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Chapter 8: Problem 57

Suppose that you have \(\$ 10,000\) in a rather risky investment recommended by your financial advisor. During the first year, your investment decreases by \(30 \%\) of its original value. During the second year, your investment increases by \(40 \%\) of its first-year value. Your advisor tells you that there must have been a \(10 \%\) overall increase of your original \(\$ 10,000\) investment. Is your financial advisor using percentages properly? If not, what is your actual percent gain or loss of your original \(\$ 10,000\) investment?

Short Answer

Expert verified
The advisor is not using percentages correctly. The actual outcome is a 2% loss of the original investment, not a 10% gain.

Step by step solution

01

Calculate the Selling Price after the first year

First year the investment decreases by 30%, this means that the investment will have a value of 70% of its initial value (since \(100\% - 30\% = 70\%\)). This is calculated by multiplying the initial value of the investment \(\$10,000\) by (0.70). So the value at the end of the first year will be \( \$10,000 \times 0.70 = \$7,000 \)
02

Calculate the Selling Price after the second year

In the second year, the value of your investment increases by 40%. To calculate the new value you need to increase the previous value (\$7,000) by 40%. This means multiplying the previous value by (1.40). So, the value at the end of second year will be \$7,000 * 1.40 = \$9,800.
03

Determine the Overall Percentage Gain or Loss

The difference between the original investment and the value after two years is the gain or loss. So, it is \$ 9,800 (\$ value at the end of second year) - \$10,000 (original price) = -\$200. To get the percentage outcome of the investment, divide the difference by the original value then multiply by 100: \((-200) / 10,000 \times 100 = -2 \%\). This reveals a 2% loss overall, not a 10% gain as the advisor suggested.

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Key Concepts

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

Understanding Percentage Calculation
Percentage calculation is key in almost all financial analyses. It helps to convey how much something has increased or decreased relative to its original value.
In the context of investments, calculating percentages accurately can reveal the real impact of changes over time.
When calculating the percentage change, it鈥檚 important to follow a few steps:
  • Identify the original value, which is your starting point.
  • Determine the new value after the change has occurred.
  • Calculate the change by subtracting the original value from the new value. If you are calculating a decrease, expect this result to be negative.
  • Divide the change by the original value. This gives you the fractional change relative to the original amount.
  • Multiply by 100 to convert this fraction into a percentage.
In our exercise, even though the investment increased by 40% in the second year, the calculation must be based on its reduced value from the first year. This underscores the importance of sequential calculations where each step is based on the most current value.
Role of a Financial Advisor
A financial advisor plays a crucial role in helping individuals make informed decisions regarding their investments.
Advisors are expected to provide clear, detailed analyses of potential risks and benefits associated with different investment options.
Part of a financial advisor鈥檚 role includes:
  • Assessing your financial situation: Understanding your financial goals, income, and current financial standings.
  • Recommending investment options: Suggesting diverse investment opportunities that align with your financial goals and risk tolerance.
  • Monitoring investment performance: Keeping a close watch on your investments, making adjustments as required.
  • Clarifying complex concepts: Explaining financial terms and helping you to understand the rationale behind your investments.
In financial scenarios, clear and accurate presentations are paramount. Misunderstandings, such as incorrectly presented percentage changes, can lead to misjudgment and poor financial decisions.
Importance of Risk Assessment
Risk assessment is a fundamental concept in investment analysis. It involves evaluating the potential risks involved in an investment and finding ways to mitigate them.
The level of risk associated with an investment often determines potential returns. Higher risks can lead to higher returns, but also greater potential losses.
There are several aspects to consider in a risk assessment:
  • Market Risk: How changes in the market conditions can affect the investment's performance.
  • Credit Risk: The potential that the borrower will not repay a loan or meet contractual obligations.
  • Liquidity Risk: The risk that comes from the lack of marketability of an investment that can't be bought or sold quickly enough to prevent a loss.
  • Operational Risk: Risks stemming from failures in internal processes, people, or systems.
In the example provided, the change in investment value over two years showcases how risk assessment can inform decision-making. Understanding risks and their implications can help investors like you make more balanced and strategic investment decisions.

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