-19

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 operating income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units

Computing Sales Needed to Computing Sales Needed to Achieve Target OperatingAchieve Target OperatingIncomeIncome

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Answer:

(Fixed Cost + Target Profit)/CM = Target Sales

($200,000 + $40,000) / 40% = $600,000

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Should Speedo spend $12,000 on advertising to increase sales by 10 percent?

Applications of CVP

Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%

Less: fixed expenses 80,000 Operating income 20,000$

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500 550Bikes Bikes

Sales 250,000$ 275,000$ Less: variable expenses 150,000 165,000 Contribution margin 100,000$ 110,000$ Less: fixed expenses 80,000 92,000 Operating income 20,000$ 18,000$

550 × $300

$80K + $12K

No, income is decreased.

550 × $500

Business Applications of CVPBusiness Applications of CVP

Should Speedo spend $12,000 on advertising to increase sales by 10 percent?

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20-27

500Bikes

Sales 250,000$ Less: variable expenses 150,000 Contribution margin 100,000$ Less: fixed expenses 80,000 Operating income 20,000$

Applications of CVPNow, in combination with advertising and a price cut, Speedo

will replace $50,000 in sales salaries with a $25 per bike commission, increasing sales by 50 percent above the

original 500 bikes. What is the effect on income?

500 750Bikes Bikes

Sales 250,000$ 337,500$ Less: variable expenses 150,000 243,750 Contribution margin 100,000$ 93,750$ Less: fixed expenses 80,000 42,000 Operating income 20,000$ 51,750$

The combination of advertising, a price cut,and change in compensation increases income.

750 × $325

$92K - $50K

750 × $450

1.5 × 500

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20-8Volume in Units

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Break-evenPoint

Profit

Loss

Summary: CVP Relationships