Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

An investor has an opportunity to invest in three companies. She researched each company and collected the information in the table below. Which company would provide the best investment?

\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{4}{|c|}{ Probability of Profit and Loss by Company } \\
\hline Company & \begin{tabular}{l}
Loss, \\
Probability of Loss
\end{tabular} & \begin{tabular}{l}
Probability to Break \\
Even
\end{tabular} & \begin{tabular}{l}
Profit, \\
Probability of Profit
\end{tabular} \\
\hline [tex]$A$[/tex] & [tex]$\$[/tex] 24,000, 16 \%[tex]$ & $[/tex]50 \%[tex]$ & $[/tex]\[tex]$ 10,000, 34 \%$[/tex] \\
\hline [tex]$B$[/tex] & [tex]$\$[/tex] 12,000, 32 \%[tex]$ & $[/tex]40 \%[tex]$ & $[/tex]\[tex]$ 21,000, 28 \%$[/tex] \\
\hline [tex]$C$[/tex] & [tex]$\$[/tex] 6,000, 23 \%[tex]$ & $[/tex]17 \%[tex]$ & $[/tex]\[tex]$ 5,000, 60 \%$[/tex] \\
\hline
\end{tabular}

A. Company [tex]$A$[/tex]
B. Company [tex]$B$[/tex]
C. Company [tex]$C$[/tex]

Sagot :

GinnyAnswer
To evaluate which company would provide the best investment for the investor, we need to calculate the expected value (EV) for each company. The expected value helps us understand the average outcome of an investment when considering all possible profits and losses along with their probabilities.

The formula to calculate the expected value is:
[tex]\[ \text{Expected Value (EV)} = (\text{Loss Amount} \times \text{Probability of Loss}) + (\text{Profit Amount} \times \text{Probability of Profit}) + (0 \times \text{Probability to Break Even}) \][/tex]

Let's calculate the expected values for each company step-by-step.

### Company A:
- Loss: \( -$24,000 \)
- Probability of Loss: \( 16\% = 0.16 \)
- Probability to Break Even: \( 50\% = 0.50 \)
- Profit: \( $10,000 \)
- Probability of Profit: \( 34\% = 0.34 \)

Expected Value for Company A:
[tex]\[ \text{EV}_A = (-24000 \times 0.16) + (0 \times 0.50) + (10000 \times 0.34) \][/tex]
[tex]\[ \text{EV}_A = -3840 + 0 + 3400 \][/tex]
[tex]\[ \text{EV}_A = -440 \][/tex]

### Company B:
- Loss: \( -$12,000 \)
- Probability of Loss: \( 32\% = 0.32 \)
- Probability to Break Even: \( 40\% = 0.40 \)
- Profit: \( $21,000 \)
- Probability of Profit: \( 28\% = 0.28 \)

Expected Value for Company B:
[tex]\[ \text{EV}_B = (-12000 \times 0.32) + (0 \times 0.40) + (21000 \times 0.28) \][/tex]
[tex]\[ \text{EV}_B = -3840 + 0 + 5880 \][/tex]
[tex]\[ \text{EV}_B = 2040 \][/tex]

### Company C:
- Loss: \( -$6,000 \)
- Probability of Loss: \( 23\% = 0.23 \)
- Probability to Break Even: \( 17\% = 0.17 \)
- Profit: \( $5,000 \)
- Probability of Profit: \( 60\% = 0.60 \)

Expected Value for Company C:
[tex]\[ \text{EV}_C = (-6000 \times 0.23) + (0 \times 0.17) + (5000 \times 0.60) \][/tex]
[tex]\[ \text{EV}_C = -1380 + 0 + 3000 \][/tex]
[tex]\[ \text{EV}_C = 1620 \][/tex]

### Comparison of the Expected Values:
- Expected Value of Company A: \( -440 \)
- Expected Value of Company B: \( 2040 \)
- Expected Value of Company C: \( 1620 \)

Based on the expected values calculated, Company B has the highest expected value of \( 2040 \), followed by Company C with \( 1620 \), and Company A with \( -440 \).

Therefore, the best investment for the investor would be Company B.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.