## Recommendation **Accept the plaintiff’s current settlement offer before it expires.** Using only the supplied probabilities and costs, the current settlement has the lowest expected cost: | Course | Decision-relevant expected cost | |---|---:| | Accept current settlement | **$1,500,000** | | Make $1,200,000 counteroffer | $1,858,750 | | Proceed directly to trial | $2,250,000 | The $300,000 already spent is sunk and does not affect the choice. If it is added back for all-in lifetime reporting, every alternative increases by $300,000, and the ranking is unchanged. --- ## 1. Expected judgment if the case proceeds to trial Counsel’s trial outcomes are mutually exclusive and total 100%: | Trial outcome | Probability | Judgment payment | Expected contribution | |---|---:|---:|---:| | Complete defense verdict | 30% | $0 | $0 | | $1,600,000 judgment | 50% | $1,600,000 | $800,000 | | $4,500,000 judgment | 20% | $4,500,000 | $900,000 | | **Total** | **100%** | | **$1,700,000** | So the **expected trial judgment is $1,700,000**. This is not a prediction that Emberline will pay exactly $1,700,000. The actual outcomes are $0, $1,600,000, or $4,500,000. But for expected-cost comparison, the probability-weighted amount is $1,700,000. --- ## 2. Total expected cost of proceeding directly to trial If Emberline proceeds directly to trial, it will incur: - Future defense cost: **$550,000** - Expected judgment: **$1,700,000** Therefore: \[ \text{Expected direct-trial cost} = \$550,000 + \$1,700,000 = \$2,250,000 \] Equivalently, by trial outcome: | Trial outcome | Probability | Cost in that outcome | Expected contribution | |---|---:|---:|---:| | Defense verdict | 30% | $0 judgment + $550,000 defense = $550,000 | $165,000 | | $1,600,000 judgment | 50% | $1,600,000 + $550,000 = $2,150,000 | $1,075,000 | | $4,500,000 judgment | 20% | $4,500,000 + $550,000 = $5,050,000 | $1,010,000 | | **Total** | **100%** | | **$2,250,000** | Thus, the decision-relevant expected cost of going directly to trial is: > **$2,250,000** If the prior $300,000 defense spend is included only as historical reporting, the all-in amount would be $2,550,000, but the sunk cost does not affect the decision. --- ## 3. Total cost of accepting the current settlement The current settlement requires: - Settlement payment: **$1,450,000** - Settlement transaction cost: **$50,000** Total: \[ \text{Settlement cost} = \$1,450,000 + \$50,000 = \$1,500,000 \] So the decision-relevant cost of accepting the current offer is: > **$1,500,000** This is a certain cost. It avoids the trial variance and caps Emberline’s exposure at $1,500,000 for this decision-relevant analysis. --- ## 4. Expected cost of making the $1,200,000 counteroffer Emberline may counter at $1,200,000. The supplied probability of acceptance is 45%, so the probability of rejection is 55%. The probabilities total 100%. The counteroffer costs $40,000 whether accepted or rejected. ### Accepted branch If accepted: - Settlement payment: **$1,200,000** - Counter cost: **$40,000** - No other settlement transaction cost, per the facts Branch cost: \[ \$1,200,000 + \$40,000 = \$1,240,000 \] Probability-weighted contribution: \[ 45\% \times \$1,240,000 = \$558,000 \] ### Rejected branch If rejected: - No $1,200,000 payment is made. - The current $1,450,000 offer is withdrawn. - The counter cost is still incurred: **$40,000** - Future defense cost rises to: **$625,000** - Expected trial judgment remains: **$1,700,000** Branch cost: \[ \$40,000 + \$625,000 + \$1,700,000 = \$2,365,000 \] Probability-weighted contribution: \[ 55\% \times \$2,365,000 = \$1,300,750 \] ### Expected cost of counteroffer \[ \text{Expected counter cost} = \$558,000 + \$1,300,750 = \$1,858,750 \] So the decision-relevant expected cost of making the $1,200,000 counteroffer is: > **$1,858,750** This is lower than direct trial, but higher than accepting the current settlement. --- ## 5. Treatment of the $300,000 already spent The $300,000 already spent is a sunk cost. It has already been incurred and is identical under every current alternative. Therefore, it should not influence the settle-or-litigate decision. For decision purposes: - Direct trial: $2,250,000 - Current settlement: $1,500,000 - Counteroffer: $1,858,750 If management wants all-in lifetime cost including the prior spend: | Course | Decision-relevant cost | Add $300,000 sunk cost | All-in cost | |---|---:|---:|---:| | Direct trial | $2,250,000 | $300,000 | $2,550,000 | | Current settlement | $1,500,000 | $300,000 | $1,800,000 | | Counteroffer | $1,858,750 | $300,000 | $2,158,750 | Adding the sunk cost to all alternatives does not change the ranking. The current settlement remains the lowest-cost option. --- ## 6. Significance of the $4,500,000 tail outcome The 20% chance of a $4,500,000 judgment is significant. Its expected contribution is: \[ 20\% \times \$4,500,000 = \$900,000 \] That $900,000 is more than half of the $1,700,000 expected trial judgment. In direct-trial terms, the $4,500,000 judgment outcome produces a total cost of: \[ \$4,500,000 + \$550,000 = \$5,050,000 \] So there is a 20% chance of a very large direct-trial cost. The expected-value calculation does not treat that tail outcome as certain; it gives it a 20% weight. But it is already built into the expected-cost comparison. The settlement eliminates that tail. Accepting the current offer caps the decision-relevant cost at $1,500,000. The counteroffer eliminates the tail only in the 45% accepted branch. In the 55% rejected branch, the tail remains, and future defense costs are higher. Under the supplied decision rules, tail exposure may be stated separately, but it may not replace the expected-cost calculation. Here, both the expected-cost calculation and the tail risk support settlement. --- ## 7. Why the 30% defense-verdict probability does not determine the decision Management’s argument is that because there is a 30% chance of a complete defense verdict, paying anything above $1,000,000 is irrational. That argument is not supported by the supplied probabilities and costs. The 30% defense-verdict chance is real, but it is only one branch of the trial decision. The other branches are: - 50% chance of a $1,600,000 judgment - 20% chance of a $4,500,000 judgment Together, those adverse outcomes produce an expected judgment of $1,700,000. Adding the $550,000 future defense cost gives an expected direct-trial cost of $2,250,000. The $300,000? No—the $300,000 is sunk and excluded from the choice. But even without it, the expected trial cost is far above the $1,500,000 settlement cost. The 30% verdict probability does not determine the decision because the decision rule requires weighting all supplied outcomes. A 30% chance of a favorable outcome does not eliminate the expected value of the remaining 70% of trial outcomes. Here, the weighted adverse outcomes make litigation more expensive, in expectation, than the current settlement. In short: > The 30% defense-verdict probability is relevant, but it does not overcome the expected cost of the 50% and 20% adverse judgment outcomes. --- ## 8. Concrete recommendation before the three-day deadline Emberline should **accept the current settlement offer** for: - Settlement amount: **$1,450,000** - Transaction cost: **$50,000** Total decision-relevant cost: > **$1,500,000** This is lower than: - Expected cost of the $1,200,000 counteroffer: **$1,858,750** - Expected cost of direct trial: **$2,250,000** Therefore, the CFO should direct that Emberline accept the settlement before the offer expires. There is no supplied nonmonetary constraint that changes the monetary expected-cost analysis.