Simple PV ? HP 12C


I recently discovered something about the way the HP12C does present value calculations I was not aware of. I'm trying to figure out if changing the way it caluculates is an easy push of a button, only solved by converting the periods to monthly etc.. In any event I can't figure out why the HP 12C calculates it like it does as, to me, it doesn't seem like the way anyone would want the calculation done. I tried it on an HP 19B and it worked as I intended. Anwyay, here is the problem.

I was trying to get a PV for annual rental payments. The term was supposed to be 68 months, so I'd used 5.667 years (end of period payments). I input the info as follows $173,250 PMT, 5.667 n, 6 i, and got a PV of $701,710. I didn't double check this anywhere. I got a call back today saying, the period should be 6 years, so I ran the same calculation with 6 n and got $851,926. I knew somethign was off, but couldn't figure out what.

I played around and realized for every "n" from 5 to 5.99 the PV number got smaller. I then figured out what the HP 12C did for my inputs was to put a zero payment in for the first period, and then discount five, $173,250 payments 1.667, 2.667, 3.667 etc. years.

Is my calculator set-up wrong or is this really how the HP 12C does this calculation? If so, it makes no sense to me as I can't imagine anyone wanting it to run that calculation with those inputs. As I said, if I put the same inputs into a 12B I get something around $830,000 which is what, I would have expected the 12C to tell me as well.


Something similar to this was discussed a few days ago.

Look through the 12c manual for how it handles odd period calculations and that should help.

When you told the 12c that n was 5.6667, it processed 5 payments of $173,250 that were put off for a 2/3 of a year handled with simple interest unless the 12c was put into the "c" mode for compound interest during an odd period.

When you changed it to N = 6, there were suddenly 6 payments and the PV went way up.

In your original problem with the period to be 68 months, how many annual rent payments were being made? On what exact months were they being made?


I agree with Gene that that the challenge here is actually setting up the cash flow diagram in a way that the calculator understands. One subtle difference with the 12c (and is part of the problem here) is that unlike most of HP's other Financial calculators, the 12c knows NOTHING of the number of annual payments, and relies on the user to enter the correct interest PER PERIOD.

In contrast the other TVM solvers require ANNUAL interest rate, and uses the P/YR setting (number of payments per year) to run calculations. So below I propose two different solutions. The first is to calculate the equivalent monthly cash flow and then determine the PV of all of the "monthly" payments. Another way (shown below in excel as a check of the former) is to SUM each annual payment's contribution to the PV (e.g. without converting to monthly payment).
As long as you are consistent matching the Periodic interest rate with the number of periods, you will get the same answer.

I propose a more meaningful solution:

12c solution:
Part 1: convert a single annual (FV) payment to equivalent monthly pmt
f CLEAR reg
173250 FV ; 173250 FV is the same as making 1 PMT at end of year
0 PV ; establish 0 balance at beginning of year
1 g N ; 12 payments/year
6 g i ; 6 percent annual interest (compounded monthly)
PMT ; = $14,044.76 per month

Part 2: Determine the present value of n months. (in this case 72)
6 g N ; Change number of pmts to 72
0 FV ; reset the FV from above since we have converted to PMT
PV ; NPV is $847,453.93

Alternative part 2: with 68 months determine the present value @ 68 months)
68 N ; Change number of pmts to 68
0 FV ; reset the FV from above since we have converted to PMT ( may be unnecessary if already cleared)
PV ; NPV is $807,928.76 <- This number will increase by $824.18 if you decide to charge $115,500
; in the 68th month rather than $14,044.76 per month for the partial year. Your example above
; did not say how the final payment was calculated.

You can easily check your work in excel:

in Month Contribution to PV Excel Formula
12 ($163,185.10) PV(0.06/12,12,0,173250)
24 ($153,704.92) PV(0.06/12,24,0,173250)
36 ($144,775.48) PV(0.06/12,36,0,173250)
48 ($136,364.80) PV(0.06/12,48,0,173250)
60 ($128,442.73) PV(0.06/12,60,0,173250)
72 ($120,980.90) PV(0.06/12,72,0,173250)
($847,453.93) SUM

Or for the 68 month example (Using pro-rated payment of $115,500 in 68th month) See comments in example above as to why PV differs.

in Month Contribution to PV Excel Formula
12 ($163,185.10) PV(0.06/12,12,0,173250)
24 ($153,704.92) PV(0.06/12,24,0,173250)
36 ($144,775.48) PV(0.06/12,36,0,173250)
48 ($136,364.80) PV(0.06/12,48,0,173250)
60 ($128,442.73) PV(0.06/12,60,0,173250)
68 ($82,279.15) PV(0.06/12,68,0,173250/12*8)
($808,752.18) SUM

Edited: 28 Jan 2008, 11:17 p.m.

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