For More Solutions to Financial Problems
In addition to the specialized solutions found in Sections 12 through 16 of this handbook, many more are available in the optional hp 12c platinum Solutions Handbook. Included are solutions to problems in lending, forecasting, pricing, statistics, savings, investment analysis, personal finance, securities, Canadian mortgages, learning curves in manufacturing, options pricing, and queuing theory. The solutions handbook is available online at the hp 12c platinum website. HP would like to thank the following for their contribution: Gene Wright, Lipscomb University, Nashville, TN, USA and Tony Hutchins, Wellington, NZ Jordi Hidalgo, Barcelona, Spain
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Contents

Introduction... 3
About This Handbook...3 Financial Calculations in the United Kingdom..4 For More Solutions to Financial Problems..4

Part I:

Problem Solving... 15
Section 1: Getting Started.. 16
Power On and Off..16 Low-Power Indication..16 Adjusting the Display Contrast..16 The Keyboard...16 Keying in Numbers...17 Digit Separators...17 Negative Numbers...17 Keying in Large Numbers..18 Backspacing...18 The CLEAR Keys...19 Undo Operation...20 The RPN and ALG Keys...20 Simple Arithmetic Calculations in RPN Mode..21 Simple Arithmetic Calculations in ALG Mode..22 Chain Calculations in RPN Mode...23 Chain Calculations in ALG Mode...26 Parentheses Calculations...26 Storage Registers...27 Storing and Recalling Numbers..27 Clearing Storage Registers..29 Storage Register Arithmetic...29
Section 2: Percentage and Calendar Functions.. 31
Percentage Functions...31 Percentages in RPN Mode..31 Percentages in ALG Mode..32 Net Amount in RPN Mode..33 Net Amount in ALG Mode..33 Percent Difference...34 Percent of Total in RPN Mode..35 5
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Percent of Total in ALG Mode.. 36 Calendar Functions... 37 Date Format... 37 Future or Past Dates... 38 Number of Days Between Dates.. 40
Section 3: Basic Financial Functions.41
The Financial Registers... 41 Storing Numbers into the Financial Registers.. 41 Displaying Numbers in the Financial Registers. 41 Clearing the Financial Registers... 42 Simple Interest Calculations... 42 Financial Calculations and the Cash Flow Diagram. 44 The Cash Flow Sign Convention... 46 The Payment Mode... 46 Generalized Cash Flow Diagrams.. 47 Compound Interest Calculations... 49 Specifying the Number of Compounding Periods and the Periodic Interest Rate... 49 Calculating the Number of Payments or Compounding Periods. 49 Calculating the Periodic and Annual Interest Rates. 55 Calculating the Present Value.. 56 Calculating the Payment Amount.. 58 Calculating the Future Value... 60 Odd-Period Calculations... 63 Amortization... 69

1.7814 12

1,781,400,000,000 entered in scientific notation.
Numbers entered in scientific notation can be used in calculations just like any other number.

Backspacing

While you are entering a number, pressing g deletes the last character you entered. After performing a calculation, pressing g deletes the current number. Keystrokes (RPN mode) 12345gg.63\ Display

123.63

Correcting removes the 4 and 5. g clears the most recent digit entered.

128.63 0.00

Clears the calculator line.
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Keystrokes (ALG mode) 12345gg.63+
Correcting removes the 4 and 5. g clears the most recent digit entered. } is also labeled the \ key. Clears the calculator line.

The CLEAR Keys

Clearing a register or the display replaces the number in it with zero. Clearing program memory replaces the instructions there with gi000. There are several clearing operations on the hp 12c platinum, as shown in the table below:

Key(s)

O fCLEAR fCLEAR fCLEARG fCLEARH Display and X-register.

Clears:

Statistics registers (R1 through R6), stack registers, and display. Program memory (only when pressed in Program mode). Financial registers. Data storage registers, financial registers, stack and LAST X registers, and display.
Note: In ALG mode, it is a good idea to begin calculations by pressing
OO. This will ensure that there are no pending arithmetic calculations that might interfere with the solution of a new problem. The reason this key is pressed twice is that pressing it the first time clears the display and X-register only, allowing you to correct an erroneous entry by keying in a correct number. The second press of O will clear any pending operations as well. Pressing the } key is another way to ensure that there are no pending operations before beginning a new calculation, since the } key will evaluate any pending expressions.
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Undo Operation

Every time you press O, g, fCLEARH, fCLEAR or fCLEARG key to clear data, the status indicator appears in the display. This means you can press g to undo the last operation (i.e., to recover the data.) Note: the Undo function is only available immediately after data has been cleared. When the Undo indicator is turned off no operation can be undone.

The RPN and ALG Keys

The calculator can be set to perform arithmetic operations in either RPN (Reverse Polish Notation) or ALG (Algebraic) mode. In Reverse Polish Notation (RPN) mode, the intermediate results of calculations are stored automatically, hence you do not have to use parentheses. In algebraic (ALG) mode, you perform addition, subtraction, multiplication, and division in the traditional way, using parentheses if needed. To select RPN mode: Press f] to set the calculator to RPN mode. When the calculator is in RPN mode, the RPN status indicator is lit. To select ALG mode: Press f[ to set the calculator to ALG mode. When the calculator is in ALG mode, the ALG status indicator is lit. Example Suppose you want to calculate 1 + 2 = 3. In RPN mode, you enter the first number, press the \ key, enter the second number, and finally press the arithmetic operator key: +. In ALG mode, you enter the first number, press +, enter the second number, and finally press the equals key: }. Dont forget to press OO before doing the calculation.

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Net Amount in RPN Mode

A net amount that is, the base amount plus or minus the percentage amount can be calculated easily with your hp 12c platinum, since the calculator holds the base amount inside after you calculate a percentage amount. To calculate a net amount, simply calculate the percentage amount, then press = or -. Example: Youre buying a new car that lists for $23,250. The dealer offers you a discount of 8%, and the sales tax is 6%. Find the amount the dealer is charging you, then find the total cost to you, including tax. Keystrokes Display (RPN mode) 23250\ 8b 6b =
23,250.00 Keys in the base amount and
separates it from the percentage.

1,860.00

Amount of discount.
21,390.00 Base amount less discount. 1,283.40
Amount of tax (on $21,390). plus tax.
22,673.40 Total cost: base amount less discount

Net Amount in ALG Mode

In ALG mode, you can calculate a net amount all in one calculation: For example, to decrease 200 by 25%, just enter 200-25b}. (Result is 150.) Example: You borrow $1,250 from a relative, and agree to repay the loan in a year with 7% simple interest. How much money will you owe? Keystrokes Display (ALG mode) 1250+7b }

87.50 1,337.50

Interest on the loan is $87.50. You owe this amount at the end of one year.
Example: Youre buying a new car that lists for $23,250. The dealer offers you a discount of 8%, and the sales tax is 6%. Find the amount the dealer is charging you, then find the total cost to you, including tax. Keystrokes Display (ALG mode) 23250-
prepares to subtract the discount percentage.
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Keystrokes (ALG mode) 8b = 6b }

Percent Difference

In RPN or ALG mode, to find the percent difference between two numbers: 1. Key in the base number. 2. Press \ to separate the other number from the base number. 3. Key in the other number. 4. Press. If the other number is greater than the base number, the percent difference will be positive. If the other number is less than the base number, the percent difference will be negative. Therefore, a positive answer indicates an increase, while a negative answer indicates a decrease. If you are calculating a percent difference over time, the base number is typically the amount occurring first. Example: Yesterday your stock fell from $58.50 to $53.25 per share. What is the percent change? (Note that the \ key is the same as the } key in ALG mode.) Keystrokes 58.5\ 53.25 Display

Simple Interest Calculations
The hp 12c platinum simultaneously calculates simple interest on both a 360-day basis and a 365-day basis. You can display either one, as described below. Furthermore, with the accrued interest in the display, you can calculate the total amount (principal plus accrued interest) by pressing + in RPN mode or +~} in ALG mode. 1. Key in or calculate the number of days, then press n. 2. Key in the annual interest rate, then press. 3. Key in the principal amount, then press $.* 4. Press f to calculate and display the interest accrued on a 360-day basis. 5. If you want to display the interest accrued on a 365-day basis, press d~. 6. In RPN mode, press + or in ALG mode, press +~} to calculate the total of the principal and the accrued interest shown in the display. The quantities n, i, and PV can be entered in any order.

* Pressing

the $ key stores the principal amount in the PV register, which then contains the
present value of the amount on which interest will accrue. The key is pressed first to change the sign of the principal amount before storing it in the PV register. This is required by the cash flow sign convention (see page 46), which is applicable primarily to compound interest calculations.
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Example 1: Your good friend needs a loan to start his latest enterprise and has requested that you lend him $450 for 60 days. You lend him the money at 7% simple interest, to be calculated on a 360-day basis. What is the amount of accrued interest he will owe you in 60 days, and what is the total amount owed? Keystrokes Display (RPN mode) 60n 7 450$ f +
60.00 7.00 450.00 5.25 455.25
Stores the number of days. Stores the annual interest rate. Stores the principal. Accrued interest, 360-day basis. Total amount: principal plus accrued interest.
In ALG mode, perform the steps in the RPN listing above, except replace the last step with the step below. Keystrokes Display (ALG mode) +~}

455.25

Total amount: principal plus accrued interest.
Example 2: Your friend agrees to the 7% interest on the loan from the preceding example, but asks that you compute it on a 365-day basis rather than a 360-day basis. What is the amount of accrued interest he will owe you in 60 days, and what is the total amount owed? Keystrokes Display (RPN mode) 60n 7 450$ fd~ +

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Compound Interest Calculations
Specifying the Number of Compounding Periods and the Periodic Interest Rate
Interest rates are usually quoted at the annual rate (also called the nominal rate): that is, the interest rate per year. However, in compound interest problems, the interest rate entered into i must always be expressed in terms of the basic compounding period, which may be years, months, days, or any other time unit. For example, if a problem involves 6% annual interest compounded quarterly for 5 years, n the number of quarters would be = 20 and i the interest rate per quarter would be 6% 4 = 1.5%. If the interest were instead compounded monthly, n would be = 60 and i would be 6% 12 = 0.5%. If you use the calculator to multiply the number of years by the number of compounding periods per year, pressing n then stores the result into n. The same is true for i. Values of n and i are calculated and stored like this in Example 2 on page 59. If interest is compounded monthly, you can use a shortcut provided on the calculator to calculate and store n and i: To calculate and store n, key the number of years into the display, then press gA. To calculate and store i, key the annual rate into the display, then press gC. Note that these keys not only multiply or divide the displayed number by 12; they also automatically store the result in the corresponding register, so you need not press the n or key next. The gA and gC keys are used in Example 1 on page 59.
Calculating the Number of Payments or Compounding Periods
1. Press fCLEARG to clear the financial registers. 2. Enter the periodic interest rate, using or gC. 3. Enter at least two of the following values: Present value, using $. Payment amount, using P. Future value, using M. Note: Remember to observe the cash flow sign convention.
4. If a PMT was entered, press g or g to set the payment mode. 5. Press n to calculate the number of payments or periods.
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If the answer calculated is not an integer (that is, there would be nonzero digits to the right of the decimal point), the calculator rounds the answer up to the next higher integer before storing it in the n register and displaying it.* For example, if n were calculated as 318.15, 319.00 would be the displayed answer. n is rounded up by the calculator to show the total number of payments needed: n1 equal, full payments, and one final, smaller payment. The calculator does not automatically adjust the values in the other financial registers to reflect n equal payments; rather, it allows you to choose which, if any, of the values to adjust. Therefore, if you want to know the value of the final payment (with which you can calculate a balloon payment) or desire to know the payment value for n equal payments, you will need to press one of the other financial keys, as shown in the following two examples. Example 1: Youre planning to build a log cabin on your vacation property. Your rich uncle offers you a $35,000 loan at 10.5% interest. If you make $325 payments at the end of each month, how many payments will be required to pay off the loan, and how many years will this take?

5. If a PMT was entered, press g or g to set the payment mode. 6. Press $ to calculate the present value.
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Example 1: Youre financing a new car purchase with a loan from an institution that requires 5.9% interest compounded monthly over the 4-year term of the loan. If you can make payments of $450 at the end of each month and your down payment will be $1,500, what is the maximum price you can pay for the car? (Assume the purchase date is one month prior to the date of the first payment.)
Keystrokes (RPN mode) fCLEARG 4gA 5.9gC 450P g $ 1500+

48.00 0.49 450.00 450.00

Calculates and stores n. Calculates and stores i. Stores PMT (with minus sign for cash paid out). Sets payment mode to End.
19,198.60 Maximum amount of loan. 20,698.60 Maximum purchase price.
In ALG mode, press the keys listed for RPN mode but replace the last step above with the step below. Keystrokes (ALG mode) +1500} Display
20,698.60 Maximum purchase price.
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Example 2: A development company would like to purchase a group of condominiums with an annual net cash flow of $17,500. The expected holding period is 5 years, and the estimated selling price at that time is $540,000. Calculate the maximum amount the company can pay for the condominiums in order to realize at least a 12% annual yield.
Keystrokes fCLEARG 5n 12 17500P

5.00 12.00 17,500.00

Stores n. Stores i. Stores PMT. Unlike in the previous problem, here PMT is positive since it represents cash received. Stores FV. Sets payment mode to End. The maximum purchase price to provide a 12% annual yield. PV is displayed with a minus sign since it represents cash paid out.

540000M g $

540,000.00 540,000.00 369,494.09
Calculating the Payment Amount
1. Press fCLEARG to clear the financial registers. 2. Enter the number of payments or periods, using n or gA. 3. Enter the periodic interest rate, using or gC. 4. Enter either or both of the following: Present value, using $. Future value, using M. Note: Remember to observe the cash flow sign convention.
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5. Press g or g to set the payment mode. 6. Press P to calculate the payment amount. Example 1: Calculate the payment amount on a 29-year, $243,400 mortgage at 5.25% annual interest, compounded monthly.
Keystrokes fCLEARG 29gA 5.25gC 243400$ g P
348.00 0.44 243,400.00 243,400.00 1,363.29
Calculates and stores n. Calculates and stores i. Stores PV. Sets payment mode to End. Monthly payment (with minus sign for cash paid out).
Example 2: Looking forward to retirement, you wish to accumulate $60,000 after 15 years by making deposits in an account that pays 9.75% interest compounded semiannually. You open the account with a deposit of $3,200 and intend to make semiannual deposits, beginning six months later, from your profit-sharing bonus paychecks. Calculate how much these deposits should be.

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150 Section 11: Multiple Programs
Example 1: Assuming that program memory still contains the last program from the preceding section (which consisted of 17 program lines in RPN mode and 23 program lines in ALG mode), store after that program the office-supplies program from Section 8 (page 104). Since this is the second program to be stored in program memory, well ensure that a i000 instruction separates it from the first program by doing step 3 in the procedure above. Furthermore, since this program does not end with a loop, well do steps 5 and 6 too. Keystrokes (RPN mode) fs gi.017 gi000 \ b 5 + t gi019 fs Display Sets calculator to Program mode.
017,43, 33,002 018,43, 33,000 019, 020, 021, 022, 023, 024, 025, 026, 12,000.31
Sets calculator to last line keyed into program memory. Ensures that second program is separated from first by i000.

Keys in program.

Halts program execution. Branches to beginning of program. Sets calculator back to Run mode. (Display shown assumes results remain from running program in previous example.)

027,43, 33,019

Keystrokes (ALG mode) fs gi.023 gi000
023,43, 33,002 024,43, 33,000
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Section 11: Multiple Programs
Keystrokes (ALG mode) b + 5 } t gi025 fs
025, 026, 027, 028, 029, 030, 031, 032, 12,000.00
Halts program execution. Branches to beginning of program. Sets calculator back to Run mode. (Display shown assumes results remain from running program in previous example.) Keys in program.

033,43, 33,025

Example 2: With the two programs now stored in program memory from the preceding examples (occupying 27 program lines in RPN mode and 33 lines in ALG mode), store the amortization program from Section 9(page 125). Since there are already two programs stored in program memory, well skip step 3 in the procedure above. Furthermore, since the amortization program ends with a loop, well skip steps 5 and 6. When the amortization program was stored at the beginning of program memory, the i instruction at the end of the program branched to the :0 instruction in line 002. In the RPN program, since the :0 instruction is now in line 029, well specify that line number with the i instruction in line 034. In the ALG program, since the :0 instruction is now in line 035, well specify that line number with the i instruction in line 041. Keystrokes (RPN mode) fs gi.027 Display Sets calculator to Program mode.

Keystrokes (ALG mode) 12

0.48 5.73

Monthly interest rate (calculated). Annual percentage rate.
Price of a Mortgage Traded at a Discount or Premium
Mortgages may be bought and/or sold at prices lower (discounted) or higher (at a premium) than the remaining balance of the loan at the time of purchase. Given the amount of the mortgage, the periodic payment, the timing and amount of the balloon or prepayment, and the desired yield rate, the price of the mortgage may be found. It should be noted that the balloon payment amount (if it exists) occurs coincident with, and does not include, the last periodic payment amount. Information is entered as follows: 1. Press g and fCLEARG. 2. Key in the total number of periods until the balloon payment or prepayment occurs; press n. (If there is no balloon payment, key in total number of payments and press n.) 3. Key in the desired periodic interest rate (yield) and press. 4. Key in the periodic payment amount; press P.* 5. Key in the balloon payment amount and press M.* (If there is no balloon payment, go to step 6.) 6. Press $ to obtain the purchase price of the mortgage. Example 1: A lender wishes to induce the borrower to prepay a low interest rate loan. The interest rate is 5% with 72 payments remaining of $137.17 and a balloon payment at the end of the sixth year of $2,000. If the lender is willing to discount the future payments at 9%, how much would the borrower need to prepay the note? Keystrokes (RPN mode) f] g fCLEARG 72n Keystrokes (ALG mode) f[ Display

g fCLEARG 72n

Months (into n).
* Positive for cash received; negative for cash paid out.
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160 Section 12: Real Estate and Lending
Keystrokes (RPN mode) 9gC 137.17P* 2000M$
Keystrokes (ALG mode) 9gC 137.17P* 2000M$

0.75 137.17 8,777.61

Discount rate (into i). Monthly payments (into PMT). Amount necessary to prepay the note.
Example 2: A 6.5% mortgage with 26 years remaining and a remaining balance of $249,350 is available for purchase. Determine the price to pay for this mortgage if the desired yield is 12%. (Since the payment amount is not given, it must be calculated.) Keystrokes (RPN mode) f] g fCLEARG 26gA 6.5gC Keystrokes (ALG mode) f[ g fCLEARG 26gA 6.5gC Display

Example 1: A property has just been purchased for $150,000. The purchase price is allocated between $25,000 for land and $125,000 for improvements (building). The remaining useful life of the building is agreed to be 25 years. There is no salvage value forecasted at the end of the useful life of the building. Thus, the depreciable value and book value is $125,000. The building was acquired 4 months before the end of the year. Using straight-line depreciation, find the amount of depreciation and remaining depreciable value for the 1st, 2nd, 25th, and 26th years. What is the total depreciation after 3 years?
* The display will pause showing the year number before showing the amount of depreciation

for that year.

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Keystrokes (RPN mode) f] fCLEARG
Keystrokes (ALG mode) f[ fCLEARG
Salvage value = 0 so FV = 0; set to 0 by CLEARG.
125000$ 25n 1\ 4t ~ t ~ t

125000$ 25n 1 4t ~ t ~ t

125,000.00 25.00 1.00 1.00 1,666.67 123,333.33 2.00 5,000.00 118,333.33 3.00 5,000.00
Book value. Life. Year desired. First year: depreciation, remaining depreciable value. Second year: depreciation, remaining depreciable value. Third year: depreciation.
~:$:3 ~:$= :3-~ +~gi000 gi000 11,666.67 fCLEARG 125000$ 25n 25\ 4t ~ t ~ fCLEARG 125000$ 25n 25 4t ~ t ~
Total depreciation through third year.
11,666.67 125,000.00 25.00 25.00 25.00 5,000.00 3,333.33 26.00 3,333.33 0.00
Book value. Life. Year desired. Twenty-fifth year: depreciation, remaining depreciable value. Twenty-sixth year: depreciation, remaining depreciable value.
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176 Section 13: Investment Analysis
Example 2: A used car was purchased for $6,730 with 4.5 months remaining in the year. If the expected life of the car is 5 years, what is the amount of depreciation in the first year? Keystrokes (RPN mode) f] gi000 fCLEARG 6730$ 5n 1\ 4.5t Keystrokes (ALG mode) f[ gi000 fCLEARG 6730$ 5n 1 4.5t Display
6,730.00 5.00 1.00 1.00 504.75

Book value. Life.

029,43, 33, 041 030, 031, 032, 033, 034, 035, 036, 037, 038, 6

038,43, 33, 000

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Section 16: Bonds

:1 :6 + $ 2 fs
DISPLAY 039, 040, 041, 042, 043, 044, 045, 046, 2 20

} g(000 :1 :6 $ 2 } fs

DISPLAY 039, 36
040,43, 33, 000 041, 042, 043, 044, 045, 046, 047, 048, 049, 36
n: days/180 FV: Red+Cpn./2 R3: Dset R7R.3: Unused 1. Key in the program. 2. If the C status indicator is not displayed, press ?. 3. Key in the annual coupon interest rate as a percentage then press ?2. 4. Key in the settlement date (MM.DDYYYY)* then press ?3. 5. Key in the maturity date (MM.DDYYYY)* then press ?4. 6. Key in the redemption value as a percentage of par then press ?5. i: Yield/2 R0: Yield R4: Dmat PV: Price R1: Price. R5: Redemption PMT: Coupon/2. R2: Coupon R6: Accrued Int.
* For information about date format see pages 37 to 38.
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220 Section 16: Bonds

7. If price is desired: a. Key in the desired yield to maturity as a percentage then press ?0. b. Press t to calculate price as a percentage of par value. c. RPN: Press ~ to display accrued interest due the seller. Press + to calculate the total price paid. c. ALG: Press +~ to display accrued interest due the seller and then press } to calculate the total price paid. For a new case return to step 3. Note that only those values which have been changed need to be reentered and stored. 8. If yield is desired: a. Press 0?0. b. Key in the price as a percentage of par value and press ?1. c. Press t to compute annual yield to maturity. For a new case return to step 3. Note that only those values which have been changed need to be reentered and stored. Example 1: What price should you pay on August 28, 2004 for a 5.5% bond (computed with a 30/360 basis) that matures on June 1, 2008, if you want a yield of 4.75%? What price should you pay for a yield of 4.5%? This problem assumes a redemption value of 100. Keystrokes (RPN mode) f] ? Keystrokes (ALG mode) f[ ? Set compound interest mode if the C indicator is not on. Display
5.5?2 8.282004?3 6.012008?4 100?5 4.75?0 t ~ 4.5?0
5.50 8.28 6.01 100.00 4.75 102.55 1.33 4.50
Coupon into R2. Settlement date into register R3. Maturity date into R4. Redemption value into R5. Yield into R0. Price (calculated). Accrued interest (calculated). New yield into R0.
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Keystrokes (RPN mode) t ~ +
Keystrokes (ALG mode) t +~

103.41 1.33 104.74

Price to yield 4.5% (calculated). Accrued interest (calculated). Total price paid.
Example 2: The market is quoting 105% for the bond described in example 1. What yield will that provide? What would be the yield to maturity if 104% were the quoted price? Keystrokes (RPN mode) Keystrokes (ALG mode) Display

The Power Function

Pressing q calculates a power of a number, that is, yx. Like the arithmetic function +, q requires two numbers: 1. Key in the base number (which is designated by the y on the key). 2. Press q and key in the exponent (which is designated by the x on the key) 3. Press } to calculate the power. Dont forget to press OO if you are unsure if there are any pending operations.

21.4 21.4 (2)

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Appendix C

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 platinum 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. Lets look at all of the possible outcomes of IRR as calculated by your hp 12c platinum: 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 79) and Changing Cash Flow Entries (page 80) 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.
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244 Appendix C: More About L
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. 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.

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Appendix D

Error Conditions
Some calculator operations cannot be performed under certain conditions (for example, z when x = 0). If you attempt such an operation under these conditions, the calculator will display the word Error followed by a digit, 0 through 9. Listed below are operations that cannot be performed under the conditions specified. The symbols x and y represent the number in the X- and Y-registers, respectively, when the operation key is pressed.

Error 0: Mathematics

Operation z y r q Condition x=0 x=0 x<0 x0 y = 0 and x 0 y < 0 and x is noninteger. Z ?z(0 through 4) e y=0 y=0 x=0 x is noninteger x<0
Page: 245 of 275 Dimension: 14.8 cm x 21 cm
246 Appendix D: Error Conditions
Error 1: Storage Register Overflow
Operation ?+(0 through ?-(0 through ?(0 through ?z(0 through A 4) 4) 4) 4) Condition
Magnitude of result is greater than 9.9999999991099.

Error 2: Statistics

Operation v Condition n (number in R1) = 0 x = 0 n=0 n=1 nx2 (x)2< 0 ny2 (y)2< 0 n=0 nx2 (x)2 = 0 n=0 ny2 (y)2 = 0 [nx2 (x)2][ny2 (y)2] 0

R Q R~ Q~

Error 3: IRR

Refer to Appendix C.

Error 4: Memory
Attempting to enter more than 400 program lines. Attempting to i to a program line that does not exist. Attempting storage register arithmetic in R5 through R9 or R.0 through R.9. Too many open parentheses.
Page: 246 of 275 Dimension: 14.8 cm x 21 cm
Appendix D: Error Conditions
Error 5: Compound Interest
Operation n Condition i = 0 and PMT = 0 PMT is between FV d and PV d, inclusive,
i ( ) 100 where d = , where S=0 for END S (1 + i ) 100
mode and 1 for BEG mode. i 100 n=0 n 1010 or n < 0 i 100 Cash flows all have same sign. $ P i 100 n=0 i 100 i 100 x0 x is noninteger. i 100 n0 n > 1010 x0 x is noninteger PMT < 0 PMT < 0

M ! l V # E S

Page: 247 of 275 Dimension: 14.8 cm x 21 cm
248 Appendix D: Error Conditions
Error 6: Storage Registers
Operation ? : K a l L a Condition Storage register specified does not exist or has been converted to program lines. n specifies a storage register that does not exist or has been converted to program lines. n > 80 n<0 n is noninteger x > 99 x<0 x is noninteger Attempted to input Nj for CF0

CPN DCS E 2

Page: 253 of 275 Dimension: 14.8 cm x 21 cm
254 Appendix E: Formulas Used
P = current asset price. r% = risk-free rate (continuous, per time unit). s% = volatility (continuous, per time unit). T = term of option (same time unit as r% and s%). X = exercise price of option. N(z) = probability that a unit normal random variable is less than z. Call Value = P N(d1) Q N(d2) Put Value = Call Value + Q P where : d1 = LN(P/Q)/v + v/2, d2-= d1 v Q = Xe( T r % / 0 ) , v=s%/100 T

Depreciation

L SBV SAL FACT j DPNj RDVj RBVj Y1 = assets useful life expectancy. = starting book value. = salvage value. = declining-balance factor expressed as a percentage. = period number. = depreciation expense during period j. = remaining depreciable value at end of period j = RDVj1 DPNj where RDV0 = SBV SAL = remaining book value = RBVj1 DPNj where RBV0 = SBV = number of months in partial first year.
Page: 254 of 275 Dimension: 14.8 cm x 21 cm

Keyboard function:

DPN J =
SBV SAL for j = 1, 2, , L L
Program for partial first year:

DPN1 =

SBV SAL Y1 L 12 SBV SAL for j = 2, 3, , L DPN J = L

DPNL + 1 = RDVL

Sum-of-the-Years-Digits Depreciation

SOYDk =

(W + 1 W + 2F ) )( 2
where W = integer part of k F = fractional part of k. (i.e., for k = 12.25 years, W = 12 and F = 0.25). Keyboard function:
(L j + 1 ) (SBV SAL ) SOYDL
Program for partial year:
L Y1 DPN1 = (SBV SAL ) SOYD 12
LADJ j + 2 (SBV D1 SAL ) for j 1 DPN j = SOYD LADJ

Y1 where LADJ = L 12

DPN j = RBVj 1
FACT for j = 1, 2, , L 100L

DPN1 = SBV

FACT Y1 100L 12
Page: 255 of 275 Dimension: 14.8 cm x 21 cm
256 Appendix E: Formulas Used

FACT for j 1 100L

n NFVP NPVN = number of compounding periods. = Net future value of the positive cash flows. = Net present value of the negative cash flows.

1 n 1

NFVP MIRR = 100 NPV N
A = number of payments made in advance.
PV FV (1 + i ) n 1 (1 + i ) (n A ) + A i
Interest Rate Conversions
C EFF NOM = number of compounding periods per year. = the effective annual interest rate as a decimal. = the nominal annual interest rate as a decimal.

Finite Compounding

NOM EFF = 1 + 1 C

Continuous Compounding

EFF = (e NOM 1 )