Expando, Incorporated is considering the possibility of building an additional factory that would produce a new addition to its product line. The company is currently considering two options. The first is a small facility that it could build at a cost of $6 million. If demand for new products is low, the company expects to receive $10 million in discounted revenues (present value of future revenues) with the small facility. On the other hand, if demand is high, it expects $12 million in discounted revenues using the small facility. The second option is to build a large factory at a cost of $9 million. Were demand to be low, the company would expect $10 million in discounted revenues with the large plant. If demand is high, the company estimates that the discounted revenues would be $14 million. In either case, the probability of demand being high is 0.40, and the probability of it being low is 0.60. Not constructing a new factory would result in no additional revenue being generated because the current factories cannot produce these new products.



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.

Expando, Incorporated is considering the possibility of building an additional factory that would produce a new addition to its product line. The company is currently considering two options. The first is a small facility that it could build at a cost of $6 million. If demand for new products is low, the company expects to receive $10 million in discounted revenues (present value of future revenues) with the small facility. On the other hand, if demand is high, it expects $12 million in discounted revenues using the small facility. The second option is to build a large factory at a cost of $9 million. Were demand to be low, the company would expect $10 million in discounted revenues with the large plant. If demand is high, the company estimates that the discounted revenues would be $14 million. In either case, the probability of demand being high is 0.40, and the probability of it being low is 0.60. Not constructing a new factory would result in no additional revenue being generated because the current factories cannot produce these new products.

Explore how Expando, Inc. can decide between building a small or large factory for a new product line using expected value analysis. This problem involves calculating expected revenues based on different demand probabilities and understanding the decision-making process under uncertainty. The solution shows a comparison of expected profits for each option, guiding Expando toward the optimal choice.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation