5.5 Break-even analysis

Contribution

The sum of money that remains after all direct / variable costs have been deducted from sales revenue of a product

• The surplus contributs to paing fixed costs

Contribution per unit

• Difference betw selling price of a product and its variable costs of production

• Aka proportion of SP per unit that goes towards paying FC

Contribution per unit formula

P - AVC

Total contribution

Surplus after all VC have been deduced from revenue, that is used to cover fixed costs

• FC / unit contribution (double check)

• Quantity of output needed to go towards paying off total fixed costs

Total contribution formula

(P-AVC) X Q

• Aka GP for a product

Formula for contribution per unit vs added value

1. CPU = P - AVC

2. VA PU = P - ATC

What is used to pay a firms fixed costs?

Positive difference betw SP - AVC

Profit

Positive difference betw TR - TC

• On BE chart: all levels of output beyond BEQ

Profit formula

• Total contribution - TFC

• TR - total costs

Simple- how to increase profit?

1. Increase revenue (via sales volume or price) → raises total contribution

2. Reduce VC

3. Reduce FC

Break-even analysis

• Quantitative decision making-tool

• Used to calc the level of sales needed to cover all COP

• Any sales beyond BEP generate a positive safety margin, hence profit for the business

Break-even chart

• Represents firms costs, revenues, profits (or loss) at various levels of output

3 diff financial situations a firm can be in (relating to BE)

1. Loss- TC > TR

2. Break-even- TR = TC

3. Profit- TR > TC

Purpose of contribution analysis

1. Determine pricing strategies

2. Prioritise products in their portfolio

3. Decide whether to make / buy in products

4. Perform BE analysis

Break even

When a firm’s sales revenues cover all of its production costs

• When a firm makes neither a profit nor a loss

• TR = TC

Break-even point

• Position of BE chart where TC line intersects TR line

• TR = TC

Break-even quantity

• Sales vol needed for a firm to reach

• BEQ = FC / (P – AVC)

What does BE analysis inform managers?

1. hether a product is financially worthwhile to produce.

2. How much profit can be earned if the business idea goes to plan.

3 methods to determine BE point

1. Unit contribution method

2. TR = TC method

3. Draw + interpret BE chart

Unit contribution method to calculate BE point

BEQ = TFC / contribution per unit

TR = TC method to calculate BE point

• Work out TR and TC

• Equate them

• Sub in values

• Solve for Q

• TR = TC

• P x Q = TFC + TVC

• 30Q = 3500 + 10Q

• 20Q = 3500

• BEQ = 175 jeans

BE chart method to calculate BE point

• Draw BEC

• Level of output on x axis at BEP

Loss

When firms TC > TR

• At all levels of output below BEQ

Break even chart

Which businesses is BE analysis especially useful for?

Business that:

1. Produce / sell 1, standardized product

2. Operate in 1 market

3. Make products to order → all output sold

Margin of safety (MOS)

• Numerical difference betw firms actual sales quantity and its BE quantity

• Positive MOS → firms can reduce output by that amt w/o making a loss

• V high positive MOS → reduce risk if adverse conditions

Margin of safety formula

Actual sales quantity - BE quantity

MOS units

The unit of output (ie jeans)

• NOT monetary

How to draw a BE chart?

1. Optional- draw TFC line (horizontal)

2. Draw TC line (starts at same level as TFC)

3. Draw TR line (starts at 0)

4. Label x axis- output (rings per month)

5. Label y axis- costs AND revenue (give specific currency)

6. Title

What happens if BE quantity is a decimal?

Always round up

Target profit

• Amt of profit (surplus) a firm intends to achieve, in a given time period

• Expected SR = TC

Target profit output

• The quantity of sales required to reach the firm’s target profit

Target profit output formula

(FC + Target profit) / contribution per unit

How to manually work out target profit output?

• Target profit = TR - TC

• Target profit = (target price x Q) - TFC - TVC

• Solve for Q

Target price

Price set by a firm in order to reach BE Q or certain target profit

• Amt customers need to pay per unit, in order for firm to BE or reach target profit

BE revenue

Value of the output needed to break-even

When does a firm generate a profit / loss on BE chart?

• Profit- output beyond BEP

• Loss- output below BEP

Effect of increase in selling price on firms BE quantity + on chart

1. Reduces firms BEQ

2. Greater gradient (steeper) of TR line (1 → 2)

Effect of higher selling price on MOS

Increases MOS (because the firm BEs earlier)

• Assumption: inelastic demand

Whether a higher price generates a greater or smaller MOS, depends on what?

PED

Effect of higher cost of production on firms BE quantity + on chart

• Increase BEQ

• If VC increase → TC line is steeper

• If FC increase → TC line shifted upwards

Summary: effect of increase in price on BEQ, profit, MOS

1. BEQ decreases

2. Profit increases

3. MOS increases

Summary: effect of increase in cost on BEQ, profit, MOS

1. BEQ increases

2. Profit decreases

3. MOS decreases

What formulas to use to quantitatively show effect of change in price and cost on BE

• BE = FC / CPU

• CPU = SP - AVC

Why are actual BE, profits / losses, MOS going to be diff from the predicted ones in BE analysis? (not in spec)

2. Non price determinants of demand → affects BEQ → affects MOS

• fashion tastes change → demand ↑ → profit ↑, MOS ↑, BEQ reached sooner

3. Innovation / new tech → demand ↑ → revenue ↑ → profit ↑, MOS ↑, BEQ reached faster

4. ST vs LT pricing

• SR- low price to attract customers: contribution ↓ → BEQ ↑, profit ↓, MOS ↓

• LR- opposite (once customers are loyal)

5. External factors (costs, interest, exchange rates)

• Increase costs → decrease contribution → BEQ ↑, profit ↓, MOS ↓

6. Risk level

• High risk project → high FC → BEQ ↑, MOS ↓ (but potential profit ↑ if successful)

Assumptions of BE analysis / charts

1. Costs are constant (linear)

2. Sales revenue is constant (linear)

3. All output will be sold

Cons of BE analysis

1. Assumption: prices are constant (TR line = constant gradient)

2. Assumption: costs are constant (TC line = constant gradient)

3. Affected by changes in external business environment

4. Ideal for businesses that sell 1 g/s that sell all their output

5. Relies on accurate cost + revenue data

6. Predictions / forecast → not guaranteed

7. Ignores qualitative factors

8. Assumption: all output will be sold

Pros of BE analysis as a planning + decision making tool

1. Product portfolio management

• Helps to assess the expected BEQ prior to the launch of a new product.

2. Risk assessment

• By calc MOS

3. Helps w make or buy decisions (CTM vs CTB)

4. Helps w special order decisions

• If a one-off orderi s worth accepting