# Calculations for Average Annual Total Return (IRR)

Because the average annual total return (IRR) is calculated as an annual percentage, if the time period you specify is less than a year, you may see distortions in the calculations-the return may seem may seem very high or very low.  Also, in the beginning of the year there may be large swings in IRR.

Similarly, if you have investment transactions that affect your cash balance, such as Sell, Dividend, and so on, these may falsely inflate your apparent return.

## Average annual return (IRR)

Definition

Often called the internal rate of return (IRR), the average annual return is usually defined as a percentage equal to the interest rate on a bank account that would give you the same total return on your investment. It takes into account money earned by the investment (interest, dividends, capital gains distributions) as well as changes in share price. Because it is an annual rate, it acts like a bank interest rate that compounds annually. For example, if you invest \$10,000 and get an average annual return of 12.0 percent over two years, you'll have \$12,544 (an increase of \$2544, or 25.4 percent) at the end of the two years.

Quicken displays the average annual return in the investment performance report and graph, in Portfolio columns, and in the Average Annual Return snapshot. A negative value indicates a loss, which can be either paper or real. If the return seems surprisingly high, it could be because you have set a short date range.

Formula

The formula Quicken uses to calculate average annual return is:

 where: cfi = cash flow or dollar amount of the ith transaction to = date of the ith transaction in days n = number of transactions for this security in the report range tj = number of days in the report range r = rate of interest (solving for r)

Example

If a mutual fund lists its one-year average annual return as 20%, and you invest \$100 in that fund, you'd have \$120 by the end of the year.

If a mutual fund lists its three-year average annual return as 20%, and you invest \$100 in that fund, you'd have \$172.80 (an increase of \$72.80 or 72.80%) at the end of three years:

 Year Beginning balance Ending balance 1 \$ 100.00 \$ 120.00 2 \$120.00 \$144.00 3 \$144.00 \$172.80

Amount invested

Amount invested is the actual dollar amount that you have invested in a security to date. Amount invested includes any expenses for that security (but excludes reinvestments).

When you change the period over which Quicken calculates returns, Quicken calculates the Amount invested to be the market value of the security at the starting date plus the dollar amount you have invested in the security since that date (excluding reinvestments). In this way, the Amount invested indicates the total cost of the security to you since the starting date.

Note that the Amount invested doesn't decrease with a sale of shares, whereas cost basis does.

## Cost Basis

Cost basis equals the total cost to you of a security you purchased. It includes commissions, fees, and mutual fund loads. It also includes all purchases, even reinvestments of dividends and capital gains distributions. However, it excludes the cost of any shares you have sold or given away. Also, it is reduced in a return-of-capital transaction.

## Note

Quicken assumes, unless you tell it otherwise, that the shares you sell are the ones you've had the longest. You can tell Quicken which lots (or portions of lots) to sell when you enter a Sell transaction.

After you set up a Quicken investment account, Quicken keeps track of the cost basis of each security. It takes the dollar amount you enter for the first transaction involving a given security and uses this as the cost basis as of the date of the first transaction. Subsequent purchase costs are added to the cost basis; the cost of shares subsequently sold and any return of capital are subtracted from it.

## Return

Return represents the total return of a security: the current market value plus the income taken out as cash, plus cash received from sales of shares, minus the amount invested.

Reinvestments are not explicitly added to the return, because they contribute to the market value, which is already factored in.

Example

Let's say you bought 100 shares for \$5 each, (\$500 total). You later sold 50 shares for \$6 each, (\$300 total). Now the market price of your 50 remaining shares is \$7 (\$350 total).

The return is \$350 (current market value), plus \$300 (sales), minus the \$500 you invested, for a total return of \$150.

## Return on investment (ROI)

Return on investment, or ROI, is defined as Return divided by Amount Invested. ROI indicates how well a security has performed: it is the total profit (if ROI is positive), or loss (if ROI is negative), you would have from a security if you sold your shares in it today. ROI is expressed as a percentage of the amount you invested in the security. ROI takes account of the current market price and includes previous sales of the security and income received from the security.

Let's say you bought shares for \$100 and received \$5 in dividends, and today the shares are worth \$120. The amount invested is \$100, the \$ Return is \$25 (\$5 dividends plus the increase in market value). The ROI is 25/100 = 0.25, displayed as 25 percent. Note: If you change the return date, the ROI will change, since either the Amount Invested amount or Return amount will not be the same if you are using a different date and closing price.

Simple example

• John's amount invested in stock ABC from 12/31/96 to 1/4/98 is (100 x 10) + (50 x 15), or \$1,750.
• John's return in stock ABC from 12/31/96 to 1/4/98 is \$3,040 - \$1,750 (current market value - amount invested), or \$1,290.
• John's ROI in stock ABC from 12/31/96 to 1/4/98 is \$1,290/ \$1,750 (return /amount invested), or 73.71%.

Example with Sell and ReInvDiv

Let's say you made the following transactions for stock XYZ:

 On this date You made this transaction At this price per share 12/31/98 Bought 100 shares \$10 7/31/99 Bought 50 shares \$15 12/31/99 Received a dividend of \$40, which you reinvested in two more shares \$20 1/4/00 Sold 20 shares \$18
• Your market value in stock XYZ as of 1/4/00 is 132 shares x \$18/share (number of shares you own x current market price per share), or \$2,376.
• Your \$ invested in stock XYZ from 12/31/98 to 1/4/00 is (100 x 10) + (50 x 15), or \$1,750.
• Your \$ return in stock XYZ from 12/31/98 to 1/4/00 is 2376 + 360 - 1,750 (current market value + cash received from sale of shares - amount invested), or \$986.
• Your ROI in stock XYZ from 12/31/98 to 1/4/00 is 986/1,750 (return/amount invested), or 56%.

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