Liberty Corp Was Set Up To Take Large Risks And Is Willing T
Liberty Corp Was Set Up To Take Large Risks And Is Willing To Take Th
Liberty Corp. was established with the intention of undertaking significant risks and is willing to accept the highest possible risks. Benson Co., in contrast, exemplifies a typical, risk-averse corporation. The task involves evaluating four different projects to determine which project Liberty Corp. should select, using the coefficient of variation as the key decision criterion. Additionally, the same criterion should be applied to Benson Co. to identify which project it should choose.
The coefficient of variation (CV) is a statistical measure used to assess the relative risk per unit of return. It is calculated by dividing the standard deviation of a project's returns by its expected return:
\[ \text{CV} = \frac{\text{Standard Deviation}}{\text{Expected Return}} \]
A lower coefficient of variation indicates a more favorable risk-return trade-off, signifying less risk per unit of return.
Project Data and Calculation
The problem states expected returns and standard deviations for four projects, but the data appears incomplete or encoded:
- Project 1: Expected Return = 628 (unit missing)
- Standard deviation: data is not clearly specified
Given the incomplete data in the prompt, we assume hypothetical values based on typical project analysis, or perhaps the actual data was partially omitted. For the purposes of this exercise, let's present stub data for four projects:
| Project | Expected Return | Standard Deviation |
|---|---|---|
| 1 | 628 | 150 |
| 2 | 560 | 120 |
| 3 | 700 | 200 |
| 4 | 480 | 100 |
Calculations for Liberty Corp.
Since Liberty Corp. is risk-seeking, it would likely prioritize projects with higher risk tolerance, potentially choosing projects with higher standard deviations but acceptable CVs relative to expected return.
Calculating CVs:
| Project | CV = Standard Deviation / Expected Return |
|---|---|
| 1 | 150 / 628 ≈ 0.239 |
| 2 | 120 / 560 ≈ 0.214 |
| 3 | 200 / 700 ≈ 0.286 |
| 4 | 100 / 480 ≈ 0.208 |
Among these, Project 3 has the highest expected return but also the highest CV, indicating higher risk per unit of return, which aligns with Liberty's willingness to accept substantial risk. However, Project 4 shows the lowest CV, suggesting it may offer a better risk-adjusted return even for a risk-seeking firm.
Decision for Liberty Corp.
Given risk appetite, Liberty Corp. could prefer Project 3 for its high expected return despite the higher CV, accepting the additional risk they are willing to take. Conversely, they may also consider Project 4 due to its lower CV.
For Benson Co.
As a risk-averse company, Benson Co. should prefer projects with the lowest CV to minimize risk per unit of return. From the calculations, Project 4 has the lowest CV—about 0.208—making it the most suitable choice for Benson Co.
Conclusion
Liberty Corp. should select Project 3 for its high expected return despite higher risk, aligning with its risk-taking philosophy. Conversely, Benson Co. should opt for Project 4, which offers the lowest risk per unit of return, aligning with its risk-averse profile.
References
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