What is expected value?

Expected value is the average payoff of a chance node, found by multiplying each outcome by its probability and adding the results. The figure is a weighted average rather than any outcome that will actually occur.

What must the probabilities at a single chance node add up to?

The probabilities at one chance node must add up to 1. If they do not, an outcome has been omitted or a figure is wrong.

How is a decision tree evaluated?

A decision tree is evaluated by rolling back from right to left. The expected value of each chance node is calculated first, and the cost of the branch leading to it is then deducted.

A launch costs £200,000. There is a 0.6 chance of returns of £500,000 and a 0.4 chance of returns of £100,000. Calculate the expected value of the chance node.

Expected value equals 0.6 multiplied by £500,000, which is £300,000. Adding 0.4 multiplied by £100,000 gives a further £40,000. The expected value of the node is therefore £340,000.

Eduqas A-Level Business A510QS

Enterprise, Business Plans and Location

Topic overview Enterprise, entrepreneurs and SMEs Needs, wants and spotting a business opportunity The role of the entrepreneur in setting up and running a business Financial and non-financial motives of entrepreneurs Characteristics and skills of entrepreneurs Entrepreneurs, SMEs and the sectors of the UK economy Stakeholders and their interests Business plans and sources of advice Choosing a business location

Markets, Demand and Market Research

Topic overview Markets and competition Types of market Market size, market share and market trends Market segmentation Market structures and degrees of competition Consumer protection Demand and the factors that shift it Supply and the factors that shift it Equilibrium price and shifts in the market Price and income elasticity of demand Primary and secondary market research Qualitative and quantitative data Sampling and bias in market research

Business Structure and Sources of Finance

Topic overview The private sector and the public sector Aims of private sector businesses Sole traders and partnerships Private and public limited companies Unlimited and limited liability Choosing a legal structure Not-for-profit organisations Internal and personal sources of start-up finance Borrowing, equity and grants for a small business

Revenue, Costs and Break-Even

Topic overview Revenue, costs and profit Fixed, variable and semi-variable costs Direct costs, indirect costs and overheads Calculating revenue, costs and profit Contribution and its uses Calculating the break-even point Break-even charts and the margin of safety What-if analysis of changes in costs and revenue The usefulness and limits of break-even

Marketing and the Marketing Mix

Topic overview The purpose of marketing and market orientation The marketing mix and the four Ps Product, brand, USP and differentiation The product life cycle Extension strategies The product life cycle and cash flow The Boston matrix Pricing strategies Choosing the right pricing strategy Promotion above the line and below the line Place and distribution channels The marketing mix in different contexts New technology in marketing

Financial Planning and Accounts

Topic overview The role of the finance department Budgets and the purpose of budgeting The benefits and drawbacks of budgets Internal sources of finance External sources of finance Choosing the right source of finance Cash flow and cash flow forecasts Constructing and interpreting a cash flow forecast Cash flow problems and how to improve cash flow The income statement, gross profit and net profit Gross and net profit margins

People in Organisations

Topic overview The role of the human resource department The flexible workforce New technology and changing working patterns Workforce planning The recruitment process, job analysis and job descriptions Internal and external recruitment Methods of selecting employees Methods of training The value of training to a business Appraisal and its methods Measuring workforce performance Organisational structures and the chain of command Delegation, empowerment and delayering

Motivation, Management and Employee Relations

Topic overview Motivation and the benefits of a motivated workforce Taylor and scientific management Mayo and the Hawthorne studies Maslow's hierarchy of needs Herzberg's two factor theory Expectancy theories of Vroom, Porter and Lawler Financial methods of motivation Non-financial methods of motivation Management, management by objectives and Theory X and Y Leadership and leadership styles Leadership theories and choosing a style Employment rights, contracts and equal opportunities Trade unions, industrial conflict and dispute resolution

Operations Management

Topic overview Operations management and added value Job, batch and flow production Productivity and how to raise it Capacity utilisation Technology in operations: IT, CAD, CAM and robotics Lean production, kaizen and just-in-time Quality control and quality assurance Total quality management Purchasing, suppliers and methods of stock control Stock control diagrams and stock levels Innovation, research and development Internal and external economies of scale Diseconomies of scale and the survival of small firms

Data and Market Analysis

Topic overview Presenting and interpreting business data Index numbers and comparing figures over time Calculating price elasticity of demand Interpreting price elasticity and its effect on revenue Income elasticity of demand Sales forecasting and the reliability of a forecast Moving averages and time-series analysis Correlation, scatter graphs and extrapolation Qualitative forecasting techniques

Analysing Business Performance

Topic overview Budget variances and how to calculate them Analysing and evaluating budget variances The balance sheet and how it is constructed Working capital, capital employed and depreciation Liquidity ratios: the current ratio and the acid test Return on capital employed and gearing Comparing accounts over time and between businesses Evaluating the financial position of a business Non-financial measures of performance and vision statements

Aims, Objectives and Strategy

Topic overview Aims, objectives and SMART targets Mission and vision statements Strategy, tactics and corporate plans SWOT analysis Porter's Five Forces The Ansoff matrix Organic growth External growth: mergers and takeovers Horizontal and vertical integration Franchising as a method of growth Rationalisation and relocation Outsourcing production

Decision-Making and Investment Appraisal

Topic overview Types of business decision Scientific and intuitive decision-making Decision trees: constructing and calculating Evaluating decision tree analysis Critical path analysis: building the network Interpreting and evaluating critical path analysis Cost benefit analysis Payback and the average rate of return Discounted cash flow and net present value Choosing between investments Special orders

Change and Risk Management

Topic overview Causes of change in a business Internal and external causes of change Planned and unplanned change Effects of change on a business Managing change and Storey's four approaches Resistance to change and how it is overcome Evaluating change and its impact on stakeholders Types of risk a business faces Risk assessment, prevention and insurance Contingency planning and crisis management

PEST Factors and the External Environment

Topic overview Political factors and the role of government Taxation and subsidies Fiscal and monetary policy Economic growth, GDP and the business cycle Inflation and how it is measured Interest rates and exchange rates Unemployment Demographic change Social and cultural change Technological factors and automation

Ethical, Legal and Environmental Factors

Topic overview Business ethics and ethical objectives Ethical issues facing a business Corporate social responsibility Ethics, profitability and stakeholder views Company law, intellectual property and pay law Employment, discrimination and health and safety law Consumer, competition and data protection law Environmental costs of business activity Controlling environmental costs and business responses

International Trade, Globalisation and the European Union

Topic overview International trade and why it happens Free trade and protectionism Trading blocs and the single market Entering new international markets Globalisation and its causes The effects of globalisation on business Strategies for global growth Glocalisation and adapting to local markets Multinational companies The European Union and the single European market The euro, the Eurozone and membership

Decision-Making and Investment Appraisal

Decision trees: constructing and calculating

3 things to know
Component 2

Overview

Decision tree analysis, expected value and payoff on a decision tree.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What is a payoff on a decision tree?

Key term

What is decision tree analysis?

Key term

What do the square and circle nodes on a decision tree represent?

Questions from this subtopic

Each one with the model answer underneath.

1
What is decision tree analysis?
Model answer
Decision tree analysis is a diagram that maps the options open to a business and the possible outcomes of each. Probabilities and payoffs are attached so that options can be compared by expected value.
2
What do the square and circle nodes on a decision tree represent?
Model answer
A square node is a decision point, where the business chooses between branches. A circle node is a chance point, where the outcome depends on probability rather than on choice.
3
What is expected value?
Model answer
Expected value is the average payoff of a chance node, found by multiplying each outcome by its probability and adding the results. The figure is a weighted average rather than any outcome that will actually occur.
4
What must the probabilities at a single chance node add up to?
Model answer
The probabilities at one chance node must add up to 1. If they do not, an outcome has been omitted or a figure is wrong.
5
How is a decision tree evaluated?
Model answer
A decision tree is evaluated by rolling back from right to left. The expected value of each chance node is calculated first, and the cost of the branch leading to it is then deducted.
6
A launch costs £200,000. There is a 0.6 chance of returns of £500,000 and a 0.4 chance of returns of £100,000. Calculate the expected value of the chance node.
Model answer
Expected value equals 0.6 multiplied by £500,000, which is £300,000. Adding 0.4 multiplied by £100,000 gives a further £40,000. The expected value of the node is therefore £340,000.

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