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T2

Toolkit: business plans, decision trees, statistics and circular models

The business management toolkit · SL and HL

The second group of toolkit items helps businesses plan and decide under uncertainty: the business plan, decision trees with expected values, descriptive statistics for summarizing data, and circular business models for sustainability. All are for SL and HL, and all can appear in Paper 1, Paper 2 or your IA.

🎯What you need to be able to do

  • Explain the purpose and main elements of a business plan.
  • Construct and interpret a decision tree, calculating expected values.
  • Calculate and interpret descriptive statistics: mean, median, mode, quartiles and standard deviation; read bar charts, pie charts and infographics.
  • Explain the circular business models and evaluate their use.

📚The business management

The business plan

A business plan is a document setting out a business’s objectives and how it will achieve them. Typical elements:

  • the business idea, vision and mission, and legal structure (1.2);
  • market research, target market and competitors (4.4);
  • the marketing plan and the seven Ps;
  • operations: location, suppliers, production methods;
  • human resources: owners, key staff, organization;
  • finance: sources of finance, cash flow forecast, break-even and projected accounts.

Why write one: to secure finance from banks and investors, to test whether the idea is viable, and to set targets to measure progress against. Limitations: based on forecasts that may be wrong; can become out of date quickly; time-consuming; may give false confidence.

Decision trees

A decision tree maps the options available, the possible outcomes of each, their probabilities and their financial results.

  • Square: a decision point (the business chooses).
  • Circle: a chance node (outcomes happen with given probabilities, which add up to 1).
  • Expected value (EV) at each chance node = sum of (probability × outcome).
  • Net EV = EV − cost of the option. Choose the highest net EV; mark rejected branches with a double line (//).
Decision tree in thousands of dollars. Open second shop, cost 120: success 0.6 gives 300, failure 0.4 gives 80, expected value 212, net 92. Launch online store, cost 50: success 0.5 gives 180, failure 0.5 gives 60, expected value 120, net 70. Do nothing: 0. The second shop has the highest net expected value.
Work from right to left: expected values at the circles, then subtract costs at the square.
\[ \text{EV(shop)} = 0.6 \times 300 + 0.4 \times 80 = 212 \qquad \text{net} = 212 - 120 = 92 \]
\[ \text{EV(online)} = 0.5 \times 180 + 0.5 \times 60 = 120 \qquad \text{net} = 120 - 50 = 70 \]

Strengths: sets out options clearly; forces managers to consider risks and probabilities; quantitative basis for comparison. Limitations: probabilities and outcomes are estimates, often subjective; ignores qualitative factors (fit with objectives, staff, brand); the EV is an average, and the actual result will be one of the outcomes, not the EV; ignores the time value of money and attitudes to risk (the shop could return only 80).

Descriptive statistics

  • Mean: sum of values ÷ number of values. Uses all the data but is pulled by extreme values.
  • Median: the middle value when the data is in order. Not affected by extremes.
  • Mode: the most frequent value. Useful for stock decisions (the most popular size).
  • Quartiles: split ordered data into four equal parts; the interquartile range (Q3 − Q1) shows the spread of the middle half.
  • Standard deviation: the typical distance of values from the mean; a large value means data is widely spread (less predictable).
  • Bar charts compare categories; pie charts show shares of a whole; infographics combine images, charts and text to communicate data quickly to non-specialists.

Circular business models

A traditional linear model takes resources, makes products and throws them away. A circular model keeps products and materials in use for as long as possible, cutting waste and dependence on new resources.

Top: a linear chain of take resources, make products, use, dispose as waste. Bottom: a loop of four stages, design and make with renewable and recyclable inputs, use and share, repair and reuse, recover and recycle, returning to design and make.
Linear versus circular: the loop keeps value in the system.
  • Circular supply models: replacing scarce or harmful inputs with renewable, bio-based or recycled ones (packaging from plant fibre).
  • Resource recovery models: recovering materials or energy from waste and by-products (turning coconut husks into fibre products).
  • Product life extension models: repair, refurbishing, upgrades and resale (refurbished phones, surfboard repair services).
  • Sharing models: making better use of products by sharing access (car-sharing, co-working spaces, rental platforms).
  • Product service system models: selling the use or performance of a product rather than the product itself (leasing, subscriptions).

Benefits: lower material costs, new revenue streams, customer loyalty, stronger CSR image, resilience to resource prices, meeting regulations. Limitations: redesign and reverse logistics are costly; customers may prefer new products; recycled inputs can be more expensive or lower quality; harder to scale.

✏️Worked example

Ombak Boards recorded daily board sales over nine days: 3, 5, 4, 7, 5, 6, 12, 5, 8. Calculate the mean, median, mode, interquartile range and standard deviation, and comment on which average the manager should use to plan daily stock.

Ordered: 3, 4, 5, 5, 5, 6, 7, 8, 12. Mean = 55 ÷ 9 = 6.1. Median (5th value) = 5. Mode = 5.

Quartiles (median of each half, excluding the median): Q1 = median of 3, 4, 5, 5 = 4.5; Q3 = median of 6, 7, 8, 12 = 7.5. IQR = 7.5 − 4.5 = 3.

Standard deviation (calculator, population): 2.5 boards.

Comment: the mean is pulled up by one unusual day (12, perhaps a surf competition). The median and mode (5) better represent a typical day, so plan around 5 boards, with buffer stock to cover the spread (SD 2.5) and extra stock for known events.

Check it. Mean > median signals a few high values (a positive skew). Different textbooks use slightly different quartile methods; show yours.
Treating the expected value as a forecast result. An EV of 212 does not mean the shop will earn 212; it will earn 300 or 80. The EV is a probability-weighted average for comparing options.

📝Practise

Work through these on paper, then reveal the answer.

1. [2 marks] State two reasons for writing a business plan.
To obtain finance from lenders or investors; to plan and test the viability of the idea and set targets for monitoring.
2. [3 marks] A campaign costs $20 000 and has a 0.7 chance of earning $50 000 and a 0.3 chance of earning $10 000. Calculate its net expected value.
EV = 0.7 × 50 000 + 0.3 × 10 000 = 35 000 + 3000 = 38 000. Net EV = 38 000 − 20 000 = $18 000.
3. [2 marks] Explain why the median may be more useful than the mean for employee salaries in a company.
A few very high executive salaries pull the mean up, so it overstates what a typical employee earns; the median is not affected by these extremes.
4. [4 marks] Explain two circular business models a hotel could adopt.
Resource recovery: composting food waste for its gardens and recycling water, cutting waste costs. Product life extension: repairing and reupholstering furniture instead of replacing it, lowering capital spending and supporting a green image with guests.
5. [4 marks] Explain two limitations of decision trees.
(1) Probabilities and financial outcomes are estimates, often subjective, so the EVs may be misleading. (2) They ignore qualitative factors such as staff morale, brand image and the business’s attitude to risk; an option with a lower EV but no chance of a large loss may be preferable.
6. [10 marks] Discuss whether a fashion retailer should adopt a product service system (clothing rental subscription).

For: recurring subscription revenue; appeals to sustainability-minded and budget-conscious customers; each garment earns revenue many times; data on preferences; CSR benefits.

Against: cleaning, repair and reverse-logistics costs; damage and loss; customers may prefer ownership; cannibalizes sales; needs new systems and skills.

Judgment: worth piloting for occasion wear (high price, rarely worn) in urban markets, alongside normal sales, before committing fully.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • Ellen MacArthur Foundation — case studies of circular business models.
  • Khan Academy — mean, median, interquartile range and standard deviation.
  • Tutor2u — decision trees with worked examples.