Decision Recognizing Risk_Engineering Economy Topic 5

1. DECISION RECOGNIZING
RISKS
Expected Monetary Value of Alternatives
and Decision Tree Analysis
TOPIC 5

2. TOPIC OUTLINE:
Decision Recognizing Risks
Expected Monetary Value of Alternatives
Decision Tree Analysis
Introduction
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3
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3. INTRODUCTION
Decision Recognizing Risks
Expected Monetary Value of
Alternatives and Decision Tree
Analysis

4. Engineers and economic analysts usually deal with
estimates about uncertain future by placing
appropriate reliance on past data, if any exist.
This means that probability and samples are used.
Actually, the use of probabilistic analysis is
not common as might expected. The reason for this
is not that the computations are difficult to
perform or understand, but that realistic
probabilities associated with cash flow estimates
are difficult to assign. Experience and judgment
can often be used in conjunction with
probabilities and expected values to evaluate the
desirability of an alternative.
INTRODUCTION

5. Decision Recognizing
Risks
Topic 5: Decision Recognizing Risks

6. •Risk-based decision making provides a process to
ensure that optimal decisions, consistent with the
goals and perception of those involved are reached.
•Risk is present when there may be two or more
observable values for a parameter and it is possible
to estimate the chance that each value may occur.
•Decision making under risk is introduced when an
annual cash flow estimate has a 50-50 chance of
being either -₱50,000 or ₱25,000.
Decision Recognizing Risks

7. Expected Monetary
Value of
Alternatives
Topic 5.1: Expected Monetary Value of
Alternatives

8. •Expected Monetary Value is a statistical
concept that calculates the average outcomes
when the future includes the scenarios that
may or may not happen.
•The expected value can be interpreted as a
long-run average observable if the project is
repeated many times.
•Since a particular alternative is evaluated
or implemented only once, a point estimate of
the expected value results.

9. EXPECTED MONETARY VALUE OF ALTERNATIVES
The expected value E(X)
is computed using the
relation
Where expected value is
simply the sum of the
probability of a specific
value multiplied by its
variable x. Expected value = E(X)
Variable x = Xi
Probability of a specific value =
P(Xi)

10. EXPECTED MONETARY VALUE OF ALTERNATIVES
•Probabilities are always correctly
stated in decimal form, but they are
routinely spoken of in percentages and
often referred to as chance, such as
the chances are about 10%.
•𝑋 represents the estimated cash flows.
It can either be positive or negative.

11. • If a cash flow sequence includes revenues
and costs, and the present worth at the MARR
(minimum acceptable rate of return) is
calculated, the result is the expected value
E(PW) of the discounted cash flows.
• If the expected value is negative, the
overall outcome is expected to be a cash
outflow. For example, if E(PW) = - ₱76,500,
this indicates that the proposal is not
expected to return the MARR.
EXPECTED MONETARY VALUE OF ALTERNATIVES

12. A downtown hotel is offering a new service for weekend travelers
through its business and travel center. The manager estimates
that for a typical weekend, there is a 50% chance of having a net
cash flow of ₱250,000 and a 35% chance of ₱510,000. He also
estimates there is a small chance (5%) of no cash flow and 10%
chance of a loss of ₱25,000, which is the estimated extra personnel
and utility costs to offer the service. Determine the expected net
cash flow.
Let X be the net cash flow in pesos, and let P(X) represent the
associated probabilities.
E(X) = ₱250,000(0.50) + ₱510,000(0.35) + ₱0(0.05) - ₱25,000(0.10)
E(X) = ₱301,000.00
Example #1

13. Example #2
An electric utility is experiencing a difficult time obtaining natural
gas for electric generation. Fuels other than natural gas are
purchased at an extra cost, which is transferred to the customer.
Total monthly fuel expenses are now averaging ₱395,000,000. A
chemical engineer with this city-owned utility has calculated the
average revenue for the past 24 months using three fuel-mix
situations-gas plentiful, less than 30% other fuels purchased, and
30% or more other fuels. The following table indicates the number
of months that each fuel-mix situation occurred. Can the utility
expect to meet future monthly expenses based on the 24 months of
data, if a similar fuel-mix pattern continues?

14. Example #2
Let X be the net cash flow in pesos, and let P(X) represent the associated probabilities.
E(X) = ₱269,104,000(0.50) + ₱400,845,000(0.25) + ₱615,400,000(0.25) – 395,000,000
E(X) = - ₱6,386,750
If this pattern continues, the utility will no longer meet the future expenses.
Using the data in months, the
probabilities are as follow:
₱
269,104,000
400,845,000
615,400,000

15. Example #3
Lite-Weight Wheelchair Company has a substantial investment
in tubular steel bending equipment. A new piece of equipment
costs ₱255,000 and has a life of 3 years. Estimated cash flows
shown in the table depend on economic conditions classified as
receding, stable, or expanding. A probability is estimated that
each of the economic conditions will prevail during the 3-year
period. Apply expected value and PW analysis to determine if
the equipment should be purchased. Use a MARR of 15% per
year.

16. Example #3
Let X be the net cash flow in pesos, and let P(X) represent the associated probabilities.
E(X) = – ₱37,814.16947(0.2) – ₱26,677.48829(0.6) + ₱60,443.41251(0.2)
E(X) = - ₱11,480.64
The equipment is not justified since E(PW)<0.
PW = (Investment cost) + (values in every year) (1 + % per year)-n
₱
-255,000 -255,000 -255,000
125,000
100,000
50,000
100,000
100,000
100,000
100,000
150,000
175,000
PWR = -255,000 + 125,000(1.15)-1 + 100,000(1.15)-2 + 50,000(1.15)-3
= -₱37,814.16947
PWS = -255,000 + 100,000(1.15)-1 + 100,000(1.15)-2 + 100,000(1.15)-3
= -₱26,677.48829
PWE = -255,000 + 100,000(1.15)-1 + 150,000(1.15)-2 + 175,000(1.15)-3
= ₱60,443.41251

17. Decision Tree
Analysis
Topic 5.2: Decision Tree Analysis

18. •Alternative evaluation may require a series of
decisions where the outcome from one stage is
important to the next stage of decision making.
When each alternative is clearly defined and
probability estimates can be made to account for
risk, it is helpful to perform the evaluation using
a decision tree.
•In decision tree analysis, a problem is depicted
as a diagram which displays all possible actions,
events, and payoffs (outcomes) needed to make
choices at different points over a period of time.
Decision Tree Analysis

19. •The decisions tree is constructed left to right and
includes each possible decision and outcome.
•A square represents decision node with the possible
alternatives indicated on the branches from the
decision node.
•A circle represents a probability node with the
possible outcomes and estimated probabilities on the
branches.
Decision Tree Analysis
Decision Node Probability Node

20. Since outcomes always follow decisions, the treelike structure will
look like the one below.
Decision Tree Analysis

21. To construct a Decision Tree Analysis:
•Determine the PW value for each outcome branch
considering the time value of money.
•Calculate the expected value for each decision
alternative.
Decision Tree Analysis
where the summation is taken over all possible
outcomes for each decision alternative.

22. To construct a Decision Tree Analysis:
•At each decision node, select the best
E(decision) value-minimum cost or maximum
value (if both costs and revenues are
estimated).
•Continue moving to the left of the tree to
the root decision in order to select the best
alternative.
•Trace the best decision path back through the
tree.
Decision Tree Analysis

23. Example #1
A decision is needed to either market or sell
a new invention. If the product is marketed,
the next decision is to take it international
or national. Assume the details of the
outcome branches result in the decision tree
given. The probabilities for each outcome
and PW of CFBT (cash flow before taxes) are
indicated. These payoffs are in millions of
pesos. Determine the best decision at the
decision node D1.
(₱ million)

24. Example #1
Therefore, the best decision is to
sell, not to market a new invention.
Computing the Expected Values:
E(X) = 0.5(12) + 0.5(16)
E(X) = 14
E(X) = 0.4(4) + 0.4(-3) + 0.2(-1)
E(X) = 0.2
E(X) = 0.8(6) + 0.2(-3)
E(X) = 4.2
E(X) = 0.4(6) + 0.4(-2) + 0.2(2)
E(X) = 2
E(X) = 14(0.2) + 04.2(0.8)
E(X) = 6.16
(₱ million)