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 Return 

Shift 





Label 
Inv 
CF Max 
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.
The interest rate that equates the present value of all future cash flows with the original investment is known as the internal rate of return (IRR, also called discounted rate of return or yield). Given a nonzero initial investment and up to 44 positive cash flows, this program calculates the periodic IRR. If there are negative as well as positive cash flows, the program accepts up to 22 cash flows.
If more than 44 positive cash flows are entered, all cash flows over 44 will be ignored. There will be no indication, however, that more than 44 cash flows have been entered. Likewise, if more than 22 positive and negative cash flows are entered, erroneous results will occur.
Zero should be entered for periods with no cash flow.
When more than 22 cash flows are involved (all of which must be positive), the user is asked to enter the largest cash flow in step 3 because of the storage techniques being used. This value is then used to scale all other cash flows, and depending on these values, accuracy may be reduced. Consequently, the resulting periodic rate of return should be considered accurate to within +/.01% (.0001 decimal). This largest cash flow must be entered again in sequence in step 4. If a cash flow larger than the value entered for CF MAX is keyed in at step 4, erroneous results may occur.
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.
In many instances another program may be more suitable for calculating IRR. If all cash flows are equal and equally spaced, or if all cash flows except the last are equal and equally spaced, Direct Reduction Loans is a better choice. If the cash flows occur in groups of uneven amounts, IRR Groups of cash Flows may be more suitable.
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 there are > 22 cash flows, key in the largest cash flow. 
CF MAX 
B 
CF MAX 
4 
Beginning with the first period, key in all cash flows in sequence, pressing C after each value. 
CF 
C 
# of CFs 
5 
Calculate the periodic internal rate of return 

D 
IRR(%) 
Income property requiring a $250,000 equity investment and to be sold in ten years is expected to generate the "after tax" cash flows shown below. What is the expected yield or IRR?
End of Year Cash Flow End of Year Cash Flow 1 $46,423 6 $23,199 2 40,710 7 21,612 3 36,638 8 20,037 4 34,097 9 18,460 5 32,485 10 311,406 (property sold)
Keystrokes Outputs 250000 A 46423 C 40710 C 36638 C 34097 C 32485 C 23199 C 21612 C 20037 C 18460 C 311406 C D 13.98 (annual IRR is 13.98%)
Property requiring a $30,000 investment will be sold at the end of 2 years. If the investment results in the monthly net cash flows shown below, what is the IRR?
End of Month Cash Flow End of Month Cash Flow 1 $16 13 $201 2 50 14 195 3 175 15 178 4 181 16 197 5 143 17 210 6 147 18 220 7 151 19 206 8 176 20 194 9 184 21 187 10 193 22 190 11 157 23 201 12 190 24 35,000 (property sold)
Keystrokes Outputs 30000 A 35000 B 16 C 50 C 175 C 181 C 143 C 147 C 151 C 176 C 184 C 193 C 157 C 190 C 12.00 (12 cash flows input) 201 C 195 C 178 C 197 C 210 C 220 C 206 C 194 C 187 C 190 C 201 C 35000 C 24.00 (all cash flows input) D 1.15 (monthly IRR) 12 x 13.79 (an annual IRR of 13.79%)
LINE KEYS 001 *LBL A Clear registers 002 CL REG 003 P<>S INV>RE 004 CL REG 005 STO E 006 CF 0 Clear flags 007 CF 1 008 RTN 009 *LBL B Input largest cash flow if #CFs > 22 010 2 011 x 012 STO 0 013 RCL E 014 X<>Y 015 ÷ INV/2 CMAX > RE 016 STO E 017 LST X 018 SF 0 Flag 0 indicates > 22 cash flows 019 2 020 ÷ 021 RTN 022 *LBL C 023 ISZ I If F0, pack data in registers 024 F0? 025 GSB c 026 STO + (i) 027 X<>Y 028 RCL I Display # of cash flows (add if > 22 CF) 029 F1? 030 + 031 RTN 032 *LBL c 033 2 034 3 035 RCL I 036 X!=Y? 23rd Cash flow? 037 GTO 0 038 1 039 STO I Reset I 040 + Drop the stack and clear x 041 CLX 042 EEX 043 5 2 CMAX/10^5 > R0 044 STO ÷ 0 045 SF 1 046 *LBL 0 047 roll dn 048 1 049  050 X<>Y Scale cash flow 051 RCL 0 052 ÷ If CFj, J>22, drop fractional part of CFj 053 F1? 054 INT 055 RTN 056 *LBL a 057 RCL I LBL fa sets up I for count down and keeps track of 058 1 original # of cash flows by storing N.N 059 0 060 1 061 x 062 STO I 063 RTN 064 *LBL e 065 F0? 066 GTO 0 Unpacks doublestored cash flows 067 INT 068 EEX 069 5 070 ÷ 071 RTN 072 *LBL 0 073 FRAC 074 RTN 075 *LBL D 076 GSB a Setup I 077 RCL I NN 078 EEX 079 2 080 ÷ 081 STO I N.N>I 082 1 083 . 084 0 085 1 1+i0>RD 086 STO D 087 *LBL 4 088 CF 0 089 0 090 STO 0 091 *LBL 5 092 RCL I 093 INT 094 F1? Get j 095 GSB d 096 RCL (i) 097 F1? 098 GSB e 099 STO + 0 Unpack CFj 100 x 101 + f(i) in R0 102 RCL D 103 STO ÷ 0 104 ÷ 105 DSZ I 106 GTO 5 107 F1? 108 GTO 0 109 *LBL 6 110 RCL 0 111 RCL E 112  113 X<>Y 114 ÷ 115 RCL D f/f' * (1+i) 116 x 117 RCL D 118 X<>Y 119 + (1+i) next 120 STO D 121 LST X 122 ABS 123 EEX f(i)/f'(i) 124 CHS 125 5 126 X>Y? 127 GTO 7 <Done! 128 GSB a 129 GTO 4 130 *LBL 0 131 F0? 132 GTO 6 133 SF 0 134 GSB b 135 GTO 5 136 *LBL b Loop back for lower 22 CFs 137 2 138 2 139 RCL I 140 + Reset I to lower 22 CFs 141 STO I 142 CLX 143 + 144 RTN 145 *LBL d 146 2 Add 22 if flag 0 clear 147 2 148 F0? 149 CLX 150 + 151 RTN 152 *LBL 7 Reset R1 for another pressing of D 153 RCL D 154 1 155  156 STO D RI must contain an integer here 157 EEX 158 2 159 x 160 RCL I 161 LST X 162 x 163 STO I 164 X<>Y 165 RTN 166 R/S
R0 Used R1 Used R2 Used R3 Used R4 Used R5 Used R6 Used R7 Used R8 Used R9 Used S0 Used S1 Used S2 Used S3 Used S4 Used S5 Used S6 Used S7 Used S8 Used S9 Used A Used B Used C Used D 1+i_{0} E Used I Used
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