Two alternate solutions for odd Cash flow Message #3 Posted by allen on 28 Jan 2008, 10:38 p.m., in response to message #1 by Matthew Call
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:
Payment
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 prorated payment of $115,500 in 68th month) See comments in example above as to why PV differs.
Payment
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.
