User Manual for Texas Instruments models including: BA II PLUS, Calculator

Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. © 2011-2021 Texas ...

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DocumentDocumentBA II PLUSTM Calculator Important Information Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. © 2011-2021 Texas Instruments Incorporated ii USA FCC Information Concerning Radio Frequency Interference Interference This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures: · Reorient or relocate the receiving antenna. · Increase the separation between the equipment and receiver. · Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. · Consult the dealer or an experienced radio/television technician for help. Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment. © 2004-2019 Texas Instruments Incorporated iii Contents Overview of Calculator Operations 1 Turning On the Calculator 1 Turning Off the Calculator 1 Selecting 2nd Functions 2 Reading the Display 2 Setting Calculator Formats 4 Resetting the Calculator 6 Clearing Calculator Entries and Memories 6 Correcting Entry Errors 7 Math Operations 8 Memory Operations 12 Calculations Using Constants 14 Last Answer Feature 15 Using Worksheets: Tools for Financial Solutions 16 Time-Value-of-Money and Amortization Worksheets 21 TVM and Amortization Worksheet Variables 21 Entering Cash Inflows and Outflows 25 Generating an Amortization Schedule 25 Example: Computing Basic Loan Interest 26 Examples: Computing Basic Loan Payments 27 Examples: Computing Value in Savings 28 Example: Computing Present Value in Annuities 29 Example: Computing Perpetual Annuities 30 Example: Computing Present Value of Variable Cash Flows 31 Example: Computing Present Value of a Lease With Residual Value 33 Example: Computing Other Monthly Payments 34 Example: Saving With Monthly Deposits 35 Example: Computing Amount to Borrow and Down Payment 36 Example: Computing Regular Deposits for a Specified Future Amount 37 Example: Computing Payments and Generating an Amortization Schedule 38 Example: Computing Payment, Interest, and Loan Balance After a Specified Pay- ment 40 Cash Flow Worksheet 42 Cash Flow Worksheet Variables 42 Uneven and Grouped Cash Flows 43 Entering Cash Flows 44 iv Deleting Cash Flows 45 Inserting Cash Flows 45 Computing Cash Flows 46 Example: Solving for Unequal Cash Flows 47 Example: Value of a Lease with Uneven Payments 50 Bond Worksheet 52 Bond Worksheet Variables 52 Bond Worksheet Terminology 54 Entering Bond Data and Computing Results 55 Example: Computing Bond Price and Accrued Interest 56 Depreciation Worksheet 58 Depreciation Worksheet Variables 58 Entering Data and Computing Results 61 Example: Computing Straight-Line Depreciation 62 Statistics Worksheet 63 Statistics Worksheet Variables 63 Regression Models 65 Entering Statistical Data 66 Computing Statistical Results 66 Other Worksheets 68 Percent Change/Compound Interest Worksheet 68 Interest Conversion Worksheet 72 Date Worksheet 74 Profit Margin Worksheet 76 Breakeven Worksheet 78 Memory Worksheet 80 APPENDIX - Reference Information 82 Formulas 82 Error Messages 93 Accuracy Information 95 AOSTM (Algebraic Operating System) Calculations 96 Battery Information 96 In Case of Difficulty 97 v General Information 99 Contact TI Support 99 Service and Warranty Information 99 vi Overview of Calculator Operations This chapter describes the basic operation of your BA II PLUSTM calculator, including how to: · Turn on and turn off the calculator · Select second functions · Read the display and set calculator formats · Clear the calculator and correct entry errors · Perform math and memory operations · Use the Last Answer feature · Use worksheets Turning On the Calculator Press $. · If you turned off the calculator by pressing $, the calculator returns to the standard-calculator mode with a displayed value of zero. All worksheets and formats for numbers, angle units, dates, separators, and calculation method retain previous values and configurations. · If the Automatic Power DownTM (APDTM) feature turned off the calculator, the calculator turns on exactly as you left it, saving display settings, stored memory, pending operations, and error conditions. Turning Off the Calculator Press $. · The displayed value and any error condition clear. · Any unfinished standard-calculator operation and worksheet calculation in progress cancel. · The Constant MemoryTM feature retains all worksheet values and settings, including the contents of the 10 memories and all format settings. Overview of Calculator Operations 1 Automatic Power DownTM (APDTM) Feature To prolong battery life, the Automatic Power Down (APD) feature turns off the calculator automatically after about five minutes of inactivity. The next time you press $, the calculator turns on exactly as you left it, saving display settings and stored memory and any pending operations or error conditions. Selecting 2nd Functions The primary function of a key is printed on the key itself. For example, the primary function of the $ key is to turn on or turn off the calculator. Most keys include a second function printed above the key. To select a second function, press & and the corresponding key. (When you press &, the 2nd indicator appears in the upper left corner of the display.) For example, pressing & U exits the selected worksheet and returns the calculator to the standard-calculator mode. Note: To cancel after pressing &, press & again. Reading the Display The display shows the selected variable labels with values up to 10 digits. (The calculator displays values exceeding 10 digits in scientific notation.) The indicators along the top of the display tell you which keys are active and offer information about the status of the calculator. Indicator Meaning Press a key to select its second function. (& 2nd To cancel, press & again. 2 Overview of Calculator Operations Indicator Meaning INV Press a key to select its inverse trigonometric function. HYP Press a key to select its hyperbolic function. COMPUTE Press C to compute a value for the displayed variable. ENTER Press ! to assign the displayed value to the displayed variable. Press & Vto change the setting of the displayed SET variable. Press # or " to display the previous or next variable in #$ the worksheet. Note: To easily scroll up or down through a range of variables, press and hold # or ". DEL Press & W to delete a cash flow or statistical data point. INS Press & X to insert a cash flow or statistical data point. BGN TVM calculations use beginning-of-period payments. When BGN is not displayed, TVM calculations use end-ofperiod payments (END). RAD Angle values appear in radians. When RAD is not displayed, angle values appear and must be entered in degrees. 1 The displayed value is entered in the selected worksheet. The indicator clears following a computation. The displayed value is computed in the selected 7 worksheet. When a value changes and invalidates a computed value, the indicator clears. = The displayed variable is assigned the displayed value. The displayed value is negative. Overview of Calculator Operations 3 Setting Calculator Formats You can change these calculator formats: To Select Press Display Number of decimal places & | DEC 09 (Press 9 for floatingdecimal) Angle units # DEG (degrees) RAD (radians) Dates # US (mm-dd-yyyy) Eur (dd-mm-yyyy) Number # separators US (1,000.00 ) Eur (1.000,00) Calculation # method Chn (chain) AOSé (algebraic operating system) Default 2 DEG US US Chn 1. To access format options, press & |. The DEC indicator appears with the selected number of decimal places. 2. To change the number of decimal places displayed, key in a value and press !. 3. To access another calculator format, press # or " once for each format. For example, to access the angle unit format, press #. To access the number-separator format, press " " " or # # #. 4. To change the selected format, press & V. 5. To change another calculator format, repeat step 3 and step 4. -- or -- To return to the standard-calculator mode, press & U. -- or -- To access a worksheet, press a worksheet key or key sequence. 4 Overview of Calculator Operations Choosing the Number of Decimal Places Displayed The calculator stores numeric values internally to an accuracy of 13 digits, but you can specify the number of decimal places you want to display. The calculator displays up to 10 digits with the floating-decimal option. Results exceeding 10 digits appear in scientific notation. Changing the number of decimal places affects the display only. Except for amortization and depreciation results, the calculator does not round internal values. To round the internal value, use the round function. Note: All examples in this guidebook assume a setting of two decimal places. Other settings might show different results. Choosing the Angle Units The angle unit value affects the display of results in trigonometric calculations. When you select radians, the RAD indicator appears in the upper right corner of the display. No indicator appears when you select the default setting of degrees. Using Dates The calculator uses dates with the Bond and Date worksheets and the French depreciation methods. To enter dates, use this convention: mm.ddyy (US) or dd.mmyy (European). After you key in the date, press !. Choosing Calculation Methods When you choose the chain (Chn) calculation method, the calculator solves problems in the order that you enter them. (Most financial calculators use Chn.) For example, when you enter 3 H 2 < 4 N, the Chn answer is 20 (3 + 2 = 5, 5 * 4 = 20). Using AOSTM (algebraic operating system), the calculator solves problems according to the standard rules of algebraic hierarchy, computing multiplication and division operations before addition and subtraction operations. (Most scientific calculators use AOS.) For example, when you enter 3 H 2 < 4 N, the AOS answer is 11 (2 Q 4 = 8; 3 + 8 = 11). Resetting Default Values To reset default values for all of the calculator formats, press & z with one of the formats displayed. Overview of Calculator Operations 5 Resetting the Calculator Resetting the calculator: · Clears the display, all 10 memories, any unfinished calculations, and all worksheet data. · Restores all default settings · Returns operation to the standard-calculator mode Because the calculator includes alternative methods that let you clear data selectively, use reset carefully to avoid losing data needlessly. (See section "Clearing Calculator Entries and Memories".) For example, you might reset the calculator before using it for the first time, when starting a new calculation, or when having difficulty operating the calculator and other possible solutions do not work. (See "In Case of Difficulty".) Pressing 2nd Reset ENTER 1. Press & }. The RST ? and ENTER indicators appear. Note: To cancel reset, press & U. 0.00 appears. 2. Press !. RST and 0.00 appear, confirming that the calculator is reset. Note: If an error condition exists, press P to clear the display before attempting to reset. Performing a Hard Reset You can also reset the calculator by gently inserting a pointed object (such as an unfolded paper clip or similar object) in the hole marked RESET in back of the calculator. Clearing Calculator Entries and Memories Note: To clear variables selectively, see the specific worksheet chapters in this guidebook. To clear One character at a time, starting with the last digit Press * 6 Overview of Calculator Operations To clear keyed in An incorrect entry, error condition, or error message The prompted worksheet and reset default values Calculator format settings and reset default values · Out of the prompted worksheet and return to standard-calculator mode · All pending operations in standard-calculator mode · In a prompted worksheet, the variable value keyed in but not entered (the previous value appears) · Any calculation started but not completed TVM worksheet variables and reset default values One of the 10 memories (without affecting the others) Press P &z &| &z &U PP &U &^ Q D and a memory number key (09) Correcting Entry Errors You can correct an entry without clearing a calculation, if you make the correction before pressing an operation key (for example, H or 4). · To clear the last digit displayed, press *. · To clear the entire number displayed, press P. Note: Pressing P after you press an operation key clears the calculation in progress. Example: You mean to calculate 3 Q 1234.56 but instead enter 1234.86. Overview of Calculator Operations 7 To Begin the expression Enter a number Erase the entry error Key in the correct number Compute the result Press 3< 1234.86 ** 56 N Display 3.00 1,234.86 1,234. 1,234.56 3,703.68 Math Operations When you select the chain (Chn) calculation method, the calculator evaluates mathematical expressions (for example, 3 + 2 Q 4) in the order that you enter them. Examples of Math Operations These operations require you to press N to complete. To Add 6 + 4 Subtract 6 N 4 Multiply 6 Q 4 Divide 6 P 4 Find universal power: 31.25 Use parentheses: 7 Q (3 + 5) Find percent: 4% of $453 Find percent ratio: 14 to 25 Find price with percent add-on: $498 + 7% sales tax Find price with percent discount: $69.99 N 10% Press 6H4N 6B4N 6<4N 664N 3 ; 1.25 N 7<93H5 :N 453 < 4 2 N 14 6 25 2 N 498 H 7 2 N 69.99 B 10 2 N Display 10.00 2.00 24.00 1.50 3.95 56.00 18.12 56.00 34.86 532.86 7.00 62.99 8 Overview of Calculator Operations To Square 6.32 Find number of combinations where: n = 52, r = 5 Find number of permutations where: n = 8, r = 3 Press 6.3 4 52 & s 5 N 8 &m3 N Display 39.69 2,598,960.00 336.00 These operations do not require you to press N to complete. To Press Find square root: 15.5 3 Find reciprocal: 1/3.2 Find factorial: 5! Find natural logarithm: ln 203.45 Find natural antilogarithm: e.69315 Round 2 P 3 to the set decimal format Generate random number* Store seed value Find sine:** sin(11.54°) Find cosine:** cos(120°) Find tangent:** tan(76°) Find arcsine:** sin-1(.2) Find arccosine:** cos-1(-.5) Find arctangent:** tan-1(4) Find hyperbolic sine: sinh(.5) Find hyperbolic cosine: cosh(.5) Find hyperbolic tangent: tanh(.5) Find hyperbolic arcsine: sinh-1(5) Find hyperbolic arccosine: cosh-1(5) 3.2 5 5& g 203.45 > .69315 & i 2 6 3 N &o &a D& a 11.54 & d 120 & e 76 & f .2 8 d .5 S 8 e 48f .5 & c d .5 & c e .5 & c f 5 &c8d 5 &c8e Display 3.94 0.31 120.00 5.32 2.00 0.67 0.86 0.86 0.20 -0.50 4.01 11.54 120.00 75.96 0.52 1.13 0.46 2.31 2.29 Overview of Calculator Operations 9 To Find hyperbolic arctangent: tanh-1(.5) Press .5 & c 8 f Display 0.55 * The random number you generate might be different. ** Angles can be computed in degrees or radians. Examples show angles in degrees. (See: Choosing the Angle Units). Universal Power ; Press ; to raise the displayed postive number to any power (for example, 2-5 or 2(1/3).) Note: Because the reciprocal of an even number (such as, 1/2, 1/4, 1/6) is a complex number, you can only raise a negative number to an integer power or the reciprocal of an odd number. Parentheses 9 : Use parentheses to control the order in which the calculator evaluates a numeric expression in division, multiplication, powers, roots, and logarithm calculations. The calculator includes up to 15 levels of parentheses and up to 8 pending operations. Note: You do not have to press : for expressions ending in a series of closed parentheses. Pressing N closes parentheses automatically, evaluates the expression, and displays the final result. To view intermediate results, press : once for each open parenthesis. Factorial & g The number for which you compute a factorial must be a positive integer less than or equal to 69. Random Numbers & a The calculator generates a random real number between zero and one (0<x<1) from a uniform distribution. You can repeat a sequence of random numbers by storing a seed value in the random number generator. Seed values help you recreate experiments by generating the same series of random numbers. To store a seed value, key in an integer greater than zero and press D & a. 10 Overview of Calculator Operations Combinations & s The calculator computes the number of combinations of n items taken r at a time. Both the n and r variables must be greater than 0. Permutations & m The calculator computes the number of permutations of n items taken r at a time. Both the n and r variables must be greater than 0. Rounding & o The calculator computes using the rounded, displayed form of a number instead of the internally stored value. For example, working in the Bond worksheet, you might want to round a computed selling price to the nearest penny (two decimal places) before continuing your calculation. Note: The calculator stores values to an accuracy of up to 13 digits. The decimal format setting rounds the displayed value but not the unrounded, internally stored value. (See "Choosing the Number of Decimal Places Displayed".) Overview of Calculator Operations 11 Scientific Notation ; When you compute a value in the standard-decimal format that is either too large or small to be displayed, the calculator displays it in scientific notation, that is, a base value (or mantissa), followed by a blank space, followed by an exponent. With AOS selected, you can press ; to enter a number in scientific notation. (See "Choosing Calculation Methods".) For example, to enter 3 Q 103, key in 3 < 10 ; 3. Memory Operations You can store values in any of 10 memories using the standard calculator keys. Note: You can also use the Memory worksheet. (See Memory Worksheet.) · You can store in memory any numeric value within the range of the calculator. · To access a memory M0 through M9, press a numeric key (0 through 9). Clearing Memory Clearing memory before you begin a new calculation is a critical step in avoiding errors. · To clear an individual memory, store a zero value in it. · To clear all 10 calculator memories, press & { & z. Storing to Memory To store a displayed value to memory, press D and a numeric key (09). · The displayed value replaces any previous value stored in the memory. · The Constant Memory feature retains all stored values when you turn off the calculator. Recalling From Memory To recall a number stored in memory, press J and a numeric key (09). Note: The recalled number remains in memory. 12 Overview of Calculator Operations Memory Examples To Clear memory 4 (by storing a zero value in it) Store 14.95 in memory 3 (M3) Recall a value from memory 7 (M7) Press 0 D4 14.95 D 3 J7 Memory Arithmetic Using memory arithmetic, you can perform a calculation with a stored value and store the result with a single operation. · Memory arithmetic changes only the value in the affected memory and not the displayed value. · Memory arithmetic does not complete any calculation in progress. The table lists the available memory arithmetic functions. In each case, the specified memory stores the result. To Press Add the displayed value to the value stored in memory 9 (M9). DH 9 Subtract the displayed value from the value stored in memory D B 3 (M3). 3 Multiply the value in memory 0 (M0) by the displayed value. D< 0 Divide the value in memory 5 (M5) by the displayed value. D6 5 Raise the value in memory 4 (M4) to the power of the displayed value. D; 4 Overview of Calculator Operations 13 Calculations Using Constants To store a constant for use in repetitive calculations, enter a number and an operation, and then press & `. To use the stored constant, key in a value and press N. Note: Pressing a key other than a number or N clears the constant. Example: Multiply 3, 7, and 45 by 8 To Clear the calculator Enter the value for the first calculation. Enter the operation and a constant value. Store the operation and value, and then calculate. Calculate 7 Q 8. Compute 45 Q 8. Press Display &U 0.00 3 3 <8 8 &` N 24.00 7N 56.00 45 N 360.00 Keystrokes for Constant Calculations This table shows how to create a constant for various operations. To* Press** Add c to each subsequent entry. nH&`cN Subtract c from each subsequent entry. nB&`cN Multiply each subsequent entry by c. n<&`cN Divide each subsequent entry by c. n6&`cN Raise each subsequent entry to the power of c. n;&`cN Add c% of each subsequent entry to that entry. nH&`c2N Subtract c% of each subsequent entry from the entry. nB&`c2N 14 Overview of Calculator Operations * The letter c denotes the constant value. ** Repeat constant calculations with n N. Last Answer Feature Use the Last Answer (ANS) feature with problems that call repeatedly for the same value or to copy a value: · From one place to another within the same worksheet. · From one worksheet to another. · From a worksheet to the standard-calculator mode. · From the standard-calculator mode to a worksheet. To display the last answer computed, press & x. Note: The calculator changes the value of the last answer whenever it calculates a value automatically or whenever you: · Press ! to enter a value. · Press C to compute a value. · Press N to complete a calculation. Example: Using the Last Answer in a Calculation To Key in and complete a calculation Key in a new calculation Recall the last answer Complete the calculation Press 3H1N 2; &x N Display 4.00 2.00 4.00 16.00 Overview of Calculator Operations 15 Using Worksheets: Tools for Financial Solutions The calculator contains worksheets with embedded formulas to solve specific problems. You apply settings or assign known values to worksheet variables and then compute the unknown value. Changing the values lets you ask what if questions and compare results. Except for TVM variables, accessed in the standard-calculator mode, all variables are prompted. For example, to assign values to amortization variables, you must first press & \ to access the Amortization worksheet. Each worksheet is independent of the others: operations in a worksheet do not affect variables in other worksheets. When you exit a worksheet or turn off the calculator, the calculator retains all worksheet data. To select Function Press TVM worksheet Analyzes equal cash flows, for example, annuities, loans, mortgages, leases, and savings ,, -, ., /, 0, or & [ Amortization worksheet Performs amortization calculations and generates an amortization schedule &\ Cash Flow worksheet Analyzes unequal cash flows by calculating net present value and internal rate of return &' Bond worksheet Computes bond price and yield to maturity or call &l Depreciation worksheet Generates a depreciation schedule using one of six depreciation methods &p Statistics worksheet Analyzes statistics on one- or two-variable data using four &k 16 Overview of Calculator Operations To select Percent Change/Compound Interest worksheet Interest Conversion worksheet Date worksheet Profit Margin worksheet Breakeven worksheet Memory worksheet Function Press regression analysis options Computes percent change, compound interest, and costsell markup &q Converts interest rates between nominal rate (or annual percentage rate) and annual effective rate &v Computes number of days between two dates, or date/day of the week a specified number of days is from a given date &u Computes cost, selling price, and profit margin &w Analyzes relationship between fixed cost, variable cost, price, profit, and quantity &r Accesses storage area for up to 10 values &{ Accessing the TVM Worksheet Variables · To assign values to the TVM worksheet variables, use the five TVM keys (,, -, ., /, 0). · To access other TVM worksheet functions, press the & key, and then press a TVM function key (xP/Y, P/Y, BGN). See: TVM and Amortization Worksheet Variables. Note: You can assign values to TVM variables while in a prompted worksheet, but you must return to the standard-calculator mode to calculate TVM values or clear the TVM worksheet. Overview of Calculator Operations 17 Accessing Prompted-Worksheet Variables After you access a worksheet, press # or " to select variables. For example, press & \ to access the Amortization worksheet, and then press # or " to select the amortization variables (P1, P2, BAL, PRN, INT). See: TVM and Amortization Worksheet Variables. Indicators prompt you to select settings, enter values, or compute results. For example, the # and " indicators remind you to press # or " to select other variables. To return to the standard-calculator mode, press & U. Types of Worksheet Variables · Enter-only · Compute-only · Automatic-compute · Enter-or-compute · Settings Note: The = sign displayed between the variable label and value indicates that the variable is assigned the value. Enter-Only Variables Values for enter-only variables must be entered, cannot be computed, and are often limited to a specified range, for example, P/Y and C/Y. The value for an enter-only variable can be: · Entered directly from the keyboard. · The result of a math calculation. · Recalled from memory. · Obtained from another worksheet using the last answer feature. When you access an enter-only variable, the calculator displays the variable label and ENTER indicator. The ENTER indicator reminds you to press ! after keying in a value to assign the value to the variable. After you press !, the 1 indicator confirms that the value is assigned. 18 Overview of Calculator Operations Compute-Only Variables You cannot enter values manually for compute-only variables, for example, net present value (NPV). To compute a value, display a compute-only variable and press C. The calculator computes and displays the value based on the values of other variables. When you display a compute-only variable, the COMPUTE indicator reminds you to press C to compute its value. After you press C, the 7 indicator confirms that the displayed value has been computed. Automatic-Compute Variables When you press # or " to display an automatic-compute variable (for example, the Amortization worksheet INT variable), the calculator computes and displays the value automatically without you having to press C. Enter-or-Compute Variables in the TVM Worksheet You can either enter or compute values for the TVM worksheet variables (N, I/Y, PV, PMT, and FV). Note: Although you do not have to be in the standard-calculator mode to assign values to these variables, you must be in the standard-calculator mode to compute their values. · To assign the value of a TVM variable, key in a number and press a variable key. · To compute the value of a TVM variable, press C, and then press the variable key. The calculator computes and displays the value based on the values of other variables. Enter-or-Compute Variables in Prompted Worksheets You can either enter or compute values for some prompted worksheet variables (for example, the Bond worksheet YLD and PRI variables). When you select an enter-or-compute variable, the calculator displays the variable label with the ENTER and COMPUTE indicators. · The ENTER indicator prompts you to press ! to assign the keyed-in value to the displayed variable. · The COMPUTE indicator prompts you to press C to compute a value for the variable. Overview of Calculator Operations 19 Selecting Worksheet Settings Many prompted worksheets contain variables consisting of two or more options, or settings (for example, the Date worksheet ACT/360 variable). When you select variables with settings, the calculator displays the SET indicator and the current setting. To scroll through the settings of a variable, press & V once for each setting. Display Indicators · The 1 indicator confirms that the calculator entered the displayed value in the worksheet. · The 7 indicator confirms that the calculator computed the displayed value. · When a change to the worksheet invalidates either entered or computed values, the 1 and 7 indicators disappear. 20 Overview of Calculator Operations Time-Value-of-Money and Amortization Worksheets Use the Time-Value-of-Money (TVM) variables to solve problems with equal and regular cash flows that are either all inflows or all outflows (for example, annuities, loans, mortgages, leases, and savings). For cash-flow problems with unequal cash flows, use the Cash Flow worksheet. (See: Cash Flow Worksheet.) After solving a TVM problem, you can use the Amortization worksheet to generate an amortization schedule. · To access a TVM variable, press a TVM key (,, -, ., /,or 0). · To access the prompted Amortization worksheet, press & \. TVM and Amortization Worksheet Variables Variable Key Number of periods , Interest rate per year - Present value . Payment / Future value 0 Number of payments per year Number of compounding periods per year &[ # Display N I/Y PV PMT FV P/Y Type of Variable Enter-orcompute Enter-orcompute Enter-orcompute Enter-orcompute Enter-orcompute Enter-only C/Y Enter-only Time-Value-of-Money and Amortization Worksheets 21 Variable End-of-period payments Beginning-of-period payments Starting payment Ending payment Balance Principal paid Interest paid Key &] Display END Type of Variable Setting & V BGN Setting & \ # # # # P1 P2 BAL PRN INT Enter-only Enter-only Auto-compute Auto-compute Auto-compute Note: This guidebook categorizes calculator variables by the method of entry. (See "Types of Worksheet Variables"). Using the TVM and Amortization Variables Because the calculator stores values assigned to the TVM variables until you clear or change them, you should not have to perform all steps each time you work a problem. · To assign a value to a TVM variable, key in a number and press a TVM key (,, -, ., /, 0). · To change the number of payments (P/Y), press & [, key in a number, and press !. To change the compounding periods (C/Y), press & [ #, key in a number, and press !. · To change the payment period (END/BGN), press & ], and then press & V. · To compute a value for the unknown variable, press C, and then press the key for the unknown variable. · To generate an amortization schedule, press & \, enter the first and last payment number in the range (P1 and P2), and press " or # to compute values for each variable (BAL, PRN, and INT). Resetting the TVM and Amortization Worksheet Variables · To reset all calculator variables and formats to default values (including TVM and amortization variables), press & } !: 22 Time-Value-of-Money and Amortization Worksheets Variable N I/Y PV PMT FV P/Y C/Y Default 0 0 0 0 0 1 1 Variable END/BGN P1 P2 BAL PRN INT Default END 1 1 0 0 0 · To reset only the TVM variables (N, I/Y, PV, PMT, FV) to default values, press & ^. · To reset P/Y and C/Y to default values, press & [ & z. · To reset the Amortization worksheet variables (P1, P2, BAL, PRN, INT) to default values, press & z while in the Amortization worksheet. · To reset END/BGN to the default value, press & ] & z. Clearing the Unused Variable For problems using only four of the five TVM variables, enter a value of zero for the unused variable. For example, to determine the present value (PV) of a known future value (FV) with a known interest rate (I/Y) and no payments, enter 0 and press PMT. Entering Positive and Negative Values for Outflows and Inflows Enter negative values for outflows (cash paid out) and positive values for inflows (cash received). Note: To enter a negative value, press S after entering the number. To change a negative value to positive, press S. Entering Values for I/Y, P/Y, and C/Y · Enter I/Y as the nominal interest rate. The TVM worksheet automatically converts I/Y to a per period rate based on the values of P/Y and C/Y. · Entering a value for P/Y automatically enters the same value for C/Y. (You can change C/Y.) Time-Value-of-Money and Amortization Worksheets 23 Specifying Payments Due With Annuities Use END/BGN to specify whether the transaction is an ordinary annuity or an annuity due. · Set END for ordinary annuities, in which payments occur at the end of each payment period. (This category includes most loans.) · Set BGN for annuities due, in which payments occur at the beginning of each payment period. (This category includes most leases.) Note: When you select beginning-of-period payments, the BGN indicator appears. (No indicator appears for END payments.) Updating P1 and P2 To update P1 and P2 for a next range of payments, press C with P1 or P2 displayed. Different Values for BAL and FV The computed value for BAL following a specified number of payments might be different than the computed value for FV following the same number of payments. · When solving for BAL, PRN, and INT, the calculator uses the PMT value rounded to the number of decimal places specified by the decimal format. · When solving for FV, the calculator uses the unrounded value for PMT. Entering, Recalling, and Computing TVM Values · To enter a TVM value, key in the value and store it by pressing a TVM key (,, -, ., /, 0). · To display a stored TVM value, press J and a TVM key. You can enter or recall a value for any of the five TVM variables (N, I/Y, PV, PMT, or FV) in either the standard calculator mode or a worksheet mode. The information displayed depends on which mode is selected. · In standard calculator mode, the calculator displays the variable label, the = sign, and the value entered or recalled. · In worksheet modes the calculator displays only the value you enter or recall, although any variable label previously displayed remains displayed. Note: You can tell that the displayed value is not assigned to the displayed variable, because the = indicator is not displayed. 24 Time-Value-of-Money and Amortization Worksheets To compute a TVM value, press C and a TVM key in standard-calculator mode. Using [xP/Y] to Calculate a Value for N 1. Key in the number of years, and then press & Z to multiply by the stored P/Y value. The total number of payments appears. 2. To assign the displayed value to N for a TVM calculation, press ,. Entering Cash Inflows and Outflows The calculator treats cash received (inflows) as a positive value and cash invested (outflows) as a negative value. · You must enter cash inflows as positive values and cash outflows as negative values. · The calculator displays computed inflows as positive values and computed outflows as negative values. Generating an Amortization Schedule The Amortization worksheet uses TVM values to compute an amortization schedule either manually or automatically. Generating an Amortization Schedule Manually 1. Press & \. The current P1 value appears. 2. To specify the first in a range of payments, key in a value for P1 and press !. 3. Press #. The current P2 value appears. 4. To specify the last payment in the range, key in a value for P2 and press !. 5. Press # to display each of the automatically computed values: · BAL -- the remaining balance after payment P2 · PRN -- the principal · INT -- the interest paid over the specified range 6. Press & \. -- or -- If INT is displayed, press # to display P1 again. Time-Value-of-Money and Amortization Worksheets 25 7. To generate the amortization schedule, repeat steps 2 through 5 for each range of payments. Generating an Amortization Schedule Automatically After entering the initial values for P1 and P2, you can compute an amortization schedule automatically. 1. Press & \. -- or -- If INT is displayed, press # to display the current P1 value. 2. Press C. Both P1 and P2 update automatically to represent the next range of payments. The calculator computes the next range of payments using the same number of periods used with the previous range of payments. For example, if the previous range was 1 through 12 (12 payments), pressing C updates the range to 13 through 24 (12 payments). 3. Press # to display P2. · If you press C with P1 displayed, a new value for P2 will be displayed automatically. (You can still enter a new value for P2.) · If you did not press C with P1 displayed, you can press C with P2 displayed to enter values for both P1 and P2 in the next range of payments. 4. Press # to display each of the automatically computed values for BAL, PRN, and INT in the next range of payments. 5. Repeat steps 1 through 4 until the schedule is complete. Example: Computing Basic Loan Interest If you make a monthly payment of $425.84 on a 30-year mortgage for $75,000, what is the interest rate on your mortgage? To Set payments per year to 12 Return to standard-calculator mode Enter number of payments Press & [ 12 ! &U 30 & Z , P/Y= N= Display 12.001 0.00 360.001 26 Time-Value-of-Money and Amortization Worksheets To using the payment multiplier Enter loan amount Enter payment amount Compute interest rate Press 75000 . 425.84 S / C- Display PV= PMT= I/Y= 75,000.00 1 -425.841 5.50 Answer: The interest rate is 5.5% per year. Examples: Computing Basic Loan Payments These examples show you how to compute basic loan payments on a $75,000 mortgage at 5.5% for 30 years. Note: After you complete the first example, you should not have to re-enter the values for loan amount and interest rate. The calculator saves the values you enter for later use. Computing Monthly Payments To Press Display Set payments per year to 12 & [ 12 ! P/Y= 12.001 Return to standard-calculator & U 0.00 mode Enter number of payments using payment multiplier 30 & Z , N= 360.001 Enter interest rate 5.5 - I/Y= 5.501 Enter loan amount 75000 . PV= 75,000.001 Compute payment C/ PMT= -425.847 Answer: The monthly payments are $425.84. Computing Quarterly Payments Note: The calculator automatically sets the number of compounding periods (C/Y) to equal the number of payment periods (P/Y). Time-Value-of-Money and Amortization Worksheets 27 To Set payments per year to 4 Return to standard-calculator mode Enter number of payments using payment multiplier Compute payment Press & [4 ! &U 30 & Z , C/ P/Y= Display 4.001 0.00 N= 120.001 PMT= -1,279.827 Answer: The quarterly payments are $1,279.82. Examples: Computing Value in Savings These examples show you how to compute the future and present values of a savings account paying 0.5% compounded at the end of each year with a 20year time frame. Computing Future Value Example: If you open the account with $5,000, how much will you have after 20 years? To Set all variables to defaults Enter number of payments Enter interest rate Enter beginning balance Compute future value Press & }! 20 , .5 5000 S . C0 Display RST 0.00 N= 20.001 I/Y= 0.501 PV= -5,000.001 FV= 5,524.487 Answer: The account will be worth $5,524.48 after 20 years. Computing Present Value Example: How much money must you deposit to have $10,000 in 20 years? To Press Display Enter final balance Compute present value 10000 0 C. FV= 10,000.001 PV= -9,050.637 28 Time-Value-of-Money and Amortization Worksheets Answer: You must deposit $9,050.63. Example: Computing Present Value in Annuities The Furros Company purchased equipment providing an annual savings of $20,000 over 10 years. Assuming an annual discount rate of 10%, what is the present value of the savings using an ordinary annuity and an annuity due? Cost Savings for a Present-Value Ordinary Annuity Cost Savings for a Present-Value Annuity Due in a Leasing Agreement To Set all variables to defaults Enter number of payments Enter interest rate per payment period Press & } ! RST 10 , N= 10 - I/Y= Display 0.00 10.001 10.001 Time-Value-of-Money and Amortization Worksheets 29 To Enter payment Compute present value (ordinary annuity) Set beginning-of-period payments Return to calculator mode Compute present value (annuity due) Press 20000 S / C. Display PMT= -20,000.001 PV= 122,891.347 & ] & V BGN &U C. PV= 0.00 135,180.487 Answer: The present value of the savings is $122,891.34 with an ordinary annuity and $135,180.48 with an annuity due. Example: Computing Perpetual Annuities To replace bricks in their highway system, the Land of Oz has issued perpetual bonds paying $110 per $1000 bond. What price should you pay for the bonds to earn 15% annually? To Calculate the present value for a perpetual ordinary annuity Calculate the present value for a perpetual annuity due Press 110 615 2 N H 110 N Display 733.33 843.33 Answer: You should pay $733.33 for a perpetual ordinary annuity and $843.33 for a perpetual annuity due. A perpetual annuity can be an ordinary annuity or an annuity due consisting of equal payments continuing indefinitely (for example, a preferred stock yielding a constant dollar dividend). 30 Time-Value-of-Money and Amortization Worksheets Perpetual ordinary annuity Perpetual annuity due Because the term (1 + I/Y / 100)-N in the present value annuity equations approaches zero as N increases, you can use these equations to solve for the present value of a perpetual annuity: · Perpetual ordinary annuity · Perpetual annuity due Example: Computing Present Value of Variable Cash Flows The ABC Company purchased a machine that will save these end-of-year amounts: Time-Value-of-Money and Amortization Worksheets 31 Year Amount 1 $5000 2 $7000 3 $8000 4 $10000 Given a 10% discount rate, does the present value of the cash flows exceed the original cost of $23,000? To Set all variables to defaults Enter interest rate per cash flow period Enter 1st cash flow Enter 1st cash flow period Compute present value of 1st cash flow Store in M1 Enter 2nd cash flow Enter 2nd cash flow period Compute present value of 2nd cash flow Sum to memory Enter 3rd cash flow. Enter period number. Compute present value of 3rd cash flow. Press &} ! 10 - 5000 S 0 1, C. D1 7000 S 0 2, C. DH1 8000 S 0 3, C. Display RST 0.00 I/Y= FV= N= PV= FV= N= PV= FV= N= PV= 10.001 -5,000.001 1.001 4,545.457 4,545.45 -7,000.001 2.001 5,785.127 5,785.12 -8,000.001 3.001 6,010.527 32 Time-Value-of-Money and Amortization Worksheets To Sum to memory. Enter 4th cash flow. Enter period number. Compute present value of 4th cash flow. Sum to memory. Recall total present value. Subtract original cost. Press Display DH1 6,010.52 10000 S 0 FV= -10,000.001 4, N= 4.001 C. PV= 6,830.137 DH1 J1 B 23000 N 6,830.13 23,171.23 171.23 Answer: The present value of the cash flows is $23,171.23, which exceeds the machine's cost by $171.23. This is a profitable investment. Note: Although variable cash flow payments are not equal (unlike annuity payments), you can solve for the present value by treating the cash flows as a series of compound interest payments. The present value of variable cash flows is the value of cash flows occurring at the end of each payment period discounted back to the beginning of the first cash flow period (time Example: Computing Present Value of a Lease With Residual Value The Peach Bright Company wants to purchase a machine currently leased from your company. You offer to sell it for the present value of the lease discounted at an annual interest rate of 22% compounded monthly. The machine has a residual value of $6500 with 46 monthly payments of $1200 remaining on the lease. If the payments are due at the beginning of each month, how much should you charge for the machine? Time-Value-of-Money and Amortization Worksheets 33 The total value of the machine is the present value of the residual value plus the present value of the lease payments. To Press Display Set all variables to defaults. & } ! RST 0.00 Set beginning-of-period payments. &]& V BGN Return to standard-calculator mode. &U 0.00 Enter number of payments. 46 , N= 46.001 Calculate and enter periodic interest rate. 22 6 12 N - I/Y= 1.831 Enter residual value of asset. 6500 S 0 FV= -6,500.001 Compute residual present value. C. PV= 2,818.227 Enter lease payment amount. 1200 S / PMT= -1,200.001 Compute present value of lease payments. C. PV= 40,573.187 Answer: Peach Bright should pay your company $40,573.18 for the machine. Example: Computing Other Monthly Payments If you finance the purchase of a new desk and chair for $525 at 20% APR compounded monthly for two years, how much is the monthly payment? 34 Time-Value-of-Money and Amortization Worksheets To Set all variables to defaults. Set payments per year to 12. Return to standard-calculator mode Enter number of payments using payment multiplier. Enter interest rate. Enter loan amount. Compute payment. Press & } ! RST & [ 12 ! P/Y= Display 0.00 12.001 &U 0.00 2 &Z , 20 525 . C/ N= I/Y= PV= PMT= 24.001 20.001 525.001 -26.727 Answer: Your monthly payment is $26.72. Example: Saving With Monthly Deposits Note: Accounts with payments made at the beginning of the period are referred to as annuity due accounts. Interest begins accumulating earlier and produces slightly higher yields. You invest $200 at the beginning of each month in a retirement plan. What will the account balance be at the end of 20 years, if the fund earns an annual interest of 7.5 % compounded monthly, assuming beginning-of-period payments? To Press Set all variables to defaults. &} ! Set payments per year to 12. & [ 12 ! Set beginning-of-period payments. &]& V Return to standard-calculator & U Display RST 0.00 P/Y= 12.001 BGN 0.00 Time-Value-of-Money and Amortization Worksheets 35 To mode. Enter number of payments using payment multiplier. Enter interest rate. Enter amount of payment. Compute future value. Press Display 20 & Z , N= 240.001 7.5 200 S / C0 I/Y= PMT= FV= 7.501 -200.001 111,438.31* Answer: Depositing $200 at the beginning of each month for 20 years results in a future amount of $111,438.31. Example: Computing Amount to Borrow and Down Payment You consider buying a car for $15,100. The finance company charges 7.5% APR compounded monthly on a 48-month loan. If you can afford a monthly payment of $325, how much can you borrow? How much do you need for a down payment? 36 Time-Value-of-Money and Amortization Worksheets To Set all variables to defaults. Set payments per year to 12. Return to standard-calculator mode Enter number of payments using payment multiplier. Enter interest rate. Enter payment. Compute loan amount. Compute down payment Press &}! & [ 12 ! &U 4 &Z , 7.5 325 S/ C. H 15,100 S N Display RST 0.00 P/Y= 12.001 0.00 N= 48.001 I/Y= 7.501 PMT= -325.001 PV= 13,441.47 * -1,658.53 Answer: You can borrow $13,441.47 with a down payment of $1,658.53. Example: Computing Regular Deposits for a Specified Future Amount You plan to open a savings account and deposit the same amount of money at the beginning of each month. In 10 years, you want to have $25,000 in the account. How much should you deposit if the annual interest rate is 0.5% with quarterly compounding? Note: Because C/Y (compounding periods per year) is automatically set to equal P/Y (payments per year), you must change the C/Y value. To Set all variables to defaults Set payments per year to 12. Press &} ! & [ 12 ! Display RST 0.00 P/Y= 12.001 Time-Value-of-Money and Amortization Worksheets 37 To Set compounding periods to 4. Set beginning-of-period payments. Return to standard-calculator mode. Enter number of deposits using payment multiplier. Enter interest rate. Enter future value. Compute deposit amount. Press #4! &]& V &U 10 & Z , .5 25,000 0 C/ C/Y= Display 4.001 BGN 0.00 N= 120.001 I/Y= FV= PMT= 0.501 25,000.001 -203.137 Answer: You must make monthly deposits of $203.13. Example: Computing Payments and Generating an Amortization Schedule This example shows you how to use the TVM and Amortization worksheets to calculate the monthly payments on a 30-year loan and generate an amortization schedule for the first three years of the loan. Computing Mortgage Payments Calculate the monthly payment with a loan amount of $120,000 and 6.125% APR. To Set all variables to defaults Set payments per year to 12 Return to standard-calculator mode Enter number of payments using payment multiplier Press &}! & [ 12 ! &U 30 & Z , RST P/Y= N= Display 0.00 12.001 0.00 360.001 38 Time-Value-of-Money and Amortization Worksheets Enter interest rate Enter loan amount Compute payment 6.125 120000 . C/ I/Y= PV= PMT= 6.131 120,000.001 -729.13* Answer: The computed monthly payment, or outflow, is $729.13. Generating an Amortization Schedule Generate an amortization schedule for the first three years of the loan. If the first payment is in April, the first year has nine payment periods. (Following years have 12 payment periods each.) To Press Display & Select the Amortization worksheet \ P1= current value Set beginning period to 1 1! P1= 1.00 Set ending period to 9 # 9 ! P2= 9.001 # Display 1st year amortization data # # BAL= PRN= INT= 118,928.63* -1071.37* -5,490.80* Change beginning period to 10 # 10 ! P1= 10.001 Change ending period to 21 # 21 ! P2= 21.001 # Display 2nd year amortization data # # BAL= PRN= INT= 117,421.60* -1,507.03* -7,242.53* Move to P1 and press C to enter # C next range of payments P1= 22.001 Display P2 # # Display 3rd year amortization data # # P2= BAL= PRN= INT= 33.001 115,819.62* -1601.98* -7,147.58* Time-Value-of-Money and Amortization Worksheets 39 Example: Computing Payment, Interest, and Loan Balance After a Specified Payment A group of sellers considers financing the sale price of a property for $82,000 at 7% annual interest, amortized over a 30-year term with a balloon payment due after five years. They want to know: · Amount of the monthly payment · Amount of interest they will receive · Remaining balance at the end of the term (balloon payment) Computing the Monthly Payment To Set all variables to defaults Set payments per year to 12 Press &}! & [ 12 ! RST P/Y= Display 0.00 12.001 Return to standard-calculator mode Enter number of payments using payment multiplier Enter interest rate Enter loan amount Compute payment &U 30 & Z , 782000 . C/ 0.00 N= 360.001 I/Y= PV= PMT= 7.001 82,000.001 -545.55* Generating an Amortization Schedule for Interest and Balloon Payment To Press Display Select Amortization worksheet & \ P1= 1.00 Enter end period (five years) #5& Z! P2= 60.001 View balance due after five # years (balloon payment) BAL= 77,187.72* 40 Time-Value-of-Money and Amortization Worksheets To View interest paid after five years Press ## INT= If the sellers financed the sale, they would receive: · Monthly payment: $545.55 for five years · Interest: $27,790.72 over the five years · Balloon payment: $77,187.72 Display -27,920.72* Time-Value-of-Money and Amortization Worksheets 41 Cash Flow Worksheet Use the Cash Flow worksheet to solve problems with unequal cash flows. To solve problems with equal cash flows, use the TVM worksheet. Time-Value-of-Money and Amortization Worksheets · To access the Cash Flow worksheet and initial cash flow value (CFo), press '. · To access the cash flow amount and frequency variables (Cnn/Fnn), press # or ". · To access the discount rate variable (I), press (. · To compute net present value (NPV), press # or " and C for each variable. · To compute the internal rate of return (IRR), press ). · To compute the modified internal rate of return (MOD), press # to access the reinvestment rate (RI) variable, key in a value, and press #. Cash Flow Worksheet Variables Variable Initial cash flow Amount of nth cash flow Frequency of nth cash flow Discount rate Net present value Internal rate of return Key ' # # ( #C ) Display CFo Cnn* Fnn* I NPV IRR Variable Type** Enter-only Enter-only Enter-only Enter-only Compute-only Compute-only * nn represents the cash flow (C01C24) or frequency (F01F24) number. 42 Cash Flow Worksheet Resetting Variables · To reset CFo, Cnn, and Fnn to default values, press ' and then & z. · To reset NPV to the default value, press ( and then & z. · To reset IRR to the default value, press ) and then & z. · To reset all calculator variables and formats to default values, including all Cash Flow worksheet variables, press & } !. Entering Cash Flows · You must enter an initial cash flow (CFo). The calculator accepts up to 24 additional cash flows (C01C24). Each cash flow can have a unique value. · Enter positive values for cash inflows (cash received) and negative values for cash outflows (cash paid out). To enter a negative value, key in a number and press S. Inserting and Deleting Cash Flows The calculator displays INS or DEL to confirm that you can press & X or & W to insert or delete cash flows. Uneven and Grouped Cash Flows Uneven Cash Flows The Cash Flow worksheet analyzes unequal cash flows over equal time periods. Cash-flow values can include both inflows (cash received) and outflows (cash paid out). Cash Flow Worksheet 43 All cash-flow problems start with an initial cash flow labeled CFo. CFo is always a known, entered value. Grouped Cash Flows Cash-flow problems can contain cash flows with unique values as well as consecutive cash flows of equal value. Although you must enter unequal cash flows separately, you can enter groups of consecutive, equal cash flows simultaneously using the Fnn variable. Entering Cash Flows Cash flows consist of an initial cash flow (CFo) and up to 24 additional cash flows (C01-C24), each of which can have a unique value. You must enter the number of occurrences (up to 9,999), or frequency (F), for each additional cash flow (C01-C24). · The calculator displays positive values for inflows (cash received) and negative values for outflows (cash paid out). · To clear the Cash Flow worksheet, press & z. To enter cash flows: 1. Press '. The initial cash-flow value (CFo) appears. 2. Key in a value for CFo and press !. 3. To select an additional cash-flow variable, press #. The C01 value appears. 4. To change C01, key in a value and press !. 5. To select the cash-flow frequency variable (F01), press #. The F01 value appears. 6. To change F01, key in a value and press !. 7. To select an additional cash-flow variable, press #. The C02 value appears. 8. Repeat steps 4 through 7 for all remaining cash flows and frequencies. 9. To review entries, press # or ". 44 Cash Flow Worksheet Deleting Cash Flows When you delete a cash flow, the calculator decreases the number of subsequent cash flows automatically. The DEL indicator confirms that you can delete a cash flow. 1. Press # or " until the cash flow you want to delete appears. 2. Press & W. The cash flow you specified and its frequency is deleted. Inserting Cash Flows When you insert a cash flow, the calculator increases the number of the following cash flows, up to the maximum of 24. Note: The INS indicator confirms that you can insert a cash flow. 1. Press # or " to select the cash flow where you want to insert the new one. For example, to insert a new second cash flow, select C02. 2. Press & X. 3. Key in the new cash flow and press !. The new cash flow is entered at C02. Cash Flow Worksheet 45 Computing Cash Flows The calculator solves for these cash-flow values: · Net present value (NPV) is the total present value of all cash flows, including inflows (cash received) and outflows (cash paid out). A positive NPV value indicates a profitable investment. · Internal rate of return (IRR) is the interest rate at which the net present value of the cash flows is equal to 0. Computing NPV 1. Press ( to display the current discount rate (I). 2. Key in a value and press !. 3. Press # to display the current net present value (NPV). 4. To compute the net present value for the series of cash flows entered, press C. Computing IRR 1. Press ). The IRR variable and current value are displayed (based on the current cash-flow values). 2. To compute the internal rate of return, press C. The calculator displays the IRR value. When solving for IRR, the calculator performs a series of complex, iterative calculations that can take seconds or even minutes to complete. The number of possible IRR solutions depends on the number of sign changes in your cashflow sequence. · When a sequence of cash flows has no sign changes, no IRR solution exists. The calculator displays Error 5. · When a sequence of cash flows has only one sign change, only one IRR solution exists, which the calculator displays. 46 Cash Flow Worksheet · When a sequence of cash flows has two or more sign changes: - At least one solution exists. - As many solutions can exist as there are sign changes. When more than one solution exists, the calculator displays the one closest to zero. Because the displayed solution has no financial meaning, you should use caution in making investment decisions based on an IRR computed for a cash-flow stream with more than one sign change. The time line reflects a sequence of cash flows with three sign changes, indicating that one, two, or three IRR solutions can exist. · When solving complex cash-flow problems, the calculator might not find , DPB, IRR, even if a solution exists. In this case, the calculator displays Error 7 (iteration limit exceeded). Example: Solving for Unequal Cash Flows These examples show you how to enter and edit unequal cash-flow data to calculate: · Net present value (NPV) · Internal rate of return (IRR) A company pays $7,000 for a new machine, plans a 20% annual return on the investment, and expects these annual cash flows over the next six years: Cash Flow Worksheet 47 Year Cash Flow Number Purchase CFo 1 C01 25 C02 6 C03 Cash Flow Estimate -$7,000 3,000 5,000 each year 4,000 As the time line shows, the cash flows are a combination of equal and unequal values. As an outflow, the initial cash flow (CFo) appears as a negative value. Entering Cash-Flow Data To Press Select Cash Flow worksheet. ' Enter initial cash flow. 7000 S! Display CFo= 0.00 -7,000.001 CFo= Enter cash flow for first year. # 3000 ! # Enter cash flows for years two through five. # 5000 ! #4! Enter cash flow for sixth year. # 4000 ! # C01= F01= C02= F02= C03= F03= 3,000.001 1.001 5,000.001 4.001 4,000.001 1.001 Editing Cash-Flow Data After entering the cash-flow data, you learn that the $4,000 cash-flow value should occur in the second year instead of the sixth. To edit, delete the $4,000 value for year 6 and insert it for year 2. 48 Cash Flow Worksheet To Move to third cash flow. Delete third cash flow. Move to second cash flow. Insert new second cash flow. Move to next cash flow to verify data. Press " &W "" & X 4000 ! # # # Display 4,000.00 C03= 1 C03= 0.00 5,000.00 C02= 1 C02= F02= 4,000.00 1 1.001 C03= F03= 5,000.00 1 4.01 Computing NPV Use an interest rate per period (I) of 20%. To Press Access interest rate variable ( Enter interest rate per period. 20 ! Compute net present value. # C Display I= 0.00 I= 20.001 7,266.447 NPV= Answers: NPV is $7,266.44. Computing IRR To Access IRR. Compute internal rate of return. Answer: IRR is 52.71%. is 35.12%. Press ) #C Display IRR= 0.00 IRR= 52.717 Cash Flow Worksheet 49 Example: Value of a Lease with Uneven Payments A lease with an uneven payment schedule usually accommodates seasonal or other anticipated fluctuations in the lessee's cash position. A 36-month lease has the following payment schedule and beginning-ofperiod payments. Number of Months 4 8 3 9 2 10 Payment Amount $0 $5000 $0 $6000 $0 $7000 If the required earnings rate is 10% per 12-month period with monthly compounding: · What is the present value of these lease payments? · What even payment amount at the beginning of each month would result in the same present value? Because the cash flows are uneven, use the Cash Flow worksheet to determine the net present value of the lease. Computing NPV The cash flows for the first four months are stated as a group of four $0 cash flows. Because the lease specifies beginning-of-period payments, you must treat the first cash flow in this group as the initial investment (CFo) and enter the remaining three cash flows on the cash flow screens (C01 and F01). Note: The BGN/END setting in the TVM worksheet does not affect the Cash Flow worksheet. 50 Cash Flow Worksheet To Press Display Set all variables to defaults. Select Cash Flow worksheet. Enter first group of cash flows. Enter second group of cash flows. &}! ' # #3! # 5000 S !#8 ! RST CFo= C01= F01= C02= F02= 0.00 0.00 0.001 3.001 -5000.00 1 8.001 Enter third group of cash flows. Enter fourth group of cash flows. # #3! # 6000 S !#9 ! C03= F03= C04= F04= 0.00 1 3.001 -6000.001 9.001 Enter fifth group of cash flows. Enter sixth group of cash flows. Select NPV. Enter monthly earnings rate. # #2! # 7000 S ! # 10 ! ( 10 6 12 ! C05= F05= C06= F06= I= I= 0.001 2.00 1 -7000.001 10.001 0.00 0.831 Compute NPV. #C NPV= 138,088.447 Cash Flow Worksheet 51 Bond Worksheet The Bond worksheet lets you compute bond price, yield to maturity or call, and accrued interest. You can also use the date functions to price bonds purchased on dates other than the coupon anniversary. · To access the Bond worksheet, press & l. · To access bond variables, press "or #. · To change the options for day-count methods (ACT and 360) and coupons per year (2/Y and 1/Y), press & V once for each option. Note: Pressing # or " to navigate through the Bond worksheet before you enter values causes an error (Error 6). To clear the error, press P. Bond Worksheet Variables Variable Key Settlement date & l Annual coupon rate in percent # Redemption date # Redemption value (percentage # of par value) Actual/actual day-count # method 30/360 day-count method &V Two coupons per year # One coupon per year &V Yield to redemption # Dollar price # Display SDT CPN RDT RV ACT 360 2/Y 1/Y YLD PRI Variable Type Enter only Enter only Enter only Enter only Setting Setting Setting Setting Enter/compute Enter/compute 52 Bond Worksheet Variable Accrued interest Key Display Variable Type # AI Auto-compute Resetting Bond Worksheet Variables · To reset the Bond worksheet variables to default values, press & z while in the Bond worksheet. Variable Default Variable Default SDT 12-31-1990 ACT/360 ACT CPN 0 2/Y, 1/Y 2/Y RDT 12-31-1990 YLD 0 RV 100 PRI 0 · To reset all calculator variables and formats to default values, including the Bond worksheet variables, press & } !. Entering Dates · Use the following convention to key in dates: mm.ddyy or dd.mmyy. After keying in the date, press !. Note: You can display dates in either US or European format. Setting Calculator Formats · You can enter dates from January 1, 1980 through December 31, 2079. · The calculator assumes that the redemption date (RDT) coincides with a coupon date: · To compute to maturity, enter the maturity date for RDT. · To compute to call, enter the call date for RDT. Entering CPN CPN represents the annual coupon rate as a percentage of the bond par value rather than the dollar amount of the coupon payment. Entering RV The redemption value (RV) is a percentage of the bond par value: · For to maturity analysis, enter 100 for RV. Bond Worksheet 53 · For to call analysis, enter the call price for RV. Setting the Day-Count Method 1. To display the day-count method, press # until ACT or 360 appears. 2. To change the day-count method, press & V. Setting the Coupon Frequency 1. To display the coupon frequency, press # until 1/Y or 2/Y appears. 2. To change the coupon frequency, press & V. Bond Worksheet Terminology Term Definition Call Date A callable bond bond can be retired by the issuing agency before the maturity date. The call date for such a bond is printed in the bond contract. The periodic payment made to the owner of the bond Coupon Payment as interest. Coupon Rate The annual interest rate printed on the bond. Dollar Price Price of the security expressed in terms of dollars per $100 of par value. Par (Face) Value The value printed on the bond. Premium Bond A bond that sells for an amount greater than the par value. Discount Bond A bond selling for less than the par value. Redemption Date The date on which the issuing agency retires the bond. This date can be the date of maturity or, for a callable bond, the call date. Redemption Value The amount paid to the owner of a bond when retired. If the bond is redeemed at the maturity date, the redemption value is the par value printed on the bond. If the bond is redeemed at a call date, the redemption value is the bond's par value plus any 54 Bond Worksheet Term Settlement Date Yield to Maturity Definition call premium. The calculator treats the redemption value in terms of dollars per $100 of par value. The date on which a bond is exchanged for funds. The rate of return earned from payments of principal and interest, with interest compounded semiannually at the stated yield rate. The yield to maturity takes into account the amount of premium or discount, if any, and the time value of the investment. Entering Bond Data and Computing Results To compute values for price (PRI) or yield (YLD) and accrued interest (AI), first enter the four known values for settlement date (SDT), coupon rate (CPN), redemption date (RDT), and redemption value (RV). If necessary, change the day-count method (ACT or 360) and couponfrequency (2/Y or 1/Y). The Bond worksheet stores all values and settings until you clear the worksheet or change the values and settings. Entering Known Bond Values 1. Press & l. The current SDT value appears. 2. To clear the worksheet, press & z. 3. If necessary, key in a new SDT value and press !. 4. Repeat step 3 for CPN, RDT, and RV, pressing # once for each variable. Note: To enter dates, use this convention: mm.ddyy (US) or dd.mmyy (European). Setting the Bond Day-Count Method and Coupon Frequency 1. To display the day-count method, press # until ACT or 360 appears. 2. To change the day-count method, press & V. 3. To display the coupon frequency, press # until 2/Y or 1/Y appears. 4. To change the coupon frequency, press & V. Computing the Bond Price (PRI) 1. Press # until YLD appears. Bond Worksheet 55 2. Key in a value for YLD and press !. 3. Press # to display PRI, and then press C. The calculator displays the computed PRI value. Computing the Bond Yield (YLD) 1. Press # until PRI appears. 2. Key in a value for PRI and press !. 3. Press # to display YLD, and then press C. The calculator displays the computed YLD value. Computing Accrued Interest (AI) To compute accrued interest, press # until the AI variable appears. The calculator automatically computes AI in terms of dollars per $100 of par value. Example: Computing Bond Price and Accrued Interest You consider buying a semiannual corporate bond maturing on December 31, 2005 and settling on June 12, 2004. The bond is based on the 30/360 daycount method with a coupon rate of 7%, redeemable at 100% of par value. For an 8% yield to maturity, compute the bond's price and accrued interest. Computing Bond Price and Accrued Interest To Select Bond worksheet. Enter settlement date. Enter coupon rate. Enter redemption date. Press &l 6.1206 ! #7! # 12.3107 ! Display SDT = SDT = CPN = RDT = 12-31-19901 6-12-20061 7.001 12-31-20071 Leave redemption value as is. Select 30/360 day-count method. Leave two coupon payments per year. # #&V # RV = 360 2/Y 100.00 56 Bond Worksheet To Enter yield. Compute price View accrued interest. Press #8! #C # Display YLD = PRI = AI = 8.001 98.567 3.157 Answer: The bond price is $98.56 per 100. The accrued interest is $3.15 per 100. Bond Worksheet 57 Depreciation Worksheet The Depreciation worksheet lets you generate a depreciation schedule using your choice of depreciation methods. · To access the Depreciation worksheet, press & p. · To change depreciation methods, press & V until the desired method appears. · To access other depreciation variables, press # or ". Note: To easily scroll up or down through a range of variables, press and hold # or ". Depreciation Worksheet Variables Variable Key Straight-line method Sum-of-the-years'-digits method Declining-balance method Declining-balance method with crossover to SL method French straight-line method* French declining balance method* Life of the asset in years Starting month Starting date for French straight-line method** &p &V &V &V &V &V # # # Display SL SYD DB DBX SLF DBF LIF M01 DT1 Variable Type** Setting Setting Setting/Enter Setting/Enter Setting/Enter Setting/Enter Enter only Enter only Enter only 58 Depreciation Worksheet Variable Key Cost of the asset # Salvage value of the asset # Year to compute # Depreciation for the year # Remaining book value at the # end of the year Remaining depreciable # value Display CST SAL YR DEP Variable Type** Enter only Enter only Enter only Auto-compute RBV Auto-compute RDV Auto-compute * SLF and DBF are available only if you select the European format for dates or separators in numbers. Setting Calculator Formats ** This guidebook categorizes variables by their method of entry. Types of Worksheet Variables Resetting the Depreciation Worksheet Variables · To reset all calculator variables and formats to default values, including the Depreciation worksheet variables, press & } !. Variable Depreciation method DB DBX LIF Default SL 200 200 1 Variable M01 YR CST SAL Default 1 1 0 0 · To clear only the LIF, YR, CST, and SAL Depreciation worksheet variables and reset default values without affecting the depreciation method or other calculator variables and formats, press & z while in the Depreciation worksheet. Computing Values for DEP, RBV, and RDV · The calculator computes one year at a time and rounds the results to the number of decimal places set. Setting Calculator Formats Depreciation Worksheet 59 · The calculator computes values for DEP, RBV, and RDV automatically when you press # to display each variable. Entering Values for DB and DBX If you choose either the declining balance (DB) or declining balance with crossover to SL (DBX) depreciation method, remember to enter a value representing the percent of declining balance for the DB or DBX variable. Note: The declining balance you enter must be a positive number. Entering Values for LIF · If SL or SLF is selected, the LIF value must be a positive real number. · If SYD, DB, DBX, or DBF is selected, the LIF value must be a positive integer. Entering Values for M01 The value you enter for the starting month (M01) has two parts: · The integer portion represents the month in which the asset is placed into service. · The decimal portion represents the fraction of the initial month in which the asset begins to depreciate. For example, to specify that the asset will begin to depreciate in the middle of the first month, enter 1.5. To specify that the asset will begin to depreciate a quarter of the way through the fourth month, enter 4.25. Working with YR · When computing depreciation, the value you enter for the year-to-compute (YR) variable must be a positive integer. · If the remaining depreciable value (RDV) variable is displayed, you can press # to return to the year to compute (YR) variable. To represent the next depreciation year, press C to increment the value for YR by one. · To compute a depreciation schedule, repeatedly return to the year to compute (YR) variable, press C to increment the value for YR, and compute values for DEP, RBV, and RDV. The schedule is complete when RDV equals zero. 60 Depreciation Worksheet Entering Data and Computing Results Because the Depreciation worksheet stores values and settings until you either change them or clear the worksheet, you should not have to perform every step each time you work a problem. Selecting a Depreciation Method 1. To access the Depreciation worksheet, press & p. The current depreciation method is displayed. 2. To clear the worksheet, press & z. 3. Press & V until you display the depreciation method you want (SL, SLF, SYD, DB, DBX, or DBF). Note: If you select DB or DBX, you must either key in a value or accept the default of 200. Entering Depreciation Data 1. To display LIF, press #. 2. Key in a value for LIF and press !. 3. Repeat steps 1 and 2 for M01, DT1 (if SLF), CST, SAL, and YR. Note: To select SLF or DBF, you must set either the European date or European separator format first. Setting Calculator Formats Computing Results for DEP, RBV, and RDV After entering the data, press # once for each of the DEP, RBV, and RDV variables to display the computed values. Note: The 7 _ indicator confirms that the displayed value is computed. Generating a Depreciation Schedule To generate a depreciation schedule and compute values for other years: 1. To display YR, press #. 2. To increment the value by one, press C. 3. To compute new values for DEP, RBV, and RDV, press # for each variable. Depreciation Worksheet 61 Example: Computing Straight-Line Depreciation In mid-March, a company begins depreciation of a commercial building with a 31½ year life and no salvage value. The building cost $1,000,000. Use the straight-line depreciation method to compute the depreciation expense, remaining book value, and remaining depreciable value for the first two years. To Access Depreciation worksheet Press &p Display SL Enter life in years # 31.5 ! LIF = 31.501 Enter starting month # 3.5 ! M01 = 3.501 Enter cost Leave salvage value as is Leave year as is Display depreciation amount, remaining book value, and remaining depreciable value # 1000000 ! # # # # # CST = 1,000,000.001 SAL = YR = 0.00 1.00 DEP = RBV = RDV = 25,132.28* 974,867.72* 974,867.72* View second year #&! YR = YR = 1.00 2.001 # Display second year # depreciation data # DEP = RBV = RDV = 31,746.03* 943,121.69* 943,121.69* Answer: For the first year, the depreciation amount is $25,132.28, the remaining book value is $974,867.72, and the remaining depreciable value is $974,867.72. For the second year, the depreciation amount is $31,746.03, the remaining book value is $943,121.69, and the remaining depreciable value is $943,121.69. 62 Depreciation Worksheet Statistics Worksheet The Statistics worksheet performs analysis on one-and two-variable data with four regression analysis models. · To enter statistical data, press & j. · To choose a statistics calculation method and compute the results, press & k. · To access statistics variables, press # or ". Statistics Worksheet Variables Variable Key Current X value Current Y value Standard linear regression Logarithmic regression Exponential regression Power regression One-variable statistics Number of observations Mean (average) of X values Sample standard deviation of X Population standard deviation of X Mean (average) of Y values Sample standard deviation of Y Population standard deviation of Y Linear regression y-intercept Linear regression slope Correlation coefficient &j # &k &V # (as needed) Display Xnn* Ynn* LIN Ln EXP PWR 1-V n v Sx sx y** Sy** sy** a** b** r** X'** Y'** GX GX2 Variable Type Enter-only Enter-only Setting Setting Setting Setting Setting Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Enter/compute Enter/compute Auto-compute Auto-compute Statistics Worksheet 63 Variable Predicted X value Predicted Y value Sum of X values Sum of X squared values Sum of Y values Sum of Y squared values Sum of XY products Key Display Variable Type GY** GY2** GXY** Auto-compute Auto-compute Auto-compute * nn represents the number of the current X or Y value. ** Not displayed for one-variable statistics. *** This guidebook categorizes calculator variables by their method of entry. Types of Worksheet Variables Resetting Statistics Worksheet Variables · To clear all X and Y values as well as all values in the statistics portion of the worksheet without affecting the statistics calculation method, press & z while in the data-entry portion of the worksheet (& j). · To reset the statistics calculation method to LIN and clear all values except X and Y, press & z while in the calculation method and computation portion of the worksheet (& k). · To reset the statistics calculation method to LIN and clear all values, including X and Y, press & } !. Entering Data Points · You can enter up to 50 (x,y) data points. · If you press # or " to move through the portion of the worksheet that displays results without entering data points, the calculator will display an error. · When you enter data for one-variable statistics, Xnn represents the value and Ynn specifies the number of occurrences (frequency). · When you enter a value for Xnn, the value for Ynn defaults to 1. Analyzing One-Variable Statistics To analyze one-variable statistics, select 1-V. Only values for n, v, Sx, sX, GX, and GX2 are computed and displayed for one-variable statistics. 64 Statistics Worksheet Analyzing Two-Variable Statistics You can choose from among these four regression-analysis methods: · LIN · Ln · EXP · PWR Computing Values Automatically Except for the predicted X' and Y' values, the calculator computes and displays values for statistics variables automatically when you access them. Using X' and Y' for Regression Predictions To use the X' and Y' variables for regression predictions, you either can enter a value for X' to compute Y' or enter a value for Y' to compute X'. Regression Models For two-variable data, the Statistics worksheet uses four regression models for curve fitting and forecasting. Model Formula Restrictions LIN Y=a+bX None Ln Y = a + b ln(X) All X values > zero EXP PWR Y = a bx Y = a Xb All Y values > zero All X and Y values > zero The calculator interprets the X value as the independent variable and the Y value as the dependent variable. The calculator computes the statistical results using these transformed values: · LIN uses X and Y. · Ln uses ln(X) and Y. · EXP uses X and ln(Y). · PWR uses ln(X) and ln(Y). The calculator determines the values for a and b that create the line or curve that best fits the data. Statistics Worksheet 65 Correlation Coefficient The calculator also determines r, the correlation coefficient, which measures the goodness of fit of the equation with the data. Generally: · The closer r is to 1 or -1, the better the fit. · The closer r is to zero, the worse the fit. Entering Statistical Data Because the Statistics worksheet lets you enter and display up to 50 data points, and then stores the values until you clear the worksheet or change the values, you probably will not have to perform every step for each Statistics calculation. 1. To select the data-entry portion of the Statistics worksheet, press & j. X01 is displayed along with any previous value. 2. To clear the worksheet, press & z. 3. Key in a value for X01 and press !. · For one-variable data, X01 is the first data point. · For two-variable data, X01 is the first X value. 4. To display the Y01 variable, press #. 5. Key in a value for Y01 and press !. · For one-variable data, you can enter the number of times the X value occurs (frequency). The default value is 1. · For two-variable data, enter the first Y value. 6. To display the next X variable, press #. 7. Repeat steps 3 through 5 until you enter all of the data points. Note: To easily scroll up or down through a range of variables, press and hold # or ". Computing Statistical Results Selecting a Statistics Calculation Method 1. Press & k to select the statistical calculation portion of the Statistics worksheet. 66 Statistics Worksheet 2. The last selected statistics calculation method is displayed (LIN, Ln, EXP, PWR, or 1-V). 3. Press & V repeatedly until the statistics calculation method you want is displayed. 4. If you are analyzing one-variable data, select 1-V. 5. Press # to begin computing results. Computing Results To compute results based on the current data set, press # repeatedly after you have selected the statistics calculation method. The calculator computes and displays the results of the statistical calculations (except for X' and Y') automatically when you access them. For one-variable statistics, the calculator computes and displays only the values for n, v, Sx, sX, GX, and GX2. Computing Y' 1. To select the Statistics worksheet, press & k. 2. Press " or # until X' is displayed. 3. Key in a value for X' and press !. 4. Press # to display the Y' variable. 5. Press C to compute a predicted Y' value. Computing X' 1. To select the Statistics worksheet, press & k. 2. Press " or # until Y' is displayed. 3. Key in a value for Y' and press !. 4. Press " to display the X' variable. 5. Press C to compute an X' value. Statistics Worksheet 67 Other Worksheets The calculator also includes these worksheets: · Percent Change/Compound Interest worksheet (& q) · Interest Conversion worksheet (& v) · Date worksheet (& u) · Profit Margin worksheet (& w) · Breakeven worksheet (& r) · Memory worksheet (& {) Percent Change/Compound Interest Worksheet Use the Percent Change/Compound Interest worksheet to solve percent change, compound interest, and costsell-markup problems. · To access the Percent Change/Compound Interest worksheet, press & q. · To access the Percent Change/Compound Interest variables, press # or ". Percent Change/Compound Interest Worksheet Variables Variable Key Display Variable Type Old value/Cost New value/Selling price &q # OLD NEW Enter/compute Enter/compute Percent change/Percent # markup Number of periods # %CH #PD Enter/compute Enter/compute Note: This guidebook categorizes variables by their method of entry. 68 Other Worksheets Resetting the Percent Change/Compound Interest Worksheet Variables · To reset the Percent Change/Compound Interest variables to default values, press & z while in the Percent Change/Compound Interest worksheet. Variable Default Variable Default OLD 0 %CH 0 NEW 0 #PD 0 · To reset default values for all calculator variables and formats, press & } !. Entering Values · For percent-change calculations, enter values for any two of the three variables (OLD, NEW, and %CH) and compute a value for the unknown variable (leave #PD=1). A positive percent change represents a percentage increase; a negative percent change represents a percentage decrease. · For compound-interest calculations, enter values for the three known variables and compute a value for the unknown fourth variable. · OLD = present value · NEW = future value · %CH = interest rate per period · #PD = number of periods · For cost-sell-markup calculations, enter values for two of the three variables (OLD, NEW, and %CH) and compute a value for the unknown. · OLD = cost · NEW = selling price · %CH = percent markup · #PD = 1 Computing Values 1. To select the Percent Change/Compound Interest worksheet, press & q. The current value for OLD is displayed. Other Worksheets 69 2. To clear the worksheet, press & z. 3. To enter values for the known variables, press # or " until the variable you want is displayed, then key in a value, and press !. (Do not enter a value for the variable you wish to solve.) · Percent Change -- Enter values for two of these three variables: OLD, NEW, and %CH. Leave #PD set to 1. · Compound Interest -- Enter values for three of these four variables: OLD, NEW, %CH, and #PD. · Cost-Sell-Markup -- Enter values for two of these three variables: OLD, NEW, and %CH. Leave #PD set to 1. 4. To compute a value for the unknown variable, press # or " until the variable you want is displayed and press C. The calculator displays the value. Example: Computing Percent Change First, determine the percentage change from a forecast amount of $658 to an actual amount of $700. Second, determine what the new amount would be if it were 7% below the original forecast. To Press Display Select Percent Change/Compound Interest worksheet &q OLD= Current value Enter original forecast amount 658 ! OLD= 658.001 Enter actual amount # 700 ! NEW= 700.001 Compute percent change #C %CH= 6.387 Enter -7 as percent change 7 S ! %CH= -7.001 Compute new actual amount "C NEW= 611.947 Answer: $700 represents a 6.38% increase over the original forecast of $658. A decrease of 7% would result in a new actual amount of $611.94. 70 Other Worksheets Example: Computing Compound Interest You purchased stock in 1995 for $500. Five years later, you sell the stock for $750. What was the annual growth rate? To Select Percent Change/Compound Interest worksheet Press &q Display OLD= Current value Enter stock purchase price 500 ! OLD= 500.001 Enter stock selling price # 750 ! NEW= 750.001 Enter number of years # #5 ! #PD= 5.001 Compute annual growth rate " C %CH= 8.457 Answer: The annual growth rate is 8.45%. Example: Computing Cost-Sell-Markup The original cost of an item is $100; the selling price is $125. Find the markup. To Select Percent Change/ Compound Interest worksheet Clear worksheet variables Press &q & z Display OLD= Current value OLD= 0.00 Enter original cost 100 ! OLD= 100.001 Enter selling price Compute percent markup # 125 ! #C NEW= %CH= 125.001 25.007 Answer: The markup is 25%. Other Worksheets 71 Interest Conversion Worksheet The Interest Conversion worksheet converts interest rates between nominal rate (or annual percentage rate) and annual effective rate. · To access the Interest Conversion worksheet, press & v. · To select interest conversion variables, press # or ". Interest Conversion Variables Variable Key Display Variable Type Nominal rate Annual effective rate & v NOM # EFF Enter/compute Enter/compute Compounding periods per # year C/Y Enter-only Note: The calculator categorizes variables by their method of entry. Comparing the Nominal Interest Rate of Investments Comparing the nominal interest rate (annual percentage rate) of investments is misleading when the investments have the same nominal rate but different numbers of compounding periods per year. To make a more valid comparison, convert the nominal interest rate (NOM) to the annual effective interest rate (EFF) for each investment. · The nominal interest rate (NOM) is the interest rate per compounding period multiplied by the number of compounding periods per year. · The annual effective interest rate (EFF) is the compound annual interest rate that you actually earn for the period of time stated. Resetting Variables · To reset all calculator variables and formats to default values, including the Interest Conversion worksheet variables, press & } !. 72 Other Worksheets Variable NOM EFF C/Y Default 0 0 1 · To clear the NOM and EFF variables and reset default values without affecting C/Y, press & z in the Interest Conversion worksheet. Converting Variables You can convert a nominal rate to an annual effective rate or vice versa. Entering Values for Nom and EFF Enter a value for NOM or EFF as an annual rate. Converting Interest Rates 1. To access the Interest Conversion worksheet, press & v. The current NOM value appears. 2. To clear the worksheet, press & z. 3. Enter a value for the known interest rate (either NOM or EFF). 4. To enter a value for a known variable, press # or " until NOM or EFF is displayed, key in a value, and press !. 5. Press # to display C/Y. If necessary, change the value and press !. 6. To compute a value for the unknown variable (interest rate), press # or " until NOM or EFF is displayed, and then press C. The calculator displays the computed value. Example: A bank offers a certificate that pays a nominal interest rate of 15% with quarterly compounding. What is the annual effective interest rate? To Press Display Select Interest Conversion worksheet. &v NOM= Current value Enter nominal interest rate. 15 ! NOM= 15.001 Enter number of compounding periods per year. ##4 ! C/Y= 4.001 Other Worksheets 73 To Compute annual effective interest rate. Press "C Display EFF= 15.877 Answer: A nominal interest rate of 15% compounded quarterly is equivalent to an annual effective interest rate of 15.87%. Date Worksheet Use the Date worksheet to find the number of days between two dates. You can also compute a date and day of the week based on a starting date and a specified number of days. · To access the Date worksheet, press & u. · To access the date variables, press # or ". · To select the day-count method (ACT and 360), press & V once for each option. Date Worksheet Variables Variable Date 1 Date 2 Days between dates Actual/actual day-count method 30/360 day-count method Key & u # # # # Display Variable Type DT1 Enter/compute DT2 DBD ACT* 360* Enter/compute Enter/compute Setting Setting Note: The calculator categorizes variables by their method of entry. Types of Worksheet Variables Resetting the Date Worksheet Variables · To reset default values for all calculator variables and formats, including the Date worksheet variables, press & } !. 74 Other Worksheets Variable DT1 DT2 Default 12-31-1990 12-31-1990 Variable DBD Day-count method Default 0 ACT · To clear Date worksheet variables and reset default values without affecting the day-count method, press & z while in the Date worksheet. Entering Dates · The calculator assumes that DT1 is earlier than DT2. · Enter dates for DT1 and DT2 in the selected US or European date format. · When you compute a date for DT1 or DT2, the calculator displays a three- letter abbreviation for the day of the week (for example, WED). Selecting the Day-Count Method Affects Calculations · When you select ACT as the day-count method, the calculator uses the actual number of days in each month and each year, including adjustments for leap years. · When you select 360 as the day-count method, the calculator assumes 30 days per month (360 days per year). You can compute DBD using this daycount method, but not DT1 or DT2. Computing Dates 1. To select the Date worksheet, press & u. The DT1 value is displayed. 2. To clear the worksheet, press & z. 3. Enter values for two of the three variables: DT1, DT2, and DBD. Note: Do not enter a value for the variable you wish to solve for. 4. To enter a value for a variable, press # or " to display the variable. 5. Key in a value and press !. 6. To change the day-count method setting, press # until ACT or 360 is displayed, and then press & V to select the other day-count method. 7. To compute a value for the unknown variable, press # or " to display the variable, and then press C. The calculator displays the computed value. Other Worksheets 75 Example: Computing Days between Dates A loan made on September 4, 2003 defers the first payment until November 1, 2003. How many days does the loan accrue interest before the first payment? To Press Display Select Date worksheet &u DT1= 12-31-1990 Enter first date 9.0403 ! DT1= 9-04-20031 Enter second date # 11.0103 ! DT2= 11-01-20031 Select actual/actual daycount method ## ACT Compute days between dates "C DBD= 58.007 Answer: Because there are 58 days between the two dates, the loan accrues interest for 58 days before the first payment. Profit Margin Worksheet The Profit Margin worksheet computes cost, selling price, and gross profit margin. Note: To perform markup calculations, use the Percent Change/Compound Interest worksheet. · To access the Profit Margin worksheet, press & w. · To access profit margin variables, press " or #. · Enter values for the two known variables, and then compute a value for the unknown variable. Profit Margin Worksheet Variables Variable Key Display Cost Selling price Profit margin &w # # CST SEL MAR Variable Type Enter/compute Enter/compute Enter/compute 76 Other Worksheets Note: This guidebook categorizes calculator variables by their method of entry. Gross Profit Margin and Markup The terms margin and markup often are used interchangeably, but each has a distinct meaning. · Gross profit margin is the difference between selling price and cost, expressed as a percentage of the selling price. · Markup is the difference between selling price and cost, expressed as a percentage of the cost. Clearing Profit Margin Worksheet Variables · To clear the Profit Margin worksheet variables and reset default values, press & z. All Profit Margin worksheet variables default to zero. · To reset default values for all calculator variables and formats, including the Profit Margin worksheet variables, press & } !. Computing Profit Margin 1. To select the Profit Margin worksheet, press & w. The CST value appears. 2. To enter a value for one of the two known variables, press # or " to select a variable, then key in a value and press !. 3. Repeat step 2 for the second known variable. 4. To compute a value for the unknown variable, press # or " to select the variable and press C. The calculator displays the computed value. Example: Computing Profit Margin The selling price of an item is $125. The gross profit margin is 20%. Find the original cost. To Press Display Select Profit Margin worksheet & w CST= 0.00 Enter selling price #125 ! SEL= 125.001 Enter profit margin # 20 ! MAR= 20.001 Compute cost ""C CST= 100.00 7 Answer: The original cost is $100. Other Worksheets 77 Breakeven Worksheet The Breakeven worksheet computes the breakeven point and sales level needed to earn a given profit by analyzing relationships between fixed costs, variable costs per unit, quantity, price, and profit. You operate at a loss until you reach the breakeven quantity (that is, total costs = total revenues). · To access the Breakeven worksheet, press & r. · To access breakeven variables, press " or #. · Enter known values for the four known variables, then compute a value for the fifth, unknown variable. Note: To solve for quantity (Q), enter a value of zero for profit (PFT). Breakeven Worksheet Variables Variable Fixed cost Variable cost per unit Unit price Profit Quantity Key &r # # # # Display FC VC P PFT Q Variable Type Enter/compute Enter/compute Enter/compute Enter/compute Enter/compute Note: This guidebook categorizes calculator variables by their method of entry. Types of Worksheet Variables Resetting the Breakeven Worksheet Variables · To reset default values for all Breakeven worksheet variables, press & z. All Breakeven worksheet variables default to zero. · To clear all calculator variables and formats and reset default values, including the Breakeven worksheet variables, press & } !. 78 Other Worksheets Computing Breakeven 1. To access the Breakeven worksheet, press & r. The FC variable appears. 2. Press # or " to select a known variable, key in the value, and press !. 3. Repeat step 3 for each of the remaining known variables. 4. To compute a value for the unknown variable, press # or " until the variable is displayed, and then press C The calculator displays the computed value. Example: Computing Breakeven Quantity A canoe company sells paddles for $20 each. The unit variable cost is $15, and the fixed costs are $3,000. How many paddles must be sold to break even? To Press Display Access Breakeven worksheet. & r FC= Current value Enter fixed costs. 3000 ! FC= 3,000.001 Enter variable cost per unit. # 15 ! VC= 15.001 Enter price. # 20 ! P= 20.001 Leave profit as is. # PFT= 0.00 Compute quantity. #C Q= 600.007 Answer: 600 paddles must be sold to break even. Other Worksheets 79 Memory Worksheet The Memory worksheet lets you compare and recall stored values by accessing the calculator's 10 memories. All memory variables are enter-only. Types of Worksheet Variables · To access the Memory worksheet, press & {. · To access memory variables, press " or #. Note: You can access memories individually using D, J, and the digit keys. Memory Operations Memory Worksheet Variables Variables Key Display Memory 0 Memory 1 Memory 2 Memory 3 Memory 4 Memory 5 Memory 6 Memory 7 Memory 8 Memory 9 &{ M0 # M1 # M2 # M3 # M4 # M5 # M6 # M7 # M8 # M9 Variable Type Enter-only Enter-only Enter-only Enter-only Enter-only Enter-only Enter-only Enter-only Enter-only Enter-only Note: This guidebook categorizes calculator variables by their method of entry. Clearing the Memory Worksheet Variables To clear all 10 memories at once, press & z in the Memory worksheet. Using the Memory Worksheet 1. To select the Memory worksheet, press & {. M0 apears. 2. Perform any of the following operations: 80 Other Worksheets · To clear all 10 memories at once, press & z. · To view the contents of the memories, press # or " once for each memory. · To store a value, select a memory (M0-M9), key in a value, and press !. · Memory arithmetic. Examples: Using the Memory Worksheet To Access Memory worksheet Select M4. Press &{ #### Display M0= Current value M4= Current value Clear M4. 0! M4= 0.001 Store 95. 95! M4= 95.001 Add 65. H 6 5 ! M4= 160.001 Subtract 30. B 3 0 ! M4= 130.001 Multiply by 95. < 9 5 ! M4= 12,350.001 Divide by 65. Raise to 2nd power. 665! ;2! M4= M4= 190.001 36,100.001 Other Worksheets 81 APPENDIX - Reference Information This appendix includes supplemental information to help you use your BA II PLUSTM calculator: · Formulas · Error conditions · Accuracy information · IRR (internal-rate-of-return) calculations · Algebraic operating system (AOSTM) · Battery information · In case of difficulty · TI product service and warranty information Formulas This section lists formulas used internally by the calculator. Time Value of Money where: C/Y = compounding periods per year P/Y = payment periods per year I/Y = interest rate per year where: The iteration used to compute i: 82 APPENDIX - Reference Information where: Gi = 1 + i k where: k = 0 for end-of-period payments k = l for beginning-of-period payments where: where: where: where: where: APPENDIX - Reference Information 83 where: where: where: Amortization If computing Let: Iterate from: to then: where: round the diplay to the number or decimal places selected round to 12 decimal places Balance, principal, and interest are dependent on the values of PMT, PV, I/ Y, and pmt1 and pmt2. 84 APPENDIX - Reference Information Cash Flow where: Net present value depends on the values of the initial cash flow (CF0), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i). IRR = 100 x i where: i satisfies Internal rate of return depends on the values of initial cash flow (CF0), subsequent cash flows (CFj). Bonds 1 Price (given yield) with one coupon period or less to redemption: 1Source for bond formulas (except duration): Lynch, John J., Jr., and Jan H. Mayle. Standard Securities Calculation Methods. New York: Securities Industry Association, 1986. APPENDIX - Reference Information 85 where: PRI = dollar price per $100 par value RV = redemption value of the security per $100 par value (RV except in those cases where call or put features must be considered) R = annual interest rate (as a decimal; CPN_100) M = number of coupon periods per year standard for the particular security involved (set to 1 or 2 Bond worksheet) DSR = number of days from settlement date to redemption date (maturity date, call date, put date, etc.) E = number of days in coupon period in which the settlement date falls Y = annual yield (as a decimal) on investment with security held to redemption (YLD 100) A = number of days from beginning of coupon period to settlement date (accrued days) Note: The first term computes present value of the redemption amount, including interest, based on the yield for the invested period. The second term computes the accrued interest agreed to be paid to the seller. Yield (given price) with one coupon period or less to redemption: Price (given yield) with more than one coupon period to redemption: 86 APPENDIX - Reference Information where: N= DSC = K= number of coupons payable between settlement date and redemption date (maturity date, call date, put date, etc.). (If this number contains a fraction, raise it to the next whole number; for example, 2.4 = 3.) number of days from settlement date to next coupon date summation counter Note: The first term computes present value of the redemption amount, not including interest. The second term computes the present values for all future coupon payments. The third term computes the accrued interest agreed to be paid to the seller. Yield (given price) with more than one coupon period to redemption: Yield is found through an iterative search process using the "Price with more than one coupon to redemption" formula. Accrued interest for securitites with standard coupons or interest at maturity: where: AI = accrued interest PAR= par value (principal amount to be paid at maturity) Depreciation accumulated depreciation Values for decimals you choose to be displayed. are rounded to the number of APPENDIX - Reference Information 87 Straight-line depreciation First year: Last year or more: DEP = RDV Sum-of-the-years'-digits depreciation First year: Last year or more: DEP = RDV Declining-balance depreciation where: is for YR First year: Unless; If ; then use , use 88 APPENDIX - Reference Information If computing last year, Statistics Note: Formulas apply to both x and y. Standard deviation with n weighting (sx): Standard deviation with n-1 weighting (sx): Mean: Regressions Formulas apply to all regression models using transformed data. APPENDIX - Reference Information 89 Interest Rate Conversions where: where: Percent Change where: OLD = old value NEW = new value %CH = percent change #PD = number of periods Profit Margin Breakeven where: PFT = profit P = price FC = fixed cost 90 APPENDIX - Reference Information VC = variable cost Q = quantity Days between Dates With the Date worksheet, you can enter or compute a date within the range January 1, 1980, through December 31, 2079. Actual/actual day-count method Note: The method assumes the actual number of days per month and per year. DBD (days between dates) = number of days II-number of days I Number of Days I = (Y1 -YB) Q 365 + (number of days MB to M1) + DT1 Number of Days II = (Y2 -YB) Q 365 + (number of days MB to M2) + DT2 where: M1 = month of first date DT 1 = day of first date Y 1 = year of first date M 2 = month of second date DT 2 = day of second date Y 2 = year of second date MB = base month (January) DB = base day (1) YB = base year (first year after leap year) APPENDIX - Reference Information 91 30/360 day-count method1 Note: The method assumes 30 days per month and 360 days per year. where: M1 = month of first date DT 1 = day of first date Y 1 = year of first date M 2 = month of second date DT 2 = day of second date Y 2 = year of second date Note: If DT1 is 31, change DT1 to 30. If DT2 is 31 and DT1 is 30 or 31, change DT2 to 30; otherwise, leave it at 31. Note: 1Source for 30/360 day-count method formula Lynch, John J., Jr., and Jan H. Mayle.Standard Securities Calculation Methods. New York: Securities Industry Association, 1986 92 APPENDIX - Reference Information Error Messages Note: To clear an error message, press P. Error Possible Causes Error 1 Overflow · A result is outside the calculator range (±9.9999999999999E99). · Tried to divide by zero (can occur internally). · Tried to compute 1/x when x is zero. · Statistics worksheet: a calculation included X or Y values that are all the same. Error 2 Invalid argument · Tried to compute x! when x is not an integer 0-69. · Tried to compute LN of x when x is not > 0. · Tried to compute yx when y < 0 and x is not an integer or the inverse of an integer. · Tried to compute when x < 0. · Amortization worksheet: tried to compute BAL, PRN, and INT when P2 < P1. · Depreciation worksheet: a calculation included SAL > CST. Error 3 Too many pending · More than 15 active levels of parentheses were tried in a calculation. APPENDIX - Reference Information 93 Error operations Error 4 Out of range Error 5 No solution exists Error 6 Invalid date Error 7 Possible Causes · A calculation tried to use more than 8 pending operations. · Amortization worksheet: the value entered for P1 or P2 is outside the range 1-9,999. · TVM worksheet: the P/Y or C/Y value 0. · Cash Flow worksheet: the Fnn value is outside the range 0.5-9,999. · Bond worksheet: the RV, CPN, or PRI value _0. · Date worksheet: the computed date is outside the range January 1, 1980 through December 31, 2079. · Depreciation worksheet: the value entered for: declining balance percent 0; LIF 0; YR _ 0; CST < 0; SAL < 0; or M01 1 M01 13. · Interest Conversion worksheet: the C/Y value 0. · The DEC value is outside the range 0-9. · TVM worksheet: the calculator computed I/Y when FV, (N Q PMT), and PV all have the same sign. (Make sure cash inflows are positive and outflows are negative.) · TVM, Cash Flow, and Bond worksheets: the LN (logarithm) input is not > 0 during calculations. · Cash Flow worksheet: the calculator computed IRR without at least one sign change in the cash-flow list. · Bond and Date worksheets: a date is invalid (for example, January 32) or in the wrong format (for example, MM.DDYYYY instead of MM.DDYY. · Bond worksheet: the calculator attempted a calculation with a redemption date earlier than or the same as the settlement date. · TVM worksheet: the calculator computed I/Y for a 94 APPENDIX - Reference Information Error Iteration limit exceeded Error 8 Canceled iterative calculation Possible Causes very complex problem involving many iterations. · Cash Flow worksheet: the calculator computed IRR for a complex problem with multiple sign changes or PB/DPB with no payback period based on input cash flow values. · Bond worksheet: the calculator computed YLD for a very complex problem. · TVM worksheet: $ was pressed to stop the evaluation of I/Y. · Amortization worksheet: $ was pressed to stop the evaluation of BAL or INT. · Cash Flow worksheet: $ was pressed to stop the evaluation of IRR. · Bond worksheet: $ was pressed to stop the evaluation of YLD. · Depreciation worksheet: $ was pressed to stop the evaluation of DEP or RDV. Accuracy Information The calculator stores results internally as 13-digit numbers but displays them rounded to 10 digits or fewer, depending on the decimal format. The internal digits, or guard digits, increase the calculator's accuracy. Additional calculations use the internal value, not the value displayed. Rounding If a calculation produces a result with 11-digits or more, the calculator uses the internal guard digits to determine how to display the result. If the eleventh digit of the result is 5 or greater, the calculator rounds the result to the next larger value for display. For example, consider this problem. 1P3Q3=? Internally, the calculator solves the problem in two steps, as shown below. 1. 1 P 3 = 0.3333333333333 APPENDIX - Reference Information 95 2. 0.3333333333333 Q 3 = 0.9999999999999 The calculator rounds the result and displays it as 1. This rounding enables the calculator to display the most accurate result. Although most calculations are accurate to within ±1 in the last displayed digit, higher-order mathematical functions use iterative calculations, in which inaccuracies can accumulate in the guard digits. In most cases, the cumulative error from these calculations is maintained beyond the 10-digit display so that no inaccuracy is shown. AOSTM (Algebraic Operating System) Calculations When you select the AOS calculation method, the calculator uses the standard rules of algebraic hierarchy to determine the order in which it performs operations. Algebraic Hierarchy The table shows the order in which the calculator performs operations using the AOS calculation method. Priority 1 (highest) 2 3 4 5 6 7 (lowest) Operations x2, x!, 1/x, %, x, LN, e2, HYP, INV, SIN, COS, TAN nCr, nPr Yx Q, P +, ) = Battery Information Replacing the Battery Replace the battery with a new CR2032 lithium battery. Caution: The calculator cannot retain data when the battery is removed or discharged. Replacing the battery has the same effect as resetting the calculator. 96 APPENDIX - Reference Information 1. Turn off the calculator and turn it over with the back facing you. 2. Using a small Phillips screwdriver, remove the four screws from the back cover. 3. Carefully pry off the back cover. 4. Using a small Phillips screwdriver, remove the screws from the metal battery cover and lift the cover off the battery. 5. Tip the calculator slightly to remove the battery. Caution: Avoid contact with other calculator components. 6. Install the new battery with the positive sign (+) sign down (not showing). 7. Replace the battery cover and the screws that hold it in place. 8. Align the screw holes in the back cover with those in the calculator, then snap the back cover onto the calculator. Replace the screws. Battery Precautions · Do not leave batteries within the reach of children. · Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. · Do not mix rechargeable and nonrechargeable batteries. · Install batteries according to polarity (+ and ) diagrams. · Do not place nonrechargeable batteries in a battery recharger. · Properly dispose of used batteries immediately. · Do not incinerate or dismantle batteries. In Case of Difficulty Use this list of possible solutions to difficulties you might encounter with the calculator to determine if you can correct a problem before having to return it for service. Difficulty Solution The calculator computes wrong answers. Check the settings of the current worksheet to make sure they are correct for the problem you are working; for example, in the TVM worksheet, check END and BGN and be sure the unused APPENDIX - Reference Information 97 Difficulty The display is blank; digits do not appear. The calculator does not display the correct worksheet variables. The calculator does not display the correct number of decimal places. The calculator does not display the correct date format. The calculator does not display the correct separator format. The calculator does not display the correct result in a math calculation. An error occurs. Solution variable is set to zero. Select the worksheet again. Be sure the battery is properly installed and replace, if necessary. Be sure you have selected the correct worksheet. Press & | to check or adjust the setting for number of decimal places displayed. Press & | # # to check or adjust the setting for date format. Press & | # # # to check or adjust the setting for separator format. Press & | # # # # to check or adjust the setting for calculation method. Error Messages If you experience difficulties other than those listed above, press & } ! to clear the calculator, and then repeat your calculations. Note: You can also perform a hard reset using the reset hole in back of the calculator. Resetting the Calculator 98 APPENDIX - Reference Information General Information Contact TI Support education.ti.com/ti-cares Select your country for technical and other support resources. Service and Warranty Information education.ti.com/warranty Select your country for information about the length and terms of the warranty or about product service. Limited Warranty. This warranty does not affect your statutory rights. General Information 99

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