# Series 65

## Quantitative Methods of Evaluating Businesses and Investments - Rates of Return - Internal Rate of Return

Different measures can be used when discussing potential rates of return.

The internal rate of return used in time value of money calculations cannot be directly found by formula. It can be approximated by trial and error, but in the real world it is simply found by inputting present value, future value, and the number of compounding periods into a financial calculator.

Several measures of return can be selected for such a calculation:

**The IRR is essentially the interest rate that makes the net present value of all cash flow equal zero. It represents the return a company would earn if it expanded or invested in itself rather than elsewhere.**

**Internal Rate of Return (IRR)**The internal rate of return used in time value of money calculations cannot be directly found by formula. It can be approximated by trial and error, but in the real world it is simply found by inputting present value, future value, and the number of compounding periods into a financial calculator.

Several measures of return can be selected for such a calculation:

- also known as inflation-adjusted return. By adjusting the stated (nominal) return of an investment to take inflation into account, the investor will have a more realistic assessment of return. So, if an investor were to earn 8% on an investment and inflation is 3%, the real rate of return would be approximately 5% (excluding any fees). Learn more about this in the section on Bond Yields.__Real return__

- this calculation allows an investor to determine if the amount of return received is commensurate with the risk taken. There are several methods to measure risk-adjusted return that incorporate either beta (a measure of a portfolio's market risk) or standard deviation (a measure of a portfolio's total risk) and the risk-free return (typically measured by the current rate on short-term Treasury bills). The most common method of measuring risk-adjusted return is the Sharpe Ratio, which is calculated by subtracting the risk-free rate of return from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns.__Risk-adjusted return__

is a measure of volatility or systematic risk relative to the market as a whole. If beta = 1, the security's price will move with the market. If beta < 1, the security will move to a lesser extent than the market. If beta > 1, the security will move at a greater pace than the market.*Beta*

__Beta - Know the Risk__

__Beta - Gauging Price Fluctuations__

is a statistical concept that measures the dispersion of a set of data from its mean (average). So, if the average return for an investment over the last 5 years was 11.5%, and yearly returns for the past 5 years was 9.5%, 8.5%, 13.9%, 9.1% and 16.5%, standard deviation would measure how the return for each of those 5 years differed from the mean. Standard deviation is a measure of total risk for an individual security or an overall portfolio. Beta, on the other hand, measures only its systematic risk relative to the market.*Standard Deviation*

- incorporates the rate of return from all sources, including appreciation (or depreciation), dividends and interest. This is the actual rate of return an investment provided over a certain period of time.__Total return__

Look Out!Look for questions on both the definition of total return and the inflation component of real return. Hint: Any answers that involve risk are normally incorrect. |

Exam Tips and TricksConsider this sample question: |

**Which of the following statements is least accurate with respect to how certain factors may impact internal rate of return (IRR)?**- If the required return exceeds the project's IRR, the project should be accepted.
- The higher the expected cash flows, the higher the IRR will be.
- IRR may be regarded as the expected return on a project or an investment.
- As the cost increases, the IRR will decrease, holding everything else constant.

The correct answer is "a". The IRR of the project is also the return expected from it. Therefore, if the required return exceeds the project's IRR (or expected return), the project should be rejected because it is not expected to generate return to compensate for the risk.

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