My HP 10bII+ is much faster than HP 12c!

[Gene]

Good question, Albert. For your example:

Example, for N=30, PV=6500, PMT=-1000, FV=50000, we have I = 8.96% or 11.10%
Does anyone knows what returns should be reported for above investments ?

Consider these results... the change of Net Present Value (NPV) as the interest rate being used to value the cash flows changes illustrates the problem. The NPV has two roots. Two interest rates make the Present value of the cash flows equal to the initial investment. To say it another way... there are two Internal Rates of Return (IRR).

That happens... so what is a calculator to do? Which is correct? Both are.

Many times, one IRR is more "meaningful" but that's a hard thing to put on a calculator algorithm to decide.

Take a look at the two attachments:

The npv.png picture is the table of NPV values for the above example with interest rates that go up by 0.5 points for each row... except I plugged in the two values for IRR that get the NPV essentially equal to zero.

The npvgraph.png picture is a graph of that table of values and shows where the graph crosses the X-axis two times, where the Y-value (which is the NPV) is equal to zero.

The equation has two roots, yet IRR seeks to return one. Choose wisely. :-)

Classical problem in cash flow analysis and a good reason to AVOID IRR and evaluate a series of cashflows at the firm's cost of capital using NPV.


EDIT: My table of numbers may be off - I did that quickly in Excel so apologies. The ** principle ** and graph isn't that far off. So don't rely on the specific numbers in the attached image of values. Sorry!