Question

A company is considering making a new product. They estimate the probability that the new product will be successful is 0.75. If it is successful it would generate $240,000 in revenue. If it is not successful, it would not generate any revenue. The cost to develop the product is $196,000. Use the profit (revenue − cost) and expected value to decide whether the company should make this new product.

Answers

GPT-4o mini
To make a decision about whether the company should develop the new product, we can calculate the expected profit based on the probabilities and potential outcomes.

1. **Define outcomes:**
- If the product is successful (with probability \( P(\text{Success}) = 0.75 \)):
- Revenue = $240,000
- Cost = $196,000
- Profit = Revenue - Cost = $240,000 - $196,000 = $44,000

- If the product is not successful (with probability \( P(\text{Failure}) = 0.25 \)):
- Revenue = $0
- Cost = $196,000
- Profit = Revenue - Cost = $0 - $196,000 = -$196,000

2. **Calculate expected profit:**
\[
\text{Expected Profit} = P(\text{Success}) \times \text{Profit from Success} + P(\text{Failure}) \times \text{Profit from Failure}
\]
Plugging in the values we have:
\[
\text{Expected Profit} = 0.75 \times 44,000 + 0.25 \times (-196,000)
\]
\[
\text{Expected Profit} = 33,000 - 49,000
\]
\[
\text{Expected Profit} = -16,000
\]

3. **Decision:**
The expected profit is calculated to be \(-16,000\). This indicates an expected loss of $16,000 if the company proceeds with the development of the new product.

Since the expected value of the profit is negative, the company should **not** make this new product. The potential for profit does not outweigh the costs and risks associated with developing the product.