return

Examples of return in the following topics:

• Dollar Returns

  • The dollar return does not take into account things like the time value of money or how the amount of return earned per year; it is simply the difference in nominal values.
  • If the first option has a $1,000,000 return over two years and the other has a $1,000,000 return over 10 years, the first option is clearly more attractive.
  • The investor will always choose the option with the higher dollar return.
  • If a firm is looking for an additional $50,000 from investment, they will only accept investments with a $50,000 dollar return, regardless of the percent return.
  • The dollar return is the difference in value from year to year, plus the previous dollar return.

• Percentage Returns

  • This type of return is also called the return on investment (ROI), where the numerator is the dollar return.
  • To find the return for the security overall, simply sum the dollar returns and divide by the initial value.
  • This is the arithmetic mean of the return.
  • CAGR is a way of measuring the return per year.
  • Another common method for finding the annual return is to calculate the internal rate of return (IRR).

• Reporting

  • A realized return is the difference between the sale price of the asset and the purchase price.
  • The difference between realized and unrealized returns is that realized returns result from the actual sale of the asset, while unrealized returns occur when the asset is not sold and result from a change in the market price.
  • Returns are reported each reporting period when the financial statements are created.
  • While realized returns are reported on the income statement (and affect the cash flow statement) and unrealized returns are reported on the balance sheet, only realized returns have tax implications.
  • The IRS taxes only realized returns, though financial reports must also include unrealized returns on the balance sheet.

• Relationships between ROA, ROE, and Growth

  • Return on assets is a component of return on equity, both of which can be used to calculate a company's rate of growth.
  • In review, return on equity measures the rate of return on the ownership interest (shareholders' equity) of common stockholders.
  • Return on assets is, however, a vital component of return on equity, being an indicator of how profitable a company is before leverage is considered.
  • In other words, return on assets makes up two-thirds of the DuPont equation measuring return on equity.
  • Discuss the different uses of the Return on Assets and Return on Assets ratios

• ROE and Potential Limitations

  • Return on equity measures the rate of return on the ownership interest of a business and is irrelevant if earnings are not reinvested or distributed.
  • What is the return on equity?
  • Return on equity (ROE) measures the rate of return on the ownership interest or shareholders' equity of the common stock owners.
  • Returns on equity between 15% and 20% are generally considered to be acceptable.
  • This is an expression of return on equity decomposed into its various factors.

• Differences Between Required Return and the Cost of Capital

  • Required return and cost of capital differ in their perspectives (investor versus company) and scope (individual versus all securities).
  • The terms "required return" and "cost of capital" essentially denote the same opportunity cost of choosing one investment over another.
  • Required return refers to an investor's point of view, while cost of capital refers to the point of view of a company.
  • However, since required return is from the investor's point of view, it refers to the rate of return necessary to compensate investors for taking on the risk of the individual investment.
  • The capital asset pricing model is a good representation of how to obtain required return.

• Calculating and Understanding Average Returns

  • Average returns are commonly found using average ROI, CAGR, or IRR.
  • This is a simple way to calculate the average return.
  • Average ROI generally does not calculate the actual average rate of return, because it does not incorporate compounding returns.
  • CAGR, unlike average ROI, does consider compounding returns.
  • The internal rate of return (IRR) is another commonly used method for calculating the average return .

• Calculating the IRR

  • Given a collection of pairs (time, cash flow), a rate of return for which the net present value is zero is an internal rate of return.
  • Given a collection of pairs (time, cash flow) involved in a project, the internal rate of return follows from the net present value as a function of the rate of return.
  • A rate of return for which this function is zero is an internal rate of return.
  • Given the (period, cash flow) pairs (n, Cn) where n is a positive integer, the total number of periods N, and the net present value NPV, the internal rate of return is given by r in:
  • Because the internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value of all cash flows (both positive and negative) from a particular investment equal to zero, then the IRR r is given by the formula:

• Calculating Expected Portfolio Returns

  • A portfolio's expected return is the sum of the weighted average of each asset's expected return.
  • The return of our fruit portfolio could be modeled as a sum of the weighted average of each fruit's expected return.
  • W is weight and E(RX) is the expected return of X.
  • A math-heavy formula for calculating the expected return on a portfolio, Q, of n assets would be:

• The Capital Asset Pricing Model

  • The market is expected to return 12% next year.
  • Expected return = 5% + 1.9*(12% - 5%).
  • Expected return = 18.3%.
  • The expected rate of return = the rate of return for a risk-free asset + beta* (the rate of return of the market - the risk-free rate).
  • The return of the market minus the risk-free rate is also known as the risk premium.