HP 12c Owners Manual

							  Section 4: Additional Financial Functions  61 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 61 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Calculating NPV for Grouped Cash Flows.
 A maximum of 20 cash flow 
amounts (in addition to the initial investment CF
0) can be stored in the hp 12c.* 
However, problems involving more than 20 cash flows can be handled if among 
the cash flows there are equal consecutive cash flows. For such problems, you 
merely enter along with the amounts of the cash flows the number of times — up to 
99 — each amount occurs consecutively. This number is designated N
j, 
corresponding to cash flow amount CF
j, and is entered using the a
 key. Each Nj 
is stored in a special register inside the calculator.   
This method can, of course, be used for problems involving fewer than 20 cash 
flows — and it will require fewer storage registers than the method described 
above under Calculating NPV for Ungrouped Cash Flows. Equal consecutive cash 
flows can be entered using that method — provided there are enough storage 
registers available to accommodate the total number of individual cash flows. The 
facility of grouping equal consecutive cash flows is provided to minimize the 
number of storage registers required. 
Note: When entering cash flow amounts — including the initial investment 
CF
0 — remember to observe the cash flow sign convention by pressing Þ 
after keying in the amount for a negative cash flow. 
In summary, to enter the amounts of the cash flows and the number of times they 
occur consecutively: 
1. Press fCLEARH to clear the financial and storage registers. 
2.  Key in the amount of the initial investment, press Þ if that cash flow is 
negative, then press gJ. If there is no initial investment, press 0gJ. 
3.  If the initial investment consists of more than one cash flow of the amount 
entered in step 2, key in the number of those cash flows, then press ga. If 
ga is not pressed, the calculator assumes that N
0 is 1. 
4.  Key in the amount of the next cash flow, press Þ if that cash flow is 
negative, then press gK. If the cash flow amount is zero in the next 
period, press 0gK. 
5.  If the amount entered in step 4 occurs more than once consecutively, key in 
the number of times that cash flow amount occurs consecutively, then press 
ga. If ga is not pressed, the calculator assumes that N
j is 1 for the CFj 
just entered.   
6.  Repeat steps 4 and 5 for each CF
j and Nj until all cash flows have been 
entered.  
With the amounts of the cash flows and the number of times they occur 
consecutively stored in the calculator, NPV can be calculated by entering the 
interest rate and pressing fl
, just as described earlier. 
                                                 
* If you have stored a program in the calculator, the number of registers available for storing 
cash flow amounts may be less than 21.  
						

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Example: 
An investor has an opportunity to purchase a piece of property for 
$79,000; and he would like a 131/2% return. He expects to be able to sell it after 
10 years for $100,000 and anticipates the yearly cash flows shown in the table 
below: 
Year Cash Flow Year Cash Flow 
1 
2 
3 
4 
5 $14,000 
$11,000 
$10,000 
$10,000 
$10,000 6 
7 
8 
9 
10 $9,100 
$9,000 
$9,000 
$4,500 
$100,000 
Since two cash flow amounts ($10,000 and $9,000) are repeated consecutively, 
we can minimize the number of storage registers required by using the method just 
described. 
Keystrokes Display  
fCLEARH 
0.00 Clears financial and storage 
registers. 
79000ÞgJ 
–79,000.00 Initial investment (with minus sign for 
a negative cash flow). 
14000gK 
14,000.00 First cash flow amount. 
11000gK 
11,000.00 Next cash flow amount. 
10000gK 
10,000.00 Next cash flow amount. 
3ga 
3.00 Number of times this cash flow 
amount occurs consecutively. 
9100gK 
9,100.00 Next cash flow amount. 
9000gK 
9,000.00 Next cash flow amount. 
2ga 
2.00 Number of times this cash flow 
amount occurs consecutively. 
4500gK 
4,500.00 Next cash flow amount. 
100000gK 
100,000.00 Final cash flow amount. 
:n 
7.00 Seven different cash flow amounts 
have been entered. 
13.5¼ 
13.50 Stores i. 
fl 
907.77 NPV. 
Since NPV is positive, the investment would increase the financial value of the 
investor’s assets by $907.77.  
						

							  Section 4: Additional Financial Functions  63 
 
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Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Calculating Internal Rate of Return (IRR) 
1.  Enter the cash flows using either of the methods described above under 
Calculating Net Present Value. 
2. Press fL. 
The calculated value of IRR appears in the display and also is automatically stored 
in the i register. 
Note: Remember that the L function may take a significant amount of 
time to produce an answer, during which the calculator displays running. 
Example:
 The NPV calculated in the preceding example was positive, indicating 
that the actual rate of return (that is, the IRR) was greater than the 13
1/2 used in the 
calculation. Find the IRR. 
Assuming the cash flows are still stored in the calculator, we need only press 
fL
: 
Keystrokes Display  
fL 
13.72 IRR is 13.72%. 
Note that the value calculated by L
 is the periodic rate of return. If the cash flow 
periods are other than years (for example, months or quarters), you can calculate 
the nominal annual rate of return by multiplying the periodic IRR by the number of 
periods per year. 
As noted above, the calculator may take several seconds or even minutes to 
produce an answer for IRR. This is because the mathematical calculations for 
finding IRR are extremely complex, involving a series of iterations — that is, a 
series of successive calculations. In each iteration, the calculator uses an estimate 
of IRR as the interest rate in a computation of NPV. The iterations are repeated 
until the computed NPV reaches about zero.
* 
If you do not want to wait for the computation of IRR to be completed, press any 
key. This halts the computation of IRR and displays the estimated value of IRR being 
used in the current iteration.
†  You can then check how good this estimate is by 
calculating NPV using this estimate: if the estimate is close to IRR, the NPV 
calculated with it should be close to zero.* The values of IRR is put into the i 
register at the end of each iteration. Therefore, to check how good an estimate of 
IRR is after that estimate is in the display, just press fl
. 
                                                 
* In practice, because the complex mathematical calculations inside the calculator are done 
with numbers rounded to 10 digits, NPV may never reach exactly zero. Nevertheless, the 
interest rate that results in a very small NPV is very close to the actual IRR. 
†  Provided the first iteration has been completed.  
						

							64  Section 4: Additional Financial Functions 
 
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The complex mathematical characteristics of the IRR computation have an 
additional ramification: Depending on the magnitudes and signs of the cash flows, 
the computation of IRR may have a single answer, multiple answers, a negative 
answer or no answer.
* 
For additional information regarding L
, refer to Appendix B. For an alternative 
method of calculating IRR, refer to Section 13. 
Reviewing Cash Flow Entries   
z  To display a single cash flow amount, press :, then key in the number of 
the register containing the cash flow amount to be displayed. Alternatively, 
store the number of that cash flow amount (that is, the value of j for the CF
j 
desired) in the n register, then press :gK. 
z  To review all the cash flow amounts, press :g K repeatedly. This 
displays the cash flow amounts in reverse order — that is, beginning with the 
final cash flow and proceeding to CF
0. 
z  To display the number of times a cash flow amount occurs consecutively — 
that is, to display the N
j for a CFj — store the number of that cash flow 
amount (that is, the value of j) in the n register, then press :ga. 
z  To review all the cash flow amounts together with the number of times each 
cash flow amount occurs consecutively (that is, to review each CF
j and Nj 
pair), press :ga:gK repeatedly. This displays N
j followed by 
CF
j beginning with the final cash flow amount and proceeding to N0 and 
CF
0. 
Note: Neither L nor l change the number in the n register. However, 
each time :gK is pressed, the number in the n register is decreased 
by 1. If this is done, or if you manually change the number in the n register 
in order to display a single N
j and/or CFj, be sure to reset the number in the 
n register to the total number of cash flow amounts originally entered (not 
including the amount of the initial investment CF
0). If this is not done, NPV 
and IRR calculations will give incorrect results; also, a review of cash flow 
entries would begin with N
n and CFn, where n is the number currently in the 
n register. 
For example, to display the fifth cash flow amount and the number of times that 
amount occurs consecutively: 
Keystrokes Display  
:5 
9,000.00 CF5 
5n 
5.00 Stores the value of j in the n
 register. 
                                                 
* In the case of multiple answers for IRR, the decision criteria listed on page 57 should be 
modified accordingly.  
						

							  Section 4: Additional Financial Functions  65 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 65 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
Keystrokes Display  
:ga 
2.00 N5 
7n 
7.00 Resets the number in the n
 register to 
its original value. 
To display all the cash flow amounts and the number of times they occur 
consecutively: 
Keystrokes Display  
:ga 
1.00 N7 
:gK 
100,000.00 CF7 
:ga 
1.00 N6 
:gK 
4,500.00 CF6 
:ga 
2.00 N5 
:gK 
9,000.00 CF5 
. 
. 
. . 
. 
. . 
. 
. 
:ga 
1.00 N1 
:gK 
14,000.00 CF1 
:ga 
1.00 N0 
:gK 
–79,000.00 CF0 
7n 
7.00 Resets the number in the n
 register 
to its original value. 
Changing Cash Flow Entries   
z  To change a cash flow amount: 
1.  Key the amount into the display. 
2. Press ?. 
3.  Key in the number of the register containing the cash flow amount to be 
changed. 
z  To change the number of times a cash flow amount occurs consecutively — 
that is, to change the N
j for a CFj: 
1.  Store the number of that cash flow amount (that is, j) in the n register. 
2.  Key the number of times the cash flow amount occurs consecutively into 
the display. 
3. Press ga.  
						

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Note: If you change the number in the n register in order to change an Nj, 
be sure to reset the number in the n register to the total number of cash flow 
amounts originally entered (not including the amount of the initial investment 
CF
0). If this is not done, NPV and IRR calculations will give incorrect results. 
Example 1: 
With the cash flows now stored in the calculator, change CF
2 from 
$11,000 to $9,000, then calculate the new NPV for a 131/2% return. 
Keystrokes Display  
9000?2 
9,000.00 Stores the new CF2 in R2. 
13.5¼ 
13.50 Stores i.* 
fl 
–644.75 The new NPV. 
Since this NPV is negative, the investment would decrease the financial value of 
the investor’s assets. 
Example 2:
 Change N
5 from 2 to 4, then calculate the new NPV. 
Keystrokes   Display   
5n 
5.00 Stores j in the n
 register. 
4ga 
4.00 Stores the new N5. 
7n 
7.00 Resets the number in the n
 register 
to its original value. 
fl 
–1,857.21 The new NPV. 
Bond Calculations 
The hp 12c enables you to solve for bond price (and the interest accrued since the 
last interest date) and the yield to maturity.
† The E
 and S
 calculations are 
done assuming a semiannual coupon payment and using an actual/actual basis 
(such as for U.S. Treasury bonds and U.S. Treasury notes). In accordance with 
market convention, prices are based on a redemption (par) value of 100. 
                                                 
* This step is necessary in this example because we have calculated IRR since the first time we 
calculated NPV. The IRR calculation replaced the 13.5 we keyed into i before calculating 
NPV with the result for IRR – 13.72. 
† All bond calculations are performed in accordance with. the Securities Industry Association’s 
recommendations as contained in Spence, Graudenz, and Lynch, Standard Securities 
Calculation Methods, Securities Industry Association, New York, 1973.  
						

							  Section 4: Additional Financial Functions  67 
 
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To calculate bond price and yield for a 30/360 bond (that is, using the basis of a 
30day month and a 360-day year — such as for municipal bonds, corporate 
bonds, and state and local government bonds), and to calculate bond price for 
bonds with an annual coupon payment, refer to Section 16: Bonds. 
Bond Price 
1.  Enter the desired yield to maturity (as a percentage), using ¼. 
2.  Enter the annual coupon rate (as a percentage), using P. 
3.  Key in the settlement (purchase) date (as described on page 29), then press 
\. 
4.  Key in the maturity (redemption) date. 
5. Press fE. 
The price is shown in the display and also is stored in the PV register. The interest 
accrued since the last interest date is held inside the calculator: to display the 
interest, press ~
; to add the interest to the price, press +
. 
Example: 
What price should you pay on April 28, 2004 for a 6
3/4% U.S. 
Treasury bond that matures on June 4, 2018, if you want a yield of 81/4%. 
Assume that you normally express dates in the month-day-year format. 
Keystrokes Display  
8.25¼ 
8.25 Enters yield to maturity. 
6.75P 
6.75 Enters coupon rate. 
gÕ 
6.75 Sets date format to month-day-year.   
4.282004\ 
4.28 Enters settlement (purchase) date.   
6.042018 
6.042018 Enters maturity (redemption) date. 
fE 
87.62 Bond price (as a percent of par). 
+ 
90.31 Total price, including accrued 
interest. 
Bond Yield 
1.  Enter the quoted price (as a percent of par), using $. 
2.  Enter the annual coupon rate (as a percentage), using P. 
3.  Key in the settlement (purchase) date, then press \. 
4.  Key in the maturity (redemption) date. 
5. Press fS. 
The yield to maturity is shown in the display and also is stored in the i register. 
Note: Remember that the S function may take a significant amount of 
time to produce an answer, during which the calculator displays running.  
						

							68  Section 4: Additional Financial Functions 
 
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Example:
 The market is quoting 883/8% for the bond described in the preceding 
example. What yield will that provide?
 
Keystrokes Display  
3\8z 
0.38 Calculates 3/8. 
88+$ 
88.38 Enters quoted price. 
6.75P 
6.75 Enters coupon rate. 
4.282004\ 
4.28 Enters settlement (purchase) date. 
6.042018 
6.042018 Enters maturity (redemption) date. 
fS 
8.15 Bond yield. 
Depreciation Calculations   
The hp 12c enables you to calculate depreciation and the remaining depreciable 
value (book value minus salvage value) using the straight-line, 
sum-of-the-years-digits, and declining-balance methods. To do so with any of these 
methods: 
1.  Enter the original cost of the asset, using $. 
2.  Enter the salvage value of the asset, using M. If the salvage value is zero, 
press 0M. 
3.  Enter the expected useful life of the asset (in years), using n. 
4.  If the declining-balance method is being used, enter the declining-balance 
factor (as a percentage), using ¼. For example, 1
1/4 times the straight-line 
rate — 125 percent declining-balance — would be entered as 125¼. 
5.  Key in the number of the year for which depreciation is to be calculated. 
6. Press: 
z fV for depreciation using the straight-line method. 
z fÝ for depreciation using the sum-of-the-years digits method. 
z f# for depreciation using the declining-balance method. 
V
, Ý
, and # 
each place the amount of depreciation in the display. To 
display the remaining depreciable value (the book value less the salvage value) 
after the depreciation has been calculated, press ~
.  
						

							  Section 4: Additional Financial Functions  69 
 
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Example:
 A metalworking machine, purchased for $10,000, is depreciated over 
5 years. Its salvage value is estimated at $500. Find the depreciation and 
remaining depreciable value for the first 3 years of the machine’s life using the 
declining-balance method at double the straight-line rate (200 percent 
declining-balance). 
Keystrokes Display  
10000$ 
10,000.00 Enters original cost. 
500M 
500.00 Enters salvage value. 
5n 
5.00 Enters expected useful life. 
200¼ 
200.00 Enters declining-balance factor. 
1f# 
4,000.00 Depreciation in first year. 
~ 
5,500.00 Remaining depreciable value after 
first year. 
2f# 
2,400.00 Depreciation in second year. 
~ 
3,100.00 Remaining depreciable value after 
second year. 
3f# 
1,440.00 Depreciation in third year. 
~ 
1,660.00 Remaining depreciable value after 
third year. 
To calculate depreciation and the remaining depreciable value when the 
acquisition date of the asset does not coincide with the beginning of the fiscal 
accounting year, refer to the procedures in Section 13. That section also includes a 
procedure for depreciation calculations when changing from the declining-balance 
method to the straight-line method, and a procedure for calculating excess 
depreciation. 
						

							 
70 
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  Section 5 
Additional Operating 
Features 
Continuous Memory 
The calculator’s Continuous Memory contains the data storage registers, the 
financial registers, the stack and LAST X registers, program memory, and status 
information such as display format, date format, and payment mode. All 
information in Continuous Memory is preserved even while the calculator is turned 
off. Furthermore, information in Continuous Memory is preserved for a short time 
when the batteries are removed, so that you can change the batteries without 
losing your data and programs. 
Continuous Memory may be reset if the calculator is dropped or otherwise 
traumatized, or if power is interrupted. You can also manually reset Continuous 
Memory as follows: 
1.  Turn the calculator off. 
2.  Hold down the - key, and press ;. 
When Continuous Memory is reset: 
z All registers are cleared.   
z Program memory consists of eight program lines, each containing the 
instruction g(00. 
z Display format is set to the standard format with two decimal places. 
z Date format is set to month-day-year. 
z Payment mode is set to End. 
Whenever Continuous Memory has been reset, the display will show Pr Error
. 
Pressing any key will clear this message from the display.