The information set forth below was written by Financial Computer Support, Inc., vendors for DbCAMS, the asset management software system used by Financial Planning Associates, Inc. It is reproduced here by permission.
Internal Rate of Return Key Concepts and Calculations
The Internal Rate of Return (IRR) is the discount rate at which the present value of cash flows of an investment or set of investments equals the cost or current value of that investment. Except in the simplest case, there is no formula that can be used to calculate the IRR. This exception is when there are no transactions during the period. In this case, and only in this case, the IRR is calculated as: [(End value - Beginning value) / Beginning value]*100. Other than this, the IRR can only be precisely calculated using a trial and error process.
An alternative definition is the interest rate that, when applied to the beginning balance and all cash flows during the period, yields a calculated end value equal to the actual end value. This process also requires a trial and error approach and is the one used in dbCAMS+. However, dbCAMS+ does not require the calculated end value to be exactly equal to the actual end value. It allows a degree of error that yields an interest rate that is usually within 1 or 2 basis points of the actual rate.
The best way to visualize the concept of the IRR is as follows. Think of an investment that compounds daily and guarantees an effective annual yield. The IRR is the yield that would have to be guaranteed, given the investment's beginning value and the timing and size of all its cash flows, to grow to the actual investment's ending value. One important thing to remember is that the value of this hypothetical account will, in almost all cases, only equal the value of the actual account on the begin and end dates.
The use of the IRR imposes two constraints: 1) The rate of return must be constant throughout the entire period; and 2) Daily compounding of earnings is assumed.
How dbCAMS+ Calculates the IRR
Using the parameters specified in the Client Financial Global Options, the IRR's individual options, and the data entered in the dbCAMS+ databases, the program uses the following routine to determine the IRR.
1. The program values the asset(s) on the begin date and applies a 10% APR (Annual Percentage Rate) for the first trial or pass. This APR is converted to a daily rate by dividing it by 365. The daily rate is applied to the beginning balance for the number of days from the begin date to the first transaction date, inclusive of the begin date. At this point the "earned" interest is added to the begin value as is the transaction amount from the transaction.
2. The daily rate is then applied to the new balance until the next transaction date, and so forth, until the end date is reached.
3. The routine compares the calculated value on the end date to the actual end value. If there is a significant difference, more than 1 or 2 basis points, a second pass is initiated using a 20 percent APR. This process is repeated until the calculated end value is approximately equal to the actual end value.
Formula for Period Rate: ((1 + (Nominal Compounded Daily Rate * .01 / 365)) ^ (# days in period) - 1) * 100
Use the IRR whenever you want to show the client the performance of their own individual assets or groups of assets. Remember, this return is unique to their cash flow pattern. It will not be comparable to the rate of return they might see in a prospectus or newspaper ad. In fact, 2 clients who own identical assets in roughly the same amounts may have drastically different IRRs if their cash flow patterns are different.
The IRR is the best rate of return to use if a client wants to find out how his historical return compares to his desired or target rate of return. Do not use the IRR to compare managers. Do not use the IRR to compare asset performance with that shown in a prospectus, newspaper or other advertising, or to compare to a benchmark index such as the S & P 500. The TWR (Time Weighted Return) is the best measure to fulfill these needs.
Common Misconceptions Regarding the Internal Rate of Return (IRR)
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