This program is Copyright © 1976 by HewlettPackard and is used here by permission. This program was originally published in the HP67 Business Decisions Pac.
This program is supplied without representation or warranty of any kind. HewlettPackard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.
Internal Rate Of ReturnGroups Of Cash Flows 

Shift 



>Recalc 

Label 
Inv 
Lrg CF 
CF^# 
>IRR 

Key 
A 
B 
C 
D 
E 
In the diagram above, the horizontal line represents the time period(s) involved, while the arrows represent the cash flows.
This program solves for the internal rate of return (IRR) when groups of uneven cash flows are involved. Given a nonzero initial investment (INV), the cash flows (CF) and the corresponding number of times each cash flow occurs (#), the periodic IRR is calculated.
Up to 20 groups of positive or negative cash flows, with each group containing a maximum of 99 cash flows, may be entered. If more than 20 groups are input, erroneous results will occur.
Zero should be entered for periods with no cash flow.
The program works with even dollar amounts. When dollars and cents are involved, the cents will be lost.
If a cash flow (other than the investment) exists with more than 8 digits (i.e., more than $99999999.00) the user is asked to enter this value in step 3 because of the storage techniques being used. The value is then used to scale all other cash flows, and depending on these values, accuracy may be reduced. This large cash flow must be entered again in sequence in step 4.
The answer produced is the periodic rate of return. If the cash flow periods are other than annual (monthly, quarterly) the answer should be multiplied by the number of periods per year to determine the annual internal rate of return.
The calculator must be in FIX mode, as the program is dependent upon the display setting. To obtain 4 decimals of accuracy, the program card should be recorded in FIX 4 mode. More or less accuracy may be obtained by changing the display setting from DSP 4 to DSP 5, DSP 6, DSP 2, etc. However, time for solution increases as accuracy is improved.
If the user wishes to recalculate the IRR without changing the data in any manner, simply input the number of groups and press f D This feature is useful if the calculator is halted prematurely, as it is not necessary to reenter all of the data.
This program was designed for optimum operation when the interest rate being solved for is between 0 and 100%. The program will often solve for interest rates outside this range, but occasionally may halt prematurely with ERROR in the display. This is an error condition generated by an intermediate calculation, and indicates that the program cannot solve that particular problem.
The calculated answer may be verified by using Discounted Cash Flow Analysis  Net Present Value, to calculate the net present value. The NPV should be close to 0.
When the sign of the cash flows is reversed more than once, more than one interest rate is considered correct in the mathematical sense. While this program may find one of the answers, it has no way of finding or indicating other possibilities.
Step 
Instructions 
Input Data/Units 
Keys 
Output Data/Units 
1 
Load side 1 and side 2. 

2 
Input initial investment. 
INV 
A 
INV 
3 
If one cash flow has more than 8 digits, key it in. 
LRG CF 
B 
LRG CF/10^{k}* 
4 
Beginning with the first period, key in each cash flow and the number of times it occurs, pressing C after each group. 
CF 
ENTER 



# 
C 
# of groups 
5 
Calculate the periodic internal rate of return 

D 
IRR(%) 
6 
To recalculate the IRR, enter number of groups. 
# of groups 
f D 
IRR(%) 

* k = 1 (LRG CF has 9 digits) 




k = 2 (LRG CF has 10 digits) 



An income property is available for $50,000. The annual income over a 23year projection period (all payments received at the end of the year) may be grouped as follows:
Number of Years Cash Flow ($) First 5 Years 9,000 Next 4 Years 7,500 Next 4 Years 6,000 Next 3 Years 7,500 Last 7 Years 5,000
If the investor wishes a 15% return, does the property meet his objectives?
Keystrokes Outputs 50000 A 9000 ENTER 5 C 7500 ENTER 4 C 6000 ENTER 4 C 7500 ENTER 3 C 5000 ENTER 7 C 5.0000 (5 groups of cash flows entered) D 15.2681 (annual IRR of 15.2681%)
Since the IRR is more than 15%, the property meets the investor's objectives.
An investment of $620,000,000 is expected to have the following annual income stream for the next 15 years.
Number of Years Cash Flow ($) First 10 Years 100,000,000 Next 5 Years 5,000,000
What is the expected rate of return?
Keystrokes Outputs 620000000 A 100000000 B 62000000.00 100000000 ENTER 10 C 5000000 ENTER 5 C D 10.0649 (annual IRR of 10.0649%)
LINE KEYS 001 *LBL A 002 CL REG 003 STO E INV>RE 004 1 005 STO D 006 X<>Y 007 RTN 008 *LBL B If large CF exists 009 ABS 010 EEX 011 7 012 ÷ 013 LOG 014 INT INT[log(large CF/10^{7})] 015 X<0? 016 CLX 017 10^{X} 018 STO D 019 RCL E 020 X<>Y INV/10^{k}>RE 021 ÷ 022 STO E k = 1 or 2 023 RTN 024 *LBL C 025 ISZ I Scaling routine 026 RCL C 027 X<>Y 028 + 029 STO C 030 CLX 031 LST X 032 x 033 STO + 0 n_{j}CF_{j} 034 LST X 035 ÷ 036 LST X 037 EEX 038 2 039 ÷ 040 X<>Y 041 RCL D 042 ÷ 043 INT 044 X<0? 045 SF 0 046 ABS 047 + 048 F0? 049 CHS 050 LST X 051 X=0? 052 GSB 5 053 ENTER 054 ABS 055 ÷ 056 x 057 STO (i) 058 RCL I CF_{j} * n_{j} > R(i) 059 CF 0 060 RTN 061 *LBL d Routine to sum cash flows and recall number 062 GSB 3 of groups before going to iteration routine. 063 0 064 STO C 065 GTO 7 066 *LBL D 067 RCL I 068 GSB 3 069 *LBL 7 070 1 071 . 1 + initial guess 072 0 073 1 074 GSB c 075 GTO 0 076 *LBL 1 077 RCL 0 078 GSB e 079 STO C 080 *LBL 0 The secant method is used to evaluate f(i) 081 RCL B 082 RCL 0 083 STO B 084  085 RCL D 086 RCL C 087 STO D 088  089 ÷ 090 x 091 STO  0 092 RCL 0 093 ÷ 094 RND 095 X!=0? 096 GTO 1 097 RCL 0 098 1 099  100 EEX 101 2 102 x 103 RTN 104 *LBL 3 105 1 1.01 (#groups) 106 . 107 0 108 1 109 x >R_{I} 110 STO I 111 RTN 112 *LBL c 113 EEX 114 CHS 115 2 116 % .01 117 STO C 118 + 119 STO 0 120 STO B 121 GSB e 122 STO D 123 RCL 0 124 RCL C 125  126 STO 0 127 GSB e 128 STO C 129 RTN 130 *LBL E 131 EEX 132 2 133 ÷ 134 1 135 + 1 + i>R0 136 STO 0 137 *LBL e 138 0 139 *LBL 4 140 RCL 0 Continued fractions are used to find the PV 141 RCL (i) of the cash flows 142 FRAC 143 ABS 144 EEX 145 2 146 x 147 CHS 148 Y^{X} 149 x 150 1 151 LST X 152  153 RCL (i) 154 INT 155 x 156 + 157 DSZ I 158 GTO 4 159 RCL I 160 1 161 0 162 1 163 x 164 STO I 165 X<>Y DCF/i  INV = NPV 166 RCL 0 167 1 168  169 ÷ 170 RCL E 171  172 RTN 173 *LBL 5 174 + 175 ENTER 176 RTN 177 R/S
R0 1+i R1 CF_{1} * n_{1} R2 CF_{2} * n_{2} R3 CF_{3} * n_{3} R4 CF_{4} * n_{4} R5 CF_{5} * n_{5} R6 CF_{6} * n_{6} R7 CF_{7} * n_{7} R8 CF_{8} * n_{8} R9 CF_{9} * n_{9} S0 CF_{10} * n_{10} S1 CF_{11} * n_{11} S2 CF_{12} * n_{12} S3 CF_{13} * n_{13} S4 CF_{14} * n_{14} S5 CF_{15} * n_{15} S6 CF_{16} * n_{16} S7 CF_{17} * n_{17} S8 CF_{18} * n_{18} S9 CF_{19} * n_{19} A CF_{20} * n_{20} B Used C f(i_{k}) D f(i_{k1}) E Investment I Used
Go back to the software library
Go back to the main exhibit hall