A Company Faces Three Choices Regarding A Potential Pro ✓ Solved
A Company Faces Three Choices With Regard To A Potential Project They
A company faces three choices with regard to a potential project they are considering with a partner company. They can choose to invest £150 million and this will entitle them to 85% of any profits made. Alternatively, they could invest £75 million, but this would only entitle them to 40% of any profits made. In either case, if a negative profit (loss) is made, the company has to fund the appropriate percentage (85% and 40%) of the loss. Of course, the company could choose not to invest at all.
There are three scenarios concerning the performance of the project: a very successful scenario with a probability of 0.3, yielding a total profit of £500 million; a moderate successful scenario with a probability of 0.5, yielding a total profit of £160 million; and an unsuccessful scenario with a probability of 0.2, resulting in a total loss of £100 million. In all cases, the total profit does not include the initial investment made by the company.
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Introduction
This analysis examines the decision-making process of a company contemplating an investment in a potential project with uncertain outcomes. The company has three options: investing £150 million for an 85% share of profits or losses, investing £75 million for a 40% share, or not investing at all. The project outcomes are probabilistically characterized as very successful, moderately successful, or unsuccessful. The goal is to guide the company's decision using payoff tables, decision criteria, and decision tree analysis.
Part A: Payoff Table and Decision Criteria Analysis
Constructing the Payoff Table
To analyze the decision options, we construct a payoff table representing the company's possible payoffs under each scenario for both investment options. The payoffs are based on the company's share of profits or losses after accounting for initial investments and the share percentages.
| Scenario | Probability | Share of Profits/(Loss) | Investment Option | Net Payoff (£ millions) |
|---|---|---|---|---|
| Very Successful | 0.3 | £500 million | £150 million investment (85%) | 0.85 * £500 million - £150 million = £425 million - £150 million = £275 million |
| £500 million | £75 million investment (40%) | 0.40 * £500 million - £75 million = £200 million - £75 million = £125 million | ||
| Moderately Successful | 0.5 | £160 million | £150 million investment (85%) | 0.85 * £160 million - £150 million = £136 million - £150 million = -£14 million |
| £160 million | £75 million investment (40%) | 0.40 * £160 million - £75 million = £64 million - £75 million = -£11 million | ||
| Unsuccessful | 0.2 | -£100 million | £150 million investment (85%) | 0.85 * (-£100 million) - £150 million = -£85 million - £150 million = -£235 million |
| -£100 million | £75 million investment (40%) | 0.40 * (-£100 million) - £75 million = -£40 million - £75 million = -£115 million |
Evaluating using Maximin, Maximax, and Minimax Regret
Maximin criterion: Focuses on the worst-case scenario for each option and chooses the best among these worst outcomes.
- £150 million investment: Worst payoff is -£235 million.
- £75 million investment: Worst payoff is -£115 million.
Decision: Choose the investment option with the higher worst-case payoff, which is the £75 million investment with -£115 million.
Maximax criterion: Focuses on the best possible outcome for each option and chooses the highest among these.
- £150 million investment: Best payoff is £275 million.
- £75 million investment: Best payoff is £125 million.
Decision: Choose the £150 million investment with the potential payoff of £275 million.
Minimax Regret criterion: Calculates the regret values associated with each decision and selects the option minimizing the maximum regret.
Calculating Regret Table
| Scenario | Best payoff | Regret for £150 million | Regret for £75 million |
|---|---|---|---|
| Very Successful | £275 million | £275m - £275m = £0 | £275m - £125m = £150m |
| Moderately Successful | £136 million (for £150m invest) | £136m - (-£14m) = £150m | £136m - (-£11m) = £147m |
| Unsuccessful | −£115m (for £75m invest) | −£115m - (−£115m) = £0 | −£115m - (−£235m) = £120m |
The maximum regret for each option is:
- £150 million investment: £150 million
- £75 million investment: £147 million
Decision: Choose the £150 million investment as it has the lower maximum regret value.
Part B: Decision Tree Analysis
Building the Decision Tree
The decision tree visualizes choices and uncertainties. The initial decision branches into two options: investing £150 million or £75 million, or abstaining. Each leads to chance events with associated probabilities and payoffs.
Analysis
Calculating the expected monetary value (EMV) for each investment decision helps determine the best course of action:
- EMV of £150 million investment:
EMV = (0.3 £275 million) + (0.5 -£14 million) + (0.2 * -£235 million) = £82.5m - £7m - £47m = £28.5m
- EMV of £75 million investment:
EMV = (0.3 £125 million) + (0.5 -£11 million) + (0.2 * -£115 million) = £37.5m - £5.5m - £23m = £9m
Considering the highest EMV, the company should opt for investing £150 million as it offers a higher expected monetary benefit.
Conclusion
Based on the payoff table analysis, the maximin approach suggests investing £75 million to minimize worst-case losses, while the maximax favors investing £150 million, aiming for the highest potential payoff. The minimax regret method also favors investing £150 million, given its lower maximum regret. The decision tree supports this, with the highest expected monetary value associated with the £150 million investment, indicating it is the optimal choice under the current risk-return profile.
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