HP 12C Instruction Manual page 2

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HP 12C Internal Rate of Return
Cash Flow and IRR calculations
Cash flow analysis is an extension of the basic TVM concepts applied to compound interest problems when payments
occur in regular periods and do not have the same value. Any financial investment can be represented as an initial
investment of money and a series of later cash flows that occur in regular periods of time. Each flow of money can be
positive (received) or negative (paid out) and considered as a cash flow. Common cash flow problems usually involve the
calculation of the Internal Rate of Return (IRR) or the Net Present Value (NPV).
The NPV expresses the amount of money resulting from the summation of the initial investment (CF
value of each anticipated cash flow (CF
applied to all future cash flows that cause NPV = 0.
The expression that calculates the Internal Rate of Return is:
Cash flow diagrams
The cash flow diagram in Figure 1 illustrates one of the many possible situations that can be handled by the HP12C.
gJ Initial
Cash Flow
The HP12C cash flow approach
In the HP12C each cash flow amount is stored in its corresponding register in memory. For each cash flow amount there
is a related register to store the number of consecutive occurrences of this amount. This approach is shown below:
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) calculated to the time of the initial investment. The IRR is the discounted rate
j
k

∑
= + ×
0 CF CF 
0 j


=
j 1
gK
ga
Number of consecutive occurrences of CFj
Registers
R
0
R
1
...
...
R
6
R
7
... ...
R
.8
R
.9
FV
( )
− 
nj
− +
1 1 IRR
(
× +
 1
IRR


Composition Period
Intermediate Cash Flow
Cash flow N
j
CF
0
CF
1
...
CF
6
CF
7
...
CF
18
CF
19
CF
20
- 2 -
) and the present
0
)
−
nj
IRR
Figure 1
gK
Figure 2
N
0
N
1
N
6
N
7
N
18
N
19
Figure 3
N
20
HP 12C Internal Rate of Return - Version 1.0
Last Cash Flow