91Ó°ÊÓ

A venture capitalist, willing to invest \(\$ 1,000,000\), has three investments to choose from. The first investment, a software company, has a 10% chance of returning \(\$ 5,000,000\) profit, a 30% chance of returning \(\$ 1,000,000\) profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning \(\$ 3,000,000\) profit, a 40% chance of returning \(\$ 1,000,000\) profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning \(\$ 6,000,000\) profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars. a. Construct a PDF for each investment. b. Find the expected value for each investment. c. Which is the safest investment? Why do you think so? d. Which is the riskiest investment? Why do you think so? e. Which investment has the highest expected return, on average?

Step by step solution

01

Construct the PDF for the Software Company

The software company has three possible outcomes: a 10% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing $1,000,000. The PDF can be represented as follows: - $5,000,000 profit: Probability = 0.10 - $1,000,000 profit: Probability = 0.30 - -$1,000,000 loss: Probability = 0.60

02

Construct the PDF for the Hardware Company

The hardware company also has three possible outcomes: a 20% chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 40% chance of losing $1,000,000. The PDF is: - $3,000,000 profit: Probability = 0.20 - $1,000,000 profit: Probability = 0.40 - -$1,000,000 loss: Probability = 0.40

03

Construct the PDF for the Biotech Firm

The biotech firm's possible outcomes include a 10% chance of returning $6,000,000 profit, a 70% chance of no profit or loss, and a 20% chance of losing $1,000,000. The PDF looks like: - $6,000,000 profit: Probability = 0.10 - $0 profit/loss: Probability = 0.70 - -$1,000,000 loss: Probability = 0.20

04

Calculate the Expected Value for the Software Company

The expected value for the software company is calculated using the formula:\[ E(X) = (0.10 \times 5,000,000) + (0.30 \times 1,000,000) + (0.60 \times -1,000,000) \]This results in:\[ E(X) = 500,000 + 300,000 - 600,000 = 200,000 \]

05

Calculate the Expected Value for the Hardware Company

The expected value for the hardware company is:\[ E(X) = (0.20 \times 3,000,000) + (0.40 \times 1,000,000) + (0.40 \times -1,000,000) \]Which simplifies to:\[ E(X) = 600,000 + 400,000 - 400,000 = 600,000 \]

06

Calculate the Expected Value for the Biotech Firm

The expected value for the biotech firm is:\[ E(X) = (0.10 \times 6,000,000) + (0.70 \times 0) + (0.20 \times -1,000,000) \]This works out to:\[ E(X) = 600,000 + 0 - 200,000 = 400,000 \]

07

Analyze the Investment Safety

Safety in investment could be defined as the potential to lose money. The software company has the highest probability (60%) of losing the entire amount, making it the riskiest (unsafe). The biotech firm's outcome has a 70% chance with no profit or loss, indicating it's the safest because the chance of losing $1,000,000 is 20% only.

08

Determine the Riskiest Investment

The software company is the riskiest investment due to the 60% probability of losing the entire investment, offering the highest risk compared to the others.

09

Identify the Investment with Highest Expected Return

The hardware company has the highest expected value of $600,000. Therefore, on average, it offers the highest return.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Expected Value

Expected value (EV) is a fundamental concept in probability and finance that helps investors weigh the potential outcomes of different decisions. It represents the average result you could anticipate from an investment over time, based on different probabilities and outcomes.

To calculate the expected value, you multiply each possible outcome by the probability of that outcome, and then add these products together. For instance, in the case of the software company, the possible outcomes are:

• Returning $5,000,000 with a 10% chance: 0.10 x 5,000,000
• Returning $1,000,000 with a 30% chance: 0.30 x 1,000,000
• Losing $1,000,000 with a 60% chance: 0.60 x (-1,000,000)

Calculating these gives:
500,000 + 300,000 - 600,000 = 200,000.

This means, on average, you would expect a $200,000 return by investing in the software company. Using this method for all investments helps in comparing different options, providing a clearer perspective on potential returns.

Risk Assessment

Risk assessment is all about analyzing the potential downsides of an investment, specifically, the likelihood of losing money. In investments, the term "risk" often refers to the probability of losing your investment or a portion of it.

In the context of the given choices, the software company is noted to have the highest risk, with a 60% probability of a complete loss of the $1,000,000 investment. Contrast this with the biotech firm, which offers a 70% chance of no profit or loss, and a lower 20% probability of a total loss.

Considering these probabilities:

• The software company poses the greatest risk.
• The biotech firm, however, stands out as the safest choice, with the least likelihood of loss.

In risk assessment, investors aim to minimize losses by choosing the option with the least risk and reasonable returns. Evaluating risk helps stakeholders make informed decisions about where to allocate resources.

Investments

Investments are ventures that involve allocating resources like money into projects, companies, or assets with expectations of generating profit. Each investment comes with its own set of potential risks and returns, which are crucial factors for decision-making.

In this scenario, the venture capitalist must weigh each company's potential returns against its associated risks. The hardware company, for example, has the highest expected value of $600,000, marking it as the option potentially yielding the best returns on average.

• Software Company: Offers a lower expected return of $200,000 with higher risks.
• Hardware Company: Balances a healthy return of $600,000 with moderate risk, making it appealing.
• Biotech Firm: Provides lower returns ($400,000) but is the safest bet.

Investors aim to select a balance between higher returns and acceptable risks. While higher returns often involve more risk, safer investments might offer stability with lower potential gains. Understanding these dynamics is key for successful investment strategies.