HP 12c Owners Manual
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Section 3: Basic Financial Functions 51
File name: hp 12c_users guide_English_HDPMBF12E44 Page: 51 of 209
Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm
You can calculate i, PV, PMT, and FV for transactions involving an odd period
simply by entering a noninteger n. (A noninteger is a number with at least one
nonzero digit to the right of the decimal point.) This places the calculator in
Odd-Period mode.
* The integer part of n (the part to the left of the decimal point)
specifies the number of full payment periods, and the fractional part (the part to the
right of the decimal) specifies the length of the odd period as a fraction of a full
period. The odd period, therefore, cannot be greater than one full period.
The fractional part of n can be determined using either the actual number of odd
days or the number of odd days counted on the basis of a 30-day month.
† The
Ò
function can be used to calculate the number of odd days either way. The
fractional part of n is a fraction of a payment period, so the number of odd days
must be divided by the number of days in a period. If interest is compounded
monthly, for this number you can use either 30, 365/12, or (if the odd period falls
entirely within a single month) the actual number of days in that month. Usually, a
monthly period is taken to be 30 days long.
At your option, the calculations of i, PV, PMT, and FV can be performed with either
simple interest or compound interest accruing during the odd period. If the C
status
indicator in the display is not lit, simple interest is used. To specify compound
interest, turn the C
indicator on by pressing ?Æ
.
‡ Pressing ?Æ
again
turns the C
indicator off, and calculations will then be performed using simple
interest for the odd period.
* Calculations of i, PMT, and FV are performed using the present value at the end of the odd
period. This is equal to the number in the PV register plus the interest accrued during the odd
period. When calculating PV in Odd-Period mode, the calculator returns a value equal to the
present value at the beginning of the odd period and stores it in the PV register.
After calculating i, PV, PMT, or FV in Odd-Period mode, you should not try to calculate n. If
you do, the calculator will switch out of Odd-Period mode and compute n without taking the
odd period into account. The values in the other financial registers will correspond to the new
n, but the original assumptions for the problem will be changed.
† The two methods of counting odd days will yield slightly different answers. If you are
calculating i to determine the annual percentage rate (APR) for an odd-period transaction, the
lower APR will result if the calculation uses the greater number of odd days determined using
the two methods.
‡ ?Æ is not programmable.
52 Section 3: Basic Financial Functions File name: hp 12c_users guide_English_HDPMBF12E44 Page: 52 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Example 1: A 36-month loan for $4,500 accrues interest at a 15% annual percentage rate (APR), with the payments made at the end of each month. If interest begins accruing on this loan on February 15, 2004 (so that the first period begins on March 1, 2004), calculate the monthly payment, with the odd days counted on the basis of a 30-day month and compound interest used for the odd period. Keystrokes Display fCLEARG Clears financial registers. gÕ Sets date format to month-day-year. g Sets payment mode to End. ?Æ Turns on the C indicator in the display, so that compound interest will be used for the odd period. 2.152004\ 2.15 Keys in the date interest begins accruing and separates it from the next date entered. 3.012004 3.012004 Keys in the date of the beginning of the first period. gÒ 15.00 Actual number of odd days. ~ 16.00 Number of odd days counted on the basis of a 30-day month. 30z 0.53 Divides by the length of a monthly period to get the fractional part of n. 36+n 36.53 Adds the fractional part of n to the number of complete payment periods, then stores the result in n. 15gC 1.25 Calculates and stores i. 4500$ 4,500.00 Stores PV. P –157.03 Monthly payment.
Section 3: Basic Financial Functions 53 File name: hp 12c_users guide_English_HDPMBF12E44 Page: 53 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Example 2: A 42-month car loan for $3,950 began accruing interest on July 19, 2004, so that the first period began on August 1, 2004. Payments of $120 are made at the end of each month. Calculate the annual percentage rate (APR), using the actual number of odd days and simple interest for the odd period. Keystrokes Display fCLEARG Clears financial registers. ?Æ Turns off the C indicator in the display, so that simple interest will be used for the odd period. 7.192004\ 7.19 Keys in the date interest begins accruing and separates it from the next date entered. 8.012004 8.012004 Keys in the date of the beginning of the first period. gÒ 13.00 Actual number of odd days. 30z 0.43 Divides by the length of a monthly period to get the fractional part of n. 42+n 42.43 Adds the fractional part of n to the number of complete payment periods, then stores the result in n. 3950$ 3,950.00 Stores PV. 120ÞP –120.00 Stores PMT (with minus sign for cash paid out). ¼ 1.16 Periodic (monthly) interest rate. 12§ 13.95 Annual percentage rate (APR).
54 Section 3: Basic Financial Functions
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Amortization
The hp 12c enables you to calculate the amounts applied toward principal and
toward interest from a single loan payment or from several payments, and also
tells you the remaining balance of the loan after the payments are made.
*
To obtain an amortization schedule:
1. Press fCLEARG to clear the financial registers.
2. Enter the periodic interest rate, using ¼ or C.
3. Enter the amount of the loan (the principal), using $.
4. Key in the periodic payment, then press ÞP (the sign of PMT must be
negative, in accordance with the cash flow sign convention).
5. Press g× or (for most direct reduction loans) g to set the payment
mode.
6. Key in the number of payments to be amortized.
7. Press f!
to display the amount from those payments applied toward
interest.
8. Press ~ to display the amount from those payments applied toward the
principal.
9. To display the number of payments just amortized, press dd.
10. To display the remaining balance of the loan, press :$.
11.To display the total number of payments amortized, press :n.
Example:
For a house you’re about to buy, you can obtain a 25-year mortgage
for $50,000 at 13
1/4% annual interest. This requires payments of $573.35 (at the
end of each month). Find the amounts that would be applied to interest and to the
principal from the first year’s payments.
Keystrokes Display
fCLEARG
13.25gC
1.10
Enters i.
50000$
50,000.00Enters PV.
* All amounts calculated when f! is pressed are automatically rounded to the number of
decimal places specified by the display format. (The display format is described in Section 5.)
This rounding affects the number inside the calculator as well as how the number appears in
the display. The amounts calculated on your hp 12c may differ from those on the statements
of lending institutions by a few cents, since different rounding techniques are sometimes used.
To calculate answers rounded to a different number of decimal places, press f followed by
the number of decimal places desired before you press f!.
Section 3: Basic Financial Functions 55 File name: hp 12c_users guide_English_HDPMBF12E44 Page: 55 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Keystrokes Display 573.35ÞP –573.35 Enters PMT (with minus sign for cash paid out). g –573.35 Sets payment mode to End. 12f! –6,608.89Portion of first year’s payments (12 months) applied to interest. ~ –271.31 Portion of first year’s payments applied to principal. :$ 49,728.69Balance remaining after 1 year. :n 12.00 Total number of payments amortized. The number of payments keyed in just before f! is pressed is taken to be the payments following any that have already been amortized. Thus, if you now press 12f! , your hp 12c will calculate the amounts applied to interest and to the principal from the second year’s payments (that is, the second 12 months): Keystrokes Display 12f! –6,570.72Portion of second year’s payments applied to interest. ~ –309.48 Portion of second year’s payments applied to principal. dd 12.00 Number of payments just amortized. :$ 49,419.21Balance remaining after 2 years. :n 24.00 Total number of payments amortized. Pressing :$ or :n displays the number in the PV or n register. When you did so after each of the last two calculations, you may have noticed that PV and n had been changed from their original values. The calculator does this so that you can easily check the remaining balance and the total number of payments amortized. But because of this, if you want to generate a new amortization schedule from the beginning, you must reset PV to its original value and reset n to 0. For example, suppose you now wanted to generate an amortization schedule for each of the first two months: Keystrokes Display 50000$ 50,000.00Resets PV to original value. 0n 0.00 Resets n to zero.
56 Section 3: Basic Financial Functions File name: hp 12c_users guide_English_HDPMBF12E44 Page: 56 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Keystrokes Display 1f! –552.08 Portion of first payment applied to interest. ~ –21.27 Portion of first payment applied to principal. 1f! –551.85 Portion of second payment applied to interest. ~ –21.50 Portion of second payment applied to principal. :n 2.00 Total number of payments amortized. If you want to generate an amortization schedule but do not already know the monthly payment: 1. Calculate PMT as described on page 46. 2. Press 0n to reset n to zero. 3. Proceed with the amortization procedure listed on page 54 beginning with step 6. Example: Suppose you obtained a 30-year mortgage instead of a 25-year mortgage for the same principal ($50,000) and at the same interest rate (13 1/4%) as in the preceding example. Calculate the monthly payment, then calculate the amounts applied to interest and to the principal from the first month’s payment. Since the interest rate is not being changed, do not press f CLEARG ; to calculate PMT, just enter the new value for n, reset PV, then press P . Keystrokes Display 30gA 360.00 Enters n. 50000$ 50,000.00Enters PV. P –562.89 Monthly payment. 0n 0.00 Resets n to zero. 1f! –552.08 Portion of first payment applied to interest. ~ –10.81 Portion of first payment applied to principal. :$ 49,989.19Remaining balance.
57
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Section 4
Additional Financial
Functions
Discounted Cash Flow Analysis: NPV and IRR
The hp 12c provides functions for the two most widely-used methods of discounted
cash flow analysis: l
(net present value) and L
(internal rate of return). These
functions enable you to analyze financial problems involving cash flows (money
paid out or received) occurring at regular intervals. As in compound interest
calculations, the interval between cash flows can be any time period; however, the
amounts of these cash flows need not be equal.
To understand how to use l
and L
, let’s consider the cash flow diagram for
an investment that requires an initial cash outlay (CF
0) and generates a cash flow
(CF
1) at the end of the first year, and so on up to the final cash flow (CF6) at the
end of the sixth year. In the following diagram, the initial investment is denoted by
CF
0, and is depicted as an arrow pointing down from the time line since it is cash
paid out. Cash flows CF
1 and CF4 also point down from the time line, because they
represent projected cash flow losses.
NPV is calculated by adding the initial investment (represented as a negative cash
flow) to the present value of the anticipated future cash flows. The interest rate, i,
will be referred to in this discussion of NPV and IRR as the rate of return.
* The
value of NPV indicates the result of the investment:
* Other terms are sometimes used to refer to the rate of return. These include: required rate of
return, minimally acceptable rate of return, and cost of capital.
58 Section 4: Additional Financial Functions File name: hp 12c_users guide_English_HDPMBF12E44 Page: 58 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm z If NPV is positive, the financial value of the investor’s assets would be increased: the investment is financially attractive. z If NPV is zero, the financial value of the investor’s assets would not change: the investor is indifferent toward the investment. z If NPV is negative, the financial value of the investor’s assets would be decreased: the investment is not financially attractive. A comparison of the NPV’s of alternative investment possibilities indicates which of them is most desirable: the greater the NPV, the greater the increase in the financial value of the investor’s assets. IRR is the rate of return at which the discounted future cash flows equal the initial cash outlay: IRR is the discount rate at which NPV is zero. The value of IRR relative to the present value discount rate also indicates the result of the investment: z If IRR is greater than the desired rate of return, the investment is financially attractive. z If IRR is equal to the desired rate of return, the investor is indifferent toward the investment. z If IRR is less than the desired rate of return, the investment is not financially attractive. Calculating Net Present Value (NPV) Calculating NPV for Ungrouped Cash Flows. If there are no equal consecutive cash flows, use the procedure described (and then summarized) below. With this procedure, NPV (and IRR) problems involving up to 20 cash flows (in addition to the initial investment CF 0) can be solved. If two or more consecutive cash flows are equal — for example, if the cash flows in periods three and four are both $8,500 — you can solve problems involving more than 20 cash flows, or you can minimize the number of storage registers required for problems involving less than 20 cash flows, by using the procedure described next (under Calculating NPV for Grouped Cash Flows, page 61). The amount of the initial investment (CF 0) is entered into the calculator using the J key. Pressing gJ stores CF 0 in storage register R0 and also stores the number 0 in the n register.
Section 4: Additional Financial Functions 59
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The amounts of the subsequent cash flows are stored – in the order they occur – in
the remaining storage registers: CF
1 thru CF9 in R1 thru R9, and CF10 thru CF19 in R.0
thru R
.9, respectively. If there is a CF20, that amount is stored in the FV register.*
Each cash flow (CF
1, CF2, etc.) is designated CFj, where j takes on values from 1
up to the number of the final cash flow. The amount of a cash flow is entered using
the K
key. Each time gK
is pressed, the amount in the display is stored in
the next available storage register, and the number in the n register is increased
by 1. This register therefore counts how many cash flow amounts (in addition to
the initial investment CF
0) have been entered.
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 a negative cash flow.
In summary, to enter the cash flow amounts:
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. Key in the amount of the next cash flow, press Þ if the cash flow is
negative, then press gK. If the cash flow amount is zero in the next
period, press 0 gK.
4. Repeat step 3 for each cash flow until all have been entered.
With the amounts of the cash flows stored in the calculator’s registers, you can
calculate NPV as follows:
1. Enter the interest rate, using ¼ or C.
2. Press fl.
The calculated value of NPV appears in the display and also is automatically
stored in the PV register.
* If you have stored a program in the calculator, the number of registers available for storing
cash flow amounts may be less than 21. (Storage registers are automatically allocated to
program lines beginning with R
.9 and proceeding in reverse order to R7, as described on
pages 93 thru 95.) The maximum number of cash flow amounts (in addition to CF
0) that can
be stored is the number that appears at the right of the display when gN is pressed. If the
maximum number of cash flow amounts is stored, the final cash flow amount is always stored
in the FV register. For example, if N displays P-08 r-20, the last cash flow amount that can
be stored – CF
20 – will be stored in FV. Similarly, if N displays P-22 r-18, the last cash
flow amount that can be stored – CF
18 – will be stored in FV.
60 Section 4: Additional Financial Functions File name: hp 12c_users guide_English_HDPMBF12E44 Page: 60 of 209 Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm Example: An investor has an opportunity to buy a duplex for $80,000 and would like a return of at least 13%. He expects to keep the duplex 5 years and then sell it for $130,000; and he anticipates the cash flows shown in the diagram below. Calculate NPV to determine whether the investment would result in a return or a loss. Note that although a cash flow amount ($4,500) occurs twice, these cash flows are not consecutive. Therefore, these cash flows must be entered using the method described above. Keystrokes Display fCLEARH 0.00 Clears financial and storage registers. 80000ÞgJ –80,000.00Stores CF0 (with minus sign for a negative cash flow). 500ÞgK –500.00 Stores CF1 (with minus sign for a negative cash flow). 4500gK 4,500.00 Stores CF2. 5500gK 5,500.00 Stores CF3. 4500gK 4,500.00 Stores CF4. 130000gK 130,000.00Stores CF5. :n 5.00 Checks number of cash flow amounts entered (in addition to CF 0 ). 13¼ 13.00 Stores i. fl 212.18 NPV. Since NPV is positive, the investment would increase the financial value of the investor’s assets.