To determine which company would provide the best investment opportunity, we need to calculate the expected value for each company. The expected value is a measure that combines potential outcomes (profit or loss) with the probabilities of those outcomes. It gives us a single numerical value to compare different investment choices.
Here's the step-by-step process to calculate the expected value for each company:
1. Company A:
- Loss amount: [tex]$24,000
- Probability of loss: 0.16
- Profit amount: $[/tex]10,000
- Probability of profit: 0.34
- Probability to break even: 0.50 (which means neither profit nor loss)
The expected value (EV) is calculated as:
[tex]\[
EV_A = (\text{Loss amount} \times \text{Probability of loss}) + (\text{Break even amount} \times \text{Probability to break even}) + (\text{Profit amount} \times \text{Probability of profit})
\][/tex]
Since the break even amount is [tex]$0$[/tex]:
[tex]\[
EV_A = (24000 \times 0.16) + (0 \times 0.50) + (10000 \times 0.34)
\][/tex]
2. Company B:
- Loss amount: [tex]$12,000
- Probability of loss: 0.32
- Profit amount: $[/tex]21,000
- Probability of profit: 0.28
- Probability to break even: 0.40
Using the same formula:
[tex]\[
EV_B = (12000 \times 0.32) + (0 \times 0.40) + (21000 \times 0.28)
\][/tex]
3. Company C:
- Loss amount: [tex]$6,000
- Probability of loss: 0.23
- Profit amount: $[/tex]5,000
- Probability of profit: 0.60
- Probability to break even: 0.17
Again, using the same formula:
[tex]\[
EV_C = (6000 \times 0.23) + (0 \times 0.17) + (5000 \times 0.60)
\][/tex]
Now, the expected values for each company are:
- EV_A = 7240.0
- EV_B = 9720.0
- EV_C = 4380.0
Finally, we compare the expected values:
The best investment is the company with the highest expected value.
From the calculated values, Company B has the highest expected value of 9720.0.
Therefore, Company B provides the best investment opportunity based on the given probabilities and amounts of profit and loss.
