Calculating Expected Costs & Benefits (AQA Level 3 Mathematical Studies (Core Maths)): Revision Note

Calculating Expected Costs & Benefits

What is cost-benefit analysis?

• When businesses or individuals make decisions, it is unlikely to be a simple case of "which option will generate the most extra income?"

• It is likely that each option, which has a benefit, will also have an associated cost

• Cost-benefit analysis is the process of evaluating both the additional benefits, and additional costs, and making an overall decision

• For example, if a restaurant is looking to open another establishment in a different location

  • There will be different additional benefits for each location

    • This could depend on the population, the number of tourists, and the average prices in each location

  • There will also be different additional costs for each location

    • This could include rent costs, the number of new employees, and cost of ingredients and products

• There may be costs which are unavoidable

  • E.g. compulsory insurance for a business, or licensing costs

• Sometimes decisions are made on the principle of minimising the maximum possible loss, rather than maximising possible benefits, or minimising total costs

  • For example, if a bicycle manufacturer is selecting which type of brakes to use

    • There may be a "cheap" option, which is not be the best quality and has a higher failure rate

    • If an accident and injury happened due to this component, the company could face extremely costly legal action

    • So the bicycle manufacturer may choose a more expensive component, to minimise the maximum potential loss

How do I use expected values in a cost-benefit analysis?

• Probabilities and expected values should be used where possible in a cost-benefit analysis

• In general, to find the overall benefit or cost:

  • Find the individual benefits and costs:

    • 

  • Then find the sum of all the additional incomes

  • And subtract the sum of all the additional costs

• These will often be estimates of costs and incomes and probabilities, and the effects of estimation should be considered

  • Underestimating costs, and overestimating benefits is risky, as there is a greater chance of losing money

  • Overestimating costs, and underestimating benefits is less risky, as there is a smaller chance of losing money