Key considerations as Allied develops its strategy for disposing of the case are the probabilities associated with John’s response to an Allied counteroffer of $400,000 and the probabilities associated with the three possible trial outcomes. John will accept a counteroffer of $400,000 is 0.10, John will reject the counteroffer of $400,000 is 0.40, and John will make a counteroffer of $600,000 is 0.50. If the case goes to court, they believe the jury will award John damages of $1,500,000 is 0.30, award John damages of $750,000 is 0.50 and the probability the jury will award John nothing is 0.20.

1.) Make a decision tree

2.) A recommendation regarding whether Allied should accept John’s offer to settle the claim for $750,000.

3.) A decision strategy that Allied should follow if they decide to make John a counteroffer of $400,000.

4.) A risk profile for your recommended strategy.

I agree on the strategy, make a decision tree, and expected value of either decision.

I assume you know how to do the decision tree.

1.) To create a decision tree, we need to map out the possible outcomes and their associated probabilities.

Start by drawing a square at the beginning of the tree and label it "Initial Decision."

From this square, draw three branches representing the three choices Allied has when John rejects their counteroffer: John accepts $400,000, John rejects $400,000, and John counteroffers $600,000.

Next, draw three more branches from each of these choices to represent the trial outcomes: Jury awards John $1,500,000, Jury awards John $750,000, and Jury awards John nothing.

Assign the corresponding probabilities to each outcome along the branches. For example, the probability that John accepts $400,000 is 0.10, so on the branch representing this outcome, write 0.10.

Finally, add the monetary values associated with each outcome, such as damages awarded by the jury. Label the end points of the branches accordingly.

2.) To determine whether Allied should accept John's offer to settle for $750,000, we need to evaluate the expected value of accepting the offer versus going to trial.

Calculate the expected value by multiplying the possible outcomes by their respective probabilities:

Expected Value of Accepting the Offer = (0.30 * $1,500,000) + (0.50 * $750,000) + (0.20 * $0)

Compare the expected value with the settlement offer of $750,000. If the expected value is higher, Allied should reject John's settlement offer. If it is lower, accepting the offer might be preferable.

3.) If Allied decides to make John a counteroffer of $400,000, a decision strategy would involve evaluating the probabilities associated with John's possible responses.

Multiply the probabilities of each outcome by their respective monetary values and add them up:

Expected Value of Counteroffer = (0.10 * $400,000) + (0.40 * ???) + (0.50 * ???)

The missing values depend on John's response to the counteroffer. If John accepts the counteroffer, substitute the corresponding value ($400,000). If he rejects and makes a counteroffer, use the probability-weighted expected value of his counteroffer.

Compare the expected value with the counteroffer of $400,000. If the expected value is higher, Allied should counteroffer. If it is lower, accepting John's offer might be preferable.

4.) The risk profile for the recommended strategy should consider the probabilities and potential outcomes in both accepting John's offer and making a counteroffer.

If Allied accepts John's offer:
- Best-case scenario: Pay only $750,000.
- Worst-case scenario: Potentially lose the trial and pay damages of $1,500,000.

If Allied makes a counteroffer:
- Best-case scenario: John accepts the counteroffer of $400,000.
- Worst-case scenario: John rejects the counteroffer and makes a counteroffer of $600,000, leading to potential trial outcomes.

The risk profile should consider the probabilities of each scenario and their associated costs. This information helps Allied assess the potential risks and rewards of their chosen strategy.