BA II PLUS™ PROFESSIONAL Calculator
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Table of Contents 1 Overview of Calculator Operations..................................1 Turning On the Calculator ............................................................. 1 Turning Off the Calculator............................................................. 1 Selecting 2nd Functions ................................................................. 2 Reading the Display ....................................................................... 2 Setting Calculator Formats .............................
Deleting Cash Flows...................................................................... 44 Inserting Cash Flows ..................................................................... 44 Computing Cash Flows ................................................................. 45 Example: Solving for Unequal Cash Flows ................................. 47 Example: Value of a Lease with Uneven Payments .................... 49 4 Bond Worksheet .............................................................
1 Overview of Calculator Operations This chapter describes the basic operation of your BA II PLUS™ PROFESSIONAL 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 $.
• The Constant Memory™ feature retains all worksheet values and settings, including the contents of the 10 memories and all format settings. 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.
The indicators along the top of the display tell you which keys are active and offer information about the status of the calculator. Indicator Meaning 2nd Press a key to select its second function. INV Press a key to select its inverse trigonometric function. HYP Press a key to select its hyperbolic function. COMPUTE Press % to compute a value for the displayed variable. ENTER Press ! to assign the displayed value to the displayed variable.
Setting Calculator Formats You can change these calculator formats: To Select Press Display Number of decimal places & | DEC 0–9 (Press 9 for floating-decimal) 2 Angle units # DEG DEG (degrees) Default RAD (radians) Dates # US (mm-dd-yyyy) US Eur (dd-mm-yyyy) Number separators # Calculation method # US (1,000.00 ) US Eur (1.000,00) Chn (chain) Chn AOSé (algebraic operating system) 1. To access format options, press & |.
Changing the number of decimal places affects the display only. Except for amortization and depreciation results, the calculator does not round internal values. To round the internal value, use the round function. (See “Rounding & o” on page 10.) Note: All examples in this guidebook assume a setting of two decimal places. Other settings might show different results. Choosing the Angle Units The angle unit value affects the display of results in trigonometric calculations.
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 “Clearing Calculator Entries and Memories” on page 6.
To clear Press The prompted worksheet and reset default values &z Calculator format settings and reset default values &| &z • Out of the prompted worksheet and return to standard-calculator mode • All pending operations in standard-calculator mode • In a prompted worksheet, the variable value keyed in but not entered (the previous value appears) • Any calculation started but not completed &U PP TVM worksheet variables and reset default values &U &^ One of the 10 memories (without affecting
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 10.00 Subtract 6 N 4 6B4N 2.00 Multiply 6 Q 4 6<4N 24.00 Divide 6 P 4 664N 1.50 3 ; 1.25 N 3.95 Find universal power: 3 1.25 Display Use parentheses: 7 Q (3 + 5) 7 <9 3 H 5 :N 56.
To Press Display .69315 & i 2.00 Round 2 P 3 to the set decimal format 2 6 3 N&o 0.67 Generate random number* &a 0.86 Store seed value D&a 0.86 Find sine:** sin(11.54°) 11.54 & d 0.20 Find cosine:** cos(120°) 120 & e Find tangent:** tan(76°) 76 & f Find natural antilogarithm: e .69315 .2 8 d -1 Find arcsine:** sin (.2) .5 S 8 e -1 Find arccosine:** cos (-.5) 4 8f -1 Find arctangent:** tan (4) -0.50 4.01 11.54 120.00 75.96 Find hyperbolic sine: sinh(.5) .5 & c d 0.
Parentheses 9 : Use parentheses to control the order in which the calculator evaluates a numeric expression in division, multiplication, powers, roots, and logarithm calculations. The calculator includes up to 15 levels of parentheses and up to 8 pending operations. Note: You do not have to press : for expressions ending in a series of closed parentheses. Pressing N closes parentheses automatically, evaluates the expression, and displays the final result.
For example, working in the Bond worksheet, you might want to round a computed selling price to the nearest penny (two decimal places) before continuing your calculation. Note: The calculator stores values to an accuracy of up to 13 digits. The decimal format setting rounds the displayed value but not the unrounded, internally stored value. (See “Choosing the Number of Decimal Places Displayed” on page 4.
Memory Operations You can store values in any of 10 memories using the standard calculator keys. Note: You can also use the Memory worksheet. (See “Memory Worksheet” on page 82.) • You can store in memory any numeric value within the range of the calculator. • To access a memory M0 through M9, press a numeric key (0 through 9). Clearing Memory Clearing memory before you begin a new calculation is a critical step in avoiding errors. • To clear an individual memory, store a zero value in it.
• Memory arithmetic changes only the value in the affected memory and not the displayed value. • Memory arithmetic does not complete any calculation in progress. The table lists the available memory arithmetic functions. In each case, the specified memory stores the result. To Press Add the displayed value to the value stored in memory 9 (M9). DH 9 Subtract the displayed value from the value stored in memory 3 (M3). DB 3 Multiply the value in memory 0 (M0) by the displayed value.
Keystrokes for Constant Calculations This table shows how to create a constant for various operations.
To Press Display Key in a new calculation 2; 2.00 Recall the last answer &x 4.00 Complete the calculation N 16.00 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.
To select Function Press Statistics worksheet (Chapter 6) Analyzes statistics on one- or two-variable data using four regression analysis options &k Percent Change/Compound Interest worksheet (Chapter 7) Computes percent change, compound interest, and costsell markup &q Interest Conversion worksheet (Chapter 7) Converts interest rates between nominal rate (or annual percentage rate) and annual effective rate &v Date worksheet (Chapter 7) Computes number of days between two dates, or date/day of
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” on page 22.) Indicators prompt you to select settings, enter values, or compute results. For example, the i# $ indicators remind you to press # or " to select other variables. (See “Reading the Display” on page 2.
When you display a compute-only variable, the COMPUTE indicator reminds you to press % to compute its value. After you press %, the indicator confirms that the displayed value has been computed. Automatic-Compute Variables When you press # or " to display an automatic-compute variable (for example, the Amortization worksheet INT variable), the calculator computes and displays the value automatically without you having to press %.
Display Indicators • The indicator confirms that the calculator entered the displayed value in the worksheet. • The indicator confirms that the calculator computed the displayed value. • When a change to the worksheet invalidates either entered or computed values, the and indicators disappear.
20 Overview of Calculator Operations
2 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. After solving a TVM problem, you can use the Amortization worksheet to generate an amortization schedule. • To access a TVM variable, press a TVM key (,, -, ., /, or 0).
TVM and Amortization Worksheet Variables Variable Key Display Type of Variable Number of periods , N Enter-or-compute Interest rate per year - I/Y Enter-or-compute Present value .
• To generate an amortization schedule, press & \, enter the first and last payment number in the range (P1 and P2), and press " or # to compute values for each variable (BAL, PRN, and INT).
Entering Values for I/Y, P/Y, and C/Y • Enter I/Y as the nominal interest rate. The TVM worksheet automatically converts I/Y to a per period rate based on the values of P/Y and C/Y. • Entering a value for P/Y automatically enters the same value for C/Y. (You can change C/Y.) 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.
• In worksheet modes the calculator displays only the value you enter or recall, although any variable label previously displayed remains displayed. Note: You can tell that the displayed value is not assigned to the displayed variable, because the = indicator is not displayed. To compute a TVM value, press % 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.
6. Press & \. — or — If INT is displayed, press # to display P1 again. 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 %. Both P1 and P2 update automatically to represent the next range of payments.
To Press Display Enter loan amount. 75000 . PV= Enter payment amount. 425.84 S / PMT= Compute interest rate. %- I/Y= 75,000.00õ -425.84 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 reenter the values for loan amount and interest rate.
To Press Compute payment. %/ Display -1,279.82 PMT= 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 20-year time frame. Computing Future Value Example: If you open the account with $5,000, how much will you have after 20 years? To Press Display Set all variables to defaults. &} ! RST Enter number of payments.
Example: Computing Present Value in Annuities The Furros Company purchased equipment providing an annual savings of $20,000 over 10 years. Assuming an annual discount rate of 10%, what is the present value of the savings using an ordinary annuity and an annuity due? Cost Savings for a Present-Value Ordinary Annuity Cost Savings for a Present-Value Annuity Due in a Leasing Agreement To Press Set all variables to defaults. &}! RST Enter number of payments. 10 , N= 10.
To Press Display Compute present value (ordinary annuity). %. PV= Set beginning-of-period payments. & ]& V BGN Return to calculator mode. &U Compute present value (annuity due). %. 122,891.34 0.00 PV= 135,180.48 Answer: The present value of the savings is $122,891.34 with an ordinary annuity and $135,180.48 with an annuity due. Example: Computing Perpetual Annuities To replace bricks in their highway system, the Land of Oz has issued perpetual bonds paying $110 per $1000 bond.
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 PMT PV = ---------------------------( I/Y ) ÷ 100 • Perpetual annuity due PMT PV = PMT + ---------------------------( I/Y ) ⁄ 100 ) Example: Computing Present Value of Variable Cash Flows The ABC Company purchased a machine that will save these end-of-year amounts:
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 Enter 1st cash flow. 5000 S 0 FV= -5,000.00 Enter 1st cash flow period. 1, N= Compute present value of 1st cash % . flow. Display PV= Store in M1. D1 Enter 2nd cash flow. 7000 S 0 FV= Enter 2nd cash flow period. 2, N= Compute present value of 2nd cash flow. %.
To Press Compute present value of 4th cash flow. %. Sum to memory. DH 1 Recall total present value. J1 Subtract original cost. B 23000 N Display PV= 6,830.13 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 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 Enter residual value of asset. 6500 S 0 FV= -6,500.00 PV= 2,818.22 Compute residual present value. % . Display 0.00 0.00 46.
To Press Return to standard-calculator mode &U Enter number of payments using 2 & Z , payment multiplier. Display 0.00 N= 24.00 Enter interest rate. 20 - I/Y= 20.00 Enter loan amount. 525 . PV= 525.00 Compute payment. %/ PMT= -26.72 Answer: Your monthly payment is $26.72. Example: Saving With Monthly Deposits Note: Accounts with payments made at the beginning of the period are referred to as annuity due accounts.
To Press Display 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. %0 FV= 240.00 7.50 -200.00 111,438.31 Answer: Depositing $200 at the beginning of each month for 20 years results in a future amount of $111,438.31. Example: Computing Amount to Borrow and Down Payment You consider buying a car for $15,100. The finance company charges 7.5% APR compounded monthly on a 48-month loan.
To Press Compute loan amount. %. Compute down payment H 15,100 S N Display PV= 13,441.47 -1,658.53 Answer: You can borrow $13,441.47 with a down payment of $1,658.53. Example: Computing Regular Deposits for a Specified Future Amount You plan to open a savings account and deposit the same amount of money at the beginning of each month. In 10 years, you want to have $25,000 in the account. How much should you deposit if the annual interest rate is 0.
Example: Computing Payments and Generating an Amortization Schedule This example shows you how to use the TVM and Amortization worksheets to calculate the monthly payments on a 30-year loan and generate an amortization schedule for the first three years of the loan. Computing Mortgage Payments Calculate the monthly payment with a loan amount of $120,000 and 6.125% APR. To Press Display Set all variables to defaults. &}! RST Set payments per year to 12. & [ 12 ! P/Y= 0.00 12.
To Press Display Display 2nd year amortization data. # # # BAL= PRN= INT= Move to P1 and press % to enter next range of payments. #% P1= 22.00 Display P2. # P2= 33.00 Display 3rd year amortization data. # # # BAL= PRN= INT= 117,421.60* _-1,507.03* -7,242.53* 115,819.62* -1601.98* -7,147.
Generating an Amortization Schedule for Interest and Balloon Payment To Press Select Amortization worksheet. & \ Display P1= 1.00 60.00 Enter end period (five years). # 5 &Z ! P2= View balance due after five years (balloon payment). # BAL= 77,187.72 View interest paid after five years. ## 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.
3 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. • 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 % for each variable.
Variable Key Display Variable Type** Net future value #% NFV Compute-only Payback #% PB Compute-only Discounted payback #% DPB Compute-only Internal rate of return )% IRR Compute-only Reinvestment rate # RI Enter-only MOD Auto Compute Modified Internal rate of return # * nn represents the cash flow (C01–C32) or frequency (F01–F32) number. ** This guidebook categorizes variables by the method of entry. (See “Types of Worksheet Variables” on page 17.
Uneven and Grouped Cash Flows Uneven Cash Flows The Cash Flow worksheet analyzes unequal cash flows over equal time periods. Cash-flow values can include both inflows (cash received) and outflows (cash paid out). 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.
5. To select the cash-flow frequency variable (F01), press #. The F01 value appears. 6. To change F01, key in a value and press !. 7. To select an additional cash-flow variable, press #. The C02 value appears. 8. Repeat steps 4 through 7 for all remaining cash flows and frequencies. 9. To review entries, press # or ". Deleting Cash Flows When you delete a cash flow, the calculator decreases the number of subsequent cash flows automatically.
1. Press # or " to select the cash flow where you want to insert the new one. For example, to insert a new second cash flow, select C02. 2. Press & X. 3. Key in the new cash flow and press !. The new cash flow is entered at C02. 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.
Computing IRR and MOD 1. Press ). The IRR variable and current value are displayed (based on the current cash-flow values). 2. To compute the internal rate of return, press %. The calculator displays the IRR value. 3. To select the reinvestment rate (RI), press #. 4. Key in the reinvestment rate value and press !. 5. To compute the modified internal rate of return, press #. The calculator displays the MOD value.
The time line reflects a sequence of cash flows with three sign changes, indicating that one, two, or three IRR solutions can exist. • When solving complex cash-flow problems, the calculator might not find PB, DPB, IRR, and MOD, even if a solution exists. In this case, the calculator displays Error 7 (iteration limit exceeded).
Entering Cash-Flow Data To Press Display Select Cash Flow worksheet. ' CFo= 0.00 Enter initial cash flow. 7000 S ! CFo= -7,000.00 Enter cash flow for first year. # 3000 ! # C01= F01= 3,000.00 1.00 Enter cash flows for years two through five. # 5000 ! #4! C02= F02= 5,000.00 Enter cash flow for sixth year. # 4000 ! # C03= F03= 4,000.00 4.00 1.
Computing NPV, NFV, PB, and DPB Use an interest rate per period (I) of 20%. To Press Display Access interest rate variable ( I= 0.00 I= 20.00 Enter interest rate per period. 20 ! Compute net present value. #% NPV= 7,266.44 Compute net future value. #% NFV= 21,697.47 Compute payback. #% PB= 2.00 DPB= 2.60 Compute discounted payback. # % Answers: NPV is $7,266.44. NFV is $21,697.47. PB is 2.00. DPB is 2.60. Computing IRR and MOD To Press Display Access IRR. ) IRR= 0.
Number of Months Payment Amount 9 $6000 2 $0 10 $7000 If the required earnings rate is 10% per 12-month period with monthly compounding: • What is the present value of these lease payments? • What even payment amount at the beginning of each month would result in the same present value? Because the cash flows are uneven, use the Cash Flow worksheet to determine the net present value of the lease. Computing NPV The cash flows for the first four months are stated as a group of four $0 cash flows.
To Press Enter third group of cash flows. # #3! C03= F03= 0.00 3.00 Enter fourth group of cash flows. # 6000 S ! C04= F04= #9! -6000.00 9.00 Enter fifth group of cash flows. # #2! Display C05= F05= 0.00 2.00 Enter sixth group of cash flows. # 7000 S ! C06= F06= # 10 ! -7000.00 10.00 Select NPV. ( I= 0.00 Enter monthly earnings rate. 10 6 12 ! I= 0.83 Compute NPV. #% NPV= Cash Flow Worksheet -138,088.
52 Cash Flow Worksheet
4 Bond Worksheet The Bond worksheet lets you compute bond price, yield to maturity or call, accrued interest, and modified duration. 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.
Bond Worksheet Variables Variable Key Display Variable Type Settlement date &l SDT Enter only Annual coupon rate in percent # CPN Enter only Redemption date # RDT Enter only RV Enter only Redemption value (percentage of # par value) Actual/actual day-count method # ACT Setting 30/360 day-count method &V 360 Setting Two coupons per year # 2/Y Setting One coupon per year &V 1/Y Setting Yield to redemption # YLD Enter/compute Dollar price # PRI Enter/compute Accrued int
Entering Dates • Use the following convention to key in dates: mm.ddyy or dd.mmyy. After keying in the date, press !. Note: You can display dates in either US or European format. (See “Setting Calculator Formats ” on page 4.) • You can enter dates from January 1, 1950 through December 31, 2049. • The calculator assumes that the redemption date (RDT) coincides with a coupon date: – To compute to maturity, enter the maturity date for RDT. – To compute to call, enter the call date for RDT.
Bond Worksheet Terminology Term Definition Call Date A callable bond can be retired by the issuing agency before the maturity date. The call date for such a bond is printed in the bond contract. 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. Par (Face) Value The value printed on the bond.
redemption value (RV). If necessary, change the day-count method (ACT or 360) and couponfrequency (2/Y or 1/Y). The Bond worksheet stores all values and settings until you clear the worksheet or change the values and settings. Note: Dates are not changed when you clear a worksheet. Entering Known Bond Values 1. Press & l. The current SDT value appears. 2. To clear the worksheet, press & z. 3. If necessary, key in a new SDT value and press !. 4.
Computing Modified Duration (DUR) To compute modified duration, press # until the DUR variable appears. The calculator automatically computes DUR. Example: Computing Bond Price, Accrued Interest, and Modified Duration You consider buying a semiannual corporate bond maturing on December 31, 2007 and settling on June 12, 2006. The bond is based on the 30/360 day-count method with a coupon rate of 7%, redeemable at 100% of par value.
5 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** 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. (See “Setting Calculator Formats ” on page 4.)**This guidebook categorizes variables by their method of entry. (See “Types of Worksheet Variables” on page 17.
Entering Values for DB and DBX If you choose either the declining balance (DB) or declining balance with crossover to SL (DBX) depreciation method, remember to enter a value representing the percent of declining balance for the DB or DBX variable. Note: The declining balance you enter must be a positive number. Entering Values for LIF • If SL or SLF is selected, the LIF value must be a positive real number. • If SYD, DB, DBX, or DBF is selected, the LIF value must be a positive integer.
Selecting a Depreciation Method 1. To access the Depreciation worksheet, press & p. The current depreciation method is displayed. 2. To clear the worksheet, press & z. 3. Press & V until you display the depreciation method you want (SL, SLF, SYD, DB, DBX, or DBF). Note: If you select DB or DBX, you must either key in a value or accept the default of 200. Entering Depreciation Data 1. To display LIF, press #. 2. Key in a value for LIF and press !. 3.
To Press Display Enter life in years. # 31.5 ! LIF = Enter starting month. # 3.5 ! M01 = Enter cost. # 1000000 ! CST = 1,000,000.00 Leave salvage value as is. # SAL = 0.00 Leave year as is. # YR = 1.00 Display depreciation amount, remaining book value, and remaining depreciable value. # # # DEP = RBV = RDV = View second year. # % YR = YR = Display second year depreciation data. # # # DEP = RBV = RDV = 31.50 3.50 25,132.28* 974,867.72* 974,867.72* 1.00 2.00 31,746.
64 Depreciation Worksheet
6 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 Number of observations # (as Mean (average) of X values needed) Sample standard deviation of X Population standard deviation of X Mean (average) of Y values Sample standard deviation of Y Population standard deviation of Y Linear regression y-intercept Linear regression slope Correlation coefficient 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 n v Sx sx y** Sy** sy** a** b** r**
• When you enter data for one-variable statistics, Xnn represents the value and Ynn specifies the number of occurrences (frequency). • When you enter a value for Xnn, the value for Ynn defaults to 1. Analyzing One-Variable Statistics To analyze one-variable statistics, select 1-V. Only values for n, v, Sx, sX, GX, and GX2 are computed and displayed for one-variable statistics.
• Ln uses ln(X) and Y. • EXP uses X and ln(Y). • PWR uses ln(X) and ln(Y). The calculator determines the values for a and b that create the line or curve that best fits the data. 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.
Computing Statistical Results Selecting a Statistics Calculation Method 1. Press & k to select the statistical calculation portion of the Statistics worksheet. 2. The last selected statistics calculation method is displayed (LIN, Ln, EXP, PWR, or 1-V). 3. Press & V repeatedly until the statistics calculation method you want is displayed. 4. If you are analyzing one-variable data, select 1-V. 5. Press # to begin computing results.
70 Statistics Worksheet
7 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 cost-sellmarkup problems.
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 1 To reset default values for all calculator variables and formats, press & } !.
3. 4. To enter values for the known variables, press # or " until the variable you want is displayed, then key in a value, and press !. (Do not enter a value for the variable you wish to solve.) • Percent Change — Enter values for two of these three variables: OLD, NEW, and %CH. Leave #PD set to 1. • Compound Interest — Enter values for three of these four variables: OLD, NEW, %CH, and #PD. • Cost-Sell-Markup — Enter values for two of these three variables: OLD, NEW, and %CH. Leave #PD set to 1.
To Press Display Enter number of years. ## 5 ! #PD= 5.00 Compute annual growth rate. "% %CH= 8.45 Answer: The annual growth rate is 8.45%. Example: Computing Cost-Sell-Markup The original cost of an item is $100; the selling price is $125. Find the markup. To Press Display Select Percent Change/Compound Interest worksheet. &q OLD= 0 Clear worksheet variables. &z OLD= 0.00 Enter original cost. 100 ! OLD= 100.00 Enter selling price. # 125 ! NEW= 125.
Comparing the Nominal Interest Rate of Investments Comparing the nominal interest rate (annual percentage rate) of investments is misleading when the investments have the same nominal rate but different numbers of compounding periods per year. To make a more valid comparison, convert the nominal interest rate (NOM) to the annual effective interest rate (EFF) for each investment.
6. To compute a value for the unknown variable (interest rate), press # or " until NOM or EFF is displayed, and then press %. The calculator displays the computed value. Example: A bank offers a certificate that pays a nominal interest rate of 15% with quarterly compounding. What is the annual effective interest rate? To Press Display Select Interest Conversion worksheet. &v NOM= 0 Enter nominal interest rate. 15 ! NOM= 15.00 Enter number of compounding periods per year. ##4 ! C/Y= 4.
Note: The calculator categorizes variables by their method of entry. (See “Types of Worksheet Variables” on page 17.) Resetting the Date Worksheet Variables • • To reset default values for all calculator variables and formats, including the Date worksheet variables, press & } !.
6. To change the day-count method setting, press # until ACT or 360 is displayed. 7. To compute a value for the unknown variable, press # or " to display the variable, and then press %. The calculator displays the computed value. 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.
Variable Key Profit margin # Display Variable Type MAR Enter/compute 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.
To Press Display Compute cost. ""% CST= 100.00 Answer: The original cost is $100. 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 %. 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. (See “Types of Worksheet Variables” on page 17.) • 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. (See “Memory Operations” on page 12.
• 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. (See “Memory Arithmetic” on page 12.) Examples: Using the Memory Worksheet To Press Display Access Memory worksheet &{ M0= 0 Select M4. #### M4= 0 Clear M4. 0! M4= 0.00 Store 95. 95! M4= 95.00 Add 65. H6 5 ! M4= 160.00 Subtract 30. B3 0 ! M4= 130.00 Multiply by 95. <95! M4= 12,350.00 Divide by 65.
84 Other Worksheets
A Appendix — Reference Information This appendix includes supplemental information to help you use your BA II PLUSé and BA II PLUSé PROFESSIONAL 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.
I/Y = 100 × C ⁄ Y × [ e ( y × ln ( x + 1 ) ) – 1] where: x = i y =P/Y P C/Y Gi = 1 + i Q k where: k =0 for end-of-period payments k =1 for beginning-of-period payments PMT × G i – FV × i ln --------------------------------------------- PMT × G i + PV × i N = ---------------------------------------------------------ln ( 1 + i ) where: i ƒ0 N = L(PV + FV) P PMT where: i =0 –i PV + FV PMT = ----- × PV + --------------------------N Gi (1 + i) – 1 where: i ƒ0 PMT = L(PV + FV) P N where: i =0 PMT ×
PMT × G PMT × G N FV = ------------------------i – ( 1 + i ) × PV + ------------------------i i i where: i ƒ0 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 I m = RND [ RND12 ( – i × bal ( m – 1 ) ) ] bal ( m ) = bal ( m – 1 ) – I m + RND ( PMT ) then: bal( ) =bal(pmt2) GPrn( ) =bal(pmt2) N bal(pmt1) GInt( ) =(pmt2 N pmt1 +1) Q RND(PMT) N GPrn( ) where: RND =round the display to the number of decimal places sele
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). p NFV = ( 1 + i ) × NPV where: i is the periodic interest rate used in the calculation of NPV. N p = ∑ nk k=1 where: n k is the frequency of the kth cash flow. IRR = 100 × i, where i satisfies npv() = 0 Internal rate of return depends on the values of the initial cash flow (CF0) and the subsequent cash flows (CFj).
Bonds1 Price (given yield) with one coupon period or less to redemption: 100 × R RV + -----------------M A 100 × R PRI = --------------------------------------- – --- × -----------------E M Y DSR 1 + ----------- × ----- E M where: PRI =dollar price per $100 par value RV =redemption value of the security per $100 par value (RV = 100 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
Price (given yield) with more than one coupon period to redemption: RV ------------------------------------------DSCY N – 1 + ----------E PRI = 1 + ----- + M R A – 100 × ----- × --M E N ∑ R 100 × ----M -----------------------------------------Y- 1 + --- M K = 1 K – 1 + DSC -----------E where: N =number of coupons payable between settlement date and redemption date (maturity date, call date, put date, etc.).
where Duration is calculated using one of the following formulas used to calculate Macaulay duration: • For a bond price with one coupon period or less to redemption: Y- Dur = 1 + --- M • 100 × R Rv + -----------------M Dsr × -----------------------------------------2Dsr ×Y 1 + ------------------- E×M ⋅ ---------------------------------------------------------------E × M × Pri For a bond price with more than one coupon period to redemption: Depreciation RDV = CST N SAL N accumulated depreci
Sum-of-the-years’-digits depreciation LIF + 2 – YR – FSTYR ) × ( CST – SAL ) -----------------------------------------------------------------------------------------------------( ( LIF × ( LIF + 1 ) ) ÷ 2 ) LIF × ( CST – SAL ) ( ( LIF × ( LIF + 1 ) ) ÷ 2 ) First year: ------------------------------------------------------------ × FSTYR Last year or more: DEP = RDV Declining-balance depreciation RBV × DB% ------------------------------LIF × 100 where: RBV is for YR - 1 CST × DB% LIF × 100 First year:
Standard deviation with n-1 weighting (s x): ∑ 2 x x 2 – -------------------n ----------------------------------------n–1 ∑ 1⁄2 (∑ x ) Mean: x = --------------- n Regressions Formulas apply to all regression models using transformed data.
where: OLD =old value NEW =new value %CH =percent change #PD =number of periods Profit Margin Selling Price – Cost Gross Profit Margin = ----------------------------------------------- × 100 Selling Price Breakeven PFT = P Q N (FC + VC Q) where: PFT =profit P =price FC =fixed cost VC =variable cost Q =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.
where: M1 =month of first date DT1 =day of first date Y1 =year of first date M2 =month of second date DT2 =day of second date Y2 =year of second date MB =base month (January) DB =base day (1) YB =base year (first year after leap year) 30/360 day-count method3 Note: The method assumes 30 days per month and 360 days per year.
Error Messages Note: To clear an error message, press P. Error Possible Causes Error 1 • A result is outside the calculator range (± 9.9999999999999E99). • Tried to divide by zero (can occur internally). • Tried to compute 1/x when x is zero. • Statistics worksheet: a calculation included X or Y values that are all the same. Error 2 • Tried to compute x! when x is not an integer 0-69. Invalid argument • Tried to compute LN of x when x is not > 0.
Error Possible Causes Error 5 • No solution exists TVM worksheet: the calculator computed I/Y when FV, (N Q PMT), and PV all have the same sign. (Make sure cash inflows are positive and outflows are negative.) • TVM, Cash Flow, and Bond worksheets: the LN (logarithm) input is not > 0 during calculations. • Cash Flow worksheet: the calculator computed IRR without at least one sign change in the cash-flow list.
Accuracy Information The calculator stores results internally as 13-digit numbers but displays them rounded to 10 digits or fewer, depending on the decimal format. The internal digits, or guard digits, increase the calculator’s accuracy. Additional calculations use the internal value, not the value displayed. Rounding If a calculation produces a result with 11-digits or more, the calculator uses the internal guard digits to determine how to display the result.
Priority Operations 4 Q, P 5 +, - 6 ) 7 (lowest) = Battery Information Replacing the Battery Replace the battery with a new CR2032 lithium battery. Caution: Risk of explosion if replaced by an incorrect type. Replace only with the same or equivalent type recommended by Texas Instruments. Dispose of used batteries according to local regulations. Note: The calculator cannot retain data when the battery is removed or discharged. Replacing the battery has the same effect as resetting the calculator.
• Install battery according to polarity (+ and - ) diagrams. • Do not place non-rechargeable batteries in a battery recharger. • Properly dispose of used batteries immediately. • Do not incinerate or dismantle batteries. • Seek Medical Advice immediately if a cell or battery has been swallowed. (In the USA, contact the National Poison Control Center collect at 202-625-3333.) Used only for small button cell batteries. Battery Disposal • Do not mutilate, or dispose of batteries in fire.
Difficulty Solution The calculator does not display Press & | # # # # to check or the correct result in a math adjust the setting for calculation calculation. method. An error occurs. If you experience difficulties other than those listed above, press & } ! to clear the calculator, and then repeat your calculations. Note: You can also perform a hard reset using the reset hole in back of the calculator. Texas Instruments Support and Service For general information Home Page: education.ti.
Texas Instruments (TI) Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments ("TI") electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This TI 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 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.
104 Appendix — Reference Information
Index Symbols #PD (number of periods) 72, 73, 74 #PD (number of periods, Percent Change/Compound Interest worksheet) 72 %CH (percent change) 72, 73, 74 (- (negative) indicator 3 (#$ indicator 3 (1 (value entered) indicator 3 (GX (sum of X) 65, 67 (GX² (sum of X²) 65, 67 (GXY (sum of XY products) 65 (GY (sum of Y) 65 (GY² (sum of Y²) 65 (sx (population standard deviation of X) 65, 67 (sy (population standard deviation of Y) 65 (v (mean of X) 65, 67 (w (mean of X) 65 * (value computed) indicator 3 = (value as
payments 22, 24 Bond accrued interest (AI) 54 price (PRI) 58 terminology 56 worksheet 53–58 Breakeven worksheet 80–81 Cost-Sell-Markup 73, 74 Coupon payment 56 CPN (annual coupon rate, percent) 54, 55, 56, 57 CST (cost) 59, 62, 79 Curve fitting 67 customer support and service 101 C D C/Y (compounding periods per year) 22, 24, 76 Calculation method 4, 5 Call date 56 Cash Flow worksheet 41–51 Cash flows computing 45 deleting 42, 44 editing 48 entering 42 formulas 87 grouped 43 inserting 44 uneven 43 CFo (
DPB (discounted payback) 41, 45 DT1 (starting date) 62 DT1, DT2 (date 1 and 2) 59, 78 DUR (modified duration) 54 E EFF (annual effective rate) 75, 76 END (end-of-period) payments 22, 24 Ending payment (P2) 22, 24 End-of-period (END) payments 22, 24 ENTER indicator 3 Error clearing 96 messages 96 Examples accrued interest 58 amortization schedule 38 amount to borrow 36 annuities 30 balloon payment 40 bond price 58 compound interest 73 computing basic loan payments 27 constants 13 converting interest 76 corr
bond price (more than one coupon period to redemption) 90 bond price (one coupon period or less to redemption) 89 bond yield (more than one coupon period to redemption) 90 bond yield (one coupon period or less to redemption) 89 bonds 89 breakeven 94 cash flow 87 days between dates 94 depreciation 91 depreciation, declining-balance 92 depreciation, straight-line 91 depreciation, sum-of-the-years’digits 92 interest-rate conversions 93 internal rate of return 88 modified duration 90 modified internal rate of r
MOD (modified internal rate of return) 41, 45 Modified duration (DUR) 54 Modified internal rate of return (MOD) 41, 45 Mortgages 21 Multiplication 8 N n (number of observations) 65, 67 N (number of periods) 24 N (number of periods, TVM worksheet) 22 Negative (–) indicator 3 Net future value (NFV) 41, 45 Net present value (NPV) 41, 45 NEW (new value) 72, 73, 74 New value (NEW) 72, 73, 74 NFV (net future value) 41, 45 NOM (nominal rate) 76 Nominal rate (NOM) 75, 76 NPV (net present value) 41, 45 Number of ob
computing net future value 45 computing net present value 45 computing payback 45 computing percent change 72 computing profit margin 79 computing statistical results 69 computing X’ 69 computing Y’ 69 constants for various operations 13 converting interest 75 deleting cash flows 44 entering bond data 57 entering data points 68 entering depreciation data 62 generating a depreciation schedule 62 generating amortization schedules 25, 26 inserting cash flows 44 selecting a depreciation method 62 selecting a st
indicator 3 Quit 2 SEL (selling price) 79 Selling price (SEL) 79 service and support 101 SET (setting) indicator 3 Setting (SET) indicator 3 Settlement date (SDT) 54, 56, 57 SL (straight line) 59, 61, 62 SLF (French straight line) 59, 61, 62 Slope (b) 65 Square 8 Square root 8 Starting date (DT1) 62 Starting month (M01) 59, 61, 62 Starting payment (P1) 22, 24 Statistical data 68 Statistics worksheet 65–69 Storing to memory 12 Straight line (SL) 59, 61, 62 Subtraction 8 Sum of the years’ digits (SYD) 59, 61,
Y-intercept (a) 65 YLD (yield to redemption) 54, 57 112 Ynn (frequency of X value) 65, 67 YR (year to compute) 59, 61, 62 Index
