BA II PLUS™ Calculator
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Contents Overview of Calculator Operations Turning On the Calculator Turning Off the Calculator Selecting 2nd Functions Reading the Display Setting Calculator Formats Resetting the Calculator Clearing Calculator Entries and Memories Correcting Entry Errors Math Operations Memory Operations Calculations Using Constants Last Answer Feature Using Worksheets: Tools for Financial Solutions Time-Value-of-Money and Amortization Worksheets 1 1 2 2 4 6 6 7 8 12 14 15 16 21 TVM and Amortization Worksheet Variable
Deleting Cash Flows Inserting Cash Flows Computing Cash Flows Example: Solving for Unequal Cash Flows Example: Value of a Lease with Uneven Payments Bond Worksheet Bond Worksheet Variables Bond Worksheet Terminology Entering Bond Data and Computing Results Example: Computing Bond Price and Accrued Interest Depreciation Worksheet Depreciation Worksheet Variables Entering Data and Computing Results Example: Computing Straight-Line Depreciation Statistics Worksheet Statistics Worksheet Variables Regression
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Overview of Calculator Operations This chapter describes the basic operation of your BA II PLUS™ calculator, including how to: • Turn on and turn off the calculator • Select second functions • Read the display and set calculator formats • Clear the calculator and correct entry errors • Perform math and memory operations • Use the Last Answer feature • Use worksheets Turning On the Calculator Press $.
Automatic Power Down™ (APD™) Feature To prolong battery life, the Automatic Power Down (APD) feature turns off the calculator automatically after about five minutes of inactivity. The next time you press $, the calculator turns on exactly as you left it, saving display settings and stored memory and any pending operations or error conditions. Selecting 2nd Functions The primary function of a key is printed on the key itself.
Indicator Meaning INV Press a key to select its inverse trigonometric function. HYP Press a key to select its hyperbolic function. COMPUTE Press C to compute a value for the displayed variable. ENTER Press ! to assign the displayed value to the displayed variable. SET Press & Vto change the setting of the displayed variable. Press # or " to display the previous or next variable in the worksheet. #$ Note: To easily scroll up or down through a range of variables, press and hold # or ".
Setting Calculator Formats You can change these calculator formats: To Select Press Number of decimal places & | Angle units # Dates # Number separators # Calculation method # Display Default DEC 0–9 (Press 9 for floatingdecimal) DEG (degrees) RAD (radians) US (mm-dd-yyyy) Eur (dd-mm-yyyy) US (1,000.00 ) Eur (1.000,00) 2 DEG US US Chn (chain) AOS é (algebraic Chn operating system) 1. To access format options, press & |.
Choosing the Number of Decimal Places Displayed The calculator stores numeric values internally to an accuracy of 13 digits, but you can specify the number of decimal places you want to display. The calculator displays up to 10 digits with the floating-decimal option. Results exceeding 10 digits appear in scientific notation. Changing the number of decimal places affects the display only. Except for amortization and depreciation results, the calculator does not round internal values.
Resetting the Calculator Resetting the calculator: • Clears the display, all 10 memories, any unfinished calculations, and all worksheet data. • Restores all default settings • Returns operation to the standard-calculator mode Because the calculator includes alternative methods that let you clear data selectively, use reset carefully to avoid losing data needlessly. (See section “Clearing Calculator Entries and Memories”.
To clear Press keyed in An incorrect entry, error condition, or error message P The prompted worksheet and reset default values &z Calculator format settings and reset default values • Out of the prompted worksheet and return to standard-calculator mode • All pending operations in standard-calculator mode • In a prompted worksheet, the variable value keyed in but not entered (the previous value appears) • &| &z &U PP Any calculation started but not completed TVM worksheet variables and rese
To Press Display Begin the expression 3< Enter a number 1234.86 Erase the entry error ** Key in the correct number 56 1,234.56 Compute the result N 3,703.68 3.00 1,234.86 1,234. Math Operations When you select the chain (Chn ) calculation method, the calculator evaluates mathematical expressions (for example, 3 + 2 Q 4) in the order that you enter them. Examples of Math Operations These operations require you to press N to complete. To Press Add 6 + 4 6H4N 10.
To Square Press 6.3 2 Display 39.69 6.3 4 Find number of combinations where: n = 52, r = 5 52 & s 5 N Find number of permutations where: n = 8, r = 3 8 &m3 N 2,598,960.00 336.00 These operations do not require you to press N to complete. To Press Find square root: 15.5 3 3.94 Find reciprocal: 1/3.2 3.2 5 0.31 Find factorial: 5! 5& g Find natural logarithm: ln 203.45 203.45 > 5.32 Find natural antilogarithm: e .69315 .69315 & i 2.
To Press -1 Find hyperbolic arctangent: tanh (.5) Display .5 & c 8 f 0.55 * The random number you generate might be different. ** Angles can be computed in degrees or radians. Examples show angles in degrees. (See: Choosing the Angle Units). Universal Power ; Press ; to raise the displayed postive number to any power (for example, 2-5 or 2(1/3).
Combinations & s The calculator computes the number of combinations of n items taken r at a time. Both the n and r variables must be greater than 0. Permutations & m The calculator computes the number of permutations of n items taken r at a time. Both the n and r variables must be greater than 0. Rounding & o The calculator computes using the rounded, displayed form of a number instead of the internally stored value.
Scientific Notation ; When you compute a value in the standard-decimal format that is either too large or small to be displayed, the calculator displays it in scientific notation, that is, a base value (or mantissa), followed by a blank space, followed by an exponent. With AOS selected, you can press ; to enter a number in scientific notation. (See “Choosing Calculation Methods”.) For example, to enter 3 Q 10 3, key in 3 < 10 ; 3 .
Memory Examples To Press Clear memory 4 (by storing a zero value in it) 0 D4 Store 14.95 in memory 3 (M3 ) 14.95 D 3 Recall a value from memory 7 (M7 ) J7 Memory Arithmetic Using memory arithmetic, you can perform a calculation with a stored value and store the result with a single operation. • Memory arithmetic changes only the value in the affected memory and not the displayed value. • Memory arithmetic does not complete any calculation in progress.
Calculations Using Constants To store a constant for use in repetitive calculations, enter a number and an operation, and then press & `. To use the stored constant, key in a value and press N. Note: Pressing a key other than a number or N clears the constant. Example: Multiply 3, 7, and 45 by 8 To Press Display Clear the calculator &U Enter the value for the first calculation. 3 3 Enter the operation and a constant value. <8 8 Store the operation and value, and then calculate. &` N 24.
* The letter c denotes the constant value. ** Repeat constant calculations with n N. Last Answer Feature Use the Last Answer (ANS ) feature with problems that call repeatedly for the same value or to copy a value: • From one place to another within the same worksheet. • From one worksheet to another. • From a worksheet to the standard-calculator mode. • From the standard-calculator mode to a worksheet. To display the last answer computed, press & x.
Using Worksheets: Tools for Financial Solutions The calculator contains worksheets with embedded formulas to solve specific problems. You apply settings or assign known values to worksheet variables and then compute the unknown value. Changing the values lets you ask what if questions and compare results. Except for TVM variables, accessed in the standard-calculator mode, all variables are prompted. For example, to assign values to amortization variables, you must first press & \ to access the Amortization
To select Function Press regression analysis options Percent Change/Compound Interest worksheet Computes percent change, compound interest, and costsell markup &q Interest Conversion worksheet Converts interest rates between nominal rate (or annual percentage rate) and annual effective rate &v Date worksheet Computes number of days between two dates, or date/day of the week a specified number of days is from a given date &u Profit Margin worksheet Computes cost, selling price, and profit margin
Accessing Prompted-Worksheet Variables After you access a worksheet, press # or " to select variables. For example, press & \ to access the Amortization worksheet, and then press # or " to select the amortization variables (P1 , P2 , BAL , PRN, INT). See: TVM and Amortization Worksheet Variables. Indicators prompt you to select settings, enter values, or compute results. For example, the # and " indicators remind you to press # or " to select other variables.
Compute-Only Variables You cannot enter values manually for compute-only variables, for example, net present value (NPV ). To compute a value, display a compute-only variable and press C. The calculator computes and displays the value based on the values of other variables. When you display a compute-only variable, the COMPUTE indicator reminds you to press C to compute its value. After you press C, the 7 indicator confirms that the displayed value has been computed.
Selecting Worksheet Settings Many prompted worksheets contain variables consisting of two or more options, or settings (for example, the Date worksheet ACT/360 variable). When you select variables with settings, the calculator displays the SET indicator and the current setting. To scroll through the settings of a variable, press & V once for each setting. Display Indicators • The 1 indicator confirms that the calculator entered the displayed value in the worksheet.
Time-Value-of-Money and Amortization Worksheets Use the Time-Value-of-Money (TVM) variables to solve problems with equal and regular cash flows that are either all inflows or all outflows (for example, annuities, loans, mortgages, leases, and savings). For cash-flow problems with unequal cash flows, use the Cash Flow worksheet. (See: Cash Flow Worksheet.) After solving a TVM problem, you can use the Amortization worksheet to generate an amortization schedule.
Variable Key Display Type of Variable End-of-period payments &] END Setting Beginning-of-period payments &V BGN Setting Starting payment & \ P1 Enter-only Ending payment # P2 Enter-only Balance # BAL Auto-compute Principal paid # PRN Auto-compute Interest paid # INT Auto-compute Note: This guidebook categorizes calculator variables by the method of entry. (See “Types of Worksheet Variables”).
Variable Default Variable Default N 0 END/BGN END I/Y 0 P1 1 PV 0 P2 1 PMT 0 BAL 0 FV 0 PRN 0 P/Y 1 INT 0 C/Y 1 • To reset only the TVM variables (N, I/Y , PV , PMT, FV ) to default values, press & ^. • To reset P/Y and C/Y to default values, press & [ & z. • To reset the Amortization worksheet variables (P1 , P2 , BAL , PRN, INT) to default values, press & z while in the Amortization worksheet. • To reset END/BGN to the default value, press & ] & z.
Specifying Payments Due With Annuities Use END/BGN to specify whether the transaction is an ordinary annuity or an annuity due. • Set END for ordinary annuities, in which payments occur at the end of each payment period. (This category includes most loans.) • Set BGN for annuities due, in which payments occur at the beginning of each payment period. (This category includes most leases.) Note: When you select beginning-of-period payments, the BGN indicator appears. (No indicator appears for END payments.
To compute a TVM value, press C and a TVM key in standard-calculator mode. Using [xP/Y] to Calculate a Value for N 1. Key in the number of years, and then press & Z to multiply by the stored P/Y value. The total number of payments appears. 2. To assign the displayed value to N for a TVM calculation, press ,. Entering Cash Inflows and Outflows The calculator treats cash received (inflows) as a positive value and cash invested (outflows) as a negative value.
7. To generate the amortization schedule, repeat steps 2 through 5 for each range of payments. Generating an Amortization Schedule Automatically After entering the initial values for P1 and P2 , you can compute an amortization schedule automatically. 1. Press & \. — or — If INT is displayed, press # to display the current P1 value. 2. Press C. Both P1 and P2 update automatically to represent the next range of payments.
To Press Display using the payment multiplier Enter loan amount 75000 . PV= Enter payment amount 425.84 S / PMT= Compute interest rate C- I/Y= 75,000.00 1 -425.84 1 5.50 Answer: The interest rate is 5.5% per year. Examples: Computing Basic Loan Payments These examples show you how to compute basic loan payments on a $75,000 mortgage at 5.5% for 30 years. Note: After you complete the first example, you should not have to re-enter the values for loan amount and interest rate.
To Press Display Set payments per year to 4 & [4 ! Return to standard-calculator mode &U Enter number of payments using payment multiplier 30 & Z , N= Compute payment C/ PMT= P/Y= 4.00 1 0.00 120.00 1 -1,279.82 7 Answer: The quarterly payments are $1,279.82. Examples: Computing Value in Savings These examples show you how to compute the future and present values of a savings account paying 0.5% compounded at the end of each year with a 20year time frame.
Answer: You must deposit $9,050.63. Example: Computing Present Value in Annuities The Furros Company purchased equipment providing an annual savings of $20,000 over 10 years.
To Press Display Enter payment 20000 S / PMT= -20,000.00 1 Compute present value (ordinary annuity) C. PV= 122,891.34 7 Set beginning-of-period payments &]&V BGN Return to calculator mode &U Compute present value (annuity due) C. 0.00 PV= 135,180.48 7 Answer: The present value of the savings is $122,891.34 with an ordinary annuity and $135,180.48 with an annuity due.
Perpetual ordinary annuity Perpetual annuity due Because the term (1 + I/Y / 100) -N in the present value annuity equations approaches zero as N increases, you can use these equations to solve for the present value of a perpetual annuity: • Perpetual ordinary annuity • Perpetual annuity due Example: Computing Present Value of Variable Cash Flows The ABC Company purchased a machine that will save these end-of-year amounts: Time-Value-of-Money and Amortization Worksheets 31
Year 1 2 3 4 Amount $5000 $7000 $8000 $10000 Given a 10% discount rate, does the present value of the cash flows exceed the original cost of $23,000? To Press Set all variables to defaults &} ! RST 0.00 Enter interest rate per cash flow period 10 - I/Y= 10.00 1 Enter 1st cash flow 5000 S 0 FV= -5,000.00 1 Enter 1st cash flow period 1, N= Compute present value of 1st cash flow C.
To Press Display Sum to memory. DH1 Enter 4th cash flow. 10000 S 0 FV= Enter period number. 4, N= Compute present value of 4th cash flow. C. PV= Sum to memory. DH1 Recall total present value. J1 Subtract original cost. B 23000 N 6,010.52 -10,000.00 1 4.00 1 6,830.13 7 6,830.13 23,171.23 171.23 Answer: The present value of the cash flows is $23,171.23, which exceeds the machine’s cost by $171.23. This is a profitable investment.
The total value of the machine is the present value of the residual value plus the present value of the lease payments. To Press Display Set all variables to defaults. &}! RST Set beginning-of-period payments. &]& V BGN Return to standard-calculator mode. &U Enter number of payments. 46 , N= Calculate and enter periodic interest rate. 22 6 12 N - I/Y= 1.83 1 Enter residual value of asset. 6500 S 0 FV= -6,500.00 1 Compute residual present value. C. PV= 2,818.
To Press Display Set all variables to defaults. &}! RST 0.00 Set payments per year to 12. & [ 12 ! P/Y= 12.00 1 Return to standard-calculator mode &U Enter number of payments using payment multiplier. 2 &Z, N= 24.00 1 Enter interest rate. 20 - I/Y= 20.00 1 Enter loan amount. 525 . PV= 525.00 1 Compute payment. C/ PMT= 0.00 -26.72 7 Answer: Your monthly payment is $26.72.
To Press Display mode. Enter number of payments using payment multiplier. 20 & Z , N= Enter interest rate. 7.5 - I/Y= Enter amount of payment. 200 S / PMT= Compute future value. C0 FV= 240.00 1 7.50 1 -200.00 1 111,438.31 * Answer: Depositing $200 at the beginning of each month for 20 years results in a future amount of $111,438.31. Example: Computing Amount to Borrow and Down Payment You consider buying a car for $15,100. The finance company charges 7.
To Press Set all variables to defaults. &}! RST 0.00 Set payments per year to 12. & [ 12 ! P/Y= 12.00 1 Return to standard-calculator mode &U Enter number of payments using payment multiplier. 4 &Z, N= Enter interest rate. 7.5 - I/Y= Enter payment. 325 S/ Compute loan amount. C. Compute down payment H 15,100 S N Display 0.00 PMT= PV= 48.00 1 7.50 1 -325.00 1 13,441.47 * -1,658.53 Answer: You can borrow $13,441.47 with a down payment of $1,658.53.
To Press Display Set compounding periods to 4. #4! C/Y= Set beginning-of-period payments. &]& V BGN Return to standard-calculator mode. &U Enter number of deposits using payment multiplier. 10 & Z , N= Enter interest rate. .5 - I/Y= 0.50 1 Enter future value. 25,000 0 FV= 25,000.00 1 Compute deposit amount. C/ PMT= 4.00 1 0.00 120.00 1 -203.13 7 Answer: You must make monthly deposits of $203.13.
Enter interest rate 6.125 - I/Y= 6.13 1 Enter loan amount 120000 . PV= 120,000.00 1 Compute payment C/ PMT= -729.13 * Answer: The computed monthly payment, or outflow, is $729.13. Generating an Amortization Schedule Generate an amortization schedule for the first three years of the loan. If the first payment is in April, the first year has nine payment periods. (Following years have 12 payment periods each.) To Press Select the Amortization worksheet & \ P1= current value Set beginning p
Example: Computing Payment, Interest, and Loan Balance After a Specified Payment A group of sellers considers financing the sale price of a property for $82,000 at 7% annual interest, amortized over a 30-year term with a balloon payment due after five years. They want to know: • Amount of the monthly payment • Amount of interest they will receive • Remaining balance at the end of the term (balloon payment) Computing the Monthly Payment To Press Display Set all variables to defaults &}! RST 0.
To Press View interest paid after five years ## Display INT= -27,920.72 * If the sellers financed the sale, they would receive: • Monthly payment: $545.55 for five years • Interest: $27,790.72 over the five years • Balloon payment: $77,187.
Cash Flow Worksheet Use the Cash Flow worksheet to solve problems with unequal cash flows. To solve problems with equal cash flows, use the TVM worksheet. Time-Value-of-Money and Amortization Worksheets • To access the Cash Flow worksheet and initial cash flow value (CFo ), press '. • To access the cash flow amount and frequency variables (Cnn/Fnn), press # or ". • To access the discount rate variable (I), press (. • To compute net present value (NPV ), press # or " and C for each variable.
Resetting Variables • To reset CFo , Cnn, and Fnn to default values, press ' and then & z. • To reset NPV to the default value, press ( and then & z. • To reset IRR to the default value, press ) and then & z. • To reset all calculator variables and formats to default values, including all Cash Flow worksheet variables, press & } !. Entering Cash Flows • You must enter an initial cash flow (CFo ). The calculator accepts up to 24 additional cash flows (C01 – C24 ).
All cash-flow problems start with an initial cash flow labeled CFo . CFo is always a known, entered value. Grouped Cash Flows Cash-flow problems can contain cash flows with unique values as well as consecutive cash flows of equal value. Although you must enter unequal cash flows separately, you can enter groups of consecutive, equal cash flows simultaneously using the Fnn variable.
Deleting Cash Flows When you delete a cash flow, the calculator decreases the number of subsequent cash flows automatically. The DEL indicator confirms that you can delete a cash flow. 1. Press # or " until the cash flow you want to delete appears. 2. Press & W. The cash flow you specified and its frequency is deleted. Inserting Cash Flows When you insert a cash flow, the calculator increases the number of the following cash flows, up to the maximum of 24.
Computing Cash Flows The calculator solves for these cash-flow values: • Net present value (NPV) is the total present value of all cash flows, including inflows (cash received) and outflows (cash paid out). A positive NPV value indicates a profitable investment. • Internal rate of return (IRR) is the interest rate at which the net present value of the cash flows is equal to 0. Computing NPV 1. Press ( to display the current discount rate (I). 2. Key in a value and press !. 3.
• When a sequence of cash flows has two or more sign changes: - At least one solution exists. - As many solutions can exist as there are sign changes. When more than one solution exists, the calculator displays the one closest to zero. Because the displayed solution has no financial meaning, you should use caution in making investment decisions based on an IRR computed for a cash-flow stream with more than one sign change.
Year Cash Flow Number Cash Flow Estimate Purchase CFo -$7,000 1 C01 3,000 2–5 C02 5,000 each year 6 C03 4,000 As the time line shows, the cash flows are a combination of equal and unequal values. As an outflow, the initial cash flow (CFo ) appears as a negative value. Entering Cash-Flow Data To Press Display Select Cash Flow worksheet. ' CFo= Enter initial cash flow. 7000 S! CFo= Enter cash flow for first year. # 3000 ! # C01= F01= 3,000.00 1 1.
To Press Display Move to third cash flow. " C03= Delete third cash flow. &W C03= Move to second cash flow. "" C02= Insert new second cash flow. & X 4000 ! # C02= F02= # # C03= F03= Move to next cash flow to verify data. 4,000.00 1 0.00 5,000.00 1 4,000.00 1 1.00 1 5,000.00 1 4.0 1 Computing NPV Use an interest rate per period (I) of 20%. To Press Display Access interest rate variable ( I= 0.00 Enter interest rate per period. 20 ! I= 20.00 1 Compute net present value.
Example: Value of a Lease with Uneven Payments A lease with an uneven payment schedule usually accommodates seasonal or other anticipated fluctuations in the lessee’s cash position. A 36-month lease has the following payment schedule and beginning-ofperiod payments.
To Press Display Set all variables to defaults. &}! RST 0.00 Select Cash Flow worksheet. ' CFo= 0.00 Enter first group of cash flows. # #3! C01= F01= Enter second group of cash flows. # 5000 S !#8 ! C02= F02= Enter third group of cash flows. # #3! C03= F03= 0.00 1 3.00 1 Enter fourth group of cash flows. # 6000 S !#9 ! C04= F04= -6000.00 1 9.00 1 Enter fifth group of cash flows. # #2! C05= F05= 0.00 1 2.00 1 Enter sixth group of cash flows. # 7000 S ! # 10 ! C06= F06= -7000.
Bond Worksheet The Bond worksheet lets you compute bond price, yield to maturity or call, and accrued interest. You can also use the date functions to price bonds purchased on dates other than the coupon anniversary. • To access the Bond worksheet, press & l. • To access bond variables, press "or #. • To change the options for day-count methods (ACT and 360 ) and coupons per year (2/Y and 1/Y ), press & V once for each option.
Variable Key Display Variable Type Accrued interest # AI Auto-compute Resetting Bond Worksheet Variables • • To reset the Bond worksheet variables to default values, press & z while in the Bond worksheet. Variable Default Variable Default SDT 12-31-1990 ACT/360 ACT CPN 0 2/Y, 1/Y 2/Y RDT 12-31-1990 YLD 0 RV 100 PRI 0 To reset all calculator variables and formats to default values, including the Bond worksheet variables, press & } !.
For to call analysis, enter the call price for RV . • Setting the Day-Count Method 1. To display the day-count method, press # until ACT or 360 appears. 2. To change the day-count method, press & V. Setting the Coupon Frequency 1. To display the coupon frequency, press # until 1/Y or 2/Y appears. 2. To change the coupon frequency, press & V. Bond Worksheet Terminology Term Definition Call Date A callable bond bond can be retired by the issuing agency before the maturity date.
Term Definition call premium. The calculator treats the redemption value in terms of dollars per $100 of par value. Settlement Date The date on which a bond is exchanged for funds. Yield to Maturity The rate of return earned from payments of principal and interest, with interest compounded semiannually at the stated yield rate. The yield to maturity takes into account the amount of premium or discount, if any, and the time value of the investment.
2. Key in a value for YLD and press !. 3. Press # to display PRI, and then press C. The calculator displays the computed PRI value. Computing the Bond Yield (YLD) 1. Press # until PRI appears. 2. Key in a value for PRI and press !. 3. Press # to display YLD, and then press C. The calculator displays the computed YLD value. Computing Accrued Interest (AI) To compute accrued interest, press # until the AI variable appears.
To Press Display Enter yield. #8! YLD = 8.00 1 Compute price #C PRI = 98.56 7 View accrued interest. # AI = 3.15 7 Answer: The bond price is $98.56 per 100. The accrued interest is $3.15 per 100.
Depreciation Worksheet The Depreciation worksheet lets you generate a depreciation schedule using your choice of depreciation methods. • To access the Depreciation worksheet, press & p. • To change depreciation methods, press & V until the desired method appears. • To access other depreciation variables, press # or ". Note: To easily scroll up or down through a range of variables, press and hold # or ".
Variable Key Display Variable Type** Cost of the asset # CST Enter only Salvage value of the asset # SAL Enter only Year to compute # YR Enter only Depreciation for the year # DEP Auto-compute Remaining book value at the end of the year # RBV Auto-compute Remaining depreciable value # RDV Auto-compute * SLF and DBF are available only if you select the European format for dates or separators in numbers.
• The calculator computes values for DEP, RBV , and RDV automatically when you press # to display each variable. Entering Values for DB and DBX If you choose either the declining balance (DB ) or declining balance with crossover to SL (DBX ) depreciation method, remember to enter a value representing the percent of declining balance for the DB or DBX variable. Note: The declining balance you enter must be a positive number.
Entering Data and Computing Results Because the Depreciation worksheet stores values and settings until you either change them or clear the worksheet, you should not have to perform every step each time you work a problem. Selecting a Depreciation Method 1. To access the Depreciation worksheet, press & p. The current depreciation method is displayed. 2. To clear the worksheet, press & z. 3. Press & V until you display the depreciation method you want (SL , SLF, SYD, DB , DBX , or DBF).
Example: Computing Straight-Line Depreciation In mid-March, a company begins depreciation of a commercial building with a 31½ year life and no salvage value. The building cost $1,000,000. Use the straight-line depreciation method to compute the depreciation expense, remaining book value, and remaining depreciable value for the first two years. To Press Display Access Depreciation worksheet &p SL Enter life in years # 31.5 ! LIF = Enter starting month # 3.5 ! M01 = 3.
Statistics Worksheet The Statistics worksheet performs analysis on one-and two-variable data with four regression analysis models. • To enter statistical data, press & j. • To choose a statistics calculation method and compute the results, press & k. • To access statistics variables, press # or ".
Variable Key Predicted X value Predicted Y value Sum of X values Sum of X squared values Sum of Y values Sum of Y squared values Sum of XY products Display Variable Type GY** GY 2** GXY** Auto-compute Auto-compute Auto-compute * nn represents the number of the current X or Y value. ** Not displayed for one-variable statistics. *** This guidebook categorizes calculator variables by their method of entry.
Analyzing Two-Variable Statistics You can choose from among these four regression-analysis methods: • LIN • Ln • EXP • PWR Computing Values Automatically Except for the predicted X' and Y' values, the calculator computes and displays values for statistics variables automatically when you access them. Using X' and Y' for Regression Predictions To use the X' and Y' variables for regression predictions, you either can enter a value for X' to compute Y' or enter a value for Y' to compute X'.
Correlation Coefficient The calculator also determines r, the correlation coefficient, which measures the goodness of fit of the equation with the data. Generally: • The closer r is to 1 or -1, the better the fit. • The closer r is to zero, the worse the fit.
2. The last selected statistics calculation method is displayed (LIN, Ln , EXP , PWR, or 1-V ). 3. Press & V repeatedly until the statistics calculation method you want is displayed. 4. If you are analyzing one-variable data, select 1-V . 5. Press # to begin computing results. Computing Results To compute results based on the current data set, press # repeatedly after you have selected the statistics calculation method.
Other Worksheets The calculator also includes these worksheets: • Percent Change/Compound Interest worksheet (& q) • Interest Conversion worksheet (& v) • Date worksheet (& u) • Profit Margin worksheet (& w) • Breakeven worksheet (& r) • Memory worksheet (& {) Percent Change/Compound Interest Worksheet Use the Percent Change/Compound Interest worksheet to solve percent change, compound interest, and costsell-markup problems. • To access the Percent Change/Compound Interest worksheet, press & q.
Resetting the Percent Change/Compound Interest Worksheet Variables • To reset the Percent Change/Compound Interest variables to default values, press & z while in the Percent Change/Compound Interest worksheet. Variable Default Variable Default OLD 0 %CH 0 NEW 0 #PD 0 • To reset default values for all calculator variables and formats, press & } !.
2. To clear the worksheet, press & z. 3. To enter values for the known variables, press # or " until the variable you want is displayed, then key in a value, and press !. (Do not enter a value for the variable you wish to solve.) 4. • Percent Change — Enter values for two of these three variables: OLD, NEW, and %CH. Leave #PD set to 1. • Compound Interest — Enter values for three of these four variables: OLD, NEW, %CH, and #PD.
Example: Computing Compound Interest You purchased stock in 1995 for $500. Five years later, you sell the stock for $750. What was the annual growth rate? To Press Display Select Percent Change/Compound Interest worksheet &q OLD= Current value Enter stock purchase price 500 ! OLD= 500.00 1 Enter stock selling price # 750 ! NEW= 750.00 1 Enter number of years # #5 ! #PD= 5.00 1 Compute annual growth rate "C %CH= 8.45 7 Answer: The annual growth rate is 8.45%.
Interest Conversion Worksheet The Interest Conversion worksheet converts interest rates between nominal rate (or annual percentage rate) and annual effective rate. • To access the Interest Conversion worksheet, press & v. • To select interest conversion variables, press # or ".
Variable Default NOM 0 EFF 0 C/Y 1 • To clear the NOM and EFF variables and reset default values without affecting C/Y , press & z in the Interest Conversion worksheet. Converting Variables You can convert a nominal rate to an annual effective rate or vice versa. Entering Values for Nom and EFF Enter a value for NOM or EFF as an annual rate. Converting Interest Rates 1. To access the Interest Conversion worksheet, press & v. The current NOM value appears. 2. To clear the worksheet, press & z.
To Press Display Compute annual effective interest rate. "C EFF= 15.87 7 Answer: A nominal interest rate of 15% compounded quarterly is equivalent to an annual effective interest rate of 15.87%. Date Worksheet Use the Date worksheet to find the number of days between two dates. You can also compute a date and day of the week based on a starting date and a specified number of days. • To access the Date worksheet, press & u. • To access the date variables, press # or ".
Variable Default Variable Default DT1 12-31-1990 DBD 0 DT2 12-31-1990 Day-count method ACT • To clear Date worksheet variables and reset default values without affecting the day-count method, press & z while in the Date worksheet. Entering Dates • The calculator assumes that DT1 is earlier than DT2 . • Enter dates for DT1 and DT2 in the selected US or European date format.
Example: Computing Days between Dates A loan made on September 4, 2003 defers the first payment until November 1, 2003. How many days does the loan accrue interest before the first payment? To Press Display Select Date worksheet &u DT1= 12-31-1990 Enter first date 9.0403 ! DT1= 9-04-2003 1 Enter second date # 11.0103 ! DT2= 11-01-2003 1 Select actual/actual daycount method ## ACT Compute days between dates "C DBD= 58.
Note: This guidebook categorizes calculator variables by their method of entry. Gross Profit Margin and Markup The terms margin and markup often are used interchangeably, but each has a distinct meaning. • Gross profit margin is the difference between selling price and cost, expressed as a percentage of the selling price. • Markup is the difference between selling price and cost, expressed as a percentage of the cost.
Breakeven Worksheet The Breakeven worksheet computes the breakeven point and sales level needed to earn a given profit by analyzing relationships between fixed costs, variable costs per unit, quantity, price, and profit. You operate at a loss until you reach the breakeven quantity (that is, total costs = total revenues). • To access the Breakeven worksheet, press & r. • To access breakeven variables, press " or #.
Computing Breakeven 1. To access the Breakeven worksheet, press & r. The FC variable appears. 2. Press # or " to select a known variable, key in the value, and press !. 3. Repeat step 3 for each of the remaining known variables. 4. To compute a value for the unknown variable, press # or " until the variable is displayed, and then press C The calculator displays the computed value. Example: Computing Breakeven Quantity A canoe company sells paddles for $20 each.
Memory Worksheet The Memory worksheet lets you compare and recall stored values by accessing the calculator’s 10 memories. All memory variables are enter-only. Types of Worksheet Variables • To access the Memory worksheet, press & {. • To access memory variables, press " or #. Note: You can access memories individually using D, J, and the digit keys.
• To clear all 10 memories at once, press & z. • To view the contents of the memories, press # or " once for each memory. • To store a value, select a memory (M0-M9 ), key in a value, and press !. • Memory arithmetic. Examples: Using the Memory Worksheet To Press Display Access Memory worksheet &{ M0= Current value Select M4 . #### M4= Current value Clear M4 . 0! M4= 0.00 1 Store 95. 95! M4= 95.00 1 Add 65. H65! M4= 160.00 1 Subtract 30. B30! M4= 130.00 1 Multiply by 95.
APPENDIX - Reference Information This appendix includes supplemental information to help you use your BA II PLUS™ calculator: • Formulas • Error conditions • Accuracy information • IRR (internal-rate-of-return) calculations • Algebraic operating system (AOS™) • Battery information • In case of difficulty • TI product service and warranty information Formulas This section lists formulas used internally by the calculator.
where: Gi = 1 + i where: k k = 0 for end-of-period payments k = l for beginning-of-period payments where: where: where: where: where: APPENDIX - Reference Information 83
where: where: where: Amortization If computing Let: Iterate from: to then: where: round the diplay to the number or decimal places selected round to 12 decimal places Balance, principal, and interest are dependent on the values of PMT, PV, I/ Y, and pmt1 and pmt2 .
Cash Flow where: Net present value depends on the values of the initial cash flow (CF0 ), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i). IRR = 100 x i where: i satisfies Internal rate of return depends on the values of initial cash flow (CF0 ), subsequent cash flows (CFj). Bonds 1 Price (given yield) with one coupon period or less to redemption: 1Source for bond formulas (except duration): Lynch, John J., Jr., and Jan H. Mayle.
where: PRI = dollar price per $100 par value RV = redemption value of the security per $100 par value (RV except in those cases where call or put features must be considered) R = annual interest rate (as a decimal; CPN_100) M = number of coupon periods per year standard for the particular security involved (set to 1 or 2 Bond worksheet) DSR = number of days from settlement date to redemption date (maturity date, call date, put date, etc.
where: N= number of coupons payable between settlement date and redemption date (maturity date, call date, put date, etc.). (If this number contains a fraction, raise it to the next whole number; for example, 2.4 = 3.) DSC = number of days from settlement date to next coupon date K= summation counter Note: The first term computes present value of the redemption amount, not including interest. The second term computes the present values for all future coupon payments.
Straight-line depreciation First year: Last year or more: DEP = RDV Sum-of-the-years’-digits depreciation First year: Last year or more: DEP = RDV Declining-balance depreciation where: is for YR First year: Unless; If 88 ; then use , use APPENDIX - Reference Information
If computing last year, Statistics Note: Formulas apply to both x and y. Standard deviation with n weighting (s x): Standard deviation with n -1 weighting (s x): Mean: Regressions Formulas apply to all regression models using transformed data.
Interest Rate Conversions where: where: Percent Change where: OLD = old value NEW = new value %CH = percent change #PD = number of periods Profit Margin Breakeven where: PFT = profit P = price FC = fixed cost 90 APPENDIX - Reference Information
VC = variable cost Q = quantity Days between Dates With the Date worksheet, you can enter or compute a date within the range January 1, 1980, through December 31, 2079. Actual/actual day-count method Note: The method assumes the actual number of days per month and per year.
30/360 day-count method 1 Note: The method assumes 30 days per month and 360 days per year. where: M1 = month of first date DT 1 = day of first date Y 1 = year of first date M 2 = month of second date DT 2 = day of second date Y 2 = year of second date Note: If DT1 is 31, change DT1 to 30. If DT2 is 31 and DT1 is 30 or 31, change DT2 to 30; otherwise, leave it at 31. Note: 1Source for 30/360 day-count method formula Lynch, John J., Jr., and Jan H. Mayle.Standard Securities Calculation Methods.
Error Messages Note: To clear an error message, press P. Error Possible Causes • A result is outside the calculator range (±€9.9999999999999E99). Error 1 • Tried to divide by zero (can occur internally). Overflow • Tried to compute 1/x when x is zero. • Statistics worksheet: a calculation included X or Y values that are all the same. • Tried to compute x! when x is not an integer 0-69. • Tried to compute LN of x when x is not > 0.
Error Possible Causes • A calculation tried to use more than 8 pending operations. • Amortization worksheet: the value entered for P1 or P2 is outside the range 1-9,999. • TVM worksheet: the P/Y or C/Y value 0. • Cash Flow worksheet: the Fnn value is outside the range 0.5-9,999. • Bond worksheet: the RV, CPN, or PRI value _0. • Date worksheet: the computed date is outside the range January 1, 1980 through December 31, 2079.
Error Possible Causes very complex problem involving many iterations. • Cash Flow worksheet: the calculator computed IRR for a complex problem with multiple sign changes or PB /DPB with no payback period based on input cash flow values. • Bond worksheet: the calculator computed YLD for a very complex problem. • TVM worksheet: $ was pressed to stop the evaluation of I/Y . • Amortization worksheet: $ was pressed to stop the evaluation of BAL or INT.
2. 0.3333333333333 Q 3 = 0.9999999999999 The calculator rounds the result and displays it as 1. This rounding enables the calculator to display the most accurate result. Although most calculations are accurate to within ±1 in the last displayed digit, higher-order mathematical functions use iterative calculations, in which inaccuracies can accumulate in the guard digits. In most cases, the cumulative error from these calculations is maintained beyond the 10-digit display so that no inaccuracy is shown.
1. Turn off the calculator and turn it over with the back facing you. 2. Using a small Phillips screwdriver, remove the four screws from the back cover. 3. Carefully pry off the back cover. 4. Using a small Phillips screwdriver, remove the screws from the metal battery cover and lift the cover off the battery. 5. Tip the calculator slightly to remove the battery. Caution: Avoid contact with other calculator components. 6. Install the new battery with the positive sign (+) sign down (not showing).
Difficulty Solution variable is set to zero. The display is blank; digits do not appear. Select the worksheet again. Be sure the battery is properly installed and replace, if necessary. The calculator does not display the correct worksheet variables. Be sure you have selected the correct worksheet. The calculator does not display the correct number of decimal places. Press & | to check or adjust the setting for number of decimal places displayed.
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