HP27S Solver Equation CFLO Cash Flow with IRR% (from TVM CFLO on HP19BII, HP17BII)

[Dale Gunns]

Description: Have you ever needed a CFLO Cash Flow equation with IRR% calculation on your HP27S, like the HP19BII and HP17BII have built-in? I have. This solver equation was written for the HP27S (which has a built-in TVM menu, but not the built-in CFLO menu). All three calculators were used to write this solver equation, along with their manuals and guides (See References).

Learning About Cash Flow, IRR% and TVM features in these HP Calculators: See the References section below. Documentation for these HP calculators is available online.

Solver Equation CFLO Menu:
1. IRR%  I%    NPV   NUS   NFV   MORE  
2. N     CF0   SUBT  TOTAL

Variables and Lists:
FLO: List Name (Create/edit in STAT menu on HP27S, SUM menu on HP19BII, HP17BII.

Variables and Lists:  
List Name: FLO (Create/edit in STAT menu on HP27S, in SUM menu on HP19BII, HP17BII).
IRR%  Solve for Internal Rate of Return %, per period. (Requires list CFLO). (Does not require any vars. Assumes NPV is 0. Solved iteratively.)
I%    Enter Interest Rate per period. (Required)
NPV   Solve for Net Present Value (Requires I%, list FLO).
NUS   Solve for Net Uniform Series (Requires I%, NPV, list FLO).
NFV   Solve for Net Future Value (Requires I%, NPV, list FLO).
N     Solve for total Number of payments. (Requires list CFLO).
CF0   Solve for initial-cash-flow-0. (Requires list CFLO).
SUBT  Solve for sub-total cash flow after ICF0. (Requires list CFLO).
TOTAL Solve for total of all cash flow amounts. (Requires list CFLO).

Solver Equation
Note: Line breaks and spaces added for clarity. Spaces are optional in the solver.

Code:


CFLO.V0.90.R3.12:
IF(S(IRR%):
  +ITEM(FLO:1)
  +Σ(J:4:SIZES(FLO):2:
    USPV(IRR%: ITEM(FLO:J) )
    ×SPPV(IRR%: Σ(K:2:J-2:2: ITEM(FLO:K))-1 )
    ×ITEM(FLO:J-1) )
  +0x(I%):
IF(S(NPV):
  -NPV +ITEM(FLO:1)
  +Σ(J:4:SIZES(FLO):2:
    USPV(I%: ITEM(FLO:J))
    ×SPPV(I%: Σ(K:2:J-2:2: ITEM(FLO:K))-1 )
    ×ITEM(FLO:J-1) ):
IF(S(NUS): -NUS +NPV ÷USPV(I%: Σ(A:4:SIZES(FLO):2: ITEM(FLO:A) ) ):
IF(S(NFV): -NFV +NPV ×SPFV(I%: Σ(B:4:SIZES(FLO):2: ITEM(FLO:B) ) ):
IF(S(N): -N +Σ(C:4:SIZES(FLO):2: ITEM(FLO:C) ):
IF(S(CF0): -CF0 +ITEM(FLO:1):
IF(S(SUBT): -SUBT +Σ(S:4:SIZES(FLO):2: ITEM(FLO:S-1)×ITEM(FLO:S)):
IF(S(TOTAL): -TOTAL +ITEM(FLO:1)
  +Σ(T:4:SIZES(FLO):2: ITEM(FLO:T-1)×ITEM(FLO:T)):
0 )) )) )) ))

Usage in STAT/SUM Menu:
Create/edit the list name FLO (in STAT menu on HP27S, in SUM menu on HP19BII/HP17BII).
Enter cash flow amount and number of times. Enter amount, then enter number of times.
ITEM(1) Enter Initial-cash-flow-0 (CF0). If none, enter 0 (required).
ITEM(2) Enter 1 (required).
ITEM(2) Enter amount (required).
ITEM(3) Enter the number of times (required).
ITEM(4) and above (optional). Enter additional amounts and number of times.
Note: Multiple lists can be created. Just re-name the current list to FLO.

Usage in SOLVE Menu:
Create/edit the list name FLO (see above).
In the Solver, CALC equation CFLO.
Press Shift-Clear Data, resetting variables to zero.

Solve for TOTAL, N and NF0 to confirm your entries in list FLO are correct.

Solve for IRR%.

Enter I%, Interest Rate % per period. May be same as IRR%, rounded, or other.
Solve for NPV (required).
Then solve for NUS and NFV (these use the NPV value).


Solver Equation Verification
To verify that the equation is entered correctly on your calculator, complete Example 1 and compare your results to the results for the example.
Note: These example values match the built-in CFLO values on HP19BII and HP17BII, for confirmation of accuracy of the equation and that it is working properly on your calculator.

Example 1:
Problem: You have an opportunity to invest $20,000, with income promised quarterly. Calculate the internal rate of return, IRR%.
Note: Example from HP27S Owner’s Manual, see References.

Example 1 Part A List name FLO:
Display All digits (MODES, press ALL).
Create/Edit the grouped cash flow list named CFLO (in STAT menu on HP27S, SUM menu on HP19BII, HP17BII).

Enter initial-cash-flow-0 and 1. Negative is outflow, positive is income.
ITEM(1) -20,000
ITEM(2) 1

Enter each cash flow and the number of times.
ITEM(3) 500
ITEM(4) 4
ITEM(5) 1,000
ITEM(6) 4
ITEM(7) 2,000
ITEM(8) 4
ITEM(9) 3,000
ITEM(10) 4

Example 1 Part B SOLVE the equation:

Confirm entries in list FLO are correct.

Total number of payments (in this case, quarterly).
Solve for: N = 16

Initial-cash-flow-0.
Solve for: CF0 = -20,000

Sub-total all cash flows, except initial-cash-flow-0.
Solve for: SUBT = 26,000

Total all cash flows (includes initial-cash-flow-0).
Solve for: TOTAL = 6,000

Solve for: IRR% = 2.43099385371
(Press Shift-SHOW for full precision)

Press STO I%, to save IRR% to I%.
Solve for: NPV = 0.00, NUS = 0.00, NFV = 0.00

For I%, enter 2.43.
Solve for: NPV = 2.0816476, NUS = 1.58584776901E-1, NFV = 3.056623682


References
Note: Publications are available for download as PDF at: https://literature.hpcalc.org/all

1. The built-in CFLO menu on the HP19BII and HP17BII:
TOTAL IRR% I% NPV NUS NFV
Note: Built-in CFLO message “I% Needed To Calculate NPV, NUS and NFV” (HP19BII), and “NPV, NUS, NFV Need I%” (HP17BII). This holds true for this solver equation.

2. Publication Title: “HP-27S Owner’s Manual”, Edition 2, 1988.
Download (PDF): https://literature.hpcalc.org/community/hp27s-om-en.pdf
Chapter 5 “Net Present Value (NPV) and Internal Rate of Return (IRR%) on the HP-27S”.
Chapter 6 “Time Value of Money”.
Appendix C “Equations Used By HP-27S Menus”, then section “Solve”, and sub-sections “Actuarial Functions”, “TVM”, and “Cash Flow Calculations”.

3. Publication Title: “Step-by-Step Solutions: Business Finance and Accounting, for HP-17B, HP-19B and HP-27S”, Edition 3, 1991.
Download (PDF): https://literature.hpcalc.org/community/...ess-en.pdf
Chapter 5 “Net Present Value and Internal Rate of Return on the HP-27S”.

4. Publication Title: “HP-19BII Owner’s Manual”, Edition 2, 1991.
Download (PDF): https://literature.hpcalc.org/community/...-om-en.pdf
Chapter 4 “Time Value of Money and Interest Rate Conversions”.
Chapter 5 “Cash Flow Calculations”.
Appendix B “More About HP-19B Calculations”, then sections on “IRR% Calculations”, “Equations Used By HP-19B Menus”, and sub-sections “Actuarial Functions”, “Time Value of Money”, and “Cash Flow Calculations”.

5. Publication Title: “HP-17BII Owner’s Manual”, Edition 2, 1991.
Download (PDF): https://literature.hpcalc.org/community/...-om-en.pdf
Chapter 4 “Time Value of Money”.
Chapter 6 “Cash Flow Calculations”.
Appendix B “More About Calculations”, then sections on “IRR% Calculations”, “Equations Used By Built-In Menus”, and sub-sections “Actuarial Functions”, “Time Value of Money (TVM)”, and “Cash Flow Calculations”.

Informal Disclaimer
For entertainment purposes only. Use at your own risk. Information herein is in the public domain, free of charge, informal, prone to numerous errors and omissions, and free and devoid of any useful content.

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