### Project Description

How much income will you collect on an investment? How quickly will your investment appreciate? In the world of finance, these questions can be answered by calculating the **Rate of Return**.

Return on a typical investment comes in two forms: **yield** and **capital gains**. The Rate of Return is the *speed *at which these two types of profit are accumulated. In other words, the rate of return is the profit or loss of a certain investment *measured over a set period of time*. This number is most often calculated as a percentage of the initial investment in order to facilitate comparisons of certain investments.

**Measuring Profit: Yield + Capital Gains**

Yield = income return on investment (interest, dividends, etc.)

When calculating rate of return, the standard is to assume a continuation of the current yield[1]. Yield will vary based on the type of investment made (low risk vs. high risk) and the nature of the economic climate when the investment is made. Yields often move counter to prices, which are used to calculate capital gains. So, when yields are low, prices (capital gains) are often high. For investors, high valuations or increases in yield mean a higher rate of return.

Capital Gains: sale of appreciated asset (Receipt of stocks or property sold)

The capital gain on a certain investment is calculated by taking the current value of an asset and subtracting the purchase price or cost “basis”. The resulting figure is the capital gain (or loss[2]). A capital gain is “realized” when the asset is sold.

**Measuring Period**

The rate of return is often calculated over the period of one year, and expressed as the annual return of an investment. Most investors assume the measuring period is one year. Alternatively, investors may calculate the return of an investment over a number of years. The latter is known as a cumulative return.

**Accounting for Inflation, the Real Return**

Rate of Return is often expressed as the value of the Nominal Return. The Nominal Return can be thought of as the “gross” return while the Real Return can be thought of as the “net” return. The Nominal Return does not account for the percentage lost to inflation, while the Real Return takes into value of your dollars against the current rate of inflation. As shown below, the Real Return can be calculated by subtracting the rate of inflation from the Nominal Return:

Nominal Return – rate of inflation = Real Return

**Calculating the Rate of Return on a Stock**

If an investor buys a stock for $40/share, owns the stock for three years, earns $30 in total dividends, and ultimately sells the stock for $50, she has a $10 gain per share and has earned $30 in income. The rate of return for the stock is $30 per share divided by the $40 cost per share, or 75%.

**Calculating the Rate of Return on a Bond**

If an investor pays $500 for a $500 par value 7% bond, the investment earns $35 in income each year. If the investor sells the bond for $550 and earns $70 in total interest, the investor’s rate of return is the $50 gain plus $70 interest income divided by the $500 cost, or 24%

[1] http://www.economist.com/blogs/buttonwood/2013/07/investing

[2] A capital loss is realized when the current value of the asset drops below the purchase price.