MODEL EL-738F FINANCIAL CALCULATOR OPERATION MANUAL Contents Page Introduction ..................... 3 Getting Started ................ 5 General Information ........ 11 Financial Functions ......... 17 Scientific Functions ........ 60 Statistical Functions ....... 64 Appendix .......................... 72 Index ................................. 83 NOTICE • SHARP makes no guarantee that this product or this manual is suitable or accurate for any purpose, commercial or otherwise. • Rules and practices in financial calculation vary according to country, locality, or financial institution. It is the consumer’s responsibility to determine whether or not the results produced by this product conform to applicable rules and regulations. • SHARP will not be liable nor responsible for any incidental or consequential economic or property damage caused by misuse and/or malfunctions of this product and its peripherals, unless such liability is acknowledged by law. • The material in this manual is supplied without representation or warranty of any kind. SHARP assumes no responsibility and shall have no liability of any kind, consequential or otherwise, from the use of this material. • SHARP assumes no responsibility, directly or indirectly, for financial losses or claims from third persons resulting from the use of this product and any of its functions, the loss of or alteration of stored data, etc. • SHARP strongly recommends that separate permanent written records be kept of all important data. Data may be lost or altered in virtually any electronic memory product under certain circumstances. Therefore, SHARP assumes no responsibility for data lost or otherwise rendered unusable whether as a result of improper use, repairs, defects, battery replacement, use after the specified battery life has expired, or any other cause. 1 Contents Introduction.................................................................. 3 Operational Notes ...............................................................3 Key Notations in This Manual ..............................................4 Chapter 1: Getting Started .......................................... 5 Preparing to Use the Calculator ..........................................5 Resetting the Calculator In Case of Difficulty ......................5 Calculator and Display Layout.............................................6 The SET UP Menu ..............................................................8 Operating Modes...............................................................10 Chapter 2: General Information ................................ 11 Basic Calculations .............................................................11 Clearing the Entry and Memories .....................................11 Editing and Correcting an Entry ........................................13 Memory Calculations ........................................................14 Chapter 3: Financial Functions ................................ 17 General Information ..........................................................17 TVM (Time Value of Money) Solver ..................................22 Amortization Calculations .................................................33 Discounted Cash Flow Analysis ........................................37 Bond Calculations .............................................................44 Depreciation Calculations .................................................48 Conversion between APR and EFF ..................................51 Day and Date Calculations................................................52 Percent Change/Compound Interest Calculations ............54 Cost/Sell/Margin/Markup Calculations ..............................56 Breakeven Calculations.....................................................58 Chapter 4: Scientific Functions ................................ 60 Constant Calculations .......................................................60 Chain Calculations ............................................................60 Scientific Calculations .......................................................61 Random Functions ............................................................62 Modify Function .................................................................63 Chapter 5: Statistical Functions ............................... 64 Statistical Calculations and Variables................................67 Appendix .................................................................... 72 Financial Calculation Formulas .........................................72 Statistical Calculation Formulas ........................................75 Errors and Calculation Ranges .........................................76 Battery Replacement ........................................................80 Priority Levels in Calculations ...........................................81 Specifications ....................................................................82 Index ........................................................................... 83 2 Introduction Thank you for purchasing a SHARP Financial Calculator. After reading this manual, store it in a convenient location for future reference. • Display of examples shown in this manual may not look exactly the same as what is seen on the product. For instance, screen examples will show only the symbols necessary for explanation of each particular calculation. • All company and/or product names are trademarks and/or registered trademarks of their respective holders. • Some of the models described in this manual may not be available in some countries. Operational Notes • Do not carry the calculator around in your back pocket, as it may break when you sit down. The display is made of glass and is particularly fragile. • Keep the calculator away from extreme heat such as on a car dashboard or near a heater, and avoid exposing it to excessively humid or dusty environments. • Since this product is not waterproof, do not use it or store it where fluids, for example water, can splash onto it. Raindrops, water spray, juice, coffee, steam, perspiration, etc. will also cause malfunction. • Clean with a soft, dry cloth. Do not use solvents or a wet cloth. Avoid using a rough cloth or anything else that may cause scratches. • Do not drop the calculator or apply excessive force. • Never dispose of batteries in a fire. • Keep batteries out of the reach of children. • This product, including accessories, may change due to upgrading without prior notice. Hard Case 3 Key Notations in This Manual Key operations are described in this manual as follows: To specify log To specify 1 To specify Σxy : . h ..................... 1 : 1 or 1 ....................... 2 : i V ..................... 3 To specify CLR-D: To specify ENT : To specify Z : To specify DATA : . ? ..................... 1 Q i Z ..................... 3 J .............................. 4 1 Functions that are printed in orange above the key require . to be pressed first before the key. 2 Number entry examples are shown with ordinary numbers (i.e., “100” will be indicated instead of “1 0 0”). 3 To specify a memory function (printed in green), press i first. 4 Functions that are printed in black adjacent to the keys are effective in specific modes. Using the . and i keys Press s . A x , 10. i πA˚_ and i A • . mean you have to press . followed by ) key and i followed by * key. -10 Notes: • The multiplication instruction “×” and alphabetic letter “X” are distinguished as follows: Key Display Multiplication instruction → x Alphabetic letter → X × X • Examples in this manual are performed using default settings (e.g., SET UP menu items) unless values are otherwise assigned. 4 Chapter 1 Getting Started Preparing to Use the Calculator Before using your calculator for the first time, you must reset (initialize) it. Resetting the calculator Press the RESET switch located on the back of the calculator with the tip of a ball-point pen or similar object. Do not use an object with a breakable or sharp tip. • After resetting the calculator, the initial display of the NORMAL mode appears. 000 Resetting the Calculator In Case of Difficulty Caution: The RESET operation will erase all data stored in memory and restore the calculator’s default setting. In rare cases, all the keys may cease to function if the calculator is subjected to strong electrical noise or heavy shock during use. If pressing any of the keys (including s) has no effect, reset the calculator. Resetting the calculator See the above procedure. Note: Pressing . k and 1 = will also erase all data stored in memory and restore the calculator’s default setting. 5 Calculator and Display Layout Calculator layout 1 Display screen 2 Power ON/OFF and Clear key 3 Key operation keys 5 Cursor keys 4 SET UP key 6 MODE key 1 Display screen: The calculator display consists of a 12-character dot matrix character line and a 12-digit 7-segment character line (10-digit mantissa and 2-digit exponent). 2 Power ON/OFF and Clear key: Turns the calculator ON. This key also clears the display. To turn off the calculator, press ., then c. 3 Key operation keys: .: Activates the second function (printed in orange) assigned to the following key. i: Activates the memory (printed in green) assigned to the following key. 4 SET UP key: Displays the SET UP menu to select the display notation, angular unit, depreciation method and date format. 5 Cursor keys: Move the cursor. 6 MODE key: Switches between NORMAL and STAT modes. 6 Display layout Symbol Equation/ variable name display Mantissa Exponent • During actual use, not all symbols are displayed at the same time. • Only the symbols required for the operation being explained are shown in the screen examples of this manual. : Appears when the entire equation cannot be displayed. Press g / y to see the remaining (hidden) part. c /d : Indicates that variables or data are present above/below the screen. Press z / i to scroll up/down. 2ndF : Appears when . is pressed, indicating that the functions shown in orange are enabled. HYP : Indicates that . ] has been pressed and the hyperbolic functions are enabled. ALPHA : Indicates that i, g or f has been pressed, and storing or recalling memory values or TVM solvers/statistics variables can be performed. BGN : Indicates that calculations are annuity due (payment at the beginning of each interval) calculations. When BGN is not displayed, calculations are ordinary annuity (payment at the end of each interval) calculations. : Indicates that date calculations are based on a 360 360-day year (12 months with 30 days). When 360 is not displayed, date calculations use the actual calendar. : Indicates that a value can be assigned to the displayed ENT variable using Q. COMP : Indicates that the displayed variable can be solved for by using @. FLOAT A / FLOAT B / TAB / SCI: Indicates the notation used to display values. It can be changed in the SET UP menu. 7 DEG / RAD / GRAD : Indicates which angular units are in use. It can be changed in the SET UP menu. : Appears when statistics mode is selected. M : Indicates that a numerical value is stored in the independent memory (M). : Indicates that the value of the displayed variable has not been calculated yet (for variables that can be calculated). The SET UP Menu Press ~ to display the SET UP menu. DSP DRG DEPR 0 1 2 → i DAtE 3 • A menu item can be selected by: • Using g / y to select a number (the selected number will blink), then pressing =, or • pressing the number key corresponding to the menu item number. • If c or d is displayed on the screen, press z or i to view the previous/next part of the menu. • Press s to exit the SET UP menu. Selecting the display notation and number of decimal places The calculator has three display notation systems (fixed decimal point, scientific notation and floating point) for displaying calculation results. • If ~ 0 0 (TAB) is pressed, “DIG(0-9)?” will be displayed and the number of decimal places can be set to any value between 0 and 9. • If ~ 0 1 (SCI) is pressed, “SIG(0-9)?” will be displayed and the number of significant digit can be set to any value between 0 and 9. Entering 0 will set a 10-digit display. • If a floating point number does not fit in the specified range, the calculator will display the result in scientific notation (exponential notation). See the next section for details. • The default setting is a fixed decimal point with two decimal places. 8 Selecting the floating point number system in scientific notation The calculator has two settings for displaying a floating point number: FLO_A (FLOAT A) and FLO_B (FLOAT B). In each display setting, a number is automatically displayed in scientific notation outside the following preset ranges: • FLO_A ~ 0 2: 0.000000001 ≤ | X | ≤ 9,999,999,999 • FLO_B ~ 0 3: 0.01 ≤ | X | ≤ 9,999,999,999 Switching the notation setting Procedure Key operation Display 100000 ÷ 3 = Fixed decimal point with two decimal places s 100000 8 3 = → Scientific notation (SCI) with two significant digits ~012 → Floating point (FLO_A) ~02 1—————©3= 3 ÷ 1000 = Floating point (FLO_A) s 3 8 1000 = 3©1———= → Floating point (FLO_B) ~03 3©1———= → Fixed decimal point with two decimal places ~002 1—————©3= 3333333 1—————©3= 33 04 3333333333 0003 3©1———= 3-03 000 Selecting the angular unit (see page 61) • DEG (°) : ~ 1 0 (default setting) • RAD (rad) : ~ 1 1 • GRAD (g) : ~ 1 2 Selecting the depreciation method (see page 48) • SL (Straight-line method): ~ 2 0 (default setting) • SYD (Sum-of-the-years’ digits method): ~ 2 1 • DB (Declining balance method): ~ 2 2 9 Selecting the date format (see page 44) • US (Month-Day-Year): ~ 3 0 (default setting) • EU (Day-Month-Year): ~ 3 1 Operating Modes This calculator has two operating modes, which can be selected using the MODE key. Selecting a mode 1. Press m. NORMAL 0 The menu display appears. 2. Press 0 or = to select NORMAL mode. StAt 1 000 • Press 1 or y = to select STAT mode. SD LINE QUAD 0 1 2 Operations available in each mode NORMAL mode: Allows you to perform financial, arithmetic, or scientific calculations. STAT (statistics) mode: Allows you to perform statistical, arithmetic, or scientific symbol appears in the display. calculations. The 10 Chapter 2 General Information Basic Calculations Entering numbers and arithmetic operations • Use the number keys 0 to 9, decimal point key ., and sign change key , to enter numbers into the calculator. To clear the display or entry, press s. • Use the S key to enter a value in scientific notation. • Use the arithmetic keys + - x 8 to perform the standard arithmetic calculations of addition, subtraction, multiplication, and division. Press = to perform each calculation. • Use the ( and ) keys to place parentheses around inner parts of expressions. The closing parenthesis ) just before = or h may be omitted. • When you enter a series of operations in one sequence, the calculator performs the calculation according to the priority levels in calculation on page 81. Example Key operation 45 + 285 ÷ 3 = s 45 + 285 8 3 = 18 + 6 = 15 – 8 ( 18 + 6 ) 8 ( 15 - 8 = 42 × (–5) + 120 = (5 × 103) ÷ (4 × 10–3) = 42 x , 5 + 120 = *1 (5 ,) *1 5S384S ,3= Result 14000 343 -9000 125000000 Clearing the Entry and Memories The following methods of clearing the calculator (restoring default settings) are available: 11 Operation Entry A-H, (display) M, X-Z ANS s .b m (Mode selection) . k 0 (MEM) × × × × Listed Cash TVM financial *3 flow variables*1 variables *4 data STAT *7 × × × *2 × × *5 × × *6 × *8 . k 1 (RESET) RESET switch : Cleared or restored to the default setting × : Retained 1 N, I/Y, PV, PMT, and FV (P/Y and C/Y are not included.) Note that listed financial variables sharing common memory with TVM variables, such as “COUPON (PMT)” used in bond calculations, are also cleared or restored to default settings. 3 * Listed variables used in financial calculations (such as “RATE (I/Y),” etc.) including P/Y and C/Y 4 * When you press * to enter a financial calculation, AMRT P1 and AMRT P2 both revert to their default values. The same holds true for YEAR when you press O. 5 * With one of the variables of a listed group (such as those used in bond calculations) displayed, when . b is pressed, all the variables in the listed group are cleared or restored to their default settings. Note that TVM variables sharing common memory with listed financial variables are also cleared or restored to default settings. 6 * Press . b when a cash flow value is displayed. *7 Statistical data (entered data) and variables (n, x, etc.) *8 Are cleared when changing between sub-modes in STAT mode. Notes: • To clear any of the “A-H, M, X-Z” or “ANS” memories, press s g and then specify the memory. • To clear or restore to the default setting one variable or value of TVM variables, listed financial variables, cash flow data, or STAT, refer to the relevant section. • If you turn off the calculator (by pressing . c or by letting it turn itself off automatically), it will resume wherever you left off when you turn it on again. * *2 Delete key To delete a number/function, move the cursor to the number/ function you wish to delete, then press L. If the cursor is located at the right end of an equation or if you are entering a value, the L key will function as a back space key. 12 Memory clear key Press . k to display the menu. MEM RESEt 0 1 • To clear all (A-H, M, X-Z, ANS, TVM variables, listed financial variables, cash flow data, and STAT), press 0 0 or 0 =. • To RESET the calculator, press 1 0 or 1 =. The RESET operation erases all data stored in memory, and restore the calculator’s default settings. Editing and Correcting an Entry Cursor keys • In a menu, such as the SET UP menu, use g or y to select a number (the selected number will blink), then press =. If you need to scroll up or down the screen, use z or i. • In financial calculations, such as bond calculations, press i or z to move through the variables (items). Playback function After obtaining an answer, pressing g brings you to the end of the equation and pressing y brings you to the beginning. Press g or y to move the cursor. Press . g or . y to jump the cursor to the beginning or end of the equation. Insert and overwrite modes in the equation display • This calculator has two editing modes: insert mode (default), and overwrite mode. Pressing . d switches between the two modes. A triangular cursor indicates an entry will be inserted at the cursor, while the rectangular cursor indicates existing data will be overwritten as you make entries. • To insert a number in the insert mode, move the cursor to the place immediately after where you wish to insert, then make the desired entry. In the overwrite mode, data under the cursor will be overwritten by the number you enter. • This mode setting will be retained until you press . d or RESET the calculator. 13 Changing “15 ÷ 3 =” into “25 ÷ 13 =” Procedure Key operation Display 15 ÷ 3 = s 15 8 3 = 15©3= Enter the playback function. y 15©3 Switch to overwrite . d mode. 15©3 Change “15” to “25” 2 y y and move the cursor to “3”. 25©3 Change to insert mode. .d 25©3 Change “3” to “13” and calculate. 1= 25©13= 500 192 Errors An error will occur if an operation exceeds the calculation ranges, or if a mathematically illegal operation is attempted. When an error occurs, pressing g or y automatically moves the cursor to the place in the equation/number where the error occurred. Edit the equation/number or press s to clear the equation. For details, see page 76. Memory Calculations This calculator has 11 temporary memories (A-H and X-Z), one independent memory (M) and one last answer memory (ANS). It also has various variables for use in financial calculations and statistical calculations. Memory use in each mode for memory calculations Mode A-H, X-Z M ANS NORMAL STAT : Available TVM Listed financial Statistical variables *1 variables *2 variables *3 × × : Unavailable 14 × × × *1 N, I/Y, PV, PMT, FV * All financial variables, except for TVM variables 2 2 *3 x, sx, σx, n, Σx, Σx , y, sy, σy, Σy, Σy , Σxy, r, a, b, c 2 Temporary memories (A-H, X-Z) Press g and the variable key to store a value in memory. Press f and the variable key to recall a value from the memory. To place a variable in an equation, press i and the variable key. Independent memory (M) In addition to all the other features of temporary memories, a value can be added to or subtracted from an existing memory value. Press s g M to clear the independent memory (M). Last answer memory (ANS) • The calculation result obtained by pressing = or any other calculation ending instruction (including storing and recalling operations) is automatically stored in the last answer memory. • Listed financial variables are automatically stored in the last answer memory by displaying the variable and the value. TVM variables TVM variables can be recalled using f in the same way as temporary memories. It is not necessary to press g to store a value. Listed financial variables Financial variables are specific to the type of calculation they are used in. For example, the variable N is available to the TVM solver but not to discounted cash flow analysis calculations. If you want to carry a value from a variable over into a different type of calculation, use one of the following methods: • Last answer memory (ANS): Within the original calculation, display the variable and value that you wish to carry over. The value is automatically entered into last answer memory. Press s to exit the calculation (the listed financial variables will disappear from the screen), and press i / to bring up the value from the previous calculation. M-D-Y (D-M-Y) 1 and M-D-Y (DM-Y) 2 are not stored in last answer memory. • Variables common to both calculations: If the value that you wish to carry over is held in a variable that exists in both types 15 of calculation (for example, both bond calculations and the TVM solver use the variable I/Y), you can retrieve the value simply by switching calculation types and bringing up the variable. Statistical variables Statistical data is not entered into variables. Statistical variables are the results of the calculation of statistical data. Therefore, you cannot enter values directly into statistical variables. After calculation, however, you can use the values held in statistical variables in subsequent calculations. Note: Use of f or i will recall the value stored in memory using up to 14 digits. Memory calculations Example 24 ÷ (8 × 2) = (8 × 2) × 5 = Key operation s8x2gM 24 8 i M = iMx5= sgM $150×3:M1 150 x 3 h +)$250:M2=M1+250 250 h –)M2×5% fMx5.% M .jfM $1 = ¥110 ¥26,510 = $? $2,750 = ¥? 110 g Y 26510 8 f Y = 2750 x f Y = r = 3 cm (r→Y) 2 πr = ? 3gY i Y* . .;= 24 24 8 ( 4 + 6 ) = = 2.4...(A) 4+6 3 x i / + 60 8 3 × (A) + 60 ÷ (A) = i / = Result 1600 150 8000 000 45000 25000 3500 66500 11000 24100 30250000 300 2827 240 3220 * Entry of the multiplication procedure is omitted between “π” and a variable. 16 Chapter 3 Financial Functions General Information Financial calculations The following financial functions are available. Use NORMAL mode to perform financial calculations. TVM (Time Value of Money) solver: Analyze equal and regular cash flows. These include calculations for mortgages, loans, leases, savings, annuities and contracts or investments with regular payments. Amortization calculations: Calculate and create amortization schedules using values stored in the TVM solver. Discounted cash flow analysis: Analyze unequal cash flows and calculate NPV (net present value) and IRR (internal rate of return). Bond calculations: Solve bond prices or yields to maturity with accrued interest. Depreciation calculations: Obtain depreciation base values using three types of calculation methods. Conversion between APR and EFF: Interest rates can be converted between APR (annual, or nominal percentage rate) and EFF (effective interest rate). Day and date calculations: Calculate dates and the number of days between dates. Percent change/Compound interest calculations: Calculate percent change (increase or decrease) and compound interest rates. Cost/Sell/Margin/Markup calculations: Calculate cost, selling price and margin/markup. Breakeven calculations: Calculate breakeven points (quantity) using fixed costs, variable costs per unit, unit prices, and profit. 17 Variables used in financial calculations Financial calculations use multiple variables. By entering known values into variables, you can obtain unknown values. Variables used in financial calculations are categorized into the following two types, depending on the entry method. TVM variables: Variables that are used in the TVM solver. These include N, I/Y, PV, PMT and FV. You can store, recall or calculate values directly using the corresponding keys. Listed financial variables: Variables that are organized into lists in different categories. These variables can be accessed using the z/i cursor keys in each calculation. P/Y and C/Y in the TVM solver are of this type of variable. Variables shared among calculations Financial variables are specific to the type of calculation they are used in. Values are stored in these variables and recalled as required. Some variables are shared (in the memory area) among calculations. If you change the value of a variable in one calculation, the value will change in all the other calculations as well. The following list shows the variables shared between calculations. While calculating, be aware of the values stored in these variables. TVM solver Discounted cash flow analysis Bond calculations N — CPN/Y (N) LIFE (N) PERIODS (N) — I/Y RATE (I/Y) YIELD (I/Y) DB (I/Y) % (I/Y) — PV — PRICE (PV) COST (PV) OLD PRC (PV) — PMT — — — — FV — SALVAGE (FV) NEW PRC (FV) — — — — — — — — — COUPON (PMT) REDEMPT (FV) M-D-Y 1* D-M-Y 1 M-D-Y 2 * D-M-Y 2 Percent change/ Depreciation Day and date Compound intercalculations calculations est calculations *The variable names vary according to the data format settings. 18 M-D-Y 1* D-M-Y 1 M-D-Y 2 * D-M-Y 2 Basic variable operations TVM variables (N, I/Y, PV, PMT, FV) A. Entering a value Enter a value and then press the corresponding TVM variable key. Note: You can also enter values into variables using arithmetic operations. Ex. 100 x 12 u B. Displaying a value Press f and the corresponding TVM variable key. C. Executing calculation Press @ and the corresponding TVM variable key. Listed financial variables A. Entering a value 1. Select the desired financial calculation method by pressing the corresponding financial calculation key. 2. Use z/i to select the variable you wish to enter. 3. Enter the value and press Q when the “ENT” symbol appears. Note: In step 3, you can also enter values into variables using arithmetic operations. Ex. 100 x 12 Q B. Displaying a value Use z/i to show the variable and value. C. Executing calculation 1. Use z/i to select the variable you wish to calculate. 2. Press @ when the “COMP” symbol appears. Note: Pressing . b resets all the variables in the displayed listed financial group to the default values. For details, see the relevant sections for each financial calculation. 19 The ENT and COMP symbols Listed financial variables are categorized by whether they are known or unknown. When the variable is selected (displayed), the “ENT” and/or “COMP” symbols will appear to indicate that the current variable may be entered (known variable) and/or calculated (unknown variable), respectively. For details, refer to the explanations or examples for each financial function. Note: TVM variables (N, I/Y, PV, PMT and FV) can be entered (known variables) and calculated (unknown variables), however, neither “ENT” nor “COMP” will appear on the display. Category For entry only For calculation only For entry or calculation Calculated automatically Display symbols Descriptions ENT Variable can be used as a known, but not as an unknown. COMP Variable can be used as an unknown, but not as a known. ENT COMP Variable can be used as either a known or an unknown. — Unknown variable, but the calculator calculates the value automatically. Notes: • During financial calculation, the word “calculating!” will be displayed on the screen. You can press s at this time to cancel the calculation. • Calculation-only and automatically calculated variables have no default values. • The symbol will be displayed if the value of the displayed variable has not been calculated yet (for variables that can be calculated). 20 Compound interest This calculator assumes interest is compounded periodically in financial calculations (compound interest). Compound interest accumulates at a predefined rate on a periodic basis. For example, money deposited in a passbook saving account at a bank accumulates a certain amount of interest each month, increasing the account balance. The amount of interest received each month depends on the balance of the account during that month, including interest added in previous months. Interest earns interest, which is why it is called compound interest. It is important to know the compounding period of a loan or investment before starting, because the whole calculation is based on it. The compounding period is specified or assumed (usually monthly). Cash flow diagrams The direction of arrows indicates the direction of cash movement (inflow and outflow) with time. This manual uses the following cash flow diagrams to describe cash inflows and outflows. Inflow (+) Present value (PV) Time Cash flow ...... Payment (PMT) Future value (FV) Outflow (–) 21 TVM (Time Value of Money) Solver Analyze equal and regular cash flows. These include calculations for mortgages, loans, leases, savings, annuities, and contracts or investments with regular payments. Note: Discounted cash flow analysis can be done using unequal cash flows (see page 37). An amortization schedule can be calculated using the information stored in the TVM solver (see page 33). Variables used in the TVM solver Variable Corresponding variable key Description Default value N N Total number of payments 1 I/Y f Interest rate per year 0 Present value 0 PV PMT u Payment 0 FV t Future value 0 P/Y .w Number of payments per year 1 C/Y . w i Number of compounding periods per year 1 Setting the payment period (payment due) You can toggle between ordinary annuity (payment at the end of the period) and annuity due (payment at the beginning of the period) using . ". The default setting is ordinary annuity (BGN is not displayed). Refer to page 28 for details. Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. • All the TVM solver variables retain their previously entered values. If you wish to clear all the data, press . b. 2. Select ordinary annuity or annuity due using . ". 22 3. Enter values into TVM solver variables. • Enter a value and press the appropriate TVM variable key , u, t). (N, f, • Press . w and then enter a value for P/Y. The same value is automatically assigned to C/Y as well. Values entered into P/Y or C/Y must be positive. After entering values, press s to quit the P/Y and C/Y settings. • After setting P/Y (number of payments per year), you can use . < to enter N (total number of payments). Enter the number of years and press . <. The calculator automatically calculates the total number of payments. • By pressing f / you can use the result of the previous normal calculation stored in ANS memory as a TVM variable. • Note that some variables are shared by other calculations and may have values assigned by those calculations. 4. Press @ and the TVM variable key that you wish to solve. • The calculation is performed and the obtained values are displayed. Basic examples for the TVM solver 1 Calculating basic loan interest A $56,000 mortgage loan (compounded monthly) requires monthly payments of $440 during its 20-year amortization period. Calculate the annual interest rate on the mortgage. PV = $56,000 FV = 0 ...... I/Y = ?% PMT = –$440 N = 12 × 20 years = 240 Default values for the number of payments per year (P/Y) and the number of compounding periods per year (C/Y) are both set to 1. Set these values before entering TVM variable values. 23 Procedure Set all the variables to default values. Key operation Display .b 000 Make sure ordinary annuity is set (BGN is not displayed). Set the number of payments per year to 12. . w 12 Q P/Y= 1200 The number of compounding periods per year is automatically set to the same value as P/Y. Confirm the number of compounding periods per year. i Quit the P/Y and C/Y settings. s C/Y= 1200 000 Calculate the total num- 20 . < N ber of payments and store in N. ANS~N Enter the present value. 56000 56———~PV 24000 5600000 Enter payment. , 440 u (-44—)~PMT Enter the future value. 0t —~FV Calculate the annual interest rate. @f I/Y= -44000 000 717 Answer: The annual interest rate is 7.17%. Note: If you make a mistake, press L to erase the number and enter the correct number to continue. After pressing the TVM variable key, you must re-enter values from the beginning. 24 2 Calculating basic loan payments Calculate the quarterly payment for a $56,000 mortgage loan at 6.5% compounded quarterly during its 20-year amortization period. PV = $56,000 I/Y = 6.5% FV = 0 ...... PMT = ? N = 4 × 20 years = 80 Procedure Set all the variables to default values. Key operation Display .b 000 Make sure ordinary annuity is set (BGN is not displayed). Set the number of payments per year to 4. .w4Q Confirm the number of i compounding periods per year. P/Y= 400 C/Y= 400 Quit the P/Y and C/Y set- s tings. 000 Calculate the total number of payments and store in N. 20 . < N Enter the present value. 56000 56———~PV Enter the future value. 0t —~FV Enter the annual interest rate. 6.5 f 6.5~I/Y Calculate the quarterly payment. @u PMT= ANS~N 5600000 Answer: The quarterly payments are $1,255.86. 25 8000 000 650 -125586 3 Calculating future value You will pay $200 at the end of each month for the next three years into a savings plan that earns 6.5% compounded quarterly. What amount will you have at the end of period if you continue with the plan? FV = ? I/Y = 6.5% (quarterly) PV = 0 ...... PMT = –$200 PMT = –$200 N = 12 × 3 years = 36 Procedure Set all the variables to default values. Key operation Display .b 000 Make sure ordinary annuity is set (BGN is not displayed). Set the number of payments per year to 12. . w 12 Q Set the number of com- i 4 Q pounding periods per year to 4. Quit the P/Y and C/Y settings. P/Y= 1200 C/Y= 400 s 000 Calculate the total num- 3 . < N ber of payments and store in N. ANS~N Enter the present value. 0 —~PV 3600 000 Enter payment. , 200 u (-2——)~PMT Enter the annual interest rate. 6.5 f 6.5~I/Y Calculate the future value. @t FV= -20000 650 792219 Answer: You will have $7,922.19 at the end of the three-year period. 26 4 Calculating present value You open an account that earns 5% compounded annually. If you wish to have $10,000 twenty years from now, what amount of money should you deposit now? FV = $10,000 N = 20 years PV = ? Procedure Set all the variables to default values. I/Y = 5% Key operation Display .b 000 Make sure ordinary annuity is set (BGN is not displayed). Set the number of payments per year to 1. .w1Q P/Y= 100 The number of compounding periods per year is automatically set to 1. Press s to exit the P/Y and C/Y settings. Enter the total number of payments. s 20 N 2—~N Enter the future value. 10000 t 1————~FV Set payment to zero. 0u —~PMT Enter the annual interest rate. 5f 5~I/Y Calculate the present value. @ PV= Answer: You should deposit $3,768.89 now. 27 2000 1000000 000 500 -376889 Specifying payments due (. ") This calculator can select ordinary annuity or annuity due depending on the regular cash flow (payment) conditions. Ordinary annuity (END): This is the default setting for financial calculations. BGN is not displayed. A regular cash flow (payment) is received at end of each payment period. Often applied to loan calculations, etc. Annuity due (BGN): BGN appears on the display. A regular cash flow (payment) is received at the beginning of each payment period. Often applied to the finance lease of an asset. To toggle between ordinary annuity and annuity due, press . ". Note: The above selection only affects the TVM solver. 1 Ordinary annuity Your company wishes to accumulate a fund of $300,000 over the next 18 months in order to open a second location. At the end of each month, a fixed amount will be invested in a money market savings account with an investment dealer. What should the monthly investment be in order to reach the savings objective, assuming the account will earn 3.6% interest compounded monthly? FV = $300,000 PV = 0 I/Y = 3.6% ...... PMT = ? N = 18 Procedure Set all the variables to default values. Key operation Display .b 000 Make sure ordinary annuity is set (BGN is not displayed). Set the number of payments per year to 12. . w 12 Q P/Y= 1200 The number of compounding periods per year is automatically set to 12. Press s to exit the P/Y and C/Y settings. 28 Procedure Key operation Display Enter the total number of payments. s 18 N 18~N Enter the future value. 300000 t 3—————~FV Set the present value to 0 zero. 1800 30000000 —~PV 000 Enter the annual interest rate. 3.6 f 3.6~I/Y Calculate payment. @u PMT= 360 -1624570 Answer: The monthly investment should be $16,245.70. 2 Calculating lease payments (Annuity due) You plan to purchase a new car with a value of $87,918 on a 60-month lease. If the annual interest rate is 6.75%, the contractual purchase option price at lease end is $17,500, and payment is due at the beginning of each month, how much should you pay each month? PV = $87,918 I/Y = 6.75% .................... PMT = ? FV = –$17,500 N = 60 Procedure Key operation Set all the variables to default values. .b Set to annuity due (BGN is displayed). ." Set the number of payments per year to 12. . w 12 Q 29 Display 000 000 P/Y= 1200 Procedure Key operation Display The number of compounding periods per year is automatically set to 12. Press s to exit the P/Y and C/Y settings. Enter the total number of payments. s 60 N 6—~N Enter the future value. , 17500 t (-175——)~FV Enter the present value. 87918 6000 -1750000 87918~PV 8791800 Enter the annual interest rate. 6.75 f 6.75~I/Y Calculate payment. @u PMt= 675 -147620 Answer: You should pay $1,476.20 each month. Calculating the present value of a lease with trade-in value Your client wishes to buy a machine currently leased from your company. On a five-year lease with payments of $200 at the beginning of each month, the machine has a trade-in value of $1,500 with 34 monthly payments remaining. If your company sells the machine at the present value of the lease, discounted at an annual interest rate of 18%, compounded monthly, how much should your company charge for the machine? 3 PV = ? I/Y = 18% ...... PMT = –$200 N = 34 30 FV = –$1,500 Procedure Key operation Set all the variables to default values. .b Set to annuity due (BGN is displayed). ." Set the number of payments per year to 12. . w 12 Q Display 000 000 P/Y= 1200 The number of compounding periods per year is automatically set to 12. Press s to exit the P/Y and C/Y settings. Enter the total number of payments. s 34 N 34~N Enter payment. , 200 u (-2——)~PMt Enter the annual interest rate. 18 f 18~I/Y Enter the future value. , 1500 t (-15——)~FV Calculate the present value. @ PV= 3400 -20000 1800 -150000 627995 Answer: $6,279.95 should be charged for the machine. 4 Calculating down payment and amount to borrow You wish to buy a house for $180,000. The finance company charges a 5.5% APR, compounded monthly, on a 25-year loan. If you can afford a monthly payment of $900, how much can you borrow? How much do you need for a down payment? PV = ? I/Y = 5.5% ...... PMT = –$900 N = 12 × 25 years = 300 31 FV = 0 Procedure Set all the variables to default values. Key operation Display .b 000 Make sure ordinary annuity is set (BGN is not displayed). Set the number of payments per year to 12. . w 12 Q P/Y= 1200 The number of compounding periods per year is automatically set to 12. Press s to exit the P/Y and C/Y settings. Enter the total number of payments. s 25 . < N ANS~N Enter payment. , 900 u (-9——)~PMT Enter the annual interest rate. 5.5 f 5.5~I/Y Set the future value to zero. 0t —~FV Calculate the present value. @ PV= Calculate the down payment. s 180000 f = 18————-PV= 30000 -90000 550 000 14655892 3344108 Answer: You can borrow $146,558.92 in total. The price of the house is $180,000, so: Down payment = $180,000 – present value = $180,000 – $146,558.92 You need $33,441.08 for a down payment. 32 Amortization Calculations Calculate and create amortization schedules using values stored in the TVM solver. Note: Prior to using amortization, you need to enter values into TVM variables. Variables used in amortization Variable Description Default value AMRT P1 Start of payment (nth time) 1 AMRT P2 End of payment (nth time) 1 BALANCE Remaining balance after payment — ΣPRINCIPAL Principal paid — ΣINTEREST Interest paid over the specified periods — • BALANCE, ΣPRINCIPAL and ΣINTEREST are calculated automatically, so no default values are set. • AMRT P1 and AMRT P2 must be between 1 and 9,999. Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. • All the TVM solver variables retain their previously entered values. If you wish to clear all the data, press . b. 2. Select ordinary annuity or annuity due using . ". 3. Enter the appropriate numeric values for the variables used in the TVM solver. • Confirm the values of N, I/Y, PV, PMT, FV, P/Y and C/Y. 4. Press * to use amortization calculation. 5. Enter a value for “AMRT P1” and press Q. AMRt P1= 100 6. Press i, enter a value for “AMRT P2” and press Q. 7. Display values for BALANCE, ΣPRINCIPAL and ΣINTEREST by pressing i once for each. Each value is calculated automatically. 33 8. Press i to calculate the next period of the amortization schedule. 9. Repeat steps 5 to 7 above. • If you press @ during “AMRT P1” and “AMRT P2” entry, the values for the next period of payment will be automatically calculated and displayed. • To end amortization calculations, press s. Pressing s during entry will clear the value entered. 1 Calculating mortgage payments and generating an amortization schedule 1. Calculate the monthly payment of a 20-year loan with a loan amount of $90,000 and a 5.45% APR. Procedure Set all the variables to default values. Key operation Display .b 000 Make sure ordinary annuity is set (BGN is not displayed). Set TVM solver variables and calculate payment. . w 12 Q s 20 . < 0 N 90000 t 5.45 f @ u PMT= -61656 Answer: The monthly payment is $616.56. Now generate an amortization schedule for the first 5 years of the loan. If the first payment is in August, the first year has 5 payment periods and the following years have 12 payment periods each. 2. Calculate the amortization schedule for the first year. Procedure Key operation Display Change to amortization * 1 Q calculation and enter 1 (August) for the starting payment. AMRT P1= Enter 5 (December) for the ending payment. i5Q AMRT P2= Display the remaining balance. i BALANCE= 100 500 8895148 34 Procedure Key operation Display Display the principal paid. i ÍPRINCIPAL= Display the interest paid. i ÍINTEREST= -104852 -203428 3. Calculate the amortization schedule for the second year. Procedure Key operation Change amortization i6Q schedule to the second year and enter 6 (January) for the starting payment. Enter 17 (December) i 17 Q for the ending payment. Display AMRT P1= 600 AMRT P2= 1700 Display the remaining balance. i BALANCE= Display the principal paid. i ÍPRINCIPAL= Display the interest paid. i ÍINTEREST= 8633592 -261556 -478316 4. Calculate the amortization schedule for the third year. Procedure Key operation Display Change amortization schedule to the third year and enter the next 12 months automatically. [email protected] Display the remaining balance. i BALANCE= Display the principal paid. i ÍPRINCIPAL= Display the interest paid. i ÍINTEREST= AMRT P2= 2900 8357421 -276171 -463701 5. Repeat the above operation for the fourth and fifth years. 35 2 Calculating payments, interest, and loan balance after a specified payment You have taken out a 30-year loan for $500,000, with an annual interest rate of 8.5%. If, after the 48th period, you want a balloon payment due, what amount of monthly payment must you make with monthly compounding and how much will the balloon payment be? Procedure Set all the variables to default values. Key operation Display s.b 000 Make sure ordinary annuity is set (BGN is not displayed). Set TVM solver variables and calculate payment. . w 12 Q s 30 . < 0 N 500000 t 8.5 f @ u PMT= -384457 Answer: The monthly payment is $3,844.57. Now generate an amortization schedule from the first to the 48th payments. Procedure Key operation Display Change to amortization * 1 Q calculation and enter 1 for the starting payment. AMRT P1= Enter 48 (December) i 48 Q for the ending payment. AMRT P2= 100 4800 Display the balance after 48 months. (balloon payment) i Display the principal paid over 48 months. i ÍPRINCIPAL= Display the interest paid over 48 months. i ÍINTEREST= BALANCE= 48275524 -1724476 -16729460 Answer: The balloon payment after the 48th period would be $482,755.24. 36 Discounted Cash Flow Analysis Analyze unequal cash flows and calculate the net present value (NPV) and the internal rate of return (IRR). Note: Use the TVM solver for equal and regular cash flow analysis (see page 22). Entering cash flow data To find NPV and IRR using discounted cash flow analysis, enter cash flow data, one data item at a time, in the following format: Single cash flows Cash flow value J Repeated cash flows Cash flow value > frequency value J Notes: • Before entering data, press > . b to clear any previously entered cash flow data. • Press , to enter a negative cash flow (outflow). • Make sure the calculator is in NORMAL mode. It is not possible to enter cash flow data when listed financial variables are shown on the display. Press s to exit. • You can enter a total of up to 100 cash flow and/or statistical data items. A single cash flow value is counted as one data item, while a cash flow value with an associated frequency value is counted as two. • Frequency values must be integers between 1 and 999. • If you wish to correct a value before pressing J, press s to delete the entry and enter the correct value. Entering cash flow data Enter cash flow data according to the following cash flow diagram. $7,000 $9,000 $5,000 $5,000 $8,000 –$25,000 37 Procedure Key operation Display Bring up the initial dis- s *1 play in NORMAL mode. Enter cash flow data. *1 *2 000 , 25000 J DATA SET:CF 000 * 7000 J DATA SET:CF 9000 J DATA SET:CF 5000 > 2 J DATA SET:CF 8000 J DATA SET:CF 2 100 200 300 400 If there is cash flow data stored, press > . b to clear it. The format of the data set (cash flow and frequency values) number, which is initially set to “0.00,” is dependent on calculator display notation settings. Confirming and editing data Confirming data Press > to display any previously entered cash flow data. The data is displayed in order by data item (identifier, number, and value). Use z/i to display a data item from a previously entered data set. Cash flow identifier Data set number CF D—= -2500000 Frequency identifier CF N—= 38 Cash flow value Data set number 100 Frequency value • Press . z or . i to jump to the first or the last data item, respectively. • Each data item is displayed in the form CF Dn= (cash flow value) or CF Nn= (frequency), where n indicates the data set number. Editing data • Display the data item you wish to modify by using z/ i, enter a new value and press J. • If a frequency value is set to zero, then the associated data set is deleted. Deleting data • Display the data item to be deleted by using z/ i, and press . ?. • If a cash flow value/frequency is deleted, the corresponding frequency/cash flow value is also deleted. • If you wish to delete all data, press . b. Inserting data Using the z and i keys, specify the correct place to insert your new data by displaying the value that is to come directly after, and then press . e. A new data set with a cash flow value of zero and a frequency value of one will be inserted. Modify the new data set to include your data. Correcting cash flow data Currently the cash flow data is that shown in chart A. Change it according to chart B. Chart A Chart B $7,000 $9,000 $5,000 $5,000 $8,000 –$25,000 Procedure $7,000 $9,000 $6,000 $5,000 $8,000 –$30,000 Key operation Display previously s> entered cash flow data. (Example on page 37) 39 Display CF D—= -2500000 Procedure Key operation Change the first cash , 30000 J flow value from –25,000 to –30,000. Display CF D—= -3000000 Change the frequency of 5000 from 2 to 1. iiii CF N3= iii1J Add a new data set (6000) immediately before 5000. . e 6000 J 100 CF D3= 600000 To confirm the corrections, press . z to jump to the first data item and press i to browse through each data item. Variables used in discounted cash flow analysis Variable Description Default value RATE (I/Y) Internal rate of return (IRR) 0 NET_PV Net present value (NPV) — • The variable RATE (I/Y) is shared by the variable I/Y. NET_PV is for calculation only and has no default value. • The BGN/END setting is not available for discounted cash flow analysis. NPV and IRR The calculator solves the following cash flow values: Net present value (NPV): The total present value of all cash flows, including cash paid out (outflows) and cash received (inflows). A profitable investment is indicated by a positive NPV value. Internal rate of return (IRR): The interest rate that gives a net present value of zero. Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. 40 2. Enter cash flow data. • Refer to page 37 for instructions on entering cash flow data. 3. Press . < to begin discounted cash flow analysis. • If a previously entered cash flow value is displayed, press s to exit and then press . <. 4. To find NPV or IRR, do the following: To obtain NPV: Enter the interest rate (discounted rate) into RATE(I/Y) and press Q. Move to NET_PV and calculate by pressing i and @. To obtain IRR: Press @ to calculate IRR (RATE(I/Y)). Note: If “Error 5” is displayed in step 4, or if you want to find another IRR, enter an estimated value into RATE(I/Y) and calculate again in step 4. 1 Solving for unequal cash flows Your company pays $12,000 for a new network system, and expects the following annual cash flows: $3,000 for the first year, $5,000 for the second to fourth years, and $4,000 for the fifth year. At what IRR does the net present value of the cash flows equal zero? $3,000 $5,000 $5,000 $5,000 $4,000 –$12,000 1. Enter cash flow data. Procedure Key operation Bring up the initial dis- s *1 play in NORMAL mode. Display 000 41 Procedure Enter cash flow data. Key operation , 12000 J DATA SET:CF 3000 J DATA SET:CF 5000 > 3 J DATA SET:CF 4000 J DATA SET:CF Return to the initial dis- s play in NORMAL mode. *1 Display 000 100 200 300 000 If there is cash flow data stored, press > . b to clear it. 2. Calculate IRR. Procedure Key operation Select discounted cash . < . b flow analysis, and set all the variables to default values. Calculate IRR (RATE (I/Y)). @ Display RATE(I/Y)= 000 RATE(I/Y)= 2314 Answer: The net present value of the cash flows equals zero at an IRR of 23.14%. 2 Calculating the present value of variable cash flows Your company has prepared forecasts for the development costs and operating profits of the next generation of your product. Development costs for each of the next three years (Years 1 to 3) will be $50,000. Manufacturing equipment costing $100,000 will be purchased at the end of Year 3. Annual profits for the five-year product life (from Year 4 to Year 8) are projected to be $80,000. The salvage value of the manufacturing equipment at the end of Year 8 is $20,000. Given a 12% discount rate, should your company proceed with the product development? 42 $80,000 $80,000 $80,000 $80,000 $80,000 –$20,000 –$50,000 –$50,000 –$50,000 –$100,000 1. Enter the cash flow data. Procedure Key operation Display Bring up the initial dis- s *1 play in NORMAL mode. Enter cash flow data. 000 , 50000 > 2 J DATA SET:CF , 150000 J DATA SET:CF 80000 > 4 J DATA SET:CF 60000 J DATA SET:CF 000 100 200 300 Return to the initial dis- s play in NORMAL mode. *1 000 If there is cash flow data stored, press > . b to clear it. 2. Calculate NPV. Procedure Key operation Display Select discounted cash . < . b flow analysis, and set all the variables to default values. RATE(I/Y)= Enter the discount rate. 12 Q RATE(I/Y)= Calculate NPV (NET_PV). [email protected] 000 1200 NET_PV= 662752 Answer: As NPV = 6,627.52 > 0, the product can be developed. 43 Bond Calculations Using bond calculations, you can obtain bond prices, yields to maturity, and accrued interest. Variables used in bond calculations Variable Description COUPON (PMT) Annual coupon rate (%) *1 Default value 0 REDEMPT (FV) Redemption value 0 M-D-Y 1 *2 Settlement date (date of bond purchase) 1-1-2001 M-D-Y 2 *2 Redemption date 1-1-2001 CPN/Y (N) *3 Number of coupons per year 1 YIELD (I/Y) Yield to maturity (%) 0 PRICE (PV) Bond price *4 0 ACCU INT Accrued interest — *1 *2 *3 Redemption value of the security per $100 par value. You can change the date format to D-M-Y (see page 10). You can only enter “1” or “2” — “1” for annual coupons and “2” for semi-annual coupons. *4 Per $100 par value. Note: Bonds are associated with payment methods known as coupons. A coupon is like an “interest-only payment,” and it is based on the future value of the bond. COUPON is a percentage of the bond par value, usually annually, by the owner of the bond. For bonds that have annual coupons, the owner receives one payment of the coupon amount each year. Some bonds have semi-annual coupons. For these, each year’s coupon amount is paid in two equal payments six months apart. The date on which a coupon payment is made is called the “coupon date.” The bond maturity date is usually the last coupon date. Setting the day-count method You can toggle between the actual calendar (365 days plus leap years) and a 360-day calendar (12 months of 30 days each) using . &. The actual calendar is set by default (360 is not displayed). The calendar range is from January 1, 1901 to December 31, 2099. 44 Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. 2. Select bond calculations by pressing #. • To end bond calculations, press s. • If you press s during entry, any entered values will be cleared. COUPON(PMt)= 000 3. Change the day-count setting, if necessary, by pressing . &. 4. Enter the coupon rate (%) into COUPON (PMT) by entering the value and pressing Q. 5. Enter the redemption value into REDEMPT (FV) by pressing i, entering the value, and pressing Q. 6. Enter the date of bond purchase into M-D-Y 1 (or D-M-Y 1) by pressing i, entering the date, and pressing Q. • For date entry, refer to page 47, ”Entering dates”. 7. Enter the redemption date into M-D-Y 2 (or D-M-Y 2) by pressing i, entering the date, and pressing Q. • For date entry, refer to page 47, ”Entering dates”. 8. Enter the number of coupon payments per year into CPN/Y (N) by pressing i, entering the value, and pressing Q. 9. To find bond price or yield to maturity, do the following: To obtain bond price (PRICE (PV)): Enter annual yield (%) into YIELD(I/Y) by pressing i, entering the value, and pressing Q. Move to PRICE (PV) and calculate by pressing i and @. Display the accrued interest (ACCU INT) by pressing i. The accrued interest is calculated automatically. To obtain yield to maturity (YIELD (I/Y)): Move to PRICE (PV) and enter the bond price by pressing i i, entering the value, and pressing Q. Move to annual yield, YIELD (I/Y) and calculate by pressing z @. Display the accrued interest (ACCU INT) by pressing i i. The accrued interest is calculated automatically. 45 Calculating bond price and accrued interest A $100, 20-year, 6.5% coupon bond is issued to mature on August 15, 2023. It was sold on November 3, 2006 to yield the purchaser 7.2% compounded semiannually until maturity. At what price did the bond sell? Also calculate the accrued coupon interest. Procedure Key operation Display Bring up the initial dis- s play in NORMAL mode. Select bond calculations. 000 COUPON(PMT)= # 000 Make sure the actual calendar is set (360 is not displayed). Enter the coupon rate (%). 6.5 Q COUPON(PMT)= Enter the redemption value. i 100 Q REDEMPT(FV)= Enter the settlement date. i 11032006 Q M-D-Y 1=[FR] Enter the redemption date. i 08152023 Q M-D-Y 2=[TU] Enter the number of coupon payments per year. i2Q Enter the annual yield (%). i 7.2 Q YIELD(I/Y)= Calculate bond price. i @ PRICE(PV)= Calculate the accrued interest. i ACCU INT= Calculate bond price including accrued interest. si + i/= PV+ANS= 650 10000 11- 3-2006 8-15-2023 CPN/Y(N)= 200 720 9323 141 9464 Answer: The bond sold at $93.23 and the accrued coupon interest was $1.41 (the bond price including accrued interest would be $94.64). The asking price on the above bond is $92.50. What will your yield be? 46 Procedure Key operation Display Change the bond price to $92.50. #iii i i i 92.5 Q PRICE(PV)= Calculate the yield. [email protected] YIELD(I/Y)= 9250 728 Answer: The yield will be 7.28%. Entering dates Refer to the following notes for date entry. • Enter using US date format (MM-DD-YYYY) or EU date format (DD-MM-YYYY). Refer to the previous example and the following explanation. Month entry Enter two digits. From 2 to 9, the preceding zero may be omitted. Day entry Enter two digits. From 4 to 9, the preceding zero may be omitted. Year entry Enter four digits. From 2010 to 2099, the zero following the first “2” may be omitted. From 1901 to 1989, the “9” following the first “1” may be omitted. • After entry, the date will be stored and the abbreviated day of the week will be displayed. • [SU]: Sunday, [MO]: Monday, [TU]: Tuesday, [WE]: Wednesday, [TH]: Thursday, [FR]: Friday, [SA]: Saturday. • The default value for dates is: January 1, 2001 (1-1-2001). • The effective range of dates is: January 1, 1901 to December 31, 2099. • If an inappropriate date is entered (e.g., February 31), an error message (Error 7) will appear immediately after pressing Q. In this case, follow either of the following procedures: • Press s to return to the display before the entry, enter the appropriate date, and press Q. • Press g/y to go back to the display that was shown before you pressed Q. Press s or L, enter the appropriate date, and press Q again. • If you wish to correct numbers during entry, use L as a backspace key. 47 Depreciation Calculations Using depreciation calculations, you can obtain depreciation base values using three types of calculation methods: the straight-line method, the sum-of-the-years’ digits method, and the declining balance method. Variables used in depreciation calculations Variable Description Default value DB (I/Y)*1 Interest per year 0 LIFE (N) Years of depreciation 1 START MONTH Starting month 1 COST (PV) Cost of asset 0 SALVAGE (FV) Salvage value 0 YEAR Year for calculating depreciation value 1 DEPRECIATE Depreciation value of above year — RBV Remaining book value — RDV Remaining depreciation value — *1 DB (I/Y) appears only when you select DB (declining balance method) for the depreciation method. Setting the depreciation method • Select the depreciation method in the SET UP menu. It is initially set to SL. Key operation Description ~20 SL (Straight-line method) ~21 SYD (Sum-of-the-years’ digits method) ~22 DB (Declining balance method) Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. 48 2. Select the depreciation method (see page 48). 3. Select depreciation calculations by pressing O. SL • When using the declining balance method, DB (I/Y) appears. Enter the number and press Q. • To end depreciation calculations, press s. If you press s during entry, any entered values will be cleared. ---------- 4. Enter the number of years of depreciation into LIFE (N) by pressing i, entering the value, and pressing Q. • When using the straight-line method, the value should be a positive real number, while for the SYD or DB methods, it should be a positive integer. 5. Enter the starting month into START MONTH by pressing i, entering the value, and pressing Q. • You can enter values between 1 and 13. • Generally, it is not necessary to enter a decimal value. However, if you wish to enter, for example, the middle of July, enter 7.5; where the decimal is equal to the number value of the given date divided by the total number of days in the month. 6. Enter the cost of asset into COST (PV) by pressing i, entering the value, and pressing Q. 7. Enter the salvage value into SALVAGE (FV) by pressing i, entering the value, and pressing Q. 8. Enter the year for calculating depreciation value into YEAR by pressing i, entering the value, and pressing Q. • The year for calculating depreciation value is initially 1. Pressing @ increments this number by 1. • This value must be a positive integer. 9. Calculate depreciation for the year by pressing i. 10. Calculate the remaining book value by pressing i. 11. Calculate the remaining depreciation by pressing i. 12. To calculate depreciation value for another year, press z three times to go back to YEAR, enter a value for the new year, and recalculate. 49 Calculating straight-line depreciation In April, your company begins depreciation of a commercial building with a 30-year life and no salvage value. The building costs $1,500,000. Calculate the depreciation amount, remaining book value and remaining depreciable value for the third year using the straight-line depreciation method. Procedure Key operation Display Bring up the initial display in NORMAL mode, and select the straight-line depreciation method. s~20 Select depreciation calculations. O SL Enter the number of years of depreciation. i 30 Q LIFE(N)= Enter the starting month. i4Q START MONTH= Enter the cost of asset. i 1500000 Q COST(PV)= 000 ---------3000 400 150000000 Enter the salvage value. i 0 Q SALVAGE(FV)= Enter the year for calcu- i 3 Q lating depreciation value. YEAR= Calculate depreciation for the year. 000 300 DEPRECIATE= i 5000000 Calculate the remaining i book value. RBV= Calculate the remaining i depreciation value. RDV= 136250000 136250000 Answer: At the third year, the depreciation amount is $50,000, the remaining book value is $1,362,500, and the remaining depreciable value is $1,362,500. 50 Conversion between APR and EFF Interest rates can be converted between APR (annual, or nominal percentage rate) and EFF (effective interest rate). • The APR is an investment’s annual rate of interest when compounding happens only once a year. The interest rate printed on a bond is an example of an APR. • The EFF is an investment’s annual rate of interest when compounding happens more often than once a year. It reflects the actual amount of return for a given nominal rate. For example, if your investment compounds monthly, then the stated nominal percentage rate becomes a monthly rate, and the EFF reflects your actual annual rate of return. Basic operations 1. Press s to clear the display. Make sure the calculator is in NORMAL mode. 2. Enter the calculation data in the following format: • To change APR to EFF: Number of compounding periods per year > Nominal percentage rate . P • To change EFF to APR: Number of compounding periods per year > Effective interest rate . ! Converting between APR and EFF Procedure Key operation Calculate the effective interest rate for twelve compounding periods with an 18% APR. s 12 > 18 . P Convert this rate back to the original APR. 12 > 19.56 . ! Display 12,18¬EFF 1956 12,19.56¬APR 1800 51 Day and Date Calculations Using day and date calculations, you can find dates and the numbers of days between dates. Variables used in day and date calculations Variable Description Default value M-D-Y 1 *1 The first date 1-1-2001 M-D-Y 2 *1 The last date 1-1-2001 DAYS Number of days *1 0 You can change the date format to D-M-Y (see page 10). Setting the day-count method You can toggle between the actual calendar (365 days plus leap years) and a 360-day calendar (12 months of 30 days each) using . &. The actual calendar is set by default (360 is not displayed). The calendar range is from January 1, 1901 to December 31, 2099. Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. 2. Select day and date calculaM-D-Y 1=[MO] tions by pressing K. • To end day and date calculations, press s. If you press s during entry, any entered values will be cleared. 1- 1-2001 3. Change the day-count method, using . &, if necessary. 4. Enter the values of any two known variables: the first date, the last date, or the number of days. • For date entry, refer to page 47, ”Entering dates”. 5. Move to the variable you wish to calculate, using the z and i keys, and press @ to calculate. • If the calculator is set to 360-day calendar mode (360 is displayed), it is not possible to obtain either the first or last dates, only the number of days. 52 1 Calculating number of days Calculate the number of days between December 25, 2008 and August 10, 2009 (using US date format and the actual calendar). Procedure Key operation Display Bring up the initial dis- s play in NORMAL mode. 000 Select day and date K.b calculations, and set all the variables to default values. M-D-Y 1=[MO] 1- 1-2001 Make sure the actual calendar is set (360 is not displayed). Enter the first date. 12252008 Q M-D-Y 1=[TH] Enter the last date. i 8102009 Q M-D-Y 2=[MO] Move to DAYS and calculate. [email protected] DAYS= 12-25-2008 8-10-2009 22800 Answer: 228 days • If the 360-day calendar is selected, the answer will be 225 days. 2 Finding a date Find the date 100 days after November 13, 2010 (using US date format and the actual calendar). Procedure Key operation Display Bring up the initial dis- s play in NORMAL mode. 000 Select day and date K.b calculations, and set all the variables to default values. M-D-Y 1=[MO] 1- 1-2001 Make sure the actual calendar is set (360 is not displayed). Enter the first date. 1113210 Q M-D-Y 1=[SA] Move to DAYS and enter the number of days. i i 100 Q DAYS= 53 11-13-2010 10000 Procedure Key operation Move to the last date and calculate. [email protected] Display M-D-Y 2=[MO] 2-21-2011 Answer: The last date is February 21, 2011. Percent Change/Compound Interest Calculations Using percent change/compound interest calculations, you can determine the values of percentage rates of change (increase or decrease) or interest rates compounding periodically. Variables used in percent change/compound interest calculations Variable OLD PRC (PV) Description Default value Old price (old value) 0 NEW PRC (FV) New price (new value) 0 % (I/Y) Percent change 0 PERIODS (N) Number of compounding periods 1 Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. 2. Select percent change/compound interest calOLD PRC(PV)= culations by pressing . B. • To end percent change/compound interest calculations, press s. • If you press s during entry, any entered values will be cleared. 000 3. Enter the values of any three known variables: old price, new price, percent change, or number of compounding periods. 4. Move to the variable you wish to calculate, using the z and i keys, and press @ to calculate. 54 1 Calculating percent change Sales in a company were $75,000 during the first year of operation. The second year’s sales were $116,000. What percentage greater were the second year’s sales than first year’s sales? In this calculation, the number of compound periods is set to 1 (default). Procedure Key operation Display Bring up the initial dis- s play in NORMAL mode. 000 Select percent change/ . B . b compound interest calculations, and set all the variables to default values. OLD PRC(PV)= 000 Enter the old value. 75000 Q OLD PRC(PV)= Enter the new value. i 116000 Q NEW PRC(FV)= Calculate the percent change. [email protected] %(I/Y)= 7500000 11600000 5467 Answer: The second year’s sales increased by 54.67% over the first year’s sales. 2 Calculating compound interest rate You opened an account compounding annually and deposited $8,000 eighteen years ago. You currently have $9,800. What is the compound interest rate? Procedure Key operation Bring up the initial dis- s play in NORMAL mode. 000 Select percent change/ . B . b compound interest calculations, and set all the variables to default values. Enter the old value. Display 8000 Q 55 OLD PRC(PV)= 000 OLD PRC(PV)= 800000 Procedure Key operation Enter the new value. i 9800 Q Set the number of com- i i 18 Q pound periods to 18. Calculate the compound interest rate. [email protected] Display NEW PRC(FV)= 980000 PERIODS(N)= 1800 %(I/Y)= 113 Answer: The compound interest rate is 1.13%. Cost/Sell/Margin/Markup Calculations Using cost/sell/margin/markup calculations, you can determine costs, selling prices, margins and markup. Variables used in cost/sell/margin/markup calculations Variable Description Default value COST Cost 0 SELL Selling price 0 MARGIN Profit margin (%) *1 0 MARK UP Markup (%) *2 — *1 *2 Profit margin (%) is calculated based on selling price. Markup (%) is calculated based on cost. Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. 2. Select cost/sell/margin/markup COSt= calculations by pressing I. • To end cost/sell/margin/markup calculations, press s. • If you press s during entry, any entered values will be cleared. 000 56 3. Enter the values of any two known variables as follows: Unknown variable Known variables COST SELL, and MARGIN or MARK UP *1 SELL COST, and MARGIN or MARK UP *1 MARGIN COST and SELL MARK UP COST and SELL *1 Because only either MARGIN or MARK UP is used in any cost/sell/margin/markup calculation, the unused variable is given a value of “----------”. Initially, MARK UP is set to “---------”. If you enter a value for MARK UP, MARGIN is set to “---------”, and vice versa. 4. Move to the variable you wish to calculate, using the z and i keys, and press @ to calculate. Determining selling price In a furniture business, it is desirable to realize a 95% markup from cost to retail price for each item. A certain sofa costs $455.60. What should its selling price be? Procedure Key operations Display Bring up the initial dis- s play in NORMAL mode. 000 Select cost/sell/margin I . b markup calculations, and set all the variables to default values. COST= 000 Enter cost. 455.6 Q COST= Enter markup rate. i i i 95 Q MARK UP= Calculate selling price. [email protected] SELL= Answer: The selling price should be $888.42. 57 45560 9500 88842 Breakeven Calculations Using breakeven calculations, you can calculate fixed cost, variable cost per unit, unit price, profit and quantity. Variables used in breakeven calculations Variable Description Default value FIXED Fixed cost 0 VARIABLE Variable cost per unit 0 PRICE Unit price 0 PROFIT Profit 0 QUANTITY Quantity 0 Basic operations Refer to page 19 for basic variable operations. 1. Press s to clear the display. • Make sure the calculator is in NORMAL mode. 2. Select breakeven calculations FIXED= by pressing $. • To end breakeven calculations, press s. • If you press s during entry, any entered values will be cleared. 000 3. Enter the values of any four known variables. 4. Move to the variable you wish to calculate, using the z and i keys, and press @ to calculate. Calculating the breakeven point Your company has developed a new product and plans to sell it at a price of $120 per unit. The variable cost per unit is $75.80 and the fixed costs total $15,000. What is the breakeven point for this product? Procedure Key operation Bring up the initial dis- s play in NORMAL mode. Display 000 58 Procedure Key operation Select breakeven $.b calculations, and set all the variables to default values. Display FIXED= 000 Enter fixed cost. 15000 Q FIXED= Enter variable cost per unit. i 75.80 Q VARIABLE= Enter unit price. i 120 Q PRICE= Leave profit as is. i PROFIT= Calculate quantity. [email protected] QUANTITY= 1500000 7580 12000 000 33937 Answer: The breakeven point of this product is 339.37 units. 59 Chapter 4 Scientific Functions This calculator has a variety of functions. Press m 0 to select NORMAL mode and perform scientific calculations. • For basic calculations, see page 11. • When a listed financial variable is displayed, you can enter the result of a scientific calculation into it by pressing Q immediately after completing the calculation. • Scientific calculations can also be performed in STAT mode. • The examples in this chapter are all performed under the SET UP menu’s default settings. Before starting calculation, press s to clear the display. Constant Calculations Example Key operation 34 + 57 = s 34 + 57 = 45 + 57 = 45 = 68 × 25 = 68 x 25 = 68 × 40 = 40 = Result 9100 10200 170000 272000 • In constant calculations, the addend becomes a constant. Subtraction and division behave the same way. For multiplication, the multiplicand becomes a constant. • In constant calculations, constants will be displayed as . Chain Calculations A calculation result (ANS memory) can be used in a subsequent calculation. However, it cannot be recalled after entering multiple instructions. Example Key operation 6 + 4 = ANS ANS + 5 = s6 +4 = +5 = 8 × 2 = ANS ANS2 = 8x2= .;= 44 + 37 = ANS ANS = 44 + 37 = .}= 60 Result 1000 1500 1600 25600 8100 900 Scientific Calculations Example sin 60 [°] = π cos — [rad] = 4 tan–1 1 [g] = –1 tan 1 [°] = Key operation Display s . { 60 = sin60= ~11. c(. 84 ) = cos(π©4)= ~12. 71 = tan-|1= ~10. 71 = tan-|1= 087 071 5000 4500 • The range of the results of inverse trigonometric functions –1 –1 θ = sin x, θ = tan x –1 θ = cos x DEG –90 ≤ θ ≤ 90 0 ≤ θ ≤ 180 RAD π π –—≤θ≤— 2 2 0≤θ≤π –100 ≤ θ ≤ 100 0 ≤ θ ≤ 200 GRAD Example Key operation (cosh 1.5 + sinh 1.5)2 = s ( . ] c1.5 + . ] {1.5 ) .;= 5 = tanh–1 — . ] 7 (5 8 7 )= log 50 = . h 50 = In 20 = . d 20 = 101.7 = . :1.7 = e3 = .R3= 7 Result 2009 090 170 300 5012 2009 6.;+7.; = 031 8 –3 ×5 = [email protected],2-3 [email protected]; = -202498 1 6 1 7 —+—= –2 4 1 3 – 4 (12 ) = 49 – 4 2 12 . @ 3 . @ 4 .;= 81 = . } 49 - 4 . : 81 = 61 645 400 Example 4! = P3 = 10 C2 = 5 What is 25% of 500? Key operation 4.o= 10 . q 3 = 5.p2= 500 x 25 . % 120 8 400 . % What percentage of 400 is 120? Result 2400 72000 1000 12500 3000 500 + (500 × 25%) = 500 + 25 . % 62500 400 – (400 × 30%) = 400 - 30 . % 28000 Random Functions This calculator has four kinds of random functions (the 2nd function of the - key). Random numbers A pseudo-random number, consisting of three significant digits from zero up to 0.999, can be generated by pressing . | 0 =. To generate further random numbers in succession, press = for each number. Press s to exit. • To display numbers with three significant digits, set the display notation settings to “floating point”. Random dice To simulate a die roll, a random integer between 1 and 6 can be generated by pressing . | 1 =. To generate further random numbers in succession, press = for each number. Press s to exit. Random coin To simulate a coin flip, 0 (heads) or 1 (tails) can be randomly generated by pressing . | 2 =. To generate further random numbers in succession, press = for each number. Press s to exit. 62 Random integer An integer between 0 and 99 can be generated randomly by pressing . | 3 =. To generate further random numbers in succession, press = for each number. Press s to exit. Example Key operation Pick a random number s . | 0 between zero and 9.99. x 10 = Display RANDOMx1—= 532 • The result will not be the same each time this operation is performed. Modify Function Calculation results are internally obtained in scientific notation with a mantissa of up to 14 digits. However, because calculation results are displayed in the form designated by the display notation and the number of decimal places indicated, a displayed calculation result may differ from that held internally. By using the modify function (the 2nd function of the + key), the internal value is converted to match that of the display, so that the displayed value can be used without change in subsequent operations. Example Key operation 5 ÷ 9 = ANS ANS × 9 = [FIX, TAB = 2] s589= x 9 = *1 589= . l x 9 = *2 5.5555555555555 × 10–1 × 9 *2 0.56 × 9 *1 63 Result 056 500 056 504 Chapter 5 Statistical Functions Statistical calculations can be performed in STAT mode. The symbol will be visible if you are in STAT mode. There are seven sub-modes within STAT mode, corresponding to each of the functions below: Key operation m10 m11 m12 m13 m14 m15 m16 Sub-mode Display SD: Single-variable statistics LINE: Linear regression QUAD: Quadratic regression EXP: Exponential regression LOG: Logarithmic regression PWR: Power regression INV: Inverse regression Stat — Stat 1 Stat 2 Stat 3 Stat 4 Stat 5 Stat 6 Entering statistical data Before you can perform statistical calculations, you will need to enter your data. In STAT mode, use > and J (the Q key) to enter the following: For a single-variable data set: Value J Value > frequency J (To enter multiples of the same value) For a two-variable data set: x value > y value J x value > y value > frequency J (To enter multiples of the same x and y values) Note: Before entering data, clear any previously entered data from memory by doing either of the following: • Press . b in STAT mode. • Switch sub-modes within STAT mode. 64 • You can enter a total of up to 100 statistical and/or cash flow data items. For single-variable data, a data set without a frequency is counted as one data item, and a data set with an assigned frequency is counted as two data items. For twovariable data, a data set without a frequency is counted as two data items, while a data set with an assigned frequency is counted as three data items. • If you wish to correct a value before pressing J, press L or s to delete the entry, then enter the correct value. Entering statistical data Enter the data in the table to the right using the “Stat 0” sub-mode. Procedure Key operation DATA 30 40 40 50 Display Enter the “Stat 0” submode. sm10 Stat — Enter statistical data. *1 30 J DATA SET= Return to the “Stat 0” display. 000 100 * 40 > 2 J DATA SET= 50 J DATA SET= s Stat — 200 300 000 there is data stored in memory, press . b (within STAT mode) to clear it. 2 * The format of the data set (the sample and frequency values) number, which is initially set to “1.00”, is dependent on calculator notation settings. *1 If 65 2 Confirming and editing data • Use z / i to display a data item from a previously entered data set. Data set number X1= 1000 x value Data set number Y1= 2000 y value Data set number FRQ1= 1100 Frequency • Press . z or . i to jump to the first or last data item, respectively. • Each data item is displayed in the form: “Xn = (x value)”, “Yn = (y value)”, or “FRQn = (frequency)”, where “n” is the data set number. Editing data • Display the data item you wish to modify by using z / i, enter a new value and press J. Deleting data • Display the data item to be deleted by using z/i, and press . ?. • If a value/frequency is deleted, the corresponding frequency/ value is also deleted. • If you wish to delete all data, press . b. Inserting data Using the z and i keys, specify the correct place to insert your new data by displaying the value that is to come directly after, and then press . e. A new data set with a value of zero and a frequency of one will be inserted. Modify the new data set to include your data. 66 Editing statistical data Change the previously entered data from page 65 as follows: DATA 30 40 40 50 Procedure Display the statistical data. DATA 30 45 45 45 60 Key operation Display X1= i Change the “40, 2” data i i 45 J set to “45, 3”. i3J FRQ2= 3000 300 Delete “50”. i.? Stat — Add “60”. 60 J DATA SET= 000 300 Statistical Calculations and Variables The following results can be obtained for each statistical calculation (refer to the table below): Single-variable statistical calculations Section 1 results only. Linear regression calculations Section 1 and 2 results, except for coefficients c. The estimate of y for a given x (estimate y´) and the estimate of x for a given y (estimate x´) can also be found. Quadratic regression calculation Section 1 and 2 results, and coefficients a, b, and c in the quadratic regression formula (y = a + bx + cx2). In quadratic regression calculations, no correlation coefficient r can be obtained. 67 The estimate of y for a given x (estimate y´) and the estimate of x for a given y (estimate x´) can also be found. When there are two x values, the COMP symbol will appear. Press @ to switch between x values. Exponential regression, logarithmic regression, power regression, and inverse regression calculations Section 1 and 2 results, except for coefficients c. The estimate of y for a given x (estimate y´) and the estimate of x for a given y (estimate x´) can also be found. Because the calculator converts each formula into a linear regression before actual calculation takes place, it obtains all statistics — except coefficients a and b — from converted data rather than from entered data. Variables 1 2 Content n Number of samples x Mean of samples (x values) sx Sample standard deviation (x values) σx Population standard deviation (x values) Σx Sum of samples (x values) Σx Sum of squares of samples (x values) 2 y Mean of samples (y values) sy Sample standard deviation (y values) σy Population standard deviation (y values) Σy Sum of samples (y values) Σy Sum of squares of samples (y values) 2 Σxy Sum of products of samples (x, y) a Coefficient of regression equation b Coefficient of regression equation c Coefficient of quadratic regression equation r Correlation coefficient • Use i or f to perform a variable calculation in STAT mode. 68 1 Single-variable statistical calculation Example Key operation m10. b DATA Result S a — 000 95 95 J DATA SET=100 80 80 J DATA SET=200 80 J DATA SET=300 75 75 75 75 > 3 J DATA SET=400 50 50 J DATA SET=500 x= f= – x= 7571 σx = f2 σ≈= 1237 n= fn n= Σx = fU Í≈= 2 Σx = f[ Í≈Œ= sx = f4 Sx= sx2 = .;= SxŒ= 700 53000 4120000 1336 17857 ( 95 - i (95 – x ) =)8i — × 10 + 50 = sx 4 x 10 + 50 = 69 6443 2 Linear regression calculation Example DATA x y Key operation m11 Result S a 1 000 2 5 2>5J DATA SET=100 2 5 J DATA SET=200 12 24 12 > 24 J DATA SET=300 21 21 21 40 40 40 21 > 40 > 3 J DATA SET=400 15 25 15 > 25 J DATA SET=500 a= fa a= b= fb b= r= fr r= sx = f4 Sx= sy = f5 Sy= 3.? 3y´ 46x´ x=3 y = 46 y´ = ? x´ = ? 46 . 9 70 105 183 100 854 1567 653 2462 3 Quadratic regression calculation Example DATA x Key operation m12 Result S a ≈¡= 000 SET=100 SET=200 SET=300 SET=400 SET=500 536 -312 050 2449 963 ≈™= -343 ≈¡= 963 y 12 41 12 > 41 J DATA 8 13 8 > 13 J DATA 5 2 5>2J DATA 23 200 23 > 200 J DATA 15 71 15 > 71 J DATA a= fa a= b= fb b= c= fa c= 10y´ x = 10 y´ = ? 10 . ? y = 22 x´ = ? 22 . 9 @ @ 71 2 Appendix Financial Calculation Formulas TVM solver PMT, PV, FV, N If PMT ≠ 0 or N ≠ 1 then find i using the following equations: Error + Error i≤ –1 Amortization calculations Calculations (for PV, PMT, and i, see the TVM solver) END INT(1) = ROUND(–PV × i) BGN INT(1) = 0 PRN(1) = –INT(1) + ROUND(PMT) BAL(1) = PRN(1) + PV INT(m) = ROUND(–BAL(m – 1) × i) PRN(m) = –INT(m) + ROUND(PMT) BAL(m) = PRN(m) + BAL(m – 1) ROUND(NUM): If a display notation tab setting has been chosen, NUM is rounded and truncated to the specified number of places after the decimal point. Results Error AMRT P1 > AMRT P2 Discounted cash flow analysis m m CF I/Y RATE(I/Y) where i = 100 , CFimax = the maximum data set number If PMT = 0 then If N = 1 then 72 IRR is obtained as i, which satisfies NPV = 0 in the above equations. Bond calculations In its bond calculations, this calculator conforms to rules set up by the book titled Standard Securities Calculation Methods, by Jan Mayle, Securities Industry Association, 1993. Bond calculation is based on the following rules: 1. Whenever the redemption date happens to be the last day of a month, coupons are also paid on the last days of months. For example, if coupon payments are semi-annual and the redemption date is September 30, coupon payments occur on March 31 and September 30. 2. If coupons are to be paid twice a year and the redemption date is set to August 29, 30, or 31, coupon payments for February occur on the 28th (29th for leap years). 3. The “Odd Coupon” is not supported. 4. All data stored or calculated for bonds are assumed to be positive values. Negative values in any of the variables used by bond calculations will cause errors. The formulas used for bond calculations are shown using the following variable definitions: TD: Total number of days in the coupon period that begins with the coupon date previous to the settlement date and ends with the first coupon date after the settlement date. (On the 360-day calendar, TD is 180 for semi-annual coupon and 360 for annual coupon.) PD: The number of days preceding the settlement date in the coupon period described above. (see “Day and date calculations”) FD: The number of days following the settlement date in the coupon period described above (in TD). FD = TD – PD NP: The number of whole coupon periods between the settlement date and the redemption date (rounded up to the next highest whole number, if necessary). For one coupon period or less until redemption of bond: For more than one coupon period until redemption: where CPN = COUPON(PMT), RDV = REDEMPT(FV), N = CPN/Y(N), YIELD = YIELD(I/Y), PRICE = PRICE(PV). Yield is obtained as YIELD, which satisfies the above equations. Error CPN < 0 or RDV < 0 or PRICE < 0 or M-D-Y 1 ≥ M-D-Y 2 or YIELD ≤ –100 73 Depreciation calculations ROUND(NUM): If a display notation tab setting has been chosen, NUM is rounded and truncated to the specified number of places after the decimal point. In the following equations, M01 = START MONTH, LIF = LIFE(N), CST = COST(PV), SAL = SALVAGE(FV), and DB = DB(I/Y). Straight-line method (SL) Results Calculations If 1 < n < end_year then Error CST < 0 SAL < 0 CST < SAL Results LIF: when SL, LIF ≤ 0 when SYD or DB, LIF is not a positive integer I/Y < 0 (DB only) Conversion between APR and EFF Sum-of-the-years’ digits method (SYD) Calculations N, EFF ¬ APR 1 EFF + 1)N –1) N 100 100 Error (( EFF ≤ –100 N, APR ¬ EFF (( Results APR N 100 N + 1) –1) 100 Error APR ≤ –100 N Day and date calculations Declining balance method (DB) In day and date calculations, this calculator conforms to rules set up in the book titled Standard Securities Calculation Methods, by Jan Mayle, Securities Industry Association, 1993. Calculations 74 30/360 Statistical Calculation Formulas 1. Adjust D1 and D2 according to the following rules: Type (1) If D2 and D1 are both the last day of February, change D2 to 30. Regression formula Linear y = a + bx (2) If D1 is the last day of February, change D1 to 30. Quadratic y = a + bx + cx2 (3) If D2 is 31 and D1 is 30 or 31, change D2 to 30. Exponential y = a • ebx Logarithmic y = a + b • Inx Power y = a • xb Inverse 1 y=a+b x (4) If D1 is 31, change D1 to 30. 2. Calculate using the following formula: DAYS = (Y2 – Y1) × 360 + (M2 – M1) × 30 + (D2 – D1) Actual x = Σnx Percent change/Compound interest calculations Σ x2 – nx2 sx = n–1 Σ x2 – nx2 n σx = Σ x = x1 + x2 + ··· + xn Σ x2 = x12 + x22 + ··· + xn2 y= where NEW = NEW PRC(FV), OLD = OLD PRC(PV), %CH = %(I/Y), PD = PERIODS(N) sy = Error %CH ≤ –100 NEW × OLD ≤ 0 σy = Cost/Sell/Margin/Markup calculations Σy n Σ y2 – ny2 n–1 Σ y2 – ny2 n Σ y = y1 + y2 + ··· + yn Σ y2 = y12 + y22 + ··· + yn2 Σ xy = x1y1 + x2y2 + ··· + xnyn where MAR = MARGIN, MU = MARK UP Breakeven calculations 75 An error will occur in a statistical calculation if: • The absolute value of an intermediate or calculation result is equal to or greater than 1 × 10100. • The denominator is zero. • An attempt is made to find the square root of a negative number. • No solution exists for a quadratic regression calculation. Errors and Calculation Ranges Errors An error will occur if an operation exceeds the calculation ranges, or if a mathematically illegal operation is attempted. When an error occurs, pressing g or y automatically moves the cursor back to the place in the equation where the error occurred. Edit the equation or press s to clear the equation. Note: If an error occurs during the automatic calculation of a listed financial variable, pressing s, g, or y displays the first variable in the function. Error codes and error types Syntax error (Error 1): • An attempt was made to perform an invalid operation. Ex. 2 + - 5 = • During the editing or insertion of cash flow or statistical data, a value was entered but . ? was pressed before J. Calculation error (Error 2): • The absolute value of an intermediate or final calculation result equals or exceeds 10100. • An attempt was made to divide by zero. • The calculation ranges were exceeded while performing calculations. • There was a financial calculation error, such as: • an error listed in “Financial Calculation Formulas” (see pages 72 – 75) occurred • an attempt was made to find I/Y when PV, PMT × N, and FV contain all negative or all positive values • an attempt was made to find IRR when the cash flow data contains all negative or all positive values • an attempt was made to find YIELD in a bond calculation when any of COUPON, REDEMPT, or PRICE contain negative values Depth error (Error 3): • The available number of buffers was exceeded. (There are 10 buffers for numeric values and 24 buffers for calculation instructions). • The number of entered cash flow and statistics data items combined exceeded 100. 76 Equation too long (Error 4): • The equation exceeded its maximum input buffer (160 characters). An equation must be shorter than 160 characters. No solution (Error 5): • The iteration limit was exceeded while calculating one of the following values in an overly complex problem: • I/Y (TVM solver) • IRR (Discounted cash flow analysis)*1 • YIELD (Bond calculations) *1 If you get an error while calculating IRR, enter an estimated value into RATE(I/Y) and calculate again. Display error (Error 6): • An attempt was made to display “9.999 × 1099” when the display notation tab number was set to “2”. If this happens, press s and ~ 0 2 to set the display notation settings to “floating point”. Then try again. Input value error (Error 7): • An attempt was made to enter a nonexistent date. Ex. February 30th • An attempt was made to enter an invalid numeric value into a financial calculation. • a negative value or 0 into P/Y or C/Y • anything except an integer between 1 and 9,999 into AMRT P1 or AMRT P2 • a non-integer into DAYS • anything except 1 or 2 into CPN/Y • anything except an integer between 1 and 999 as a cash flow frequency • anything except a positive integer into YEAR • anything except a value between 1 and 13 into START MONTH 77 Calculation ranges of functions • Within the ranges specified, this calculator is accurate to within ±1 of the least significant digit of the mantissa. However, a calculation error increases in continuous calculations due to accumulation of each calculation error. (This is the same for financial calculations, x x x , e , ln, n!, etc.], where continuous scientific calculations [y , calculations are performed internally.) Additionally, a calculation error will accumulate and become larger in the vicinity of inflection points and singular points of functions. In financial calculations, a calculation error increases if the interest is low or the number of payments is high. Press s if you’d like to cancel the calculation while the “calculating!” screen is displayed. • Calculation ranges ±10–99 to ±9.999999999 × 1099 and 0. If the absolute value of an entry or a final or intermediate result of a calculation is less than 10–99, the value is considered to be 0 in calculations and in the display. Function Calculation range sin x, cos x, tan x DEG: | x | < 1010 (tan x : | x | ≠ 90 (2n – 1))* π RAD: | x | < — × 1010 180 π (tan x : | x | ≠ — (2n – 1))* 2 10 × 1010 GRAD: | x | < — 9 (tan x : | x | ≠ 100 (2n – 1))* sin–1 x, cos–1 x |x|≤1 tan–1 x | x | < 10100 In x, log x 10–99 ≤ x < 10100 yx • y > 0: –10100 < x log y < 100 • y = 0: 0 < x < 10100 • y < 0: x = n 1 (0 < | x | < 1: — = 2n – 1, x ≠ 0),* x –10100 < x log | y | < 100 78 Function Calculation range x y 1 • y > 0: –10100 < — log y < 100 (x ≠ 0) x • y = 0: 0 < x < 10100 • y < 0: x = 2n – 1 1 (0 < | x | < 1: — = n, x ≠ 0),* x 1 100 –10 < — log | y | < 100 x ex –10100 < x ≤ 230.2585092 10x –10100 < x < 100 sinh x, cosh x, tanh x | x | ≤ 230.2585092 sinh–1 x | x | < 1050 cosh–1 x 1 ≤ x < 1050 tanh–1 x |x|<1 x2 | x | < 1050 x 0 ≤ x < 10100 1/x | x | < 10100 (x ≠ 0) n! 0 ≤ n ≤ 69* nPr 0 ≤ r ≤ n ≤ 9,999,999,999* n! — < 10100 (n – r)! nCr 0 ≤ r ≤ n ≤ 9,999,999,999* 0 ≤ r ≤ 69 n! — < 10100 (n – r)! * n, r: integer 79 Battery Replacement Notes on battery replacement Improper handling of battery can cause electrolyte leakage or explosion. Be sure to observe the following handling rules: • Make sure the new battery is the correct type. • When installing, orient the battery correctly, as indicated in the calculator. • The factory-installed battery may be exhausted before it reaches the service life stated in the specifications. Note on the erasure of memory contents When the battery is replaced, the memory contents are erased. Erasure can also occur if the calculator is defective or when it is repaired. Make a note of all important memory contents in case accidental erasure occurs. When to replace the battery If the display has poor contrast, or if nothing appears on the screen, even when s is pressed, it is time to replace the battery. Caution • Fluid from a leaking battery accidentally entering an eye could result in serious injury. Should this occur, wash with clean water and immediately consult a doctor. • Should fluid from a leaking battery come into contact with your skin or clothes, wash them immediately with clean water. • If the product is not to be used for some time, to avoid damage to the unit from leaking battery, remove it and store in a safe place. • Keep battery out of the reach of children. • Exhausted battery that is left in the calculator may leak and damage the unit. • Explosion risk may be caused by incorrect handling. • Do not throw battery into a fire, as it may explode. 80 Replacement procedure 1. Turn the power off by pressing . c. 2. Loosen the screw and remove the battery cover. (see fig. 1) 3. Remove the used battery using a ball-point pen or similar object. Do not use a mechanical pencil or any sharp or pointed object to remove the battery. (see fig. 2) 4. Install a new battery into the battery housing with the positive side (+) facing up. (see fig. 3) fig. 1 fig. 2 5. Replace the battery cover and the screw. 6. Press the RESET switch located on the back of the calculator with the tip of a ball-point pen or similar object. Do not use an object with a breakable or sharp tip. (see fig. 4) • Make sure that the display appears as shown. If not, remove the battery, reinstall, and check the display again. fig. 3 fig. 4 000 Automatic power-off function This calculator will turn its power off automatically if no key is pressed for about 10 minutes. Priority Levels in Calculations This calculator performs operations according to the following priority: 1. Functions preceded by their argument (x2, n!, etc.) 2. yx, x 3. Implied multiplication of a memory value (2Y, etc.) 4. Functions followed by their argument (sin, cos, etc.) 5. Implied multiplication of a function (2sin 30, etc.) 6. nCr, nPr 7. ×, ÷ 8. +, – 9. =, M+, M–, ⇒M, and any other calculation ending instructions 81 Key operation and calculation priority 5 + 2 x . { 30 + 25 x 5 . @ 3 = • Parenthesized operations take precedence over other operations. Specifications Calculations: Financial calculations General arithmetic calculations Scientific calculations Statistical calculations Calculation method: D.A.L. (Direct Algebraic Logic) Internal calculations: Mantissas of up to 14 digits Pending operations: 24 calculations, 10 numeric values Power source: 3.0 V … (DC) Lithium battery (CR2032) × 1 Operating life: Approx. 5 years (with 1 hour of daily use) • May vary depending on the operating environment and operation method. Operating temperature: 0°C – 40°C (32°F – 104°F) External dimensions: 77 mm (W) × 144 mm (D) × 10.8 mm (H) 3-1/32” (W) × 5-21/32” (D) × 7/16” (H) Weight: Approx. 82.5 g (0.19 lb.) (including battery) Accessories: Battery × 1 (installed), operation manual, and hard case For more information about financial calculators Visit us on the Internet at: http://sharp-world.com/calculator/ For USA only: This product contains a CR Coin Lithium Battery which contains Perchlorate Material – special handling may apply, California residents, See www.dtsc.ca.gov/hazardouswaste/perchlorate/ 82 Index >, 37, 51, 64 + - x 8, 4, 11 =, 11, 15 ,, 11, 37, 61 ( ), 11, 16, 61 <, 23 } :, 60, 61 %, 16, 62 B, 54 z i g y, 6, 13 ! P, 51 ., 11 , 16, 61 ;, 61 :, 61 ., 4, 6, 7 &, 44, 45, 52 i, 4, 6, 7, 15 *, 33 /, 15, 16, 23 ", 22, 28, 33 #, 45 $, 58 b, 12, 19 <, 41 >, 37, 38 ?, 39, 66 @, 7, 19 I, 56 J, 37, 64 K, 52 L, 12 O, 49 Q, 7, 19 R, 61 S, 11 t, 22, 23 ], 7, 61 f, 22, 23 d, 13 e, 39, 66 d, 61 h, 61 M, 15 h, 11, 16 j, 16 k, 5, 12, 13 l, 63 m, 6, 10, 12 N, 22, 23 o, 62 p q, 62 c, 6 s, 6, 12 w, 22, 23 u, 22, 23 , 22, 23 |, 62, 63 f, 7, 15 ~, 6, 8–10 g, 7, 15 ;, 16, 60, 61, 69 @, 61 % (I/Y), 18, 54, 75 ∑INTEREST, 33, 72 ∑PRINCIPAL, 33, 72 ACCU INT, 44 Amortization calculations, 17, 33–36, 72 AMRT P1, AMRT P2, 12, 33, 77 Angular unit, 8, 9, 61 Annuity due, 7, 22, 28 ANS (last answer memory), 14, 15 APR, 17, 51, 74 Arithmetic calculations, 11 Arithmetic operations (+, –, ×, ÷), 11 Automatic power-off function, 81 BALANCE, 33, 72 Battery replacement, 80, 81 Bond calculations, 17, 18, 44–47, 73 Breakeven calculations, 17, 58, 59, 75 (symbol), 8, 20 Calculation ranges, 78, 79 Calculator layout, 6 Calendar range, 44, 47, 52 Cash flow data, 12, 37–40, 76 Cash flow diagrams, 21 Chain calculations, 60 COMP (symbol), 7, 20 Compound interest, 21, 54–56, 75 Constant calculations, 60 Conversion between APR and EFF, 17, 51 COST, 56, 75 COST (PV), 18, 48, 74 Cost/sell/margin/markup calculations, 17, 56, 57, 75 COUPON (PMT), 18, 44, 73, 76 CPN/Y (N), 18, 44, 77 Cursor key, 6, 13 C/Y, 18, 22, 72, 77 Date format, 10, 44, 47, 52 Day and date calculations, 17, 18, 52–54, 74 Day-count method (ACT/360), 44, 52 DAYS, 52, 53, 75 DB, 9, 48, 74 DB (I/Y), 18, 48, 74 Decimal place, 8, 9, 63 DEG, 8, 9, 61, 78 Delete key, 12 DEPRECIATE, 48 Depreciation calculations, 17, 18, 48–50, 74 Depreciation method, 9, 48 83 Discounted cash flow analysis, 17, 18, 37–43, 72 Display layout, 7 Display notation, 8 EFF, 17, 51, 74 ENT (symbol), 7, 20 Entering dates, 47 Entering numbers, 11 Error, 14, 76–78 EXP, 64 Financial calculations, 17, 18, 72 FIXED, 58, 75 FLO_A (FLOAT A), FLO_B (FLOAT B), 7, 9 Floating point, 8, 9 Formulas, 72–75 FV, 18, 22, 72 GRAD, 8, 9, 61, 78 Independent memory (M), 8, 12, 14, 15 Insert mode, 13 INV, 64 IRR, 40, 41, 72, 77 I/Y, 18, 22, 72, 77 LIFE (N), 18, 48, 74 LINE, 64 Listed financial variables, 12, 14, 15, 18, 19 LOG, 64 M (symbol), 8 MARGIN, 56, 75 MARK UP, 56, 75 M-D-Y 1, M-D-Y 2, 18, 44, 52, 73, 75 Memory clear key, 5, 12, 13 Modify function, 63 N, 18, 22, 72 NET_PV, 40 NEW PRC (FV), 18, 54, 75 NORMAL mode, 10, 17, 60 NPV, 40, 41, 72 OLD PRC (PV), 18, 54, 75 Ordinary annuity, 7, 22, 28 Overwrite mode, 13 Payment period (payment due), 22, 28 Percent change/compound interest calculations, 17, 18, 54–56, 75 PERIODS (N), 18, 54, 75 Playback function, 13 PMT, 18, 22, 72 PRICE, 58, 75 PRICE (PV), 18, 44, 45, 73, 76 Priority levels in calculations, 81, 82 PROFIT, 58 PV, 18, 22, 72 PWR, 64 P/Y, 18, 22, 72, 77 QUAD, 64 QUANTITY, 58 RAD, 8, 9, 61, 78 Random coin, 62 Random dice, 62 Random functions, 62–63 Random integer, 63 Random numbers, 62 RATE (I/Y), 18, 40, 72 RBV, 48, 74 RDV, 48, 74 REDEMPT (FV), 18, 44, 73, 76 RESET switch, 5, 12, 81 Resetting the calculator, 5 SALVAGE (FV), 18, 48, 74 SCI, 7, 8 Scientific calculations, 60–63 Scientific notation, 8, 9, 11, 63 SD, 64 SELL, 56, 75 SET UP menu, 8–10 SL, 9, 48, 74 Specifications, 82 START MONTH, 48, 74, 77 (symbol), 8, 10, 64 STAT (statistics) mode, 10, 64 Statistical calculations, 10, 64–71 Statistical data, 12, 64–67, 76 Statistical variables, 12, 14, 16, 68 Symbol, 7 SYD, 9, 48, 74 TAB, 7, 8 Temporary memory (A-H, X-Z), 12, 14, 15 TVM (time value of money) solver, 17, 22–32, 72 TVM variable, 12, 14, 15, 18, 19, 22 VARIABLE, 58, 75 YEAR, 12, 48, 77 YIELD (I/Y), 18, 44, 45, 73, 76, 77 84 PRINTED IN CHINA / IMPRIMÉ EN CHINE / IMPRESO EN CHINA 13KC(TINSEA042THZZ)

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