Rate of Return Lecture Notes

Introduction to Rate of Return

• Definition: Rate of return is the gain or loss of an investment over a certain period.
  • Positive Rate of Return: Indicates a gain on investment.
  • Negative Rate of Return: Indicates a loss on investment.

Formula for Rate of Return

• Formula: [ \text{Rate of Return} = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \times 100 ]
• Note: Include any gains during the investment period (e.g., dividends).

Example Calculation

• Scenario:
  • Purchase: 1 share at $10
  • Current Price: $15
  • Dividend Received: $1
• Calculation: [ \text{Rate of Return} = \frac{(15 + 1 - 10)}{10} \times 100 = 60% ]

Detailed Example of Rate of Return

• Investor Scenario:
  • Buys 10 shares of Company A at $20 each
  • Holds shares for 2 years
  • Receives $1 dividend per share annually
  • Sells shares at $25 each
• Steps:
  1. Calculate Dividends:
     • [ 10 \times 1 \times 2 = $20 ]
  2. Calculate Selling Gain:
     • [ 10 \times 25 = $250 ]
  3. Calculate Purchase Cost:
     • [ 10 \times 20 = $200 ]
  4. Plug into Formula:
     • [ \text{Rate of Return} = \frac{(250 + 20 - 200)}{200} \times 100 = 35% ]
• Result: 35% return over 2 years

Annualized Rate of Return

• Definition: Rate of Return over one year
• Formula: [ \text{Annualized Rate of Return} = \left(\frac{\text{Ending Value}}{\text{Beginning Value}}\right)^{\frac{1}{n}} - 1 ]
  • ( n ) is the number of years
• Include all gains, including dividends

Example of Annualized Rate of Return

• Using Previous Example:
  • Calculation: [ \left(\frac{250 + 20}{200}\right)^{\frac{1}{2}} - 1 = 16.19% ]
• Result: 16.19% annualized return

Conclusion

• Summarized the calculation of both simple and annualized rates of return.
• Emphasized the inclusion of dividends and gains in calculations.