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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 (CF0) and the present
value of each anticipated cash flow (CFj) calculated to the time of the initial investment. The IRR is the discounted rate
applied to all future cash flows that cause NPV = 0.

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Cash flow and IRR calculations

Cash flow diagrams

The HP12C cash flow approach

Practice with solving cash flow problems related to IRR

How to modify cash flow entries

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 (

The NPV expresses the amount of money resulting from the summation of the initial investment (CF0) and the present

value of each anticipated cash flow (CFj) calculated to the time of the initial investment. The IRR is the discounted rate

applied to all future cash flows that cause NPV = 0.

The expression that calculates the Internal Rate of Return is:

1− (1+

0 =

−

0

∑

×(1+

Figure 1

1

The cash flow diagram in Figure 1 illustrates one of the many possible situations that can be handled by the HP12C.

Composition Period

gK Last Cash Flow

gK Intermediate Cash Flow

gJ Initial Cash Flow

ga Number of consecutive occurrences of CFj

Figure 2

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:

Registers

Cash flow

Nj

R0

CF0

N0

R1

CF1

N1

...

...

...

R6

CF6

N6

R7

CF7

N7

...

...

...

R.8

CF18

N18

R.9

CF19

N19

Figure 3

FV

CF20

N20

hp calculators

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The HP12C memory organization al ows up to 20 different cash flow amounts plus the initial investment to be stored and

handled according to the diagram in Figure 2. If any cash flow amount repeats consecutively, then it can be stored as a

grouped cash flow CFj and its corresponding Nj holds the number of occurrences, up to 99. TVM register

index to control CF operations.

The keys to enter cash flow data are:

gJ - stores the number in the display in R0 and sets

gK - adds 1 unit to current

ga - stores the number in the display(∗) in Nj;

(∗) The number in the display must be a positive integer from 1 to 99, otherwise ga returns

to the display and

no operation is performed.

If the last available register has already been used, gK adds 1 unit to current

the display in TVM register FV. Any attempt to add a cash flow amount with gK after FV has already been used

or when

to be shown in the display and no

operation is performed.

Example 1: The cash flow diagram below represents a possible investment and you were chosen to determine if it is

feasible. The success of this investment dictates your future in the company, so the analysis must be

precise and error free. What is the correct keystroke sequence to fill the HP12C registers with all data?

$ 178,500.00

$ 20,000.00

CF6

CF3

$ 7,000.00

$ 12,000.00

CF

CF4

1

3 consecutive occurrences

N3

$-10,000.00

$-8,000.00

$-130,000.00

CF

CF

CF

2

5

0

Figure 4

Solution:

Clearing all registers is not necessary to start cash flow analysis because only the registers updated with

cash flow data are used.

130000 Þ gJ

7000 gK

10000 Þ gK

Figure 5

hp calculators

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The next cash flow amount occurs three times in a sequence, so it can be entered as a grouped cash flow.

20000 gK

3 ga

Figure 6

The remaining data is entered with the following keystroke sequence:

12000 gK

8000 Þ gK

178500 gK

Figure 7

Answer:

The keystrokes presented above indicate the correct entries.

Example 2: The cash flow diagram had all of its information used to compose the cash flow data in the HP12C

memory. Show how to check that they were entered correctly.

Solution:

Now that all data is entered, checking for its correctness is possible in two ways. The most common way is

the sequential check and the keystroke sequence for this checking is as follows:

:w

Figure 8

This is the number of the last register used to store the cash flow data. It will be needed later.

:gK

Figure 9

This is the amount of CF6. The sequential checking works backwards, and each time :gK is

pressed,

:gK

:gK

:ga

Figure 10

hp calculators

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This is the N3 value. Whenever Nj needs to be checked, it must be recalled first. Now check the CF3 value:

:gK

Figure 11

Continue checking CF2, CF1 and stop when CF0 is shown in the display.

:gK

:gK

:gK

Figure 12

Recal

:w

Figure 13

Answer:

The entries are correct.

Example 3: The investment is considered attractive if it shows at least 8% of internal rate of return. Calculate the IRR.

Solution:

To perform either IRR or NPV calculations,

6 w fL

(flashing)

Figure 14

Answer:

Yes, the investment is attractive based on its 9.37% internal rate of return.

If it happens that a cash flow entry was wrongly entered, modifying its amount is not difficult and there is no need to

enter all data again. In fact there are two ways for doing this.

hp calculators

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Example 4: Update the amount of CF2 for $-9,500.00 and compute the new IRR after this change.

Solution 1: Type in the correct amount and store it in R2:

9500 Þ ?2 fL

Figure 15

Solution 2: Set

1n 9500 Þ gK 6n fL

Figure 16

Answer:

The investment is still attractive based on revised IRR of 9.42%.

To modify a wrongly entered Nj, it is necessary to change the value stored in the register

Example 5: Now change both N3 and N4 to 2 and calculate the IRR again. The cash flow diagram now looks like this:

$ 178,500.00

$ 20,000.00

CF6

CF

$ 12,000.00

3

$ 7,000.00

CF4

CF1

2 consecutive occurrences

2 consecutive occurrences

N3

N4

$-9,500.00

$-8,000.00

CF2

CF

$-130,000.00

5

CF0

Figure 17

Solution:

For each correction, set

its original value and press fL.

3n 2 ga 4n 2 ga 6 n fL

Figure 18

Answer:

The newly computed IRR is 8.77%.

hp calculators

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