Why does the internal rate of return result differ slightly from the nominal annual rate?

Problem

It sometimes happens that the internal rate of return result displays a slightly different value than the value in the nominal annual rate field.

For instance, you've entered 48 % as the nominal annual rate and, after solving for an unknown, the IRR result displays 47.99891 %.

Answer 1

This is usually due to rounding: FinFlow calculates unknowns and interest fractions up to the precision that's specified in the Options dialog. As a result, the ending balance is usually not exactly zero, but a few cents less or more.

When solving for the internal rate of return, FinFlow tries to find a rate that will make the ending balance or the net future value zero, or as close to zero as possible.
To check this, Control-click the IRR result: you'll see that the ending balance is closer to zero.

Another way to handle it would be to increase the precision for amounts: choosing a higher precision for amounts will usually make the IRR result correspond with the nominal annual rate and result in an ending balance that's closer to zero.

Answer 2

The internal rate of return result is calculated independently from the value in the nominal annual rate field.

It is calculated using a complex series of iterations which uses a slightly different technique than the one used for calculating the net present value and the net future value of the cash flow. This different method also serves as a double-check on the normal amortization method, which is why we prefer to keep it that way.

Since the method for calculating the IRR doesn't take into account the percentage rounding that is used when generating an amortization schedule, minor differences may occur.

Please also note that there may be a range of possible solutions for the given percentage rounding, for instance, values which differ by 0.0001 % or more may very well lead to the same net present value. The method we use simply stops at the first value that produces a zero net present or future value. By graphing the slightly different values (and turning off rounding), it's possible to obtain a result with an even higher precision.