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Understanding Compound Annual Return

Figuring Out Just How Much Money an Investment Made Can Be Confusing

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The return figures on a valuation statement are often misunderstood. The accuracy of the calculations is the biggest question. The compound annual return (CAR) uses internal rate of return (IRR) calculations, which take into account not only the size but also the timing of investments. They also use all cash flows into and out of an investment, including partial sales, dividends and additions to the position.

Most questions about the accuracy reveal the investor used a simple return calculation that doesn’t take into account the timing of the investments. A simple comparison can show how IRR works.

Here are two scenarios: 

•    Scenario A: $1,000 invested on Jan. 1, 2010. On Dec. 31, 2010, that’s worth $1,050.  

•    Scenario B: $250 invested on the first day of each quarter — Jan. 1, 2010, April 1, 2010, July 1, 2010 and Oct. 1, 2010. On Dec. 31, 2010, this investment is also worth $1,050.
In both cases, a total of $1,000 was invested and both had the same value at the end of the investment period.
At this time, it may be useful to introduce the concept of “dollar-months.” This is just the product of dollars invested times months invested. In scenario A, $1,000 is invested for 12 months. So the investment had 12,000 dollar-months invested. Scenario B is different. It has four different investments of $250 for four different periods: 12 months, nine months, six months and three months. Multiplying each $250 investment by its time period and then adding all the results together leads to a total of 7,500 dollar-months invested:

(250 x (12+9+6+3) = 250 x 30 = 7,500)
For this investment to be worth the same amount as scenario A, it must have a higher return, as it has less dollar months invested. Scenario A is pretty easy — it’s 5 percent. Scenario B is slightly over 8 percent. This accounting for the timing effect is essentially what IRR does. The CAR figure on the valuation statement is an IRR calculation. Checking this figure manually can be daunting. Fortunately, a spreadsheet can do this easily. In Excel, for evenly spaced cash flows the IRR function will work. For cash flows with unevenly spaced dates, use the XIRR function. The convention is to use negative numbers for amounts invested and positive numbers for money returned to the investor.
Although CAR on the valuation statement provides an accurate return figure, it does have some weaknesses. The most obvious is seen in short periods. For periods of less than a year, it’s more a projection of what an investment will earn if kept a year at the current growth rate. This can result in some very large numbers when a security experiences a larger-than-usual change in a short time. Although accurate, the figures aren’t very useful. As you near a one-year holding period, the figures become more meaningful.
The second shortfall is in using CAR to compare the performance of investments in different securities. Although a good tool for comparing the returns on investments, the greater the time difference between the investments, the less useful the comparison of CAR figures. For example, comparing the CAR of two investments — one held four years and one held five — is more useful than comparing the CAR of an investment held one year with one held seven years. I suggest a better comparison is the current CAR of an investment to your expected CAR from your SSG when the decision to buy was made.

Russell Malley is the Club Accounting Adviser for ICLUBcentral.

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