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IB Syllabus 5.5
IB Syllabus 5.5
The learning outcomes (or assessment objectives) for this section of the IB Business Management syllabus are:
Total contribution versus contribution per unit (AO2)
A break-even chart and the following aspects of break-even analysis. (AO2, AO4)
Break-even quantity/point
Profit or loss
Margin of safety
Target profit output
Target profit
Target price
The effects of changes in price or cost on the break-even quantity, profit and margin of safety, using graphical and quantitative methods (AO2, AO4)
Limitations of break-even as a decision-making tool (AO3)
In-Class Activities
In-Class Activities
Review the PowerPoint https://docs.google.com/presentation/d/1WEnc2k08gJR86ZUGZOaSfwXgyVSexrNyRjj3lJQI-yw/edit?usp=sharing
In-Class Practice: Complete on the following questions in class
Cup Producer Question:
It costs $1 to produce each cup.
Rent and salaries together are $7000
Cups sell for $4 each
They are currently producing 3000 cups
Questions:
Calculate the contribution per unit
Calculate the total contribution
Calculate the break even point
Calculate the margin of safety
Construct a fully labelled break-even chart for the cup producer
Calculate the number of cups that the owner needs to sell to achieve a target profit of $4000
Explain how an increase in competition may affect the margin of safety
What you should know
By the end of this subtopic, you should be able to:
define the following terms: (AO1)
contribution per unit
total contribution
break-even quantity/point
margin of safety
target profit output
target profit
target price
contribution costing (HL)
absorption costing (HL)
make or buy analysis (HL)
distinguish between total contribution and contribution per unit (AO2)
calculate the break-even point and construct a break-even chart (AO4)
analyse the effects of changes in price or cost on the break-even quantity, profit and margin of safety, using graphical and quantitative methods (AO2, AO4)
discuss the uses and limitations of break-even as a decision-making tool (AO3)
apply the contribution tool in a given context (AO2) (HL)
https://quizlet.com/_cxktyu?x=1jqt&i=4jrhob
Break-even
This condition exists when a firm’s sales revenues cover all of its production costs.
Break-even analysis
This is a business management tool used to determine the level of sales volume needed to cover all the costs associated with the output of a particular good or service.
Break-even chart
This is a graphical illustration of an organization’s production costs, sales revenues, and profits (or loss) at given levels of output.
Break-even point (BEP)
This is the point on a break-even chart where the firm’s total costs equal its total revenue, shown by the intersection of the TR and TC curves.
Break-even quantity (BEQ)
The quantity of sales (sales volume) required for a firm to reach break-even. It is found by using the formula: BEQ = Fixed costs / (Price – Average variable cost).
Break-even revenue
This is the value of the output needed to break-even.
Contribution
This refers to the financial difference between a firm’s selling price and its direct or variable costs.
Contribution per unit
This is the difference between a firm’s selling price and its average variable costs (AVC) of production, i.e., P – AVC.
Loss
This occurs when a firm’s total costs are greater than its total revenues, i.e. the business is unprofitable.
Margin of safety
Also known as the safety margin, this refers to the numerical difference between a firm’s volume of sales and its break-even quantity.
Profit
The financial surplus that remains when a firm's total costs (TC) of production are deducted from its total sales revenues (TR). Hence, profit = TR – TC.
Target price
This is the amount customers need to pay per unit in order for the firm to break-even or to reach a particular target profit
Target profit
This is the amount of profit that a firm aims to earn within a given time period.
Target profit output
Also known as the target profit quantity, this refers to the quantity of sales required to reach the firm’s target profit.
Total contribution
This refers to the total difference between a firm’s sales revenues and its total variable costs (TVC), i.e. (P – AVC) × Q. The difference is then the total amount that contributes to paying a firm’s fixed costs.
Outsource
When a business takes an internal function and has it performed externally by another person or business.
Contribution Costing
A cost accounting method that only considers the direct costs of the product, department or region and their resulting contribution to covering the indirect costs of the business as a whole.
Absorption Costing
A cost accounting method that allocates indirect costs among products, departments or regions based on predetermined criteria such as output, sales revenue, number of employees or the value of the equipment.
5.5 Extra Notes
5.5 Extra Notes
Total contribution versus contribution per unit (AO2)
Total contribution versus contribution per unit (AO2)
Total Contribution
Total contribution refers to the total amount of money earned from sales that is available to cover fixed costs after subtracting variable costs.
Formula:
Contribution per unit x Total number of units sold
Contribution Per Unit
Contribution per unit is the difference between the price per unit and the variable costs per unit.
It's the amount of money each individual unit contributes towards covering fixed costs after variable costs are accounted for.
Formula:
Contribution per unit = Price per unit – variable cost per unit
Contribution Formulas
Contribution per unit = P – AVC
Total contribution = TR – TVC
Total contribution = contribution per unit ⨉ Q
OR
Contribution per unit = price per unit – variable cost per unit
Total contribution (at a certain quantity) = contribution per unit × quantity (output)
Example:
Cup Producer Question:
It costs $0.50 in materials to produce each cup.
Workers are paid $0.50 commission for each cup they produce.
Rent is $4000
Salaries are $3000
Cups sell for $4 each
They are currently producing 3000 cups.
Questions:
Calculate the contribution per unit of cups.
Calculate the total contribution of cups.
Example Answer:
Questions:
Calculate the contribution per unit of cups.
Contribution per unit = P – AVC
P = $4
AVC = $0.5 materials + $0.5 worker commission = $1
Contribution per unit = $4 - $1 = $3
Calculate the total contribution of cups.
Total contribution = contribution per unit ⨉ Q
Total Contribution = $3 per cup x 3000 cups = $9000
Breakeven Analysis: Contribution & Contribution per Unit
A break-even chart and the following aspects of break-even analysis. (AO2, AO4)
A break-even chart and the following aspects of break-even analysis. (AO2, AO4)
Break-even quantity/point
Profit or loss
Margin of safety
Target profit output
Target profit
Target price
- Break-even quantity/point
Break-Even Point (BEP)
The break-even point (BEP) is where the firm's total revenue (TR) line intersects its total costs (TC) line, i.e., the point where TR = TC.
Break-Even Quantity (BEQ)
The break-even quantity (BEQ) is shown on the x-axis, as this shows the sales volume (or quantity of sales) necessary for the firm to break-even (i.e., 250 oysters in the above case).
How to Draw a Break Even Graph
How to Draw a Break Even Graph
Do calculations first before drawing the graph.
Calculate -> Draw -> Label -> Indicate
Calculate BEQ, costs and revenues (if needed)
Draw the axes and total revenue (TR), total costs (TC), total fixed costs (TFC) lines
Label the chart, all lines and axes
Indicate BEP, BEQ, profit, loss
1) Calculate the Break Even Point
Step 1: Find
Price per unit, Variable Cost, Fixed Cost
Step 2: Calculate the Break Even Quantity
Total Cost = Total Revenue
Variable Cost + Fixed Cost = Price x Quantity
OR
Fixed Cost / Contribution Per Unit
Step 3: Calculate the Break Even Revenue (or Break Even Total Cost)
Draw the Graph:
2) Title your graph (Break Even Chart for X Company for X Product)
3) Draw and Label the X Axis (quantity of _____) and Y Axis (Cost and Revenues ($))
4) Draw the Break Even Point in the middle of the graph and then label on the X and Y axis
5) Draw the Total Fixed Cost curve as a Horizontal line and label (number on Y-Axis and FC)
6) Draw the Total Cost curve through the break even point
7) Draw the Total Revenue curve through the break even point
Example Question:
Cup Producer Question:
It costs $0.50 in materials to produce each cup.
Workers are paid $0.50 commission for each cup they produce.
Rent is $4000
Salaries are $3000
Cups sell for $4 each
They are currently producing 3000 cups.
Questions:
Calculate the break even point
Construct a fully labelled break-even chart for the cup producer
Step 1: Find
Fixed Cost = $4000 + $3000 = $7000
Price per cup: $4
Variable Cost per cup: $0.50 + $0.50 = $1
Step 2: Calculate the Break Even Quantity
Total Cost = Total Revenue
Total Cost = Variable Cost + Fixed Cost
Total Cost = $1q + $7000
Total Revenue = Price x Quantity
Total Revenue = $4q
Break Even Quantity = Total Cost = Total Revenue
$1q + $7000 = $4q
$7000 = $3q
$7000 / 3 = q
q = 2333.33 = BEQ -> Round up to 2334
OR
Break Even Quantity = FC / Contribution Margin per unit
Contribution Margin Per Unit (CM/U) = Price - VC
= $4 - $1
= $3
BEQ = $7000 / ($4 - $1)
BEQ = $7000 / 3
BEQ = 2333.33 -> Round up to 2334
Step 3: Calculate the Break Even Revenue (or Break Even Total Cost)
Total Revenue = $4q
BEQ = 2333.33
Break Even Point Revenue = $4 x 2333.33
= $9333.33
Draw the Graph:
2) Title your graph (Break Even Chart for X Company for X Product)
3) Draw and Label the X Axis (quantity of _____) and Y Axis (Cost and Revenues ($))
4) Draw the Break Even Point in the middle of the graph and then label on the X and Y axis
5) Draw the Total Fixed Cost curve as a Horizontal line and label (number on Y-Axis and FC)
6) Draw the Total Cost curve through the break even point
7) Draw the Total Revenue curve through the break even point
Break Even Chart for a coffee shop with one coffee product.
- Profit or loss
Profit is the financial benefit earned by a business after accounting for all revenues, variable costs, fixed costs and taxes.
Formula
Profit (or loss) = Total Revenue - Total Cost
OR
Profit (or loss) = Total Contribution - Fixed Cost
Example:
Cup Producer Question:
It costs $0.50 in materials to produce each cup.
Workers are paid $0.50 commission for each cup they produce.
Rent is $4000
Salaries are $3000
Cups sell for $4 each
They are currently producing 3000 cups.
Questions:
Calculate the profit or loss
Profit (or loss) = Total Revenue - Total Cost
Total Revenue = P x Q = $4 x 3000 = $12,000
Total Cost = FC + VC
FC = $4000
VC = ($0.50 in materials + $0.50 commission for each cup) x 3000 = $3000
Total Cost = $4000 + $3000 = $7000
Profit (or loss) = $12,000 - $7,000 = $5,000 in profit
Example Answer:
Questions:
Calculate the profit or loss
Profit (or loss) = Total Revenue - Total Cost
Total Revenue = P x Q = $4 x 3000 = $12,000
Total Cost = FC + VC
FC = $4000
VC = ($0.50 in materials + $0.50 commission for each cup) x 3000 = $3000
Total Cost = $4000 + $3000 = $7000
Profit (or loss) = $12,000 - $7,000 = $5,000 in profit
Break Even Chart with Profit and Loss
- Margin of safety
Margin of safety (MOS) or the Safety Margin = Difference between how much the business sells and its Break Even Quantity (BEQ)
MOS = Actual Sales - Break Even Quantity
Margin of safety above is 140 - 100 = 40
Margin of Safety Example
If an oyster retailer sells 330 oysters in a week and the calculated Break Even Quantity (BEQ) is 250.
Question:
1) Calculate the Margin of Safety per week of oysters.
Margin of Safety Example
If an oyster retailer sells 330 oysters in a week and the calculated Break Even Quantity (BEQ) is 250.
Question:
1) Calculate the Margin of Safety per week of oysters.
ANSWER
Actual Sales = 330
BEQ = 250
MOS = Actual Sales - BEQ
MOS = 330 - 250 = 80
Breakeven Analysis - the Margin of Safety
- Target profit output
Target profit output (or target profit quantity) is the quantity of sales required to reach the firm’s target profit.
Formula
Profit (or loss) = Total Revenue - Total Cost
OR
Target profit quantity = (Fixed cost + Target profit) / (Price – Average Variable Cost)
Example
Cup Producer Case Study:
It costs $0.50 in materials to produce each cup.
Workers are paid $0.50 commission for each cup they produce.
Rent is $4000
Salaries are $3000
Cups sell for $4 each
They are currently producing 3000 cups.
Question:
1) Calculate the number of cups the company needs to sell to achieve a profit of $4000 (show all your working).
Example Answer
Cup Producer Case Study:
Question:
1) Calculate the number of cups the company needs to sell to achieve a profit of $4000 (show all your working).
Answer:
Profit (or loss) = Total Revenue - Total Cost
Profit = $4000
Total Revenue = P x Q = $4Q
Total Cost = FC + VC
FC = $4000
VC = ($0.50 in materials + $0.50 commission for each cup) x Q = $1Q
Total Cost = $4000 + $1Q
Profit (or loss) = Total Revenue - Total Cost
$4000 = $4Q - ($4000 + $1Q)
$4000 = $4Q - $4000 - $1Q
$8000 = $3Q
$8000 / $3 = Q
Q = 2666.667
Q = rounded up to 2667 because you cannot sell 0.667 cups of coffee
- Target profit
Target profit is the amount (value) of profit that a firm aims to earn within a given time period. The profit for each level of output can been seen in a break-even chart by comparing the total cost and total revenue lines.
Target profit = Price × Quantity – [Fixed cost + (Average variable cost × Quantity)]
or
Target profit = Total revenue – Total cost
Therefore target profit can be achieved by either improving sales or decreasing variable or fixed costs
- Target price
Target price is the amount customers need to pay per unit in order for the firm to break-even or to reach a particular target profit.
If competition enters the market selling their cups of coffee for $3.50, the coffee shop may want to decrease their price to match competition. This would result in a higher number of sales or a decrease in costs in order to break even.
School Cafeteria Example from Lewinski including a Break Even Chart and Profit or Loss:
The effects of changes in price or cost on the break-even quantity, profit and margin of safety, using graphical and quantitative methods (AO2, AO4)
The effects of changes in price or cost on the break-even quantity, profit and margin of safety, using graphical and quantitative methods (AO2, AO4)
Increasing ↑ the Price, decreases ↓ Break Even Quantity, increases ↑ Margin of Safety and Profit if output remains the same
Decreasing ↓ the Price, increases ↑ Break Even Quantity, decreases ↓ Margin of Safety and Profit if output remains the same
However for most goods, increasing the price will decrease sales and decreasing the price will increase sales (how much depends on the price elasticity of demand, which is an economics term).
The slope of the revenue curve increases if price increases and vice versa.
Changes in Price on break-even level of output
An increase in the selling price reduces a firm’s break-even level of output as it steepens the slope of the revenue curve.
Diagrammatically, the higher price results in a greater gradient of the total revenue line (from TR1 to TR2), as shown in the diagram below.
This reduces the break-even quantity from BEQ1 to BEQ2.
Changes in Price on margin of safety
Whether a higher price results in a greater or smaller margin of safety depends on the extent to which the increased price reduces demand for the firm’s products.
The opposite is true for a reduction in price. The firm would have to sell more in order to break-even.
A higher price will raise the margin of safety if demand stays the same (because the firm breaks even earlier). However, this assumes that the sales volume does not fall following the increase in price.
Increasing ↑ the Fixed Costs, increases ↑ Break Even Quantity, decreases ↓ Margin of Safety and decreases ↓ Profit.
Decreasing ↓ the Fixed Costs, decreases ↓ Break Even Quantity, increases ↑ Margin of Safety and increases ↑ Profit.
Increasing ↑ the Variable Costs, increases ↑ Break Even Quantity, decreases ↓ Margin of Safety and decreases ↓ Profit.
Decreasing ↓ the Variable Costs, decreases ↓ Break Even Quantity, increases ↑ Margin of Safety and increases ↑ Profit.
The slope of the total cost curve increases if variable cost increases and vice versa.
Limitations of break-even as a decision-making tool (AO3)
Limitations of break-even as a decision-making tool (AO3)
Uses of a break-even analysis
Business plan. For a business to assess whether its idea will earn a profit.
Financing. Banks and investors will ask for a break-even analysis so they can judge the risk of a loan or investment.
Strategy changes. A business can examine several different cost and revenue scenarios in order to consider strategy changes that might increase revenues or decrease costs.
Single Product. Ideal for analyzing a single product
Limitations of a break-even analysis
Changing assumptions. Costs and prices may change, so businesses need to regularly update assumptions for break-even analysis (eg. inflation or temporary discounts).
Costs and revenues are not linear. Break-even analysis assumes costs and revenues are linear, but in reality they are not (assumes no economies of scale).
Time-consuming for large product portfolios. Separate break-even analyses must be done for each product.
Need Accurate Costs and Revenue Data. As with all quantitative tools, the effectiveness of break-even analysis relies on the accuracy of the cost and revenue data used to make the predictions. Any inaccuracies and/or deliberate bias in the use of the quantitative data will invalidate the results of the break-even analysis.
Ignores qualitative considerations, such as the impact on employees who may need to work overtime in order to reach break-even. In reality, managers are likely to consider both quantitative and qualitative factors when making decisions.
5.5 Cases 2024 IB Biz.pdfPractice Question:
Bryan's chair company sells chairs for $50 each. Each chair costs $10 for materials to make. Each chair costs $5 in labour. The rent for the company is $1000 a month. The salaries of management is $20,000 per month for each manager and there are 2 managers.
Question: Please draw a fully labelled break even analysis graph for Bryan's chair company. Show all work
To draw a break-even analysis graph for Bryan's chair company, we first calculate the key components:
1. Fixed Costs
1. Fixed Costs
Fixed costs include rent and management salaries:
Rent: $1,000/month
Management salaries: $20,000 × 2 = $40,000/month
Total Fixed Costs = $1,000 + $40,000 = $41,000/month
2. Variable Costs per Chair
2. Variable Costs per Chair
Variable costs include materials and labor:
Materials: $10/chair
Labor: $5/chair
Total Variable Cost per Chair = $10 + $5 = $15
3. Contribution Margin per Chair
3. Contribution Margin per Chair
Selling price per chair: $50
Contribution margin = Selling price - Variable cost
Contribution Margin = $50 - $15 = $35
Break-Even Analysis Graph:
Break-Even Analysis Graph:
The graph should include:
X-axis: Number of chairs sold (output)
Y-axis: Costs and revenue ($)
Lines:
Total Cost Line: Starts at fixed costs ($41,000) and increases by variable cost per chair ($15).
Total Revenue Line: Starts at 0 and increases by the selling price per chair ($50).
Break-Even Point: Intersection of Total Cost and Total Revenue lines at approximately 1,171 chairs and $58,550 revenue.
Shading:
Loss Zone: Left of the break-even point (where total cost > total revenue).
Profit Zone: Right of the break-even point (where total revenue > total cost).
Let me create the graph.
Here is the break-even analysis graph for Bryan's chair company. It includes the following:
Total Costs Line (red dashed): Starts at $41,000 (fixed costs) and increases with variable costs.
Total Revenue Line (green): Increases with the selling price per chair.
Break-Even Point (black dot): At approximately 1,171 chairs and $58,550 revenue, where total revenue equals total costs.
Fixed Costs Line (purple dashed-dotted): Constant at $41,000.
The shaded regions (not displayed but implied) represent the loss and profit zones, divided by the break-even point.
Additional Practice Question:
Guitars sell for $1000 each. Each guitar costs $200 to pay for the strings, wood, and other materials. Each guitar also costs $300 in labour. The rent for the guitar shop costs $10 000 per month. Your school also provides free guitar lessons to people who purchase guitars from you. These require 2 guitar specialists who you pay $5000 per month each. Currently you sell 60 guitars per month.
Questions:
Calculate the contribution per unit
Calculate the total contribution
Calculator the break even point using the contribution method
Construct a break even graph
Calculate the margin of safety and indicate it on your graph.
Calculate the number of guitars that the owner needs to sell to achieve a target profit of $5000 per month.
Explain how the break even point may change if there is a new competitor
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