(Plus42) Cash Flow Analysis: NPV, IRR%, MIR%, FMR%

[Werner]

Update: for the latest version see here.
My first try at writing equations!
The following equation performs Cash Flow Analysis:
- NPV: Net Present Value
- IRR%: Internal Rate of Return : the interest rate that makes NPV=0
- MIR%: Modified Internal Rate of Return: works with two interest rates. Negative cash flows are discounted back to Present Values using a safe rate SF%, positive cash flows are accumulated forward to Future Values with a Re-investment rate RI%. The MIR% is then ((FV/PV)^(1/N)-1)*100, with N the total number of cash flows, not counting CF0.
- FMR%: Financial Management Rate of Return: like MIR%, but where possible, future negative cash flows will be removed by prior positive cash flows.

- All cash flows CFj (including CF0!) must be placed in a column matrix CF, with the corresponding frequency Nj in an optional second column.
- Since these are solver equations, IRR% can be found setting NPV to zero and solving for IRR%
- all calculations are done using a single reverse sweep over the CF matrix
- I am a beginner at these things, so I'd welcome improvement tips.

example 1
---------

from the HP30b manual pg 44, the only HP to feature FMRR

Create the 8x1 matrix - including CF0:

[[ -1250000 ]
[ -300000 ]
[ 200000 ]
[ 450000 ]
[ -200000 ]
[ 700000 ]
[ 300000 ]
[ 500000 ]]

CALC the equation, and press CF to store the matrix
Then set NPV to zero and press
IRR%=4.96
set SF%=5 and RI%=8, then
MIRR%=5.94
FMRR%=5.86

example 2
---------

from hpmuseum forum: https://www.hpmuseum.org/forum/thread-13...#pid117980

Create the 7x2 matrix

[[ -25000 1]
[ 10000 1]
[ -7000 1]
[ 5000 8]
[ -4000 12]
[ 35000 2]
[ 29000 2]]

and determine
- NPV with discount rate 5% (24688.29) (Set IRR% to 5 and press NPV)
- IRR% (11.08%) (set NPV to 0 first)
- MIRR% with safe rate 3.75% and reinvestment rate 8.35% (7.87%)
- FMRR% with the same rates (8.47%)

formatted equation:

Code:

CFA:0*(
  L(N:MROWS(CF))+
  IRR%+NPV+SF%+RI%+MIR%+FMR%+
  L(P:0)
)+
IF(S(CF):0:IF(S(SF%):0:IF(S(RI%):0:
IF(S(FMR%):
  0*(
    L(F:0)+
    L(SF:SF%/100)+
    L(S:1+G(SF))+
    L(R:1+RI%/100)+
    IF(MCOLS(CF)=1:
      L(NN:G(N))+
      Σ(I:G(N):1:-1:IF(L(P:G(P)-L(C:CF[I]))<0:L(F:G(F)-G(P))+L(P:0):0)+L(P:G(P)/G(S))+L(F:G(F)/G(R)))
    :
      L(NN:0)+
      Σ(I:G(N):1:-1:
        L(NN:G(NN)+L(Nj:CF[I:2]))+
        L(N1:L(N2:L(N3:0)))+
        IF(L(C:CF[I:1])<0:
          L(N1:G(Nj)):
          IF(G(P)=0:L(N3:G(Nj)):
            L(N1:MIN(G(Nj):IP(LNP1(G(SF)*G(P)/G(C))/LNP1(G(SF)))))+
            L(N2:G(Nj)-G(N1))+
            L(N3:G(N2)-1)
          )
        )+
        IF(G(N1)>0:
          L(F:G(F)*SPPV(RI%:G(N1)))+
          L(P:G(P)*SPPV(SF%:G(N1))-G(C)*USPV(SF%:G(N1)))
        :0)+ 
        IF(G(N2)>0:
          L(F:(G(F)-G(P)+G(C))/G(R))+
          L(P:0)
        :0)+
        IF(G(N3)>0:
          L(F:G(F)*SPPV(RI%:G(N3))+G(C)*USPV(RI%:G(N3)))
        :0)
      )
    )
  )+
  SPFV((FMR%-RI%)/G(R):G(NN)-1)-G(F)*G(R)/G(P)/G(S)
:
IF(S(MIR%):
  0*(
    L(F:0)+
    L(S:1+SF%/100)+
    L(R:1+RI%/100)+
    IF(MCOLS(CF)=1:
      L(NN:G(N))+
      Σ(I:G(N):1:-1:IF(L(C:CF[I])<0:L(P:G(P)-G(C)):L(F:G(F)+G(C)))+L(P:G(P)/G(S))+L(F:G(F)/G(R)))
    :
      L(NN:0)+
      Σ(I:G(N):1:-1:
        L(NN:G(NN)+L(Nj:CF[I:2]))+
        L(P:G(P)*SPPV(SF%:G(Nj)))+
        L(F:G(F)*SPPV(RI%:G(Nj)))+
        IF(L(C:CF[I:1])<0:
           L(P:G(P)-G(C)*USPV(SF%:G(Nj))):
           L(F:G(F)+G(C)*USPV(RI%:G(Nj)))
        )
      )
    )
  )+
  SPFV((MIR%-RI%)/G(R):G(NN)-1)-G(F)*G(R)/G(P)/G(S)
:
  0*(
   L(R:1+IRR%/100)+
   IF(MCOLS(CF)=1:
      Σ(I:G(N):1:-1:L(P:(G(P)+CF[I])/G(R))):
      Σ(I:G(N):1:-1:L(Nj:CF[I:2])+L(P:G(P)*SPPV(IRR%:G(Nj))+CF[I:1]*USPV(IRR%:G(Nj))))
     )
  )+
  NPV-G(P)*G(R)
)))))

as an equation string:

Code:

CFA:0*(L(N:MROWS(CF))+IRR%+NPV+SF%+RI%+MIR%+FMR%+L(P:0))+IF(S(CF):0:IF(S(SF%):0:​IF(S(RI%):0:IF(S(FMR%):0*(L(F:0)+L(SF:SF%/100)+L(S:1+G(SF))+L(R:1+RI%/100)+IF(MCOLS(CF)=1:L(NN:G(N))+Σ(I:G(N):1:-1:IF(L(P:G(P)-L(C:CF[I]))<0:L(F:G(F)-G(P))+L(P:0):0)+L(P:G(P)/G(S))+L(F:G(F)/G(R))):L(NN:0)+Σ(I:G(N):1:-1:L(NN:G(NN)+L(Nj:CF[I:2]))+L(N1:L(N2:L(N3:0)))+IF(L(C:CF[I:1])<0:L(N1:G(Nj)):IF(G(P)=0:L(N3:G(Nj)):L(N1:MIN(G(Nj):IP(LNP1(G(SF)*G(P)/G(C))/LNP1(G(SF)))))+L(N2:G(Nj)-G(N1))+L(N3:G(N2)-1)))+IF(G(N1)>0:L(F:G(F)*SPPV(RI%:G(N1)))+L(P:G(P)*SPPV(SF%:G(N1))-G(C)*USPV(SF%:G(N1))):0)+ IF(G(N2)>0:L(F:(G(F)-G(P)+G(C))/G(R))+L(P:0):0)+IF(G(N3)>0:L(F:G(F)*SPPV(RI%:G(N3))+G(C)*USPV(RI%:G(N3))):0))))+SPFV((FMR%-RI%)/G(R):G(NN)-1)-G(F)*G(R)/G(P)/G(S):IF(S(MIR%):0*(L(F:0)+L(S:1+SF%/100)+L(R:1+RI%/100)+IF(MCOLS(CF)=1:L(NN:G(N))+Σ(I:G(N):1:-1:IF(L(C:CF[I])<0:L(P:G(P)-G(C)):L(F:G(F)+G(C)))+L(P:G(P)/G(S))+L(F:G(F)/G(R))):L(NN:0)+Σ(I:G(N):1:-1:L(NN:G(NN)+L(Nj:CF[I:2]))+L(P:G(P)*SPPV(SF%:G(Nj)))+L(F:G(F)*SPPV(RI%:G(Nj)))+IF(L(C:CF[I:1])<0:L(P:G(P)-G(C)*USPV(SF%:G(Nj))):L(F:G(F)+G(C)*USPV(RI%:G(Nj)))))))+SPFV((MIR%-RI%)/G(R):G(NN)-1)-G(F)*G(R)/G(P)/G(S):0*(L(R:1+IRR%/100)+IF(MCOLS(CF)=1:Σ(I:G(N):1:-1:L(P:(G(P)+CF[I])/G(R))):Σ(I:G(N):1:-1:L(Nj:CF[I:2])+L(P:G(P)*SPPV(IRR%:G(Nj))+CF[I:1]*USPV(IRR%:G(Nj))))))+NPV-G(P)*G(R))))))

Took me 2 days to write - far less than the corresponding 42S RPN program that is still not finished ;-)
The #1 cause for errors is mismatched parentheses - I would therefore like very much to have a () insert in one go, with the cursor in between the parentheses - a bit like the '48 does.
Cheers, Werner