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HP 12c Financial Calculator  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_{0}) and the present
value of each anticipated cash flow (CF_{j}) 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:
Figure : Expression calculating Internal Rate of Return
Cash flow diagrams
The cash flow diagram in Figure 1 illustrates one of the many possible situations that can be handled by the HP 12c.
Figure : Cash flow diagram
The HP 12c cash flow approach
In the HP 12c 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:
Figure : Diagram showing different cash flow amounts can be stored
The HP 12c memory organization allows 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 CF_{j} and its corresponding N_{j} holds the number of occurrences, up to 99. TVM register 'n' is used as an
index to control CF operations.
The keys to enter cash flow data are:
Keystroke

Description


Stores the number in the display in R_{0} and sets 'n' to zero.


Adds 1 unit to current 'n' contents (j) and then stores the number in the display in R_{j}.


Stores the number in the display in N_{j}; 'n' contents (j) are not changed.

note:
The number in the display must be a positive integer from 1 to 99, otherwise returns to the display and no operation is performed.
If the last available register has already been used, adds 1 unit to current 'n' contents and stores the number in
the display in TVM register FV. Any attempt to add a cash flow amount with after FV has already been used
or when 'n' contents refer to a register that is not available causes to be shown in the display and no
operation is performed.
Practice solving IRR problems
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 HP 12c registers with all data?
Figure : Values entered in the cash flow diagram
Solution
Clearing all registers is not necessary to start cash flow analysis because only the registers updated with
cash flow data are used.
Keystroke

Display


Figure : Entering the first set of values

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

Display


Figure : Entering the next set of values

The remaining data is entered with the following keystroke sequence:
Keystroke

Display


Figure : Entering the remaining set of values

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 HP 12c
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:
Keystroke

Display


Figure : Displaying the number of the last register

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

Display


Figure : Displaying the amount of CF_{6}

This is the amount of CF_{6}. The sequential checking works backwards, and each time is
pressed, 'n' is decreased by one unit. Now check CF_{5}, CF_{4} and when checking CF_{3} verify N_{3} as well.
Keystroke

Display


Figure : Checking the cash flow data entered

This is the N_{3} value. Whenever N_{j} needs to be checked, it must be recalled first. Now check the CF_{3} value:
Keystroke

Display


Figure : Checking the CF_{3} value

Continue checking CF_{2}, CF_{1} and stop when CF_{0} is shown in the display.
Keystroke

Display


Figure : Displaying the value of CF_{0}

Recall 'n' contents to the display:
Keystroke

Display


Figure : Recalling the contents

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, 'n' must have its contents restored to the correct value:
Keystroke

Display


(flashing)
Figure : Calculating the Internal Rate of Return

Answer
Yes, the investment is attractive based on its 9.37% internal rate of return.
How to modify cash flow entries
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.
Example 4
Update the amount of CF_{2} for $9,500.00 and compute the new IRR after this change.
Solution 1
Type in the correct amount and store it in R_{2}:
Keystroke

Display


Figure : Updating the amount of CF_{2}

Solution 2
Set 'n' register to (j1), type in the correct amount, press , then restore 'n' prior to compute IRR:
Keystroke

Display


Figure : Calculating the Internal Rate of Return

Answer
The investment is still attractive based on revised IRR of 9.42%.
To modify a wrongly entered N_{j}, it is necessary to change the value stored in the register 'n'.
Example 5
Now change both N_{3} and N_{4} to 2 and calculate the IRR again. The cash flow diagram now looks like this:
Solution
For each correction, set 'n' to match 'j,' type in the correct N_{j} and press . After all corrections, set 'n' to
its original value and press .
Keystroke

Display


Figure : Calculating the new Internal Rate of Return

Answer
The newly computed IRR is 8.77%.
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