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# HP 12C TVM bugs!?

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I have a TVM question as follows:

A Company bought a debt securities at \$102.70 on 1 July 20X4. The debt security carried a fixed interest of 4.5% per annum, payable on 31 December of each year. The principal \$100 is repayable on 31 December 20X10.

Relevant particulars are as follows:
Investment cost .............................................................................................\$102.70
Principal at maturity.......................................................................................\$100.00
Coupon rate.......................................................................................................... 4.5%
Cash interest income per annum........................................................................\$4.50
Years to maturity from inception................................................................... 6.5 years
Cash interest income for half-year 20x4............................................................\$2.25

Now I have to calculate the effective interest rate.

The input parameters should be:

PV = -102.70

FV = 100.00

PMT = 4.5

n = 6.5

When I use the Texas Instrument BA II+ to calculate, i = 4.02; however, when I use the HP 12C to calculate, i = 3.64.

Further, when I use Excel or other TVM programme to calculate, I get i = 4.02 too!!

So I wonder if it is a bug for HP 12C?

I would be appreciate if some gentlement can help me!

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Hi!, marcuslsw:

You can see, for learning TVM ... http://h20331.www2.hp.com/Hpsub/downloads/HP12CTVMbasics.pdf

Too, the other function's, from ... http://h20331.www2.hp.com/Hpsub/cache/299940-0-0-225-121.html

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I guess I don't really understand the problem, as I think this is a problem of determining the effective interest on a cash flow rather than on a traditional TVM problem. I looked at the definitions at the Wikipedia entry on Internal Rate of Return, and figure that the equation to solve, for r, in this case is:

-102.5+2.25/(1+r/2)+104.5/(1+r)^6.5+4.5/(1+r)^5.5+4.5/(1+r)^4.5+4.5/(1+r)^3.5+4.5/(1+r)^2.5+4.5/(1+r)^1.5 =0

My HP50g and Mathematica 9 both give r=0.0405862  (i.e., approx 4.058%).

I also tried entering this as a cash flow problem on the HP30b, using a cash flow of :

-102.5, 2.25, 0, 4.50, 0, 4.50, 0, 4.50, 0, 4.50, 0, 4.50, 0, 104.50.

The 30b returned an IRR of 3.95% and an MIRR of 3.301%.

So, I'd really appreciate it if someone in finance could straighten out my misunderstandings of this problem as well!

--Leopold Bloom

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Thanks for replies!

I got confused since, for the same input parameters, HP 12C can't get the same  (or similar) result with TI BAII+ or other programme like Excel. The input parameters are as follows:

PV = -102700

PMT = 4500

FV = 100000

N = 6.5

HP 12C returns 3.64

TI BAII+ returns 4.02

Excel returns 4.02

So I wonder if it is a bug for HP 12C! Or else, how should I input the parameters in order to get the same result as TI BAII+ or Excel?

On the other hand, I've drafted a spreadsheet about the computation logic of TI BAII+ and HP 12C (for both END and BEG mode). See if it helps.

Thanks very much in advance! Hope someone can help!

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4.02% appears to be correct.

My bad! I really should have read and copied more carefully, as I used the initial payment as \$102.50 when it should have been \$102.70 as stated in the problem.

As a correction, using the given figures, the problem is

-102.5+2.25/(1+r/2)+104.5/(1+r)^6.5+4.5/(1+r)^5.5+4.5/(1+r)^4.5+4.5/(1+r)^3.5+4.5/(1+r)^2.5+4.5/(1+r)^1.5 =0

and Mathematica gives r=0.0402355 (which is the value shown in the spreadsheet)!

My HP30b still shows a different amount: 3.9104% (assuming 2 cash flows per year) if the cash flow is entered explicitly and IRR is computed. On the other hand, if the problem is set up as TVM using the implied parameters (N=6.5, P/Yr=1, PV=-102.70, PMT=4.50, FV=100.00, then I/Yr comes out as 4.01974066689% which is pretty close to the 4.02% marcuslsw gets on his spreadsheet and TI calculator).

So, again, it would be very helpful if a financial person could explain what is going on in the HP calculators' logic for this kind of problem.

--Leopold Bloom

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I got 4.0197% here too using the Hp50g finance tool! {LEFT_**bleep**} + {9}

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Gosh... Anyone can tell me whether it is a bug of HP12C? Or how should I handle such situation correctly?

I would be appreciate if any gentlement can give me a hand. Thanks! orz...

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Try with the simulator and see if the error persists:

I don't know how to use this calculator!

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Well, the first step was determining whether or not the 12C was correct, and that required finding a solution that fit the definition of IRR. As near as I can tell, it's approximately 4.02% -- different degrees of precision calculate different results because of roundoff error, but 4.02% either the slightly smaller or your slightly larger quantity, both produce very small errors in the calculated present value summation.

Thus, one can only conclude that there is an error in the 12C if you set it for 1 payment per year and 6.5 periods as I did on the 30b, 50g, and 39gii). There also appears to be an error in either my understanding of how the 30b's CashFlow calculation of IRR is supposed to work, or it also has an error (even though the 30b does get the 'correct' result using its TVM function).

I'll call this to the attention of a friend at HP to see if he can get an opinion registered.

--Leopold Bloom

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MarcioB: Thanks! I've tried the simulator, but the problem persists!

LeopoldBloomThanks! I think the most important point is that. TI BAII+ calculate only half of the coupon for 0.5 period, but HP just wait and count when there is a full period. You can refer to "TVM.xlsx" in my pervious message and you will know my meaning. I've draft out the cash flow I think the TI BAII+ and HP 12C are using.

I think there should be a way to handle this problem using HP 12C. Let's wait for reply from your HP friend!

Thanks again for your kind help!

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