HP 12c Owners Manual

							  Appendix A: The Automatic Memory Stack  171 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 171 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Now let’s see what happens in the stack during a chain calculation: 
7) 6 5 ( ) 4 3 (
×+×=
=
See how the intermediate results are not only displayed when they are calculated, 
but also automatically stored and available in the stack at just the right time!=
That
						

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File name: hp 12c_users guide_English_HDPMBF12E44  Page: 172 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Termination of Digit Entry 
The first digit keyed in after digit entry has been terminated replaces the number 
already in the displayed X-register. Digit entry is automatically terminated when 
any key is pressed (except for digit entry keys — digit keys,.
, Þ
, and É 
— 
and prefix keys — f
, g
,?
, :
, and i
). 
Stack Lift 
When the stack lifts, the number in each stack register is copied into the register 
above, and the number formerly in the T-register is lost. The number formerly in the 
X-register is then contained in both the X-register and the Y-register. 
When a number is entered into the displayed X-register — either from the 
keyboard, from a storage register (using :
), or from the LAST X register (using 
F
) — the stack usually lifts first. The stack does not lift if the last key pressed 
before a number is entered was one of the following: \
, O
, _
, ^
, A 
or 
C
.
*  If one of these keys was the last key pressed, the number in the displayed 
X-register is replaced when a new number is entered. 
Rearranging Numbers in the Stack 
The  key 
Pressing ~
 exchanges the numbers in the X- and 
Y-registers. 
 
Certain functions (Ò
, Ï
, !
, E
, V
, Ý
, #
, Ö
, v
, R
, and Q
) 
return answers to the Y-register as well as to the displayed X-register. The ~
 key, 
since it exchanges the number in the Y-register with that in the displayed X-register, 
is used to display the second number calculated. 
The  Key 
When d
 (roll down) is pressed the number in each 
stack register is copied into the register below, and the 
number formerly in the X-re
gister is copied into the 
T-register.  
                                                 
* In addition, the stack does not lift when a number is entered if the last operation performed 
was storing a number into a financial register. For example, the stack will not lift when a 
number is entered following the sequence 100000$, but will lift when a number is entered 
following the sequence 100000$M. Note also that although the stack lifts when \ is 
pressed, it does not lift when a number is entered after \ is pressed.  
						

							  Appendix A: The Automatic Memory Stack  173 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 173 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Pressing d
 four times successively displays the numbers in the Y-, Z-, and 
T-registers and returns the numbers to their original registers. 
 
One-Number Functions and the Stack 
One-number mathematics and number-alteration functions — y
, r
, °
, >
, 
e
, B
, Ñ
, and T
 — use only the number in the displayed X-register. 
When the key is pressed, the function is performed upon the number in the 
X-register, and the answer is then placed into the X-register. The stack does not lift, 
so the number formerly in the X-register does not get copied into the Y-register; but 
this number is copied into the LAST X register. The numbers in the Y-, Z-, and 
T-registers are not affected when a one number function is performed. 
 
Two-Number Functions and the Stack 
Two-number functions — +
, -
, §
, z
, q
, b
, à
, and Z
 — use the 
numbers in both the X- and the Y-registers. 
Mathematics Functions   
To perform an arithmetic operation, the numbers are positioned in the X- and 
Y-registers just as you would write them vertically on paper: the number you would 
write on top goes in the Y-register, and the number you would write on the bottom 
goes in the X-register. For example, to do each of the four arithmetic calculations 
shown below, you would put the 8 in the Y-register (using \ 
and then key the 2 
into the displayed X-register.)  
						

							174  Appendix A: The Automatic Memory Stack 
 
 
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Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
 
When an arithmetic operation or q
 is performed, the answer is placed in the 
X-register, the number formerly in the X-register is copied into the LAST X register, 
and the stack drops. When the stack drops, the number in the Z-register is copied 
into the Y-register, and the number in the T-register is copied into the Z-register but 
also remains in the T-register. 
The diagram on the next page illustrates the stack operation when 8 ÷ 2 is 
calculated. (Assume that the stack and LAST X registers have already been loaded 
with the numbers shown as the result of previous calculations.) 
 
Percentage Functions 
When any of the three percentage functions is performed, the answer is placed in 
the X-register, the number formerly in the X-register is copied into the LAST X 
register, but the stack does not drop. The numbers in the Y-, Z-, and T-registers are 
not changed when a percentage function is performed. 
  
						

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Calendar and Financial Functions 
The following table shows what quantity is in each stack register after the indicated 
calendar or financial function key is pressed. The symbols x, y, z, and t represent 
the number that was in the corresponding register (X, Y, Z, or T, respectively) at 
the time the function key was pressed. 
Register 
D Ò Ï n, ¼, $, 
P, M, l,
L
* ! 
T t t x  t  y 
Z t z INT365 z x (number of 
payments) 
Y z ∆DYS30-day 
						

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File name: hp 12c_users guide_English_HDPMBF12E44  Page: 176 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
The LAST X Register and the  Key 
The number in the displayed X-register is copied into the LAST X
 register 
whenever any of the following function keys is pressed: 
+
 -
 §  z
 y
 
q
 >
 ¿
 r
 B
 
T
 Ñ  _
 ^
 Q
 
R
 e
 b
 à
 Z
 
D
 Ò
    
Pressing gF
 lifts the stack (unless \
, O
, _
, ^
, A
, or C
 was the 
last key pressed, as described on page 172), then copies the number from the 
LAST X register into the displayed X-register. The number remains also in the LAST 
X register. 
 
Chain Calculations 
The automatic stack lift and stack drop make it possible to do chain calculations 
without the necessity for keying in parentheses or storing intermediate results, as 
are required on some other calculators. An intermediate result in the displayed 
X-register is automatically copied into the Y-register when a number is keyed in 
after a function key is pressed.
* Therefore, when a two-number function key is 
then pressed, that function is performed using the number keyed into the displayed 
X-register and the intermediate result in the Y-register. The number then in the 
Y-register, if remaining as an intermediate result from an earlier calculation, can 
then be used with the intermediate result in the X-register for another calculation. 
                                                 
* Except for \, O, _, ^, A or C, and — under certain circumstances — n, ¼, 
$, P, and M. For more information, refer to Stack Lift, page 172.  
						

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The diagram on page 171 illustrates how the automatic stack lift and stack drop 
make chain calculations quick and error-free. 
Virtually every chain calculation you are likely to encounter can be done using 
only the four stack registers. However, to avoid having to store an intermediate 
result in a storage register, you should begin every chain calculation at the 
innermost number or pair of parentheses and then work outward — just as you 
would if you were doing the calculation manually (that is, using pencil and paper). 
For example, consider the calculation of   
3 [4 + 5 (6 + 7)] 
If this calculation were done from left to right — as were the (simpler) examples 
under Chain Calculations on page 20 and page 22 — you would have to enter 
five numbers into the calculator before doing the first operation possible (6 + 7). 
But since the stack holds only four numbers, this calculation cannot be done 
left-to-right. However, it can easily be done if you begin with the calculation in the 
innermost pair of parentheses — again, (6 + 7). 
Keystrokes Display  
6\7+ 
13.00 Intermediate result of (6+7). 
5§ 
65.00 Intermediate result of 5 (6+7). 
4+ 
69.00 Intermediate result of [4 + 5(6 + 7)]. 
3§ 
207.00 Final result: 3 [4 + 5 (6 + 7)].   
Arithmetic Calculations with Constants 
Because the number in the T-register remains there when the stack drops, this 
number can be used as a constant in arithmetic operations. To place the constant 
into the T-register, key it into the display (that is, into the X-register), then press 
\ 
three times. This also places the constant in the Y and Z-registers. Each time 
an arithmetic operation is then performed — using the constant in the Y-register 
and a number keyed into the displayed X-register — the constant will be 
“dropped” back into the Y-register. 
Example:
 The annual sales of solar engineering hardware your firm — currently 
$84,000 — are projected to double each year for the next 3 years. Calculate the 
annual sales for each of those years. 
Keystrokes Display  
2\\ 
  
\ 
2.00 Enters constant into Y, Z, and 
T-registers.  
						

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Keystrokes Display  
84000 
84,000. Enters base amount into displayed 
X-register. 
§ 
168,000.00 Annual sales after first year. 
§ 
336,000.00 Annual sales after second year. 
§ 
672,000.00 Annual sales after third year. 
In the example above, the constant was repeatedly multiplied by the result of the 
previous operation, which was already in the displayed X-register. In another class 
of calculations with constants, the constant is multiplied by (or added to, etc.) a 
new number keyed into the displayed X-register. For these calculations, you must 
press O 
before keying in a new number after having pressed an operator key. If 
this were not done, the stack would lift when you keyed in a new number after 
pressing the operator key, and the Y-register would no longer contain the constant. 
(Recall — from page 172 — that the stack does not lift when a number is keyed 
into the displayed X-register after O
 is pressed.) 
Example:
 At Permex Pipes a certain pipe fitting is packaged in quantities of 15, 
75, and 250. If the cost per fitting is $4.38, calculate the cost of each package.
* 
Keystrokes Display  
4.38\\   
\ 
4.38 Enters constant into Y-, Z-, and 
T-registers. 
15 
15. Enters first quantity into displayed 
X-register. 
§ 
65.70 Cost of a package of 15. 
O75 
75. Clears display and enters second 
quantity into displayed X-register. 
§ 
328.50 Cost of a package of 75. 
O250 
250. Clears display and enters third 
quantity into displayed X-register. 
§ 
1,095.00 Cost of a package of 250. 
 
                                                 
* You may want to compare this method of arithmetic calculations with constants to the method 
using F
 described on page 74.  
						

							 
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  Appendix B 
More About L 
Given a sequence of positive and negative cash flows, we hope that there is 
enough information to determine whether an IRR answer exists, and what that 
answer is. For the vast majority of cases, your hp 12c will find the unique IRR 
answer if it exists. But the IRR computation is so complex that if the cash flow 
sequence does not meet certain criteria, then sometimes the calculator is unable to 
determine whether or not an answer or answers exist. 
Let’s look at all of the possible outcomes of IRR as calculated by your hp 12c: 
Case 1:
 A positive answer. If a positive answer is displayed, it is the only such 
answer. One or more negative answers may also exist. 
Case 2:
 A negative answer. If a negative answer is displayed, there may be 
additional negative answers, and there may be a single positive answer. If 
additional answers (negative or positive) exist, they can be calculated using the 
procedure described below. 
Case 3:
 The calculator displays Error 3
. This indicates that the computation is 
very complex, possibly involving multiple answers, and cannot be continued until 
you give the calculator an estimate of IRR. The procedure for doing so is described 
below. 
Case 4:
 The calculator displays Error 7
. This indicates that there is no answer to 
the computation of IRR with the cash flow amounts you have entered. This situation 
is probably the result of a mistake in entering the magnitudes or signs of the cash 
flows or the number of times a cash flow amount occurs consecutively. Refer to 
Reviewing Cash Flow Entries (page 64) and Changing Cash Flow Entries (page 
65) to check and correct the entries. Error 7
 will result if there is not at least one 
positive cash flow and at least one negative cash flow. 
Although the calculator will eventually reach one of the above outcomes, it may 
take a long time to get there. You may wish to terminate the IRR iterative process, 
by pressing any key, to see what interest rate the calculator has computed at that 
point. If you stop the calculation, you may continue searching for IRR as described 
below. 
Searching for IRR.
 You can continue searching for IRR solutions, even after an 
Error 3
 indication, as follows: 
1.  Make a guess for the interest rate and key it in. 
2. Press:gt.  
						

							180  Appendix B: More About L 
 
 
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Your guess will aid the calculator in its search, and if it finds an IRR answer near 
your guess, that answer will be displayed. Since the calculator cannot tell you the 
number of solutions that exist when there is more than one mathematically correct 
answer, you can continue to make guesses, pressing :gt
 after each one, 
to search for IRR solutions. 
You can hasten this process by using the l 
function to help you make a good 
guess. Remember that a correct IRR solution will make the calculated NPV very 
small. So continue to guess interest rates and solve for NPV until the answer you 
obtain is reasonably close to zero. Then press :gt
 to calculate the IRR 
answer near your guess. 
How would this work in case 2 above?
 The calculator displays a negative answer 
and you wish to check for a unique positive IRR. Key in successively larger guesses 
for i (starting from 0) and solve for NPV until you reach a sign change in your NPV 
outcomes. Then press :gt
 to find an IRR solution near the last interest rate 
obtained using the l
 key. 
If you stop the IRR iterative process, you can test the interest obtained using l
, 
and then restart the process by pressing :gt
.