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

[AndiGer]

To see it is true I did it the other way round with HP67 standard pac card SD05 on Legendary 67 on iFon 4s. PV has to be set to -1,000 to get 50,000 with interest rate 3.652.
When I then calculate i it returns 3.6520 after a few seconds less than 2 minutes at DSP 4.

[lrdheat]

On the Prime G2, if I uncheck “End” and make N=29, FV=49,000, P/Yr=1: I get I=3.64 Is this coincidental?

What is happening here? (If, in the above, I make N=30, FV=50,000, I get I=3.43

[Albert Chan]

(01-06-2020 11:07 PM)lrdheat Wrote:  On the Prime G2, if I uncheck “End” and make N=29, FV=49,000, P/Yr=1: I get I=3.64 Is this coincidental?

With End Off, it is identical to End On, but with payments shifted up:

PV ← PV + PMT
FV ← FV − PMT

Above is plain savings plan (with "End" On): N=29, PV=0, PMT=-1000, FV=50000 → I=3.639%

You can visualize it as original N=30 example, PV=1000 getting no interest, and got cancelled by first PMT.
The error is tiny, but to correct for this, we can iterate again.

PV gives up 1000 * 3.639% = 36.39
FV correction = 36.39 * 1.03639²⁹ = 102.60

Rerun solver, with N=29, PV=0, PMT=-1000, FV=50102.60 → I=3.652%

[lrdheat]

(Prime G2) Makes sense. At the expense of showing what remains my misunderstanding, when I input an i=3.652 and solve for N, I get 30.00 (result rounded by FIX 2). Indeed, if I choose an arbitrary i, and solve for N, a result will come up that makes sense if one is fine with a non integer N. If, however, I enter a N that is identical to an N that appears in the command line when I choose “edit”, and solve for i, it throws the many or no solutions error. This is true for all values that I experimented with. What am I not seeing here?

[SlideRule]

From my Texas Instruments Financial Investment Anayst:
PMT = -1,000
  FV = 50,000
  PV =  1,000
   N =       30
 I/Y =      43.82 *

BEST!
SlideRule

[Albert Chan]

(01-07-2020 02:48 AM)lrdheat Wrote:  If, however, I enter a N that is identical to an N that appears in the command line when I choose “edit”, and solve for i, it throws the many or no solutions error. This is true for all values that I experimented with. What am I not seeing here?

We have N+1 cash flows: PV , PMT × (N-1) , FV+PMT

If the cash flows has more than one sign changes, you may have multiple roots for rate, see post #19

Unlike my example, sometimes solved rates are close to each other.

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 ?

[ijabbott]

(01-06-2020 01:04 AM)Albert Chan Wrote:  My guess so many calculators failed this is because we have multiple solutions.
For my posted example, we have 2 (real) solutions for I.

Using HP-12C IRR (with the good guess), it did solve them.

Clear Reg
1000 CF0      ; PV
CHS CFj        ; PMT
29 Nj            ; N-1
49000 CFj     ; FV + last payment

IRR                             → Error 3
3 [i] RCL [g] [R/S]       → 3.651974353
100 [i] RCL [g] [R/S]    → 99.99999525

Same thing for HP 17BII+:

[FIN] [CFLO]
[SHIFT] [CLR DATA] [YES]
"FLOW(0)=?" 1000
"FLOW(1)=?" -1000
"#TIMES(1)=1" 29
"FLOW(2)=?" 49000
"#TIMES(2)=1"
[EXIT]
[CALC]
0 [STO] [IRR%] → 3.65197435259
100 [STO] [IRR%] → 99.9999952503

[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!

[Gene]

One other comment. This multiple root IRR problem happens ** whenever ** there is a series of cash flows with multiple sign changes.

+ - + as in this case.

- + - + - etc, etc.

That is the initial sign something will be wrong with an IRR approach. NPV does not suffer this problem. It ** always ** gives the best answer when your cost of funds is known.

[jthole]

(01-06-2020 02:11 AM)SlideRule Wrote:  

(01-06-2020 01:04 AM)Albert Chan Wrote:  My guess so many calculators failed this is because we have multiple solutions.

My HP-19BII Business ConsultantII concurs with MANY OR NO SOLUTIONS message.

The same for my HP 17Bii, which by the way solves the TVM equation of the thread starter almost immediately as well.

[SteveC]

I found this thread trying to verify if the HP 10Bii+ solves the two or more sign
change cash flow IRR problem. Simply answering 3.652% to the cf0 +1000,
cf 1-29 -1000, cf30 +49,000, is inferior and misleading as it makes no hint that
there may be more to the answer.

One more point in favor of the Gold Standard 12C that I trust.
The "Error 3" telling me there are multiple solutions is the best solution.
My 17B from 1989 also get the right answer of 3.652 & 100 after asking for
seeds and then running pretty quickly.

A Quick wrong or misleading answer is not at all superior to a slightly delayed
correct answer. The 12C Platinum runs this example quickly.

NPV does not have these problems.

-sc

[Gene]

Biggest lesson from this is don't use IRR.

:-)
Gene

[SteveC]

Today, a new to me HP 38C just arrived with looking pretty amazing for having
been made in 1979. I tried the same cf0 +1000, cf 1-29 -1000, cf30 +49,000
and it yields the correct 3.652% & 100% IRRs after the reassuring Error 3 and
seeding. The 100% comes up pretty quick. The 3.652 takes about 23 seconds.

The bright red LED display took me back to the calculators I remember using in
high school. Cost effective LCDs were hitting the market as I graduated so college
was all LCD displays.