Question

Question 9 Use the following decision tree, but update the probabilities as follows: Probability of Small Demand = 20% Probability of Medium Demand = 14% Probability of Large Demand = remaining probability What is the expected value with perfect information (in millions)?

Answer 1

As per the revise information given in the question for the probabilities values, the probability of the small demand is 20% which 0.2. the probability of the medium demand is 14% which is 0.14 and the remaining is the large demand probability which is (100 - (20 + 14) = 66% or 0.66 is the probability of the large demand.

So, we have to replace the values of the new probabilities in the given decision tree to calculate the expected value. The expected value for a project is calculated by multiplying each of the possible outcomes of that project by the likelihood each outcome will occur and then summing all of those values. As a final decision, we have to choose the higher value as the Expected Value (EV) of the project. So, now based on this understanding, let's find out the expected value of all 3 projects mentioned in the given picture.

Project A (Subcontract):-

1 x 0.2 + (1.3 x 0.14 + 1.3 x 0.14) + ( 1.5 x 0.66 + 1.6 x 0.66 + 1.8 x 0.66) = 0.2 + (0.182 + 0.182) + (0.99 + 1.056 + 1.188) = 0.2 + 0.364 + 2.244 = 2.808

So the EV of Subcontract is 2.808 $

Project B ( Expand):-

0.2 x ( 0.7 + 1.5 + 1.0) + 0.14 x 1.6 + 0.66 x ( 1.6 + 1.5 + 1.7) = 0.64 + 0.224 + 3.168 = 4.032

So the EV of Expand is 4.032 $

Project C ( Build) :-

0.2 x (0.9 + 1.4 + 1.0) + 0.14 x ( 1.0 + 1.1 + 0.9 ) + 0.66 x 2.4 = 0.66 + 0.42 + 1.584 = 2.664

So the Ev of the Build is 2.664 $.

Since the largest of all of the above three projects is, 4.032 million $ that is the Expected Value.