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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 (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:
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 CFj and its corresponding Nj 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 R0 and sets 'n' to zero.
Adds 1 unit to current 'n' contents (j) and then stores the number in the display in Rj.
Stores the number in the display in Nj; '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 CF6
This is the amount of CF6. The sequential checking works backwards, and each time is pressed, 'n' is decreased by one unit. Now check CF5, CF4 and when checking CF3 verify N3 as well.
Keystroke
Display
Figure : Checking the cash flow data entered
This is the N3 value. Whenever Nj needs to be checked, it must be recalled first. Now check the CF3 value:
Keystroke
Display
Figure : Checking the CF3 value
Continue checking CF2, CF1 and stop when CF0 is shown in the display.
Keystroke
Display
Figure : Displaying the value of CF0
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 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:
Keystroke
Display
Figure : Updating the amount of CF2
Solution 2
Set 'n' register to (j-1), 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 Nj, it is necessary to change the value stored in the register 'n'.
Example 5
Now change both N3 and N4 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 Nj 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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