# Chapter 10 Dealing with Uncertainty (Graphical Methods)

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Chapter 10 Dealing with Uncertainty (Graphical Methods)

Overview Language: Definitions of risk, uncertainty, sensitivity, as used in ECON115 Consequences of poor risk management and poor communications about risk Risk vs. Uncertainty Graphical methods for communicating about options under uncertainty Breakeven plots Spider plot Problems with Risk-adjusted interest rates

Risk, Uncertainty, Sensitivity Risk and uncertainty are both words to describe situations where the future is unknown. Risk describes situations with known probabilities or probabilities that have been estimated. Uncertainty describes situations with unknown probabilities. Sensitivity indicates how a decision or worth estimate (PW, AW,etc.) changes when a factor (e.g. useful life, certain revenues or costs, MARR) changes.

Why should we care? Engineers often have valuable information about the risks of technology. Engineers and Management need to communicate effectively about risk and uncertainty. Engineers need to assist Management in maintaining a scientific approach towards risk and uncertainty. Otherwise, bad things can happen.

A Famous Example Click for movie Alternate link (note: some versions of Microsoft Internet Explorer can not play the files. Netscape needs either real-player or windows- media-player to play the movie.)

A famous example The US Space Shuttle Challenger exploded on 28/Jan/1986, killing 7 including a teacher in space. It cost over us\$3 billion to replace the shuttle, and the accident temporarily halted the US space program. Why did this happen? What does it have to do with Econ 115?

Why? US President Reagan ordered an investigation. They found two main causes: Technical reasons [not relevant to Econ115] –The center fuel tank exploded. It contains the liquid hydrogen and liquid oxygen. –A rubber joint in the solid rocket, called an O-ring failed. A flame escaped from the bad joint, and burned a hole in the center tank, causing the explosion. Managerial reasons [relevant to Econ115] –Problems with managers and engineers communicating. –Lack of scientific approach to risk and uncertainty.

Econ115: Problems with managers and engineers communicating. Engineers knew the system could fail. Est. Probability of Failure = 0.003 to 0.01 Managers took previous successes to indicate that it would not fail. Est. Probability of Failure =0.00001 Engineers had evidence that cold weather (-3C) would increase likelihood of failure in the solid rocket booster O-ring. This is a critical component. The rubber O-ring required a temperature of 10-15C to seal correctly. BUT…. Managers didnt care.

Lack of scientific approach to risk and uncertainty. NASA never officially estimated shuttle failure probabilities. No statistical experts. No mathematical analysis. Only opinions and guesses. NASA Managers estimated shuttle failure rates at 10,000-100,000 to 1. (that is, 0.001-0.01%) NASA Engineers estimated shuttle failure rates at around 100 to 1 (1%). The historical failure rate for solid rocket boosters is much higher (25 to 1 or 4%). Source: Feynman, Richard P., Personal Observations on the Reliability of the Space Shuttle, Report of the Presidential Commission on the Space Shuttle Challenger Accident, Appendix F, US Government Printing Office, 1986.Personal Observations on the Reliability of the Space Shuttle, Report of the Presidential Commission on the Space Shuttle Challenger Accident

Overview Risk Uncertainty (known probabilities) (unknown probabilities) Chapter 13 Chapter 10 This week: focus on uncertainty. Sensitivity analysis –Breakeven analysis (1 unknown factor) –Spider plot graphs (many unknown factors; 1 at a time) –Multiple factors; optimistic/pessimistic Commonly-used methods for dealing with uncertainty -- that can fail and give the wrong answer (revisits Ch.4 material) –Risk Adjusted MARR –Reduction in useful life

Risk: Examples Betting on a coin toss. Many coins have a persons head on one side, and so the outcomes are called heads and tails. If the coin is fair: – the probability of heads is 50% – the probability of tails is 50% Insurance companies offer a contract to protect customers against risky events (accident, health, death, fire, etc.) –Cost of contract = probability of event * payoff for event –Company needs to know probability to establish a price –With lots of data, the probabilities can be estimated and the insurance company can use this to set prices. Young people are more likely to have accidents. Affects automobile insurance rates. Old people are more likely to die from health problem. Affects health and life insurance rates.

Uncertainty: Examples Will interest rates rise or fall? Future prices –Costs: price of company inputs (land/rent, labor, machinery, software, etc.) –Revenues: price of finished products and services (Sometimes can be resolved through futures markets) Life –Equipment life (when will a product wear out?) –Market life (when will a product become obsolete?)

Single-factor Uncertainty Vary one unknown factor or element of the problem All other factors are constant Goal is to make a go-no go decision, compare designs or other alternative choices. Breakeven Analysis

Breakeven analysis One unknown factor Two or more designs A do-nothing design is allowed. –The do-nothing design usually has 0 revenue, and 0 costs, but not always. For example, failing to fix a hill slide or a defective space shuttle component could be expensive. Goal is to compare PW or AW graphically as a function of the unknown factor –And never IRR

Breakeven analysis example go-no go decision An expenditure of \$20,000 is made in a small workshop. The modification will result in first year savings of \$2,000, second year savings of \$4,000, and savings of \$5,000 per year thereafter. How many years must the system (the savings annuity) last if a 20% return on investment is required? Because it is custom made, the system has no salvage value at any time.

Breakeven: Go/no-go decision Year 0, -\$20000 Year 1 \$2000 Year 2 \$4000 Year 3 through ………..Year L \$5000/year Cash flow diagram. L = life in years. If we assume L > 3, PW(build) = -20000 + 2000 (P/F,20%,1) + 4000 (P/F,20%,2) + 5000 (P/F,20%,2)(P/A,20%,L-2) PW(dont build) = 0

Breakeven: Go/no-go decision Break even point

Breakeven: Go/no-go decision Break even point Recommendation: If L is 14 years or less, dont build. If L is 15 years or more, build.

Breakeven analysis: comparing 2 designs Fall 2000 final 2(b) Equipment choice. Either Machine A or Machine B can be used for the same task. Machine A has a capital cost of \$1,000,000, lasts 5 years, and has an operating cost of \$240,000/year. Machine B has a capital cost of \$2,000,000, lasts 6 to 10 years, and has an operating cost of \$120,000/year. Both machines have zero salvage value. The MARR is 20%/year. The machine is essential and an identical replacement will be purchased at the end of its useful life. Which machine should be chosen? If you are not sure, use a graph to explain why.

Breakeven: comparing 2 designs Machine A Initial Cost \$1,000,000 Annual O&M \$240,000 Savage Value \$0 Life 5 years, certain AW = \$1,000,000 (A/P,20%,5) + \$240,000/year =\$334379/year + \$240,000/year =\$574379/year Machine B Initial Cost \$2,000,000 Annual O&M \$120,000 Salvage Value \$0 Life 6-10 years,uncertain AW= \$2,000,000(A/P,20%,L)+ \$120,000/year MARR = 20 %

Breakeven analysis: comparing 2 designs

Breakeven analysis: 2 designs The breakeven point between A and B occurs around 12 years. If B lasts 6 to 10 years, it will never be as economical as A. We can safely recommend A.

Breakeven Analysis: unknown i% Investment A Cash Flows Year 0 -90 000 Year 1 30 000 Year 2 30 000 Year 3 30 000 Year 4 30 000 Investment B Cash Flows Year 0 -10 000 Year 1 -6 000 Year 2 20 000 Year 3 15 000 Year 4 -10 000 MARR is unknown. What should we do? Graph PW vs. i% Suppose that A and B are mutually exclusive. Should we choose invest A or investment B?

Breakeven analysis: unknown i%

Goal: max PW of investment Recommend: Invest in A if i 10% Breakeven point

Multiple Factors: the SpiderPlot Origin assumes some set of values for the unknown factors We vary only one unknown factor at a time. X-axis indicates % change in an unknown factor Y-axis indicates PW, AW or other criteria PW % Life Salvage Value Initial Cost +50% - 50% L=5 years S=\$10000 C0=\$20000

Multiple Factors: Pessimistic-Expected-Optimistic Multiple factors can vary => hard to graph The result has to be a table, not a graph The pessimistic analysis is made with factors chosen to produce a possible bad outcome – i.e. low profit or high cost The optimistic analysis is made with factors chosen to produce a possible good outcome – i.e. high profit or low costs. The expected analysis is made with factors chosen in the middle -- neither pessimistic nor optimistic.

Commonly-used methods for dealing with uncertainty -- that can fail and give the wrong answer (revisits Ch.4 material) Method 1. Risk Adjusted MARR MARR [risky project] = MARR [no risk projects] + risk adjustment Increasing MARR makes future cash flows (both costs and revenues) appear smaller in year 0 dollars. Method 2. Truncated cash flows Cut off cash flows after a certain year. Problem: Ignoring future cash flows or making them less important can lead to some unusual decisions.

Risky investment Suppose we have two investments A = School Bus Company B = Nuclear Waste Disposal Company Suppose our expert engineer determines that B is more risky than A.

Here are the Cash flows (stolen from unknown i% example) Investment A Year 0 -90 000 Year 1 30 000 Year 2 30 000 Year 3 30 000 Year 4 30 000 Investment B Year 0 -10 000 Year 1 -6 000 Year 2 20 000 Year 3 15 000 Year 4 -10 000 Somewhat risky The company no-risk MARR is 8%. Very risky Engineers risk assessment

unknown i%

Analysis At MARR=8%, PW[A] = \$9363 PW[B] = \$6148 So PW[A] > PW[B] => A more profitable We were also told that A is also less risky. So A should be the preferred investment.

Adjustment of MARR for Risk Suppose we adjust MARR upwards for Risk (We will see that this is a bad idea) 1.Choose MARR[A]=12%, MARR[B]=15%, since A is a little risky and B is very risky. 2.Checking the table (or graph): PW[A,12%]=\$1120 PW[B,15%]=\$4050 => this says choose B! But clearly, A is the better choice. –A had higher PW than B at marr of 8%; AND –A was less risky than B => adjusting MARR for risk can sometimes lead to bad decisions

Summary Uncertainty occurs we do not know the probabilities for unknown future events. This chapter looked at methods for dealing with uncertainty. Breakeven methods involve simple graphs that vary one factor. Spiderplot varies many factors, but only one at a time. Tables with optimistic, pessimistic, and expected outcomes can also be useful to discuss uncertain factors. Adjusting MARR for uncertainty or risk is commonplace in business decision making, but it can yield strange results.

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