Lecture No. 41
Chapter 12
Contemporary Engineering Economics
Copyright © 2010
Contemporary Engineering Economics, 5th edition, © 2010

 A graphical tool for describing
(1) the actions available to the decision-maker,
(2) the events that can occur, and
(3) the relationship between the actions and events.
Contemporary Engineering Economics, 5th edition, © 2010

Constructing a
Decision Tree
A Company is considering marketing a new product. Once the product is introduced, there is a 70% chance of encountering a competitive product. Two options are available each situation.
Decision Points
Events
( ) Probability
Market
 Option 1 (with competitive product):
Raise your price and see how your competitor responds. If the competitor raises price, your profit will be $60. If they lower the price, you will lose $20.
 Option 2 (without competitive product): You still two options: raise your price or lower your price.
Do not market
First Decision Point
$0
Our Price
High
Competitor’s price
High
(0.5)
Conditional
Profit
$60
(0.5)
Low
-$20
Competitive
Product (0.7)
High
(0.2)
$40
Low
No Competitive
Product (0.3) Low
(0.8)
$10
High
$100
Low
$30
Second Decision Point
The conditional profits associated with each event along with the likelihood of each event is shown in the decision tree.
Contemporary Engineering Economics, 5th edition, © 2010

 To analyze a decision tree, we begin at the end of the tree and work backward.
 For each chance node, we calculate the expected monetary value (EMV), and place it in the node to indicate that it is the expected value calculated over all branches emanating from that node.
 For each decision node, we select the one with the highest EMV (or minimum cost). Then those decision alternatives not selected are eliminated from further consideration.
Contemporary Engineering Economics, 5th edition, © 2010

$20
Set High Price
High
(0.5)
(0.5)
Low
$60
-$20
$44
Market
$44
Competitive
Product (0.7)
$20
Do not market
No Competitive
Product (0.3)
Low
High
(0.2)
$40
$16
Set High Price
Low
(0.8)
$10
$100
$100
Low
$0
$30
Contemporary Engineering Economics, 5th edition, © 2010

 Market the new product.
 Whether or not you encounter a competitive product, raise your price.
 The expected monetary value associated with marketing the new product is $44.
Contemporary Engineering Economics, 5th edition, © 2010

 A company is considering the purchase of a new laborsaving machine.
 The machine’s cost will turn out to be $55 per day. Each hour of labor that is saved reduces costs by $5.
However, there is some uncertainty over the number of hours that actually will be saved.
 It is judged that the hours of labor saved per day will be
10, 11, or 12, with probabilities of 0.10, 0.60, 0.30, respectively.
 Let us define “profit” as the excess of labor-cost savings over the machine cost.
Contemporary Engineering Economics, 5th edition, © 2010

-$5
0.10
$1.0
10
$1
Invest
0.60
11 0
12
0.30
Do not invest
$5
EMV = $1.0
Decision: Purchase the equipment
Contemporary Engineering Economics, 5th edition, © 2010
0



What is EVPI? This is equivalent to asking yourself how much you can improve your decision if you had perfect information.
Mathematical Relationship:
EVPI = EPPI – EMV = EOL where EPPI (Expected profit with perfect information) is the expected profit you could obtain if you had perfect information, and EMV
(Expected monetary value) is the expected profit you could obtain based on your own judgment. This is equivalent to expected opportunity loss ( EOL ).
Contemporary Engineering Economics, 5th edition, © 2010

State of
Nature
10
11
12
Best
Strategy
Don’t Buy
Indifferent
Buy
Maximum
Payoff
0
0
5
Probability the State of
Nature
Occurs
0.10
0.60
0.30
Expected
Payoff or each State
0
0
1.5
 Expected Profit with Perfect Information (EPPI):
(0.10)(0) + (0.60)(0) + (0.30)(5) = $1.5
 Expected Value of Perfect Information (EVPI) = EPPI – EMV
$1.5 - $1 = $0.5
Contemporary Engineering Economics, 5th edition, © 2010

Bill’s Decision Problem – $50,000 to Invest
 Decision Problem:
 Buying a highly speculative stock (d
1
) with three potential levels of return – High (50%),
Medium (9%), and Low (-
30%).
 Buying a very safe U.S.
Treasury bond (d
2
) with a guaranteed 7.5% return.
 Seek advice from an expert?
 Seek professional advice before making the decision
 Do not seek professional advice – do on his own.
Contemporary Engineering Economics, 5th edition, © 2010

Contemporary Engineering Economics, 5th edition, © 2010

Evaluating Options in Bill’s Investment Problem
• Option 1:
1) Period 0: (-$50,000 - $100) = -$50,100
Period 1: (+$75,000 - $100) - 0.20($24,800) =$69,940
PW(5%)=-$50,100 + $69,940 ( P/F , 5%, 1) = $16,510
2) Period 0: (-$50,000 - $100)= -$50,100
Period 1: (+$54,500 - $100)- (0.20)($4,300) = $53,540
PW(5%) = -$50,100 + $53,540 ( P/F , 5%, 1) = $890
3) Period 0: (-$50,000 - $100) = -$50,100
Period 1: (+$35,000 - $100) – (0.20)(-$14,800) = $37,940
PW(5%)= - $50,100 + $37,940 ( P/F , 5%, 1) = -$13,967
• Option 2:
Period 0: (- $50,000 - $150) = -$50,150
Period 1: (+$53,750 - $150) = $53,600
PW (5%)= -$50,150 + $53,600 ( P/F , 5%, 1) = $898
EMV = $898
Or, prior optimal decision is Option 2
(c) 2001 Contemporary Engineering Economics 13

Decision Option
Potential
Return Level
High (A)
Medium (B)
Probability Option1:
Invest in
Stock
0.25
$16,510
0.40
890
(Prior
Optimal)
Option 2:
Invest in
Bonds
$898
898
Low(C) 0.35
-13,967 898
EMV -$405 $898
EPPI = (0.25)($16,510) + (0.40)($898)
+ (0.35)($898) = $4,801
EVPI = EPPI – EV
= $4,801 - $898
= $ 3,903
Optimal
Choice with
Perfect
Information
Stock
Bond
Opportunity
Loss
Associated with Investing in Bonds
$15,612
0
Bond
$3,903
EOL = (0.25)($15,612)
+ (0.40)(0) + (0.35)(0)
= $ 3,903
0
Contemporary Engineering Economics, 5th edition, © 2010

Bill’s Investment Problem with an Option of Getting
Professional Advice
Updating Conditional Profit (or Loss) after
Paying a Fee to the Expert (Fee = $200)
Revised Decision Tree
Contemporary Engineering Economics, 5th edition, © 2010

Conditional Probabilities of the Expert’s Prediction,
Given a Potential Return on the Stock
What the Report
Will Say
Favorable (F)
Unfavorable (UF)
Given Level of Stock Performance
High
(A)
0.80
0.20
Medium
(B)
0.65
0.35
Low
(C)
0.20
0.80
Contemporary Engineering Economics, 5th edition, © 2010

Nature’s Tree Joint & Marginal Probabilities
 P(A,F) = P(F|A)P(A) = (0.80)(0.25) = 0.20
 P(A,UF|A)P(A) = (0.20)(0.25) = 0.05
 P(B,F) = P(F|B)P(B) = (0.65)(0.40) = 0.26
 P(B,UF) = P(UF|B)P(B) = (0.35)(0.40) = 0.14


P(F) = 0.20 + 0.26 + 0.07 = 0.53
P(UF) = 1 – P(F) = 1 – 0.53 =
0.47
Contemporary Engineering Economics, 5th edition, © 2010

What the Report Will Say
Joint Probabilities
When Potential
Level of Return is
Given
High (A)
Favorable (F)
0.20
Unfavorable (UF)
0.05
Medium (B)
Low (C)
Marginal
Probabilities
0.26
0.07
0.53
0.14
0.28
0.47
Contemporary Engineering Economics, 5th edition, © 2010
Marginal
Probabilities of
Return Level
0.25
0.40
0.35
1.00

P(A|F) = P(A,F)/P(F) = 0.20/0.53 = 0.38
P(B|F) = P(B,F)/P(F) = 0.26/0.53 = 0.49
P(C|F) = P(C,F)/P(F) = 0.07/0.53 = 0.13
P(A|UF) = P(A,UF)/P(UF) = 0.05/0.47 = 0.11
P(B|UF) + P(B,UF)/P(UF) = 0.14/0.47 = 0.30
P(C|UF) = P(C,UF)/P(UF) = 0.28/0.47 = 0.59
Contemporary Engineering Economics, 5th edition, © 2010

Decision Making after Having Imperfect Information
- $6,319
Contemporary Engineering Economics, 5th edition, © 2010