BA II PLUS™ Calculator ©1997, 2002 Texas Instruments Incorporated
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1: Overview of Calculator Operations Turning the Calculator On and Off.............................. Resetting the Calculator ....................................... Keys and 2nd Functions ....................................... The Display .................................................. Display Indicators ............................................ Setting Calculator Formats .................................... Clearing the Calculator ........................................ Correcting Entry Errors ...
iv 2: Time-Value-of-Money and Amortization Worksheets 27 TVM and Amortization Worksheet Labels .................... Time-Line Diagrams ..................................... Procedure: Using the TVM Worksheet ...................... Procedure: Generating an Amortization Schedule ............. Procedure: Automatically Generating a Schedule ............. Basic Loan Calculations—Interest ......................... Basic Loan Calculations—Payments ........................ Future Value of Savings ...............
4: Bond Worksheet 73 Terminology ........................................... Entering Bond Data and Computing Results.................. Bond Price and Accrued Interest Example ................... 76 77 79 5: Depreciation Worksheet 81 Depreciation Worksheet Labels ............................ Entering Data and Computing Results ...................... Declining Balance with Straight-Line Crossover Example .......... Straight-Line Depreciation Example ........................
Appendix: Reference Information Formulas ............................................. Error Conditions ....................................... Accuracy Information ................................... IRR Calculations ....................................... AOSé (Algebraic Operating System) Calculations ............. Battery Information ..................................... In Case of Difficulty ..................................... Texas Instruments (TI) Support and Service Information .......
1 Overview of Calculator Operations This chapter contains information on: • Basic calculator operation • Clearing and correcting • Math operations • Memory • Last Answer • Worksheets 1: Overview of Calculator Operations 1
Turning the Calculator On and Off Turning the Calculator On Press $ to turn the calculator on. • If you turned the calculator off by pressing $, the calculator returns to operation in the standard-calculator mode. A value of zero is displayed and the values in all of the worksheets are the same as you left them, as are the formats for numbers, angle units, dates, separators, and calculation method.
Resetting the Calculator Resetting the calculator restores all default settings and clears all data. Because you can clear only selected portions of data, you should reserve the reset function for appropriate situations. You might choose to reset when you first purchase the calculator or when you start a new project. Effects of Resetting • Clears the display and any unfinished calculation. • Clears all 10 memories. • Clears all worksheet data and restores the default settings.
Keys and 2nd Functions The primary function of each key is printed on the key. For example, press $ to turn the calculator on or off. Some keys provide a secondary function. which is printed in yellow above the key. When you press &, the character, abbreviation, or word printed above a key becomes active for the next keystroke. For example, press & U to leave a worksheet and return to standard-calculator mode. The Display The display shows entries and results with up to 10 digits.
Display Indicators Indicator Meaning 2nd The calculator will access the second function of the next key pressed. INV The calculator will access the inverse function of the next key or key sequence pressed. HYP The calculator will access the hyperbolic function of the next key or key sequence pressed. COMPUTE You can compute a value for the displayed variable by pressing %. ENTER You can enter a value for the displayed variable by keying in a value and pressing !.
Setting Calculator Formats You can set formats for five aspects of the calculator. Format Options Default Number of decimal 0 – 9 places (floating-decimal format = 9) 2 places Angle units DEG degrees (DEG) or radians (RAD) (degrees) Dates US format mm-dd-yyyy or Eur US format (European) format dd-mm-yyyy Number separators US format 1,000.00 or Eur (European) format 1.
Procedure: Changing the Number of Decimal Places 쐃 Press & |. DEC= is displayed with the current decimal-place setting. 쐇 Enter the number of decimal places to be displayed (0 through 9) and press !. To specify a floating-decimal format, enter 9. 쐋 Choose one of the following to continue: < To continue setting formats, press #. < To return to the standard-calculator mode, press & U . < To access a worksheet, press the appropriate worksheet key or key sequence.
Date Format Both the Bond and Date worksheets use dates. You can select either the US or the European display format. The default setting for dates is the US format. US format (US): Month European format (EUR): Day 12 31 Day - 31 Year - Month - 12 1990 Year - 1990 Procedure: Changing the Date Format 쐃 If necessary, press & | # #. The most recently selected date format is displayed, either US or EUR. 쐇 Press & V repeatedly to select either US or EUR.
Separator Format You can select either the US or the European format for the display of separators in numbers. The default setting for separators is the US format. US and UK format (US): 1,000.00 European format (EUR): 1.000,00 Procedure: Changing the Separator Format 쐃 If necessary, press & | # # #. The most recently selected separator format is displayed, either US or EUR. 쐇 Press & V repeatedly to select either US or EUR.
Calculation Method You can select either the chain calculation method or the AOS (algebraic operating system) calculation method. The default setting for calculation method is chain (Chn). When the calculation method is set to Chn (chain), the calculator solves problems in the order that you enter them. This calculation method is used in most financial calculators. For example, in Chn when you enter 3 H 2 < 4 N, the answer is 20 (3 + 2 = 5, 5 * 4 = 20).
Clearing the Calculator To clear . . . Keystrokes . . . one character at a time from the display (including decimal points). * . . . an incorrect entry, an error condition, or an error message from the display. P . . . out of a worksheet and return to standard-calculator mode. &U . . . all pending operations in the standard-calculator mode and display zero. &U . . . in a worksheet, a value you have keyed into the display but not yet entered as a variable value. The previous value PP* returns. . .
Correcting Entry Errors If you enter an incorrect number but have not yet pressed an operation key (such as H or 4), you can correct the number without clearing the calculation. • Remove the last digit or decimal point from a number you have keyed in by pressing the backspace key * and then enter the correct digit. • Erase the entire number by pressing P once, then key in the correct number and continue with your calculation.
Math Operations When the calculation method is set to chain (Chn), mathematical expressions, such as 3 + 2 Q 4, are evaluated in the order that you enter them. The N key completes an operation and displays the result. Operation Example Keystrokes Addition 6+4 6H4N 10.00 Subtraction 6N4 6B4N 2.00 Multiplication 6Q4 6<4N 24.00 Division 6P4 664N 1.50 Universal power 3 1.25 3 ; 1.25 N 3.95 Parentheses 7 Q (3 + 5) 7<93H5:N 56.00 Percent 4% of $453 453 < 4 2 N 18.
Math Operations (cont.) Some operations are performed immediately and do not require that you press N. Operation Example 15.5 Square root Keystrokes Display 15.5 3 3.94 0.31 Reciprocal 1/3.2 3.2 5 Factorial 5! 5&g Natural logarithm ln 203.45 203.45 > 5.32 .69315 & i 2.00 263N&o 0.67 Generate random number &a 0.86 Store “seed” value D&a 0.86 sin(11.54°) 11.54 & d 0.20 Cosine** cos(120°) 120 & e N0.50 Tangent** tan(76°) 76 & f 4.01 -1 .2 8 d 11.54 -1 .
More on Selected Math Operations Universal Power ; lets you raise a positive number to any power (2 or 2 , for example). However, you can raise a negative number only to an integer power or the reciprocal of an odd number. In either case, the power can be either positive or negative. .5 (1/3) Parentheses Parentheses let you control the order in which a numeric expression is evaluated. The portion of an expression enclosed in parentheses is evaluated separately.
Permutations & m computes the number of permutations of n items taken r at a time. n Pr = n! ( n − r )! Rounding The round function is useful when you need to perform a calculation using the displayed form of a number rather than the unrounded value that the calculator stores internally. The decimal format setting does not round the calculator’s internally stored value, only the displayed value. & o lets you change the internal value to match its displayed form.
Memory Operations Your calculator always has 10 memories available. • The memories can hold any numeric value within the range of the calculator. • The memories are numbered M0 through M9. This lets you access each memory using a single keystroke. Clearing Memory There are two ways to clear memory. • Storing a zero in an individual memory clears the memory (shown in “Memory Examples” below). • To clear all of the memories simultaneously, press & { & z to clear the Memory worksheet.
Memory Arithmetic Memory arithmetic allows you to perform a calculation on a stored value and then store the result with a single operation. • Memory arithmetic does not change the displayed value, only the value in the affected memory. • Memory arithmetic does not complete any calculation in progress. The table below shows the memory arithmetic functions available with the calculator. In each case, the result is stored in the specified memory. These examples assume that a value is already in the display.
Calculations Using Constants & ` stores a number and an operation for use in repetitive calculations. After you store the constant, you can use it in subsequent calculations by entering a new value and pressing N. The constant is cleared when you press any key other than a numeric entry key or N. Example: Multiply 3, 7, and 45 by 8. Procedure Keystrokes Display Clear calculator. &U Begin first calculation. 3 Store Q 8 in the constant register. <&`8N Compute 7 Q 8. 7N 56.00 Compute 45 Q 8.
Last Answer Feature To display the last answer, press & x. If your current equation calls for the last answer repeatedly, you can retrieve the value of ANS more than once. You can use the last answer feature to copy a value: • From one place to another within the same worksheet. • From one worksheet to another. • From a worksheet to the standard-calculator mode. • From the standard-calculator mode to a worksheet. ANS is updated when: • You enter a value by pressing !. • You compute a value by pressing %.
Using Worksheets: Tools for Financial Solutions What Is a Worksheet? Each worksheet is designed as a framework for a set of variables. The formulas that define the relationships between the variables, though not visible, are built into each worksheet. • Each worksheet is designed to solve specific types of problems such as time-value-of money, cash-flow, bond, or depreciation problems.
Types of Worksheets The calculator has two modes. • In the standard-calculator mode, you can perform standard math operations and compute TVM values (N, I/V, PV, PMT, FV). • In the prompted worksheet modes, you are guided through specialized tasks such as amortization calculations and cash-flow analyses. Worksheet Variables TVM Variables You access the five time-value-of-money variables with the five TVM keys on the third row of the keyboard.
Prompted-worksheet Variables To access the column of variables within a prompted worksheet (or portion of a prompted worksheet), press the appropriate worksheet key or key sequence. For example, to access the amortization variables P1, P2, BAL, PRN, and INT (first payment in a range, last payment in a range, remaining balance, principal, and interest), press & \. This is the prompted worksheet for amortization calculations. Press # and " to move to the next or previous variable in a prompted worksheet.
Compute-Only Variables For compute-only variables, you compute values by displaying the appropriate label and pressing %; you cannot enter a value for this type of variable. When you access a compute-only variable, the variable label and the COMPUTE indicator are displayed. This indicator reminds you to press % to compute a value for the displayed variable. An = sign is displayed between the label and the value when the value has been assigned to the variable.
Enter-or-Compute Variables in Prompted Worksheets Some prompted worksheets contain variables that you can either enter or compute. When you access an enter-or-compute variable, the variable label is displayed along with both the ENTER and COMPUTE indicators. • The ENTER indicator reminds you that if you key in a value for the variable, you must press ! to assign the value to the variable. • The COMPUTE indicator reminds you that if you want to compute a value for the variable, you must press %.
Clearing Worksheets and Setting Defaults &} !* &^ N 0 0 I/Y 0 0 PV 0 0 PMT 0 0 FV 0 0 P/Y 12 12 C/Y 12 12 Label END / BGN END &[ &] &\ &z &z &z END P1 1 1 P2 1 1 BAL 0 0 PRN 0 0 INT 0 0 Note: & } ! also sets the calculator formats (2 decimal places, DEG, US dates, US number separators, CHN calculations).
2 Time-Value-of-Money and Amortization Worksheets The Time-Value-of-Money and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or all outflows. They help you solve problems involving annuities, loans, mortgages, leases, and savings. You can also generate an amortization schedule. Press # and " to move through each set of variables. Z , [ \ ]^ .
TVM and Amortization Worksheet Labels Type of Variable Keys Label Meaning , N Number of periods Enter/compute - I/Y Interest rate per year Enter/compute .
Notes about TVM and Amortization Worksheets (cont.) ♦ Enter values for PV, PMT, and FV as negative if they are outflows (cash paid out) or as positive if they are inflows (cash received). To enter a negative value, press S after entering the number. ♦ Enter I/Y as the nominal interest rate. The TVM worksheet automatically converts I/Y to a “per period” rate based on the values for P/Y and C/Y. ♦ When you enter a value for P/Y, the same value is automatically entered for C/Y. (You can change C/Y.
Entering, Recalling, and Computing TVM Values You enter a TVM value by keying in a value and pressing the appropriate TVM key (,, -, ., /, or 0). The value is stored in the TVM variable (N, I/Y, PV, PMT, or FV). You recall a TVM value to the display by pressing J and the TVM key. When you enter or recall a value for any of the five TVM variables (N, I/Y, PV, PMT, or FV), you can be in either standard calculator mode or a worksheet mode. The display responds differently according to the mode you are in.
Compound Interest Many lending institutions add the interest you earn to the principal. The interest you earn from the previous compounding period becomes part of the principal for the next compounding period. Compound interest enables you to earn a greater amount of interest on your initial investment. In order to earn compound interest, the interest must remain with the principal. For example, if you invest $100 at an annual interest rate of 10% compounded annually, you earn $10 interest after one year.
Time-Line Diagrams A time-line diagram can help you visualize cash flows by showing the amounts paid or received (cash outflows or cash inflows) at various points in time. • Cash flows received are shown with arrows pointing up, as with the loan amount at the left. • Cash flows invested have arrows pointing down, as with the 35 regular payments and the balloon payment at the right. Loan amount 23,000 Enter inflows as positive.
Procedure: Using the TVM Worksheet The worksheet stores the values and settings you enter until you clear the worksheet or change the values or settings. Therefore, you may not need to do all the steps in the procedure every time you work a TVM problem. 쐃 Press & } ! to reset all variables to their defaults (N=0, I/Y=0, PV=0, PMT=0, FV=0; P/Y=12, C/Y=12; END; P1=1, P2=1; BAL=0, PRN=0, INT=0). 쐇 If P/Y (payments per year) should not be 12, press & [, key in the number of payments per year, and press !.
Procedure: Generating an Amortization Schedule The worksheet for amortization calculations uses the values you entered and computed in the TVM worksheet to compute amortization data. The procedures on these pages give you two ways to generate an amortization schedule. 쐃 Press & } ! to reset all variables to their defaults (N=0, I/Y=0, PV=0, PMT=0, FV=0; P/Y=12, C/Y=12; END; P1=1, P2=1; BAL=0, PRN=0, INT=0). 쐇 Press & \. P1= and its current value are displayed. 쐋 Specify the range of payments.
Procedure: Automatically Generating a Schedule After you enter the initial values for P1 and P2, as described above, you can automatically compute an amortization schedule. 쐃 Press & \ or, if INT is displayed, press # to display P1= and its current value. 쐇 Press %. This automatically updates both P1 and P2 to represent the next range of payments. The calculator computes the next range of payments using the same number of periods as in the previous range of payments.
Basic Loan Calculations—Interest Example: Interest Rate You have a 30-year mortgage for $75,000 and make payments each month of $576.69. What is the interest rate of your mortgage? Procedure Keystrokes Display Set all variables to defaults. &}! RST Enter number of payments using payment multiplier. 30 & Z , N= Enter loan amount. 75000 . PV= Enter payment amount. 576.69 S / PMT= Compute interest rate. %- I/Y= 0.00 360.00 75,000.00 -576.69 8.50 The interest rate is 8.5% per year.
Basic Loan Calculations—Payments Example: Monthly Payment You are considering a 30-year mortgage at 8.5% for $75,000. How much would the monthly payment be? Procedure Keystrokes Display Set all variables to defaults. &}! RST Enter number of payments using payment multiplier. 30 & Z , N= Enter interest rate. 8.5 - I/Y= 8.50 Enter loan amount. 75000 . PV= 75,000.00 Compute payment. %/ PMT= 0.00 360.00 -576.69 The monthly payment would be $576.69.
Future Value of Savings Example: Future Value of Savings You have opened a savings account with $5,000. The bank pays 5%, compounded at the end of each year. What is the future value of the account after 20 years? Procedure Keystrokes Display Set all variables to defaults. &}! RST 0.00 Set payments per year to 1. &[1! P/Y= 1.00 Return to calculator mode. &U Enter number of payments. 20 , N= 20.00 Enter interest rate. 5- I/Y= 5.00 Enter beginning balance. 5000 S . PV= -5,000.
Present Value of Savings Example: Future Value of Savings You are opening a savings account that you want to be worth $10,000 in 20 years. The bank pays 5%, compounded at the end of each year. How much do you need to deposit now? Procedure Keystrokes Display Set all variables to defaults. &}! RST 0.00 Set payments per year to 1. &[1! P/Y= 1.00 Return to calculator mode. &U Enter number of payments. 20 , N= 20.00 Enter interest rate. 5- I/Y= 5.00 Enter final balance.
Present Value in Present-Value Annuities Example: Present Value of Cost Savings The Furros Company purchased a machine that provides annual savings of $20,000 per year for the next 10 years. Using an annual discount rate of 10%, compute the present value of the savings using an ordinary annuity and an annuity due. • For a present value ordinary annuity: PV = ? $20,000 $20,000 $20,000 9 N = 10 ...
Example: Present Value of Cost Savings (cont.) Procedure Keystrokes Set all variables to defaults. &}! RST 0.00 Set payments per year to 1. &[1! P/Y= 1.00 Return to calculator mode. &U Enter number of payments. 10 , N= 10.00 Enter interest rate per payment period. 10 - I/Y= 10.00 Enter payment. 20000 S / PMT= -20,000.00 Compute PV for an ordinary annuity. %. PV= 122,891.34… Set beginning-of-period payments. &] &V BGN Return to calculator mode.
Perpetual Annuities A perpetual annuity consists of equal payments that continue indefinitely. An example of a perpetual annuity is a preferred stock that yields a constant dollar dividend. These time-line diagrams represent a perpetual annuity as an ordinary annuity and as an annuity due. • For a perpetual ordinary annuity: PV PMT PMT 1 2 . . . to infinity 0 • For a perpetual annuity due: PV PMT PMT PMT 0 1 2 . . .
Example: Present Value of Perpetual Annuities The Land of OZ has issued perpetual bonds for replacing bricks in their highway system. The bonds pay $110 per $1000 bond. You plan to purchase the bonds if you can earn 15% annually. What price should you pay for the bonds? Procedure Keystrokes Clear. &UPP Display Calculate PV for a perpetual ordinary annuity. 110 6 15 2 N 733.33 Calculate PV for a perpetual annuity due. H 110 N 843.33 0.00 You should pay $733.
Variable Cash Flows In annuities, all payments are equal. In variable cash flows, however, the payments are unequal. You can solve for the present value of variable cash flows by treating the cash flows as a series of compound interest payments. The present value of variable cash flows is the value of cash flows occurring at the end of each payment period discounted back to the beginning of the first cash flow period (time zero). PV = ? CF1 CFj-1 Cfj NN1 N ...
Example: Present Value of Annual Savings Procedure Keystrokes Set all variables to defaults. &}! RST 0.00 Set payments per year to 1. &[1! P/Y= 1.00 Return to calculator mode. &U Enter interest rate per cash flow period. 10 - I/Y= 10.00 Enter 1st cash flow. 5000 S 0 FV= -5,000.00 Enter period number of 1st cash flow. 1, N= Compute present value of 1st cash flow. %. PV= 4,545.45… Store in M1. D1 Enter 2nd cash flow. 7000 S 0 FV= -7,000.00 Enter period number.
Lease-or-Buy Decision Your business is considering getting a new computer server. If you lease, you would pay $36,000 per year for five years at the first of each year. You could buy it for $125,000. The server is expected to save the company $46,000 per year. It will have no resale value at the end of the five years. The company can borrow at 15% annual interest. You require a 20% annual return on projects and investments of this kind.
Example: Present Value of Lease Payments Procedure Keystrokes Set all variables to defaults. &}! RST 0.00 Set payments per year to 1. &[1! P/Y= 1.00 Set beginning-of-period payments. &] &V BGN Return to calculator mode. &U Enter number of periods. 5, Enter periodic interest rate at which your firm can borrow. 15 - Display 0.00 N= 5.00 I/Y= 15.00 Enter annual lease payment. 36000 S / PMT= -36,000.00 Compute present value of lease payments. %. PV= 138,779.
Present Value of Lease with Residual Value The Peach Bright Company wants to purchase a machine that it is currently leasing from your company. You offer to sell it for the present value of the lease discounted at an annual interest rate of 22% compounded monthly. The machine has a residual value of $6500, and 46 monthly payments of $1200 remain on the lease.
Monthly Payments You are planning to purchase a new small desk and chair set that is sale priced at $525. You can finance your purchase at 20% APR, compounded monthly, for two years. How much is the monthly payment? PV = $525 FV = $0 PMT = ? PMT = ? PMT = ? 23 N = 24 ... 0 1 I/Y = 20 ÷ 12 Example: Monthly Payments Procedure Keystrokes Set all variables to defaults. &}! RST Display Enter number of payments using payment multiplier. 2&Z, N= 24.00 Enter interest rate. 20 - I/Y= 20.
Yield to Maturity on Bond Purchased on Interest Date A 9% $1,000 semiannual commercial bond has 13 remaining coupon payments. You can purchase the bond for $852.50 (ignoring commissions). At this price, what is your yield to maturity and the annual effective rate? Example: Yield to Maturity Procedure Keystrokes Display Set all variables to defaults. &}! RST 0.00 Set payments per year to 2. &[2! P/Y= 2.00 Return to calculator mode. &U Enter number of remaining coupon payments.
Saving for the Future by Making Monthly Deposits Accounts with payments made at the beginning of the period are referred to as “annuity due” accounts. Interest on annuity due accounts starts accumulating earlier and produces slightly higher yields. An individual has decided to invest $200 at the beginning of each month in a retirement plan. What will the account balance be at the end of 20 years if the fund earns an annual interest of 7.
Amount to Borrow and Down Payment You want to buy a car that sells for $5,100. The finance company charges 13.51% APR, compounded monthly, on a 48-month loan. If you can afford a monthly payment of $125, how much can you borrow? How much do you need for the down payment? Example: Loan Amount and Down Payment Calculate the loan amount. Then subtract it from the cost of the car to find the down payment. PV = ? FV = $0 $125 $125 $125 47 N=48 ... 0 1 I/Y = 13.
Regular Deposits for a Specified Future Amount You plan to open a savings account and deposit the same amount of money at the beginning of each month. In 10 years, you want to have $25,000 in the account. How much should you deposit if the annual interest rate is 7% with quarterly compounding? C/Y (compounding periods per year) is automatically set to equal P/Y (payments per year), so you need to set C/Y. Example: Monthly Deposits Compounded Quarterly Procedure Keystrokes Set all variables to defaults.
Time Value of Money/Amortization Schedule This two-part example shows you how to use the TVM and Amortization worksheets to compute the monthly payment on a 30-year loan and then generate an amortization schedule for the first three years of the loan. Example: Mortgage Payment Using the TVM worksheet, determine the monthly payment on a 30-year mortgage with a loan amount of $120,000 and an annual percentage rate of 9.125%. Procedure Keystrokes Display Set all variables to defaults.
Example: Loan Amortization (continued from previous example) Use the Amortization worksheet to generate an amortization schedule for the first three years of the loan. Assume that the first payment is in April; therefore, the first year has 9 payment periods. There are 12 payment periods per year thereafter. Procedure Keystrokes Select the Amortization worksheet. &\ P1= 1.00 # 9! P2= 9.00 Set ending period to 9. Display first year amortization # # data. # Display BAL= 119,407.46 PRN= -592.
Interest and Loan Balance after Specified Payment To evaluate the financial advisability of financing all or some of the sale price of a property, a seller must know the amount of interest that will be received and the remaining balance at the end of the term (balloon payment). A seller is asked to finance $82,000 at 10% annual interest, amortized over a 30-year term but with a balloon payment due after five years. The seller wants to know: • The amount of the monthly payment.
Canadian Mortgages Canadian mortgages typically require the borrower to make monthly payments, although interest is compounded semiannually. Additionally, mortgages are usually refinanced at the end of a fixed period of time, such as five years. A home buyer borrows $60,000 for 20 years at an annual interest rate of 13 % compounded semiannually.
58 BA II PLUS™ Calculator
3 Cash Flow Worksheet Three keys are used for performing cash-flow calculations. ' lets you enter cash flow data. ( lets you compute net present value. ) lets you compute internal rate of return. Press # and " to move through each set of variables.
Cash Flow Worksheet Labels Key Label Meaning Variable Type ' CFo Initial cash flow Enter-only # Cnn* Amount of n th cash flow Enter-only # Fnn* Frequency of n th cash flow Enter-only ( Z Discount rate Enter-only # NPV Net present value Compute-only ) IRR Internal rate of return Compute-only * nn represents the number of the cash flow (C01–C24) or the number of the corresponding frequency (F01–F24). Notes about the Cash Flow Worksheet ♦ ' & z sets all variable values to zero.
Interpreting the Results of IRR Calculations When you compute a value for IRR (internal rate of return), the calculator displays either a solution or an error message. When a solution is displayed, there are two possibilities. • The displayed solution is the only solution. • There may be additional solutions. This occurs when there are two or more sign changes in the cash flow sequence. When an error message is displayed, there are two possibilities. • No solution for IRR exists (Error 5).
Uneven and Grouped Cash Flows Uneven Cash Flows The Cash Flow worksheet lets you analyze the value of money over equal time periods. It allows you to enter uneven values, each of which can be either an inflow (cash received) or an outflow (cash paid out). Similar to an annuity’s present value (PV) in the TVM worksheet, a typical cash-flow problem usually has an initial cash flow (labeled CFo). This is always a known, entered value.
Entering Cash Flows You can enter the initial cash flow and up to 24 additional cash flows, each of which can be a unique value. Enter inflows as positive and outflows as negative. If you have consecutive cash flows of equal value, you can enter the cash-flow value and then a frequency of up to 9,999 for the number of times the value occurs. Procedure: Entering Cash Flows 쐃 Press ' to select the cash flow entry portion of the Cash Flow worksheet. CFo= and its current value are displayed.
Deleting Cash Flows When you delete a cash flow, the calculator decreases the numbers of subsequent cash flows . Before deleting 8,000 cash flow After deleting 8,000 cash flow Procedure: Deleting a Cash Flow The DEL indicator lets you know when you can delete a cash flow. 쐃 Press # or " until the cash flow you want to delete is displayed. 쐇 Press & W. The cash flow you specified (and its frequency) is deleted. The calculator decreases the numbers of subsequent cash flows so that there is no gap.
Inserting Cash Flows When you insert a cash flow, the calculator increases the numbers of the current and subsequent cash flows. When inserting cash flows, remember that the most cash flows you can enter is 24. Procedure: Inserting a Cash Flow The INS indicator lets you know when you can insert a cash flow. 쐃 Press # or " until the display shows the current cash flow where you want to insert the new cash flow. For example, if you want to insert a new second cash flow, display C02. 쐇 Press & X.
Computing NPV and IRR IRR (internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero. NPV (net present value) is the sum of the present values for the cash inflows (cash received) and outflows (cash paid out). A positive value for NPV indicates a profitable investment. Procedure: Computing Net Present Value 쐃 Press (. Z= and its current value are displayed. 쐇 Key in a value for Z (discount rate) and press !.
Uneven Cash Flows A company plans to pay $7,000 for a new machine. The company would like a 20% annual return on its investment. Over the next six years, the company expects to receive the annual cash flows shown below. Year Cash Flow Number Cash Flow Estimate 1 1 3,000 2–5 2 5,000 each year 6 3 4,000 The following time line shows that these cash flows are a combination of equal and unequal values. Because the initial cash flow (CFo) is an outflow, it is a negative value.
Example: Editing Cash Flow Data (continued from previous example) After entering the data, you learn that the cash flow projections you were given were incorrect. The $4,000 cash-flow value should occur in the second year instead of the sixth. Otherwise, the entries are correct.
Example: Computing Net Present Value (continued from previous example) Compute the net present value (NPV) using an interest rate per period ([) of 20%. Procedure Keystrokes Display Access NPV. ( [= 0.00 Enter interest rate per period. 20 ! [= 20.00 Compute net present value. #% NPV= 7,266.44 Example: Computing Internal Rate of Return (continued from previous example) Compute the internal rate of return (IRR). Procedure Keystrokes Display Access IRR. ) IRR= 0.
Value of a Lease with Uneven Payments A lease with an uneven payment schedule usually accommodates seasonal or other anticipated fluctuations in the lessee’s cash position. Suppose a 36-month lease has the following payment schedule, with beginning-of-period payments.
Example: Compute Net Present Value of Cash Flows The cash flows for the first four months are stated as a group of four $0 cash flows. Because the lease specifies beginning-ofperiod payments, you must treat the first cash flow in this group as the initial investment (CFo) and enter the remaining three cash flows on the cash flow screens (C01 and F01). Note: The BGN/END setting in the TVM worksheet does not affect the Cash Flow worksheet.
Example: Compute Equivalent Monthly Payments (continued from previous example) Use the net present value (NPV) from the Cash Flow worksheet as the present value (PV) in the TVM worksheet to compute the equivalent even monthly payment that is equivalent to the uneven cash flows. Present value (PV) = NPV from Cash Flow worksheet Interest (I/Y) = 10% Number of payments (N) = 36 ... Payment amount (PMT) = ? Procedure Keystrokes Display Set beginning-of-period payments. &] &V Return to calculator mode.
4 Bond Worksheet To access the Bond worksheet, press & l. Press # and " to move through each set of variables.
Bond Worksheet Labels Label Meaning Variable Type SDT Settlement date Enter-only CPN Annual coupon rate in percent Enter-only RDT Redemption date Enter-only RV Redemption value (percentage of par value) Enter-only ACT* Actual/actual day-count method Setting 360* 30/360 day-count method Setting 2/Y* Two coupons per year Setting 1/Y* One coupon per year Setting YLD Yield to redemption Enter/compute PRI Dollar price Enter/compute AI Accrued interest Auto-compute * Press & V re
Notes about the Bond Worksheet (cont.) ♦ Enter a date for RDT (redemption date) in the date format you selected (U.S. or European). The calculator assumes that the redemption date (RDT) coincides with a coupon date. < For “to maturity” calculations, enter the maturity date for RDT. < For “to call” calculations, enter the call date for RDT. ♦ Redemption value (RV) is a percentage of the bond’s par value. < For “to maturity” analysis, enter 100 for RV. < For “to call” analysis, enter the call price for RV.
Terminology The following terminology applies to the Bond worksheet. Call Date — A bond that can be retired by the issuing agency before the bond’s maturity date is a callable bond. The call date for such a bond is printed in the bond contract. Coupon Payment — The periodic payment made to the owner of the bond as interest. Coupon Rate — The annual interest rate printed on the bond. Dollar Price — Price of the security expressed in terms of dollars per $100 of par value.
Entering Bond Data and Computing Results Before computing values for price or yield and accrued interest, enter the four known values (settlement date, coupon rate, redemption date, and redemption value). If necessary, change the day-count method and coupon frequency settings. The worksheet stores values and settings until you clear the worksheet or change the values and settings. Procedure: Entering Bond Data First enter the known values: 쐃 Press & l. SDT is displayed, along with the previous date.
Procedure: Computing Bond Price (PRI) 쐃 Press # until YLD is displayed. 쐇 Key in a value for YLD and press !. 쐋 Press # to display PRI, and then press %. A value for PRI is computed and displayed. Procedure: Computing Bond Yield (YLD) 쐃 Press # until PRI is displayed. 쐇 Key in a value for PRI and press !. 쐋 Press # to display YLD, and then press %. A value for YLD is computed and displayed.
Bond Price and Accrued Interest Example You want to purchase a semiannual corporate bond that matures on 12/31/97 to settle on 6/12/96. The bond is based on the 30/360 day-count method with a coupon rate of 7%. It will be redeemed at 100% of its par value. For an 8% yield to maturity, compute the bond’s price and the accrued interest. Example: Entering Bond Data Procedure Keystrokes Display Set all variables to defaults. &}! RST Select Bond worksheet. &l SDT = 12-31-1990 Enter settlement date.
80 BA II PLUS™ Calculator
5 Depreciation Worksheet To access the Depreciation worksheet, press & p. Then choose a depreciation method, enter the known values, and compute the unknown values. To choose a depreciation method, press & V repeatedly until the desired method is displayed. Press # and " to move through each set of variables.
Depreciation Worksheet Labels Label Meaning Variable Type SL* Straight line method Setting SYD* Sum-of-the-years’-digits method Setting DB* Declining-balance method Setting/Enter DBX* DB method with crossover to SL Setting/Enter SLF* French straight-line method Setting/Enter DBF* French declining balance method Setting/Enter LIF Life of the asset in years Enter-only M01 Starting month Enter-only DT1 Starting date (SLF) Enter-only CST Cost of the asset Enter-only SAL Salvage
Notes about the Depreciation Worksheet (cont.) ♦ Values for DEP, RBV, and RDV are computed and displayed automatically when you press # to display each variable. ♦ If you choose DB or DBX as the depreciation method, enter a value for declining-balance percent when you display the DB or DBX label. The value you enter must be a positive number. (The default value is 200.) ♦ The value you enter for LIF must be: < If SL or SLF is selected, a positive real number.
Entering Data and Computing Results Because the worksheet stores previous values and settings until you change them or clear the worksheet, you may not need to do all the steps every time you work a depreciation problem. Procedure: Selecting a Depreciation Method 쐃 Press & p to select the Depreciation worksheet. The label for the current depreciation method is displayed. 쐇 Press & z to clear the worksheet.
Declining Balance with Straight-Line Crossover Example In mid-May, a company begins to depreciate a machine with a seven-year life and no salvage value. The machine cost is $100,000. Use the declining-balance with straight-line crossover method to compute the depreciation expense, remaining book value, and remaining depreciable value for the first two years. The declining-balance percent is 200. Example: Declining-Balance Data Procedure Keystrokes Display Set all variables to defaults.
Straight-Line Depreciation Example In mid-March, a company begins depreciation of a commercial building with a 31½ year life and no salvage value. The building cost $1,000,000. Use the straight-line depreciation method to compute the depreciation expense, remaining book value, and remaining depreciable value for the first two years. Example: Entering Straight-Line Depreciation Data Procedure Keystrokes Set all variables to defaults. & } ! RST Select Depreciation worksheet. &p SL Enter life in years.
6 Statistics Worksheet Two keys are used for performing statistics calculations. & j lets you enter statistical data. & k lets you choose a statistics calculation method and compute results. Press # and " to move through each set of variables.
Statistics Worksheet Labels Keys Label Meaning &j # Xnn* Ynn* Current X value Current Y value Enter-only Enter-only &k &V LIN Ln EXP PWR 1-V Standard linear regression Logarithmic regression Exponential regression Power regression One-variable statistics Setting Setting Setting Setting Setting # n (as needed) x Variable Type Number of observations Mean (average) of X values Sample standard deviation of X Sx sx Population standard deviation of X y** Mean (average) of Y values Sample standard devi
Notes about the Statistics Worksheet & j & z sets all X and Y values and all values in the Stat portion of the worksheet to zero, but does not affect the statistics calculation method. & k & z sets the statistics calculation method to LIN and all values to zero. & } ! sets the statistics calculation method to LIN and X, Y, and all other values to zero. You can enter up to 50 (x,y) data points.
Regression Models For two-variable data, the Statistics worksheet has four regression models for curve fitting and forecasting. The X value is interpreted as the independent variable and the Y value as the dependent variable.
Entering Statistical Data & j lets you enter and display up to 50 data points. The Statistics worksheet stores the values you enter until you clear the worksheet or change the values. Therefore, you may not need to do all the steps each time you perform a Statistics calculation. Procedure: Entering Data Points 쐃 Press & j to select the data-entry portion of the Statistics worksheet. X01 is displayed, along with any previous value. 쐇 Press & z to clear the worksheet. 쐋 Key in a value for X01 and press !.
Editing Statistical Data Pressing & j also lets you insert or delete data points. You may not need to do all the steps each time you perform a Statistics calculation. Procedure: Deleting a Data Point When the DEL indicator is displayed, you can delete a data point. 쐃 Press # or " until the data point you want to delete is displayed. 쐇 Press & W. The data point you specified (both X and Y) is deleted. The calculator decreases the numbers of subsequent data points so that there is no gap.
Computing Statistical Results Procedure: Selecting a Statistics Calculation Method 쐃 Press & k to select the statistical calculation portion of the Statistics worksheet. The most recently selected statistics calculation method is displayed (LIN, Ln, EXP, PWR, or 1-V). 쐇 Press & V repeatedly until the statistics calculation method you want is displayed. If you are analyzing one-variable data, select 1-V. 쐋 Press # to begin computing results.
Procedure: Computing X' 쐃 If necessary, press & k. 쐇 Press " or # until Y' is displayed. 쐋 Key in a value for Y' and press !. 쐏 Press " to display the X' variable. 쐄 Press % to compute an X' value.
One-Variable Statistics Example You randomly select a sample of 10 stores to see how much they charge for a particular item. You find the following prices: $63, $69, $71, $69, $74, $74, $72, $66, $74, $76 Note that $69 occurs twice and $74 occurs three times. You can save time entering by using the frequency factor (Ynn) for them. Find the mean and the sample standard deviation.
Example: Computing One-Variable Statistical Results Procedure Keystrokes Display Select and clear statistical calculation portion of Statistics worksheet. &k &z LIN &V &V &V &V 1-V Display sample size. # n= 10.00 Display mean. # x= 70.80 Display sample standard deviation. # Sx= Select one-variable calculation method. 4.08 Two-Variable Statistics Example A life insurance company wants to explore the relationship between the number of salespeople in an office and the volume of sales.
Example: Entering Two-Variable Statistical Data Procedure Keystrokes Display Select and clear data-entry portion of Statistics worksheet. &j &z X01 7! # 99000 ! X01= Y01= 7.00 99,000.00 # 12 ! # 152000 ! X02= Y02= 12.00 152,000.00 #4! # 81000 ! X03= Y03= 4.00 81,000.00 #5! # 98000 ! X04= Y04= 5.00 98,000.00 # 11 ! # 145000 ! X05= Y05= 11.00 145,000.00 #9! # 112000 ! X06= Y06= 9.00 112,000.00 Enter data set. 6: Statistics Worksheet 0.
Example: Computing Two-Variable Statistical Results (continued from previous example) Procedure Keystrokes Display Select and clear statistical calculation portion of Statistics worksheet. &k &z LIN #### #### a= 47,115.38 Display slope. # b= 8,423.08 Display correlation. # r= Enter X' (people). # 10 ! X'= 10.00 Compute Y' (sales). #% Y'= 131,346.15 Enter Y' (sales). 115000 ! Y'= 115,000.00 Compute new X' (people). "% X'= 8.06 Display intercept. 0.
7 Other Worksheets This chapter contains information about six worksheets: • Percent Change/Compound Interest Worksheet • Interest Conversion Worksheet • Date Worksheet • Profit Margin Worksheet • Breakeven Worksheet • Memory Worksheet 7: Other Worksheets 99
Percent Change/Compound Interest Worksheet To access the Percent Change/Compound Interest worksheet, press & q. You can also compute compound interest or perform cost-sell-markup calculations.
Procedure: Computing Percent Change, Compound Interest, or Cost-Sell-Markup 쐃 Press & q to select the worksheet. OLD is displayed, along with the previous value. 쐇 Press & z to clear the worksheet. 쐋 Enter the known values. Do not enter a value for the variable you wish to solve for. < Percent Change — Enter values for two of the three variables: OLD, NEW, and %CH. Leave #PD set to 1. < Compound Interest — Enter values for three of the four variables: OLD, NEW, %CH, and #PD.
Example: Percent Change First, determine the percentage change from a forecast amount of $658 to an actual amount of $700, and then determine what the new amount would be if it were 7% below the original forecast. Procedure Keystrokes Display Select and clear Percent Change/Compound Interest worksheet. &q &z OLD= 0.00 Enter original forecast amount. 658 ! OLD= 658.00 Enter actual amount. # 700 ! NEW= 700.00 Compute percent change. #% %CH= 6.38 Enter -7 as percent change.
Example: Cost-Sell-Markup The original cost of an item is $100; the selling price is $125. Find the markup. Procedure Keystrokes Display Select and clear Percent Change/Compound Interest worksheet. &q &z OLD= 0.00 Enter original cost. 100 ! OLD= 100.00 Enter selling price. # 125 ! NEW= 125.00 Compute percent markup. #% %CH= 25.00 The markup is 25%.
Interest Conversion Worksheet Interest Conversion Worksheet Labels Press & v to access the Interest Conversion worksheet. Label Meaning Variable Type NOM Nominal rate Enter/compute EFF Annual effective rate Enter/compute C/Y Compounding periods per year Enter-only Notes about the Interest Conversion Worksheet ♦ You may need to compare interest rates on investments that have the same nominal interest rate (annual percentage rate) but a different number of compounding periods per year.
Procedure: Converting Interest 쐃 Press & v to select the worksheet. NOM is displayed, along with the previous value. 쐇 Press & z to clear the worksheet. 쐋 Enter a value for the known interest rate, either NOM or EFF. To enter a value for a known variable, press # or " until the variable label you want (NOM or EFF) is displayed, and then key in a value and press !. 쐏 Press # until C/Y is displayed. If necessary, key in a value for number of compounding periods per year and press !.
Date Worksheet Press & u to access the Date worksheet. This worksheet can help you find the number of days between two dates. You can also compute a date and day of the week based on a starting date and a specified number of days.
Procedure: Computing Dates 쐃 Press & u to select the worksheet. DT1 is displayed, along with the previous date. 쐇 Press & z to clear the worksheet. 쐋 Enter values for two of the three variables: DT1, DT2, and DBD. Do not enter a value for the variable you wish to solve for. Press # or " until the variable label you want is displayed, and then key in a value and press !. 쐏 If necessary, change the day-count method setting.
Profit Margin Worksheet To access the Profit Margin worksheet, press & w. This worksheet lets you solve for cost, selling price, or profit margin. Profit Margin Worksheet Labels Label Meaning Variable Type CST Cost Enter/compute SEL Selling price Enter/compute MAR Profit margin Enter/compute Notes about the Profit Margin Worksheet ♦ Gross profit margin is a term commonly used in business. Sometimes the terms margin and markup are used interchangeably, but each has a distinct meaning.
Procedure: Profit Margin Calculations 쐃 Press & w to select the worksheet. CST is displayed, along with the previous value. 쐇 If necessary, press & z to clear the worksheet. 쐋 Enter values for two of the three variables; for example, enter values for SEL and MAR. Press # or " until the variable label you want is displayed, and then key in a value and press !. 쐏 Compute a value for the unknown variable; for example, compute a value for CST.
Breakeven Worksheet Press & r to access the Breakeven worksheet. This worksheet allows you to determine the breakeven point and sales level necessary to earn a given level of profit.
Procedure: Computing Breakeven 쐃 Press & r to select the worksheet. FC is displayed, along with the previous value. 쐇 If necessary, press & z to clear the worksheet. 쐋 Enter values for four of the five variables; for example, enter values for FC, VC, P, and PFT. Press # or " until the variable label you want is displayed, and then key in a value and press !. 쐏 Compute a value for the unknown variable; for example, compute a value for Q.
Memory Worksheet To access the Memory worksheet, press & {. This worksheet lets you display the calculator’s 10 memories. The Memory worksheet makes it easy to compare stored values and reduces the chance of recalling the wrong value.
Procedure: Using the Memory Worksheet 쐃 Press & { to select the worksheet. M0 is displayed, along with any value you may have stored in this memory. 쐇 Perform any of the following operations. < To clear all 10 memories at once, press & z. < To view the contents of the memories, press # or ". < To store a value in a memory, key in the value when the memory you want is displayed (M0 through M9) , and then press !.
Procedure: Multiplying a Value in a Memory To multiply the value in memory 0 by 95. 쐃 Press # or " until M0 is displayed. 쐇 Press < 95 !. Procedure: Dividing a Value in a Memory To divide the value in memory 6 by 95. 쐃 Press # or " until M6 is displayed. 쐇 Press 6 95 !. Procedure: Raising a Value in Memory to a Power To raise the value in memory 7 to the 66th power. 쐃 Press # or " until M7 is displayed. 쐇 Press ; 66 !.
APPENDIX Reference Information This appendix provides supplemental information on formulas, error conditions, and accuracy that may be helpful as you use your calculator.
Formulas Formulas used internally by your calculator are included here for your information. Time Value of Money i = [e ( y × ln( x + 1))] − 1 where: PMT ƒ y= x= C/Y = P/Y = I/Y = 0 C/Y P P/Y (.
PMT = where: −i Gi PV + FV × PV + ( 1 + i) N − 1 iƒ 0 PMT = L(PV + FV) P N where: i= 0 PMT × Gi 1 PMT × Gi PV = − FV × − N i i (1 + i) iƒ 0 where: PV = L(FV + PMT Q N) where: FV = i= 0 PMT × Gi PMT × Gi − ( 1 + i )N × PV + i i where: iƒ 0 FV = L(PV + PMT Q N) where: i= 0 Amortization If computing bal(), pmt2 = npmt Let bal(0) = RND(PV) Iterate from m = 1 to pmt2 [ ] Im = RND RND12( − i × bal( m − 1)) bal ( m) = bal( m − 1) − Im + RND( PMT ) then
Cash Flow N NPV = CF0 + ∑ CF (1 + i) j − Sj − 1 j =1 j ni where: Sj = i = 1 0 ∑ (1 − (1 + i) i −n j ) j ≥1 j=0 Net present value is dependent on the values of the initial cash flow (CF0), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i). IRR = 100 × i, where i satisfies npv() = 0 Internal rate of return is dependent on the values of the initial cash flow (CF0) and subsequent cash flows (CFj).
E = number of days in coupon period in which the settlement date falls Y = annual yield (as a decimal) on investment with security held to redemption (YLD P 100) A = number of days from beginning of coupon period to settlement date (accrued days) Note: The first term computes present value of the redemption amount, including interest, based on the yield for the invested period. The second term computes the accrued interest agreed to be paid to the seller.
Yield (given price) with more than one coupon period to redemption: Yield is found through an iterative search process using the “Price with more than one coupon period to redemption” formula. Accrued interest for securities with standard coupons or interest at maturity: AI = PAR × where: R A × M E AI = accrued interest PAR = par value (principal amount to be paid at maturity) Source for bond formulas: Lynch, John J., Jr., and Jan H. Mayle. Standard Securities Calculation Methods.
Sum-of-the-years’-digits depreciation ( LIF + 2 − YR − FSTYR) × (CST − SAL) (( LIF × ( LIF + 1)) ÷ 2) First year: LIF × (CST − SAL) (( LIF × ( LIF + 1)) ÷ 2) × FSTYR Last year or more: DEP = RDV Declining-balance depreciation RBV × DB % LIF × 100 where: RBV is for YR - 1 First year: Unless CST × DB % × FSTYR LIF × 100 CST × DB % > RDV ; then use RDV Q FSTYR LIF × 100 If DEP > RDV, use DEP = RDV If computing last year, DEP = RDV Statistics (Formulas apply to both x and y.
Regressions Formulas apply to all regression models using transformed data. b= a= r= n( ∑ xy) − ( ∑ y)( ∑ x ) n( ∑ x 2) − ( ∑ x )2 (∑ y − b ∑ x) n bσx σy Interest Rate Conversions EFF = 100 × (e C / Y where: × ln( x + 1) − 1) x = .01 Q NOM P CàY NOM = 100 × C / Y × (e1 ÷ C / Y where: × ln( x + 1) − 1) x = .
Breakeven PFT = P Q N (FC + VC Q) where: PFT = P= FC = VC = Q= profit price fixed cost variable cost quantity Days between Dates With the Date worksheet, you can enter or compute a date within the range January 1, 1950, through December 31, 2049.
30/360 day-count method (assumes 30 days per month and 360 days per year): DBD = (Y 2 − Y 1) × 360 + ( M 2 − M 1) × 30 + ( DT 2 − DT 1) where: M1 = DT1 = Y1 = M2 = DT2 = Y2 = month of first date day of first date year of first date month of second date day of second date year of second date Note: If DT1 is 31, change DT1 to 30. If DT2 is 31 and DT1 is 30 or 31, change DT2 to 30; otherwise, leave it at 31. Source for 30/360 day-count method formula: Lynch, John J., Jr., and Jan H. Mayle.
Error Conditions The calculator reports error conditions by displaying the message Error n, where n is the number of the error. Error messages are listed in numerical order on the next few pages. Use this table to determine the cause of the error. You cannot make any keyboard entries until you clear an error condition by pressing P. Error Possible Causes Error 1 Attempted a calculation whose result is outside the range of the calculator (± 9.9999999999999E99). Overflow Attempted to divide by zero.
Error Possible Causes Error 4 In Amortization worksheet, attempted to enter a value for P1 or P2 that is outside the range 1-9,999. Out of range In TVM worksheet, attempted to enter a value for P/Y or C/Y that is 0. In Cash Flow worksheet, attempted to enter a value for Fnn (frequency) that is outside the range 11-9,999. In Bond worksheet, attempted to enter a value for RV or CPN that is less than zero. In Bond worksheet, attempted to enter a value for PRI 0.
Error Possible Causes Error 8 In TVM worksheet, pressed $ to stop the evaluation of I/Y. Canceled iterative calculation In Amortization worksheet, pressed $ to stop the evaluation of BAL or INT. In Cash Flow worksheet, pressed $ to stop the evaluation of IRR. In Bond worksheet, pressed $ to stop the evaluation of YLD. In Depreciation worksheet, pressed $ to stop the evaluation of DEP or RDV.
Accuracy Information Internally, the calculator stores results as 13-digit numbers. In the display, however, results are rounded to 10 digits or fewer, depending on the decimal format. The internal digits, called “guard” digits, increase the calculator’s accuracy. Any later calculations are performed using the internal value, not on the value in the display.
IRR Calculations When you solve for IRR, the calculator performs a series of complex, iterative calculations. An IRR problem may have one solution, multiple solutions, or no solution. The number of possible solutions depends on the number of sign changes in your cash-flow sequence. When There Are No Sign Changes When a sequence of cash flows has no sign changes, there is no solution for IRR. The calculator displays Error 5 (no solution exists).
When There Are Two or More Sign Changes When a sequence of cash flows has two or more sign changes, there may be multiple solutions for IRR. • There is at least one solution. • There may be as many solutions as there are sign changes. If there are multiple solutions, the calculator displays the one closest to zero. However, the displayed solution has no financial meaning.
AOS™ (Algebraic Operating System) Calculations If you select AOS (rather than Chn) as the calculation method, the calculator uses the standard rules of algebraic hierarchy to determine the order in which operations are performed. Algebraic Hierarchy The table below shows the order in which operations are performed when AOS is selected as the calculation method.
Battery Information Replacing the Battery If it becomes necessary to replace the battery, you must use an Eveready E-2032, Duracell DL2032, or the equivalent. The calculator cannot retain data when the battery is removed or becomes discharged. Replacing the battery has the same effect as resetting the calculator. 쐃 Turn off the calculator and place it face down. 쐇 Using a small Phillips screwdriver, remove the screws from the back case and put them in a safe place.
In Case of Difficulty If you have difficulty operating the calculator, you may be able to correct the problem without returning the calculator for service. This table lists several problems and possible solutions. Difficulty Solution The calculator computes wrong answers. Check the settings of the current worksheet to make sure they are right for the problem you are working; for example, check END and BGN in the TVM worksheet.
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Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction.
Index x (mean of X), 88, 89 y (mean of Y), 88 .
BAL (balance), 28, 29 Balance (BAL), 28, 29 Balloon payment, 32 Batteries, 132 Beginning of period (BGN), 5, 28, 29 BGN (beginning of period), 5, 28, 29 Bond worksheet, 73–79 Breakeven worksheet, 110–11 —C— C/Y (compounding periods per year), 28, 29, 104, 105 Calculation method, 6, 10 Call date, 76 Cash Flow deleting, 64 editing, 68 entering, 63 formulas, 118 grouped, 62 inserting, 65 uneven, 62 worksheet, 59–69 CFo (initial cash flow), 60 Chain (Chn) calculation, 6, 10, 13, 131 Chn (chain) calculation, 6,
Examples accrued interest, 79 accumulated interest and loan balance, 56 amortization, 55 amortization schedule, 50, 54, 55, 56, 57 annual savings, 44 annuities, 42, 43 bond price, 79 bond price and accrued interest, 79 Canadian mortgage, 57 cash flow, 67 compound interest, 102 compounding periods, 53 correcting an entry error, 12 cost savings, 40 cost-sell-markup, 103 days between dates, 107 declining balance with straight-line crossover, 85 down payment, 52 editing cash flow data, 68 entering cash flow dat
—I— —N— I (discount rate), 60 I/Y (interest rate per year), 28, 29, 30 Indicators, 5 Inflows, 27, 29, 32 Initial cash flow (CFo), 60 INS (insert), 5 Insert (INS), 5 INT (interest paid), 28, 29 Interest Conversion worksheet, 104–5 Interest paid (INT), 28, 29 Interest rate per year (I/Y), 28, 29, 30 Internal rate of return (IRR), 60, 61, 66, 129, 130 INV (inverse function), 5 Inverse function (INV), 5 IRR (internal rate of return), 60, 61, 66, 129, 130 n (number of observations), 88, 89 N (number of period
Predicted Y value (Y'), 88, 89, 93 Premium bond, 76 Present value (PV), 28, 29, 30 PRI (dollar price), 74, 75, 76, 78, 79 Principal paid (PRN), 28, 29 PRN (principal paid), 28, 29 Procedures adding to memory, 113 clearing memory, 113 computing bond price, 78 computing bond yield, 78 computing breakeven, 111 computing breakeven quantity, 111 computing compound interest, 101 computing cost-sell-markup, 101 computing dates, 107 computing internal rate of return, 66 computing net present value, 66 computing per
Starting date (DT1), 84 Starting month (M01), 82, 83, 84 Starting payment (P1), 28, 29 Statistical data, 91–92 Statistics worksheet, 87–97 Storing to memory, 17 Straight line (SL), 82, 83, 84 Subtraction, 13 Sum of the years’ digits (SYD), 82, 83, 84 Sum of X (∑X), 88, 89 Sum of X2 (∑X2), 88, 89 Sum of XY products (∑XY), 88 Sum of Y (∑Y), 88 Sum of Y2 (∑Y2), 88 Sx (sample standard deviation of X), 88, 89 Sy (sample standard deviation of Y), 88 SYD (sum of the years’ digits), 82, 83, 84 —T— Tangent, 14 Time
