10. Project risk and uncertainty

Question 1

What are the two types of decisions?

Answer 1

1. Decisions making under uncertainty

2. Decisions under risk

Question 2

What are the methods for describing project risk?

Answer 2

• Sensitivity analysis: a way to find which project variables have the greatest effect on the acceptability of the project (project’s sensitivity to variables)
• Scenario analysis: a means of comparing a “base-case” or expected project measurement (ex: NPW) with 1 or more other scenarios to find the extreme and most likely outcomes

Question 3

Describe a Decision under uncertainty.

Answer 3

Maximax - choose the alternative that maximizes the maximum outcome for every alternative
Maximin - choose the alternative that maximizes the minimum outcome for every alternative
Equally likely - choose the alternative with the highest average outcome

Question 4

Describe decision under risk.

Answer 4

• This is where we use decision tree
• [Square] Decision node: from which an alternative may be selected
• (circle) State of nature node: where a state of nature will occur

-States of nature have a probability of occurrence and an estimated monetary pay-off expressed in actual/real dollars
- Each option has an Expected Monetary Value (EMV)
EMV = (sum of estimated monetary pay-off of each state of nature) x (its probability of occurrence)
->The alternative with the largest EMV should be selected

Question 5

Which option should we choose?

Answer 5

Invest $50,000, because EMV is higher

Question 6

What does this mean?

Answer 6

The probability of event B, given that event A has already occurred.

*If B and A are independent, we know P(B|A) = P(B)

Question 7

What’s Bayes’ Theorem?

Answer 7

Its used to calculate the probability of an event based on its association with another event.

We will it to calculate the Probability of each Path/Branch in the tree or Joint Probabilities.
P(A∩B) means “the probability of both A and B happening”

Question 8

Marginal Probabilities - How do you calculate how probable it is for there to be favourable conditions?

Answer 8

Calculate joint probability from cond. probabilities:
P(A)P(F|A) = P(A∩F)
Then sum all the joint probabilities that have F in them P(F) = 0.2+0.26+0.07 = 0.53

Question 9

ex: How did they get the Marginal probabilities of favourable or unfavourable scenario?

Answer 9

They followed the favourable node:

0.750.75+0.250.45 = 67.5%

Question 10

How do you get the final probabilities of each decision?

How do you calculate EMV at every node?

Answer 10

Multiply probabilities down the chain - ex: 0.750.25 = 18.75%
Sum for all branches (End of branch value * probability)
ex: $ 180,869,4570.75 + $ 109,951,470*0.25 = $ 163,139,960