STATISTICS FOR BUSINESS

1. STATISTICS FOR BUSINESS Chapter 11. Business decisions and risk Mountain climbing and the inherent risks

2. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Before a final decision is made, it may be helpful to develop a model A model is a representation of reality MATHEMATICAL MODELS Pro-forma statements • Forecasts • Supply chain • Inventory • Linear programming • Project management PHYSICAL (prototype) or computer-based three- dimensional model Nuclear reactor • Airplane (wind tunnel) • Skyscraper • Automobile • Mobile phone • kitchen A model is a management tool that: Minimizes risk • Aids planning • Ultimately reduces cost • Exposes potential problems • Improves decisions

3. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks A tradeoff – pros and cons of one decision or another INVENTORY MANAGEMENT 1. Keep large inventories - always satisfying customers but at a high cost 2. Low inventories - risk of stockout Trade-off between high and low inventories OPERATIONS 1. Manufacture in Europe - high cost, better control, low lead times. 2. Manufacture in China - Low cost, long lead times, less control Trade-off between locations QUALITY CONTROL 1. High level of product inspections (direct product cost) 2. Low inspection and a number of defects slip through production (indirect cost to company) Trade-off between level of inspection, and permitted defects FINANCE Float new shares or increase debt Trade-off between decisions Advantages/disadvantages with either selection.

4. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Environment in which we live CERTAIN • You are going to die, or physically disappear from this earth ………….some day • If you are honest, and earn income, you will pay taxes • If you were born outside the US, you can never be president of the USA – under current law Risky – probability or chance • If you marry, on average there is a 30% chance you will divorce …..based on statistics • If you climb in Tibet, there is a risk of having an accident • When you have sex without precaution your partner risks getting pregnant or being infected UNCERTAIN – you have never been there before • You do not know at what age you will die • Will you be always be happy if you marry the person you love? • If you are currently unmarried or have no partner, you do not know how many children you will have

5. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Magnitude and cost of making a decision • Intuition (Based on experience) 2. Quick and dirty (Back of the envelope type calculations) 3. Simple computations 4. Financial models, simulations, linear programming 5. A 3D computer display, physical model 6. Project task force on site) 7. Prototype Cost increases with level of effort

6. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Steps in decision making process • Reason for decision • Changing markets • New technology • Increased competition • • Declining market share 2. Define current or future situation •Collect data • Benchmark • Market research 3. Objectives of decision • Increase profit • Reduce costs • Improve quality • Increase market share • Improve employee motivation • Reduce activity times 4. Consider alternatives • Joint venture or new facility • Produce in-house or purchase; • Hire new staff, or use overtime • Remain in location or move to low cost area. 5. Analyze alternatives • Quantitative methods • Subjective approach • “What-if” analysis • Weighting analysis 6. Select best alternative • Highest on weighted criteria • Less risky • Most profitable • Lowest cost 7. Firm-up operating plan • Personnel involved •Timing of investments • Schedule 8. Implement plan 9. Monitor results Profits as expected • Quality improving • Costs declining?

7. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Decision making under certainty Here the outcome is known with a certain confidence Take retirement as annuity: Annual amount is known Alternative is a lump sum Take a fixed rate mortgage on purchase of property: Monthly payment is known and fixed Alternative is a variable rate mortgage Invest in US Government Certificates of deposit. Interest return each year is known Alternative is to purchase stocks or shares in companies Take a fixed rate mortgage on purchase of property: Monthly payment is known and fixed Alternative is a variable rate mortgage Alternatives are uncertain

8. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Decision making under uncertainty Little idea of outcome. Assigning probabilities is wild. YOU HAVE NEVER DONE IT BEFORE If we build new hotels in Africa, will this increase tourism in this continent? Will the effort, and expenditures to reduce global warming be successful by 2050? In 10 years, will the economy of the former Eastern Europe be equal to that of the European Union? If we invest in new nuclear technology will this industry be profitable in the next 20 years? Will new chemicals to replace chlorofluorocarbons, eventually prove hazardous to the environment? • Decisions made under uncertainty are often: • Long-term • Complex • Involve many players • Political • Emotional

9. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Methods for making decisions under uncertainty – risk but no probabilities MAXIMAX – Optimistic approach Criteria that chooses alternative that maximizes, the maximum outcome of every alternative. The best MAXIMIN – pessimistic approach Criteria that chooses alternative that maximizes, the minimum outcome of every alternative. “Best of worst” EQUALLY LIKELY –moderate approach Criteria that chooses alternative with highest averageoutcome. Middle of the road MINIMAXREGRET – least “painfull” Criteria that analyses the "regret" or disappointmentif the best decision is not selected. Selects the minimum, or the least disappointing. Approach used often depends on personality of decision maker - utility

10. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Decision making under risk Probabilities can be assigned Situation, environment, or action is similar to past events. Risk can be evaluated. YOU HAVE BEEN THERE BEFORE 70% probability will receive contract ; 30% will not 90% certain revenues will exceed forecast; 10% will not 60% certain that your suppliers respect delivery dates; 40% they will be unable 80% sure hotel will be at full capacity; 20% will not Procedure is to multiply outcomes by probability to obtain an expected value This gives a guideline for the decision. However expected value cannot be the numerical outcome. Ultimate objective is to maximize benefits of expected outcome

11. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Expected values Used for quantifying decisions when probabilities are known for the states of nature (external environment) Expected value (EV) Total of each estimated outcome multiplied by probability EV= p1*payoff1 + p2*payoff2 + p3*payoff3 Also called expected value under risk (EVUR) Expected payoff under certainty (EVUC) Best EV if you knew in advance the state of nature EVUC = p1*best payoff1 + p2*best payoff2 + p3* bestpayoff3 Expected value of perfect information (EVPI) EVPI= Expected payoff under certainty - Expected payoff under risk EVPI = EVUC - EVUR You would not pay more than the EVPI in order to be certain of information In order to minimize your risk Analyze using a decision tree or payoff table

12. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Decision tree Diagram showing alternatives and outcomes in decision making. It has nodes and branches Useful visual display for decision making under risk when there are probabilities. CIRCULAR NODE: State of nature external chance event Decision maker has little or no control SQUARE NODE: Denotes decision point. Choice available Manager controls alternative BRANCH: Direction of next decision point • UTILIZATION • Draw tree • Analyze by proceeding from right to left choose alternative that maximizes return • "De-branch" alternatives not selected

13. STATISTICS FOR BUSINESS (Business decisions and risk) Layout of decision tree Mountain climbing and inherent risks EV1= p1*Payoff1+ p2*Payoff2+ p3*Payoff3 (Payoff 3 > Payoff 4) Payoff 1 p1 probability occurrence Payoff 2 2 p2 p3 Payoff 3 choice C EV1 > EV2 4 choice A Payoff 4 choice D Next decisions 1 choice E Payoff 5 choice B 5 Initial decision Payoff 6 p1 choice F 3 p2 Payoff 7 p3 probability occurrence Payoff 8 EV2= p1*Payoff6+ p2*Payoff7+ p3*Payoff8(Payoff 6 > Payoff 5) Decision point. One has control Chance Event. No control

14. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Payoff table

15. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Marginal analysis Probability evaluation that considers benefit of an action as opposed to not taking that action CONSIDER a production and selling operation, (bread, cakes, sandwiches….) • p is probability of selling the product that is made • (1 - p) is probability of not selling product (binomial) • MP is marginal profit from making additional product. It is sold • ML is marginal loss from making additional product. It is not sold • Expected marginal profit = p*MP • Expected marginal loss = (1 – p)*ML • For optimum operation production would not be made unless: • p*MP ≥ (1 – p)*ML • Reorganizing p*MP ≥ ML – p*ML • Giving p ≥ ML/(MP + ML)

16. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Marginal analysis with Normal distribution y1 x1 m - 3s m m + 3s

17. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Utility curves: Managers with different personalities (utility)

18. STATISTICS FOR BUSINESS (Business decisions and risk) Mountain climbing and inherent risks Insurance and expected loss • TRANSPORTATION • Equipment value is $4 million • Probability of a loss is 0.01% • EL = $4,000,000*0.01% = $400 • Insurance premium = $2,000 • $400 < $2,000 • Why insure? • INDUSTRIAL INSURANCE • Building value is £2 million • Probability of a fire is 0.001% • EL = £2,000,000*0.001% = £20 • Insurance premium = £2,500 • £20 < £2,500 • Why insure? • EARTHQUAKE INSURANCE (California) • Value of home is $1 million • Probability of destructive earthquake is 0.02% • EL = $1,000,000*0.02% = $200 • Insurance premium = $2,000 • $200 < £2,000 • Why insure? • FLIGHT INSURANCE • Value of life insurance is $1,000,000 • Probability of plane crashing is 0.0002% • EL = $1,000,000*0.0002 = $2.00 • Insurance premium cost $20 • $ 2.00 < $20.00 • Why insure? However insurance is taken out. We are “afraid”: Concept of utility