Question

XYZ Company is considering digging an oil well. The cost of the well is \(\$ 50,000\). If the well is successful \(X Y Z\) will make a profit of \(\$ 400,000\), otherwise zero. The probability of the well being successful is \(0.1 .\) Is it worthwhile to dig the well?

Short answer

The expected value of the profit for the oil well is \(40,000, which is less than the cost of digging the well (\)50,000). Therefore, it is not worthwhile for XYZ Company to dig the well, as they are more likely to lose money on the investment than to profit from it.

Step-by-step solution

Identify the information given in the problem.

We are given the following pieces of information: - Cost of the well: $50,000 - Profit if successful: $400,000 - Probability of success: 0.1

Calculate the expected value of the profit.

The expected value (EV) of the profit is given by the probability of success multiplied by the profit if successful, plus the probability of failure multiplied by the profit if the well is unsuccessful (in this case, zero). Expected value (EV) = (probability of success × profit if successful) + (probability of failure × profit if unsuccessful) Here we have, the probability of success = 0.1, the probability of failure = 1 - 0.1 = 0.9. Also, the profit if successful = \(400,000, and the profit if unsuccessful = \)0. EV = (0.1 × \(400,000) + (0.9 × \)0)

Calculate the expected value.

Now, calculate the expected value using the given values. EV = (0.1 × \(400,000) + (0.9 × \)0) = $40,000 The expected value of the profit is $40,000.

Compare the expected value to the cost of the well.

Lastly, compare the expected value of the profit (\(40,000) to the cost of digging the well (\)50,000). Since the expected value of the profit is less than the cost of the well, it is not worthwhile to dig the well. The company is more likely to lose money on the investment than to profit from it.

Key concepts

Probability Theory

Understanding probability is key to making predictions about future events. In our exercise, the concept of probability helps XYZ Company assess their chances of success in digging an oil well. Probability measures how likely an event is to occur. In this scenario, the probability of success is 0.1, which means there is a 10% chance that the well will be successful.

Probability is often expressed as a fraction or a decimal. It ranges between 0 and 1, where 0 means the event will not happen, and 1 means it will definitely happen. In our oil well problem, the probability of success is low, suggesting that the likelihood of achieving profit from the well is also low.

By calculating the probability of failure as well (1 - probability of success), we determine the chance of not finding oil is 90%. Understanding these probabilities allows us to make informed predictions about the future outcomes of investments, as seen in this decision-making process.

Investment Decision Analysis

Investment decision analysis involves evaluating the potential outcomes and risks associated with investment opportunities. It is an essential process for companies, like XYZ, to determine if a project is financially viable. In our exercise, the focus is on deciding whether to dig the oil well.

• Expected Value (EV): Calculating the expected value is a primary step in investment decision analysis. It involves assessing the potential returns of an investment against the likelihood of those returns.
• Risk Assessment: We must also consider the risks involved, like the high probability of failure.
• Cost-Benefit Analysis: Comparing the expected return to the costs involved is crucial for making wise investment decisions.

Here, the company calculates a potential expected value of $40,000, but the cost to drill is $50,000, indicating a loss. Such an analysis helps the company determine that this investment may not be worth pursuing, as the expected profit does not cover the cost, portraying a rational and data-driven approach to decision-making.

Profit and Loss Analysis

Profit and loss analysis is a fundamental tool for determining the economic viability of a business decision. In our scenario with XYZ Company, this analysis helps in deciding if the venture will be profitable. To find out, it’s important to look at various factors:

• Profit Potential: How much could be earned if the project succeeds?
• Cost Analysis: What are the expenses involved in the project?
• Expected Outcomes: How do different scenarios affect the financial projections?

In the oil well example, the profit if successful stands at $400,000. However, the high expense of $50,000 for drilling gives a negative indication when compared to the expected value of only $40,000. This detailed profit and loss analysis enables XYZ to conclude that the anticipated loss overshadows the slim chance of success, thus the venture is economically unsound.