This scenario involves a decision-making process under uncertainty, where Expando, Incorporated is trying to choose between building a small or large factory to produce a new product, or doing nothing. The decision depends on the expected revenues based on different demand levels (high or low) and their respective probabilities.

Let’s break down the expected outcomes for each option.

1. Small Factory:

• Cost: $6 million.
• Revenue if demand is low: $10 million.
• Revenue if demand is high: $12 million.
• Probability of low demand: 0.60.
• Probability of high demand: 0.40.

The expected revenue from the small factory is calculated by the weighted average of revenues based on the probabilities of demand: $\text{Expected revenue} = (0.60 \times 10 \, \text{million}) + (0.40 \times 12 \, \text{million})$ $\text{Expected revenue} = 6 \, \text{million} + 4.8 \, \text{million} = 10.8 \, \text{million}$ Now, the expected profit is the expected revenue minus the cost: $\text{Expected profit} = 10.8 \, \text{million} - 6 \, \text{million} = 4.8 \, \text{million}$

2. Large Factory:

• Cost: $9 million.
• Revenue if demand is low: $10 million.
• Revenue if demand is high: $14 million.
• Probability of low demand: 0.60.
• Probability of high demand: 0.40.

The expected revenue from the large factory is: $\text{Expected revenue} = (0.60 \times 10 \, \text{million}) + (0.40 \times 14 \, \text{million})$ $\text{Expected revenue} = 6 \, \text{million} + 5.6 \, \text{million} = 11.6 \, \text{million}$ Now, the expected profit is: $\text{Expected profit} = 11.6 \, \text{million} - 9 \, \text{million} = 2.6 \, \text{million}$

3. Do Nothing:

• Cost: $0.
• Revenue: $0.

The expected profit here is simply: $\text{Expected profit} = 0$

Conclusion:

• Small factory: Expected profit = $4.8 million.
• Large factory: Expected profit = $2.6 million.
• Do nothing: Expected profit = $0.

Therefore, based on expected profits, Expando should choose to build the small factory, as it yields the highest expected profit of $4.8 million.

Would you like more details or have any questions on this analysis?

Here are 5 related questions:

1. How would changes in the probability of high demand affect the decision?
2. What would happen if the costs of the factories increased due to inflation?
3. Could Expando reduce risk by considering an option to expand in the future?
4. How could this decision be influenced by financing or cash flow constraints?
5. What non-financial factors should Expando consider when making this decision?

Tip: When calculating expected values, always account for both probabilities and potential payoffs to ensure a balanced decision.