Chapter 10Dealing 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

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(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 didn’t 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.

OverviewRisk 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 person’s 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 examplego-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(don’t build) = 0

Breakeven Analysis

-10000

-8000

-6000

-4000

-2000

0

2000

0 5 10 15 20 25

Life L(years)

Pre

sen

t W

ort

h

Breakeven: Go/no-go decision

Break even point

Breakeven Analysis

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0 5 10 15 20 25

Life L(years)

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Breakeven: Go/no-go decision

Break even point

Recommendation: If L is 14 years or less, don’t 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 BInitial Cost $2,000,000Annual O&M $120,000Salvage Value $0Life 6-10 years,uncertain

AW=$2,000,000(A/P,20%,L)+$120,000/year

MARR = 20 %

Breakeven analysis: comparing 2 designs

Breakeven comparison of machines A and B

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

0 2 4 6 8 10 12 14 16

L = Life of B

An

nu

aliz

ed

Co

st A

W[C

ost

]

AW[A]

AW[B]

Breakeven analysis: 2 designsBreakeven comparison of machines A and B

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

0 2 4 6 8 10 12 14 16

L = Life of B

An

nu

alize

d C

ost

AW

[Co

st]

AW[A]

AW[B]

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 BCash 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%PW[A] vs. PW[B]

-15000

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0

5000

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15000

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0% 5% 10% 15% 20% 25%

interest rate i%

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year

0 $

]

PW[A]

PW[B]

Breakeven analysis: unknown i%PW[A] vs. PW[B]

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PW[A]

PW[B]

Goal: max PW of investmentRecommend: Invest in A if i<10%, Invest in B 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

%

LifeSalvage 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 Engineer’s risk assessment

unknown i%PW[A] vs. PW[B]

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-5000

0

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10000

15000

20000

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0% 5% 10% 15% 20% 25%

interest rate i%

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year

0 $

]

PW[A]

PW[B]

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 RiskSuppose 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%]=$1120PW[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.