The Settlement Offer and the Decision Tree

Question 66: The Settlement Offer and the Decision Tree

Your role

You represent Emberline Systems, the defendant in a contract case. Trial is four months away. The plaintiff's current settlement offer expires in three days, and the chief financial officer wants a settle-or-litigate recommendation based only on the supplied probabilities and costs.

Governing law

Use the following decision rules for this assignment:

1. Expected monetary cost is the sum of each possible outcome multiplied by its supplied probability, plus future legal and transaction costs attributable to that course.

2. Probabilities in a branch must total 100 percent. Do not replace the supplied probabilities with intuitive estimates.

3. Costs already incurred are sunk and do not affect the choice among current alternatives.

4. A future litigation cost is counted whenever the branch requiring that work occurs, regardless of who ultimately wins, unless the facts state otherwise.

5. A settlement amount and the transaction cost required to complete it are both counted in the settlement branch.

6. If a counteroffer is rejected and the current offer will no longer be available, the rejected branch proceeds to trial on the supplied trial economics.

7. Expected value is not a prediction that the average result will occur. Tail exposure and cash timing may be stated separately, but they may not replace the expected-cost calculation.

8. Recommend the course with the lowest expected cost unless a supplied nonmonetary constraint changes the decision. No such constraint is supplied here.

Facts

Emberline has already spent $300,000 defending the case. That amount cannot be recovered and is the same under every current choice.

If the case proceeds directly to trial, future defense cost will be $550,000. Counsel supplies the following mutually exclusive trial outcomes:

• 30 percent probability of a complete defense verdict and no payment to plaintiff.
• 50 percent probability of a $1,600,000 judgment.
• 20 percent probability of a $4,500,000 judgment.

There is no fee shifting, insurance, interest, appeal, or collection discount in this assignment.

The plaintiff offers a complete release for $1,450,000. Completing the settlement will cost Emberline an additional $50,000 in legal, accounting, and closing work.

Emberline may instead counter at $1,200,000. The supplied probability of acceptance is 45 percent. Negotiating and documenting the counter costs $40,000 whether it is accepted or rejected. If accepted, no other settlement transaction cost applies. If rejected:

• The current $1,450,000 offer is withdrawn.
• The case proceeds to the same trial outcomes.
• Future defense cost rises from $550,000 to $625,000 because expert and trial deadlines will then be compressed.

Management argues that a 30 percent defense-verdict chance means paying anything above $1 million is irrational. Counsel has not identified any operational, reputational, insurance, or precedent effect outside the supplied monetary record.

Assignment

Analyze:

• Expected judgment if the case proceeds to trial.
• Total expected cost of proceeding directly to trial.
• Total cost of accepting the current settlement.
• Expected cost of making the $1,200,000 counteroffer, showing accepted and rejected branches.
• The treatment of the $300,000 already spent.
• The significance of the $4,500,000 tail outcome.
• Why the defense-verdict probability does or does not determine the decision.
• The concrete recommendation before the three-day deadline.

Q66 key (Settlement Decision Tree)

1. Expected trial judgment is 30 percent of $0 plus 50 percent of $1,600,000 plus 20 percent of $4,500,000, equaling $1,700,000. Add $550,000 future defense cost for total direct-to-trial expected cost of $2,250,000. Missed: the defense-verdict branch is discussed without weighting all outcomes.
2. Accepting now costs $1,450,000 plus $50,000 completion cost, or $1,500,000. The $300,000 already spent is sunk and excluded from every comparison. Missed: past spend distorts the current choice or the transaction cost disappears.
3. The counter branch costs $40,000 regardless. Acceptance contributes 45 percent of $1,200,000, or $540,000. Rejection contributes 55 percent of $2,325,000, consisting of $1,700,000 expected judgment plus $625,000 future defense cost, or $1,278,750. Total expected counter cost is $1,858,750. Missed: the rejected branch keeps an offer that the facts withdraw or uses the lower defense cost.
4. Ranking by expected cost is accept now at $1,500,000, counter at $1,858,750, and direct trial at $2,250,000. The $4.5 million judgment branch is already weighted in expected cost and separately shows material tail exposure. Missed: tail risk is ignored or counted twice.
5. A 30 percent defense verdict does not make a payment irrational because the other 70 percent carries much larger outcomes and unavoidable defense expense. No supplied nonmonetary factor overrides the calculation. Missed: one branch is treated as the entire decision tree.
6. Accept the $1.45 million complete-release offer before it expires. Do not risk its withdrawal for the $1.2 million counter on these inputs. Missed: Emberline pays an expected $358,750 premium for the counter strategy or $750,000 for trial relative to settlement.