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## Contribution Break-Even

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Source: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

Fixed- & Variable-Cost Formulas

- Fixed Costs = Total Costs – Variable Costs
- Variable Costs = Total Costs – Fixed Costs
- Total Costs = Fixed Costs + Variable Costs
- Total Variable Costs = Unit variable costs * Units Sold
- Unit Variable Costs = Total Variable Costs / Units Sold
- Total Revenue = Unit Selling Price * Units Sold
- Average Costs = Total Costs / Units Sold
- Profits = Total Revenues – Total Cost

Fixed Costs

- Are the costs of production that stay the same
- Examples: rent for facilities, management salaries, interest on loans.
- Don’t change with volume sold (up to some limit).
- Don’t change regardless of whether you produce a lot, a little bit, or even if you produce zero.

Source: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

Variable Costs

- Vary as you produce more or less.
- Examples: construction materials, packaging, sales commissions
- Are unit costs that remain more or less constant on a unit basis
- In other words, total variable costs increase at a constant rate with increases in units produced and sold
- Producing more adds to Total Variable Costs. Producing less reduces them.

Source: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

Total Costs

- What it costs to operate at some particular rate of output.
- Total Costs = Fixed Costs + Variable Costs

Source: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

Truth or Consequences: Fixed or Variable?

Fixed

1____

2____

3____

4____

5____

6____

7____

8____

Variable

1____

2____

3____

4____

5____

6____

7____

8____

Do the costs vary as you

produce more/less?

- Rent for office space
- Packaging Material
- Sales Force Base Salaries
- Sales Force Commission
- TV Advertisement
- Shipping charges
- CEO’s limo lease payment
- Warranty expenses

Click to see each answer…

Total vs. Fixed vs. VariableSource: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

Fixed Cost$ 1000

Fixed Cost$ 1000$ 1000$ 1000$ 1000$ 1000$ 1000$ 1000$ 1000$ 1000$ 1000

Number of TVs Total Cost 0 $ 1000 1 $ 4500 2 $ 7500 3 $ 10000 4 $ 12000 5 $ 14500 6 $ 17500 7 $ 21000 8 $ 25000 9 $ 30000

How much is the fixed cost?

Total vs. Fixed vs. VariableSource: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

Variable Cost

$ 0

$ 3500

$ 6500

$ 9000

$ 11000

$ 13500

$ 16500

$ 20000

$ 24000

$ 29000

Number of TVs Total Cost 0 $ 1000 1 $ 4500 2 $ 7500 3 $ 10000 4 $ 12000 5 $ 14500 6 $ 17500 7 $ 21000 8 $ 25000 9 $ 30000

How much is the variable cost?

Distinguish variable from fixed costs to see how total costs will increase with units sold.

Total Revenues

Total Fixed Costs + Total Variable Costs = Total Costs

Total Costs

Total Variable Costs (change at a constant rate)

Total costs ($)

Total Fixed Costs

(don’t change with units sold)

0

Units

Click to continue at each pause...

Variable costs increase with unit volume (production and sales)

Fixed costs don’t – so, over the short-term, fixed costs may be “sunk” costs.

And of course:

Total Revenues – Total Costs = Profits (losses)

Def: Sunk Costs

Variable Costs, Average Costs

Units Sold 1 10 100 1,000

Fixed Costs $500 $500 $500 $500

Variable costs

Packaging $2 $20 $200 $2,000

Material $3 $30 $300 $3,000

Total Costs $505 $550 $1,000 $5,500

Average Costs $505 $55 $10 $5.50

Unit Variable Cost $5 $5 $5 $5

Average Costs = Total Costs / Units Sold

Total costs = Fixed Costs + (unit variable costs * units sold)

In this example, as the number of units sold increases, fixed costs stay fixed at $500, unit variable costs remain constant at $5, total variable costs increase with each additional unit sold, and the average cost per unit decreases as more units are sold.

A Digression for those Remembering Economics 101:Marginal Costs and Variable Costs

- Almost the same concept: marginal costs refer to what it costs to produce an additional unit; variable cost analysis usually assumes constant marginal cost.
- Over a wide range of output, the unit variable costs may not change (as in previous slide’s example). Therefore the “marginal costs” of producing an additional unit and the variable costs will be the same.
- Over some range, variable costs might change (discounts from suppliers for a larger order of packaging materials, for example), but still would not be fixed costs.

Marginal CostsSource: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

Marginal cost is the difference

between one rate of output and another.

# of Total

TVs Cost 0 $ 1000 1 $ 4500 2 $ 7500 3 $ 10000 4 $ 12000

You may take the difference between the total costs or the variable costs. The two ways result in the same answer.

Variable Cost

$ 0$ 3500$ 6500$ 9000$ 11000

Marginal Cost

$ NA

$ 3500

$ 3000

$ 2500

$ 2000

The difference between one rate of output and another.

In other words:

- The marginal cost of changing from one rate of output to another is how much total cost increases when the output rate goes up.
- When the output rate changes, the fixed cost doesn't change. That's why it's called "fixed." The variable cost is what changes, so the difference in total cost is just the difference in the variable cost.
- When there are only fixed costs, marginal costs will be zero, and any increase of production does not change costs.
- If there are only proportionally-growing variable costs, marginal costs will be equal to variable costs.

Marginal CostsSource: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

The difference between one rate of output and another.

Here's the table with all the variable and marginal costs:

Marginal CostsSource: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

Here's the cost data in a graph:

― Total Cost

― Fixed Cost

― Variable Cost

― Marginal Cost

TVs per Year

Marginal CostsSource: University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management, Economics Interactive Tutorials

- Total cost and variable cost are cumulative. That's why they go up and up.
- Fixed cost is not cumulative because it's fixed at $1000, regardless of the output rate.
- Variable cost parallels total cost, always below it by $1000.

- Marginal cost on this graph is the difference in cost between the given output rate and the next lower one. Marginal cost dips for the first few TVs, indicating increasing returns to scale. ("Scale" means size, which here means output rate.) After the fourth TV, diminishing returns to scale set in, and marginal cost per added TV rises. The total cost curve bends down a bit for output rates from 0 to 4, because the marginal cost is falling. For output rates from 4 to 9, marginal cost is increasing, so the total cost curve bends up a bit.

Supplemental descriptions and information regarding Marginal Costs available at

http://www.amosweb.com/cgi-bin/wpd_prv.pl?fcd=dsp&key=marginal+cost

For Tests #2 and #3

- Test #2 will include the information in this presentation up to this slide, i.e. Fixed Costs, Variable Costs, Unit Variable Costs, Total Variable Costs, Total Costs, Marginal Costs, and Profits. But the test will not include the information on the following slides.
- Test #3 will include the information on the following slides in the remainder of this presentation, i.e. Contribution and Break-Even

Decisions That Might Be Affected By Unit Contribution

- Will our unit prices cover unit variable costs?
- Target unit volumes: will the additional contribution cover our fixed costs and make a “profit”?
- We want to sell 10,000 units. Will the contribution cover our fixed costs?
- How much can we afford to pay marketing to sell an additional unit?
- If an advertisement costs $1,000, how many units will we need to sell to make it worthwhile?

Unit Contribution = Selling Price per unit – Variable Costs per unit

Unit Contribution = Total Contribution/Units Sold

Total Contribution = Total Revenues – Total Variable Costs

Total Contribution = Unit Contribution * Units Sold

Total Variable Costs = Unit Variable Costs * Units Sold

Total Revenues = Selling Price per unit * Units Sold

Formulas for Break-Even

Unit Break-even = Fixed Costs / Unit Contribution

Unit Break-even = Fixed Costs / (Selling Price – Variable Cost per unit)

$ Break-even = Fixed Costs / ((Selling Price – unit Variable Cost)/Selling Price)

$ Break-even = Fixed Costs / (Unit Contribution / Selling Price)

$ Break-even = Unit Break-even * Selling Price

Contribution

Total Contribution = Total Revenues - Total Variable Costs

Total Revenues

Total Contribution

Net Income

Total variable costs and revenues ($)

Total Variable Costs

Fixed costs don’t figure

in when calculating

Contribution

0

Units

Click to continue at each pause...

Unit Contribution = Selling Price per unit – Variable Costs per unit

This is significant because it measures a net income of funds to a company as additional units are sold.

Unit Contribution = Selling Price per unit – Variable Costs per unit

Think for a moment about why this quantity might be meaningful to a company.

Unit Contribution Examples

Unit Contribution = Selling Price per unit – Variable Costs per unit

Unit Contribution = Total Contribution/Units Sold

Total Contribution = Total Revenues – Total Variable Costs

Total Contribution = Unit Contribution * Units Sold

Total Variable Costs = Unit Variable Costs * Units Sold

Total Revenues = Selling Price per unit * Units Sold

Unit Contribution = Selling Price per unit – Variable Costs per unit

If a firm receives $12 revenue from each unit it sells, and pays $5 per unit in variable costs, then what is the contribution of each unit? (click for answer)

Unit Contribution = SP per unit – VC per unit

Unit Contribution = $12 - $5

Unit Contribution = $7

Total Contribution

Total Var. Costs

Unit Contribution ExamplesUnit Contribution = Selling Price per unit – Variable Costs per unit

Unit Contribution = Total Contribution/Units Sold

Total Contribution = Total Revenues – Total Variable Costs

Total Contribution = Unit Contribution * Units Sold

Total Variable Costs = Unit Variable Costs * Units Sold

Total Revenues = Selling Price per unit * Units Sold

Unit Contribution = Selling Price per unit – Variable Costs per unit

If a firm realizes $50 in total contribution by selling 10 units of a product at a selling price of $20, what is the variable cost per unit? (click for answer)

Total Contribution = Unit Contribution * Units Sold

$50 = Unit Contribution * 10

Unit Contribution = $5

Unit Contribution = Selling Price per unit – Variable Cost per unit

$5 = $20 - Unit Variable Cost

Unit Variable Cost = $20 - $5

Unit Variable Cost = $15

Or:

$200 - $50 = $150

$150/10 = $15

Unit Var. Costs

Total Var. Costs

Total Contrib.

Unit Contribution ExamplesUnit Contribution = Selling Price per unit – Variable Costs per unit

Unit Contribution = Total Contribution/Units Sold

Total Contribution = Total Revenues – Total Variable Costs

Total Contribution = Unit Contribution * Units Sold

Total Variable Costs = Unit Variable Costs * Units Sold

Total Revenues = Selling Price per unit * Units Sold

Unit Contribution = Selling Price per unit – Variable Costs per unit

If a firm receives $100 revenue from selling 5 units of a product, and pays $25 in total variable costs, then what is the contribution of each unit? (click for answer)

Total Revenues = Selling Price per unit * Units Sold

$100 = SP * 5; Selling Price = $20

Total Variable Costs = Unit Variable Costs * Units Sold

$25 = Unit Variable Costs * 5; Unit Variable Costs = $5

Unit Contribution = SP per unit – VC per unit

Unit Contribution = $20 - $5

Unit Contribution = $15

Or:

$100 - $25 = $75

$75/5 = $15

The Break-even Point

- Definition: the volume of sales needed to at least cover all your costs.
- Break-even means zero profit, but not a loss.

- Once you know what your variable costs are, as well as your overall fixed costs for the business, you can determine your breakeven point.
- You can also compute the new breakeven point that you'd need to meet if you decided to increase your fixed costs (for example, if you undertook a major expansion project or bought some new office equipment).

Source: Business Owner’s Toolkit

Break-even Formulas

Unit Break-even = Fixed Costs / Unit Contribution

Unit Break-even = Fixed Costs / (Selling Price – Variable Cost per unit)

$ Break-even = Fixed Costs / ((Selling Price – unit Variable Cost)/Selling Price)

$ Break-even = Fixed Costs / (Unit Contribution / Selling Price)

Notice that multiplying the first formula by the selling price yields the second formula. Thus…

Unit Break-even * Selling Price = $ Break-even

Break-even Point:

Total Costs = Total Revenues

Profit!

Break-even Volume in Units

The Break-even PointTotal Revenues

Total Fixed Costs + Total Variable Costs = Total Costs

Total Costs

Total Variable Costs (change at a constant rate)

Total costs ($)

Total Fixed Costs

(don’t change with units sold)

0

Units

Click to continue at each pause...

The Break-even Point is where…

Total Costs = Total Revenues

Two Types of Break-even

- Unit break-even – how many unit sales have to be made to cover fixed costs?
- Dollar break-even – what level of dollar sales are required to break even?

Dollar Break-even = Break-even in units * Unit Price

Break-even in Units = Dollar Break-even / Unit Price

A Few Examples…

BE (units) = FC / (SP-VC) BE ($) = FC / ((SP - VC)/SP)

A

Mickey’s Mousetraps wants to know how many of its “Magic Mouse Trappers” it needs to sell in order to break-even on costs. The product sells for $20, it costs $5 per unit to make, and the company’s fixed costs are $30,000.

BE (units) = FC / (SP – VC)

BE (units) = $30,000 / ($20 - $5) = 2000 mousetraps

A Few Examples…

BE (units) = FC / (SP-VC) BE ($) = FC / ((SP - VC)/SP)

A

Mickey’s Mousetraps wants to know how many dollars worth of its “Deluxe Mighty Mouse Trappers” it needs to sell in order to break-even on costs. The product sells for $40, it costs $10 per unit to make, and the company’s fixed costs are $30,000.

BE ($) = FC / ((SP – VC)/SP)

BE ($) = $30,000 / (($40 - $10)/$40) = ($30,000 / 0.75) = $40,000

Sample Problem

BE (units) = FC / (SP-VC) BE ($) = FC / ((SP - VC)/SP)

Swiss entrepreneur Herr Zeitgeist buys watch faces from Italy for 5 Euros, buys watch mechanisms for 15 Euros from Spain, and hires assembly in Portugal for 10 Euros per watch. His only other expense is 100,000 Euros he pays the Zuricher Flughafen ad agency to place ads in in-flight magazines to build the Zeitgeist brand.

Herr Zeitgeist sells each watch for 50 Euros to airport duty-free shops, earning the retailer an 80% margin.

How many watches must he sell to break-even?

Click for answer…

The formula for break-even in units is:

BE (units) = FC / (SP-VC)

By reading the information provided, we see that fixed costs are 100,000 Euros, and variable costs are 5+15+10 = 30 Euros per watch.

BE (units) = 100,000 / (50 – 30) = 100,000 / 20 = 5,000 watches

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