BA II PLUS™
PROFESSIONAL
Calculator
Table of Contents
Example: Computing Present Value of a Lease With Residual
Value........................................................................................ 33
Example: Computing Regular Deposits for a Specified Future
Amount ................................................................................... 37
Example: Computing Payments and Generating an
Amortization Schedule........................................................... 38
Example: Computing Payment, Interest, and Loan Balance
After a Specified Payment ..................................................... 39
Table of Contents
iii
Modified Duration..................................................................58
.......................................................................................................83
Index.............................................................................. 105
iv
Table of Contents
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 $.
•
If you turned off the calculator by pressing $, the
calculator returns to the standard-calculator mode
with a displayed value of zero.
All worksheets and formats for numbers, angle units,
dates, separators, and calculation method retain
previous values and configurations.
•
If the Automatic Power Down™ (APD™) feature
turned off the calculator, the calculator turns on
exactly as you left it, saving display settings, stored
memory, pending operations, and error conditions.
Turning Off the Calculator
Press $.
•
•
The displayed value and any error condition clear.
Any unfinished standard-calculator operation and worksheet
calculation in progress cancel.
Overview of Calculator Operations
1
•
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.
Selecting 2nd Functions
The primary function of a key is printed on the key itself.
For example, the primary function of the $ key is to
turn on or turn off the calculator.
Most keys include a second function printed above the key.
To select a second function, press & and the
corresponding key. (When you press &, the 2nd indicator
appears in the upper left corner of the display.)
For example, pressing & U exits the selected
worksheet and returns the calculator to the standard-
calculator mode.
Note: To cancel after pressing &, press & again.
Reading the Display
The display shows the selected variable labels with values up to 10 digits.
(The calculator displays values exceeding 10 digits in scientific notation.)
2
Overview of Calculator Operations
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
INV
HYP
Press a key to select its second function.
Press a key to select its inverse trigonometric function.
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.
Press & V to change the setting of the displayed
SET
variable.
Press " or # to display the previous or next variable in the
# $
worksheet.
Note: To easily scroll up or down through a range of
variables, press and hold # or ".
DEL
INS
Press & W to delete a cash flow or statistical data point.
Press & X to insert a cash flow or statistical data point.
BGN
TVM calculations use beginning-of-period payments. When
BGN is not displayed, TVM calculations use end-of-period
payments (END).
RAD
Angle values appear in radians. When RAD is not displayed,
angle values appear and must be entered in degrees.
The displayed value is entered in the selected worksheet.
The indicator clears following a computation.
The displayed value is computed in the selected worksheet.
When a value changes and invalidates a computed value,
the_indicator clears.
=
The displayed variable is assigned the displayed value.
The displayed value is negative.
–
Overview of Calculator Operations
3
Setting Calculator Formats
You can change these calculator formats:
To Select Press Display
Number of & | DEC 0–9 (Press 9 for
Default
2
decimal
places
floating-decimal)
DEG
US
Angle units
#
#
#
#
DEG (degrees)
RAD (radians)
Dates
US (mm-dd-yyyy)
Eur (dd-mm-yyyy)
US
Number
separators
US (1,000.00 )
Eur (1.000,00)
Chn
Calculation
method
Chn (chain)
AOSé (algebraic
operating system)
1. To access format options, press & |. The DEC indicator
appears with the selected number of decimal places.
2. To change the number of decimal places displayed, key in a value
and press !.
3. To access another calculator format, press # or " once for each
format.
For example, to access the angle unit format, press #. To access the
number-separator format, press " " "or # # #.
4. To change the selected format, press & V.
5. To change another calculator format, repeat step 3 and step 4.
— or —
To return to the standard-calculator mode, press & U.
— or —
To access a worksheet, press a worksheet key or key sequence.
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.
4
Overview of Calculator Operations
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. When you select radians, the RAD indicator appears in the
upper right corner of the display. No indicator appears when you select
the default setting of degrees.
Using Dates
The calculator uses dates with the Bond and Date worksheets and the
French depreciation methods. To enter dates, use this convention:
mm.ddyy (US) or dd.mmyy (European). After you key in the date, press
!.
Choosing Calculation Methods
When you choose the chain (Chn) calculation method, the calculator
solves problems in the order that you enter them. (Most financial
calculators use Chn.)
For example, when you enter 3 H 2 < 4 N, the Chn answer is 20 (3 + 2 = 5,
5 * 4 = 20).
Using AOSé (algebraic operating system), the calculator solves problems
according to the standard rules of algebraic hierarchy, computing
multiplication and division operations before addition and subtraction
operations. (Most scientific calculators use AOS.)
For example, when you enter 3 H 2 < 4 N, the AOS answer is 11 (2 Q 4 =
8; 3 + 8 = 11).
Resetting Default Values
To reset default values for all of the calculator formats, press &
z with one of the formats displayed.
Overview of Calculator Operations
5
Resetting the Calculator
Resetting the calculator:
•
Clears the display, all 10 memories, any unfinished
calculations, and all worksheet data.
•
•
Restores all default settings
Returns operation to the standard-calculator mode
Because the calculator includes alternative methods that let you clear
data selectively, use reset carefully to avoid losing data needlessly. (See
“Clearing Calculator Entries and Memories” on page 6.)For example, you
might reset the calculator before using it for the first time, when starting
a new calculation, or when having difficulty operating the calculator and
other possible solutions do not work. (See “In Case of Difficulty” on
page 100.)
Pressing & } !
1. Press & }. The RST ? and ENTER indicators appear.
Note: To cancel reset, press & U. 0.00 appears.
2. Press !. RST and 0.00 appear, confirming that the calculator is
reset.
Note: If an error condition exists, press P to clear the display before
attempting to reset.
Performing a Hard Reset
You can also reset the calculator by gently inserting a pointed object
(such as an unfolded paper clip or similar object) in the hole marked
RESET in back of the calculator.
Clearing Calculator Entries and Memories
Note: To clear variables selectively, see the specific worksheet chapters in
this guidebook.
To clear
Press
One character at a time, starting with the last digit
keyed in
*
An incorrect entry, error condition, or error
message
P
6
Overview of Calculator Operations
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 & U
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)
P P
•
Any calculation started but not completed
TVM worksheet variables and reset default values
& U
& ^
One of the 10 memories (without affecting the
others)
Q D and a
memory number
key (0–9)
Correcting Entry Errors
You can correct an entry without clearing a calculation, if
you make the correction before pressing an operation key
(for example, H or 4).
•
•
To clear the last digit displayed, press *.
To clear the entire number displayed, press P.
Note: Pressing P after you press an operation key clears
the calculation in progress.
Example: You mean to calculate 3 Q 1234.56 but instead enter 1234.86.
To
Press
3 <
Display
3.00
Begin the expression.
Enter a number.
1234.86
* *
56
1,234.86
1,234.
Erase the entry error.
Key in the correct number.
Compute the result.
1,234.56
3,703.68
N
Overview of Calculator Operations
7
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
Display
10.00
Add 6 + 4
Subtract 6 N 4
Multiply 6 Q 4
Divide 6 P 4
6 H 4 N
6 B 4 N
6 < 4 N
6 6 4 N
3 ; 1.25 N
2.00
24.00
1.50
1.25
3.95
Find universal power: 3
56.00
18.12
56.00
Use parentheses: 7 Q (3 + 5)
Find percent: 4% of $453
Find percent ratio: 14 to 25
7 < 9 3 H 5 : N
453 < 4 2 N
14 6 25 2 N
34.86
532.86
Find price with percent add-on:
$498 + 7% sales tax
498 H 7 2
N
7.00
62.99
Find price with percent discount:
$69.99 N 10%
69.99 B 10 2
N
2,598,960.00
336.00
Find number of combinations where: 52 & s 5 N
n = 52, r = 5
Find number of permutations where: 8 & m 3 N
n = 8, r = 3
These operations do not require you to press N to complete.
To
Press
Display
39.69
2
6.3 4
Square 6.3
3.94
15.5 3
Find square root: 15.5
Find reciprocal: 1/3.2
0.31
120.00
5.32
3.2 5
Find factorial: 5!
5 & g
203.45 >
Find natural logarithm: ln 203.45
8
Overview of Calculator Operations
To
Press
Display
2.00
.69315
.69315 & i
Find natural antilogarithm: e
0.67
0.86
Round 2 P 3 to the set decimal format
Generate random number*
Store seed value
2 6 3 N & o
& a
0.86
D & a
11.54 & d
120 & e
76 & f
0.20
Find sine:** sin(11.54°)
-0.50
4.01
Find cosine:** cos(120°)
Find tangent:** tan(76°)
-1
11.54
.2 8 d
Find arcsine:** sin (.2)
-1
120.00
75.96
.5 S 8 e
Find arccosine:** cos (-.5)
-1
4 8 f
Find arctangent:** tan (4)
0.52
1.13
0.46
2.31
Find hyperbolic sine: sinh(.5)
Find hyperbolic cosine: cosh(.5)
Find hyperbolic tangent: tanh(.5)
.5 & c d
.5 & c e
.5 & c f
5 & c 8 d
-1
Find hyperbolic arcsine: sinh (5)
-1
2.29
0.55
5 & c 8 e
Find hyperbolic arccosine: cosh (5)
-1
.5 & c 8 f
Find hyperbolic arctangent: tanh (.5)
*
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” on page 5.)
Universal Power ;
Press ; to raise the displayed positive number to any power (for
-5
(1/3)
example, 2 or 2
).
Note: Because the reciprocal of an even number (such as, 1/2, 1/4, 1/6) is
a complex number, you can only raise a negative number to an integer
power or the reciprocal of an odd number.
Overview of Calculator Operations
9
Parentheses 9 :
Use parentheses to control the order in which the calculator evaluates a
numeric expression in division, multiplication, powers, roots, and
logarithm calculations. The calculator includes up to 15 levels of
parentheses and up to 8 pending operations.
Note: You do not have to press : for expressions ending in a series of
closed parentheses. Pressing N closes parentheses automatically,
evaluates the expression, and displays the final result. To view
intermediate results, press : once for each open parenthesis.
Factorial & g
The number for which you compute a factorial must be a positive integer
less than or equal to 69.
Random Numbers & a
The calculator generates a random real number between zero and one
(0<x<1) from a uniform distribution.
You can repeat a sequence of random numbers by storing a seed value in
the random number generator. Seed values help you recreate
experiments by generating the same series of random numbers.
To store a seed value, key in an integer greater than zero and press D
& a.
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 or equal to 0.
n!
nCr = -----------------------------
(n – r)! × r!
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 or equal to 0.
n!
nPr = ------------------
(n – r)!
Rounding & o
The calculator computes using the rounded, displayed form of a number
instead of the internally stored value.
10
Overview of Calculator Operations
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.)
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” on page 5.)
For example, to enter 3 Q 103, key in 3 < 10 ; 3.
Overview of Calculator Operations
11
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.
To clear all 10 calculator memories, press & { & z.
Storing to Memory
To store a displayed value to memory, press D and a numeric key (0–9).
•
The displayed value replaces any previous value stored in the
memory.
•
The Constant Memory feature retains all stored values when you
turn off the calculator.
Recalling From Memory
To recall a number stored in memory, press J and a numeric key (0–9).
Note: The recalled number remains in memory.
Memory Examples
To
Press
Clear memory 4 (by storing a zero value in it)
Store 14.95 in memory 3 (M3)
Recall a value from memory 7 (M7)
0 D 4
14.95 D 3
J 7
Memory Arithmetic
Using memory arithmetic, you can perform a calculation with a stored
value and store the result with a single operation.
12
Overview of Calculator Operations
•
•
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
D H 9
(M9).
Subtract the displayed value from the value stored in
D B 3
memory 3 (M3).
Multiply the value in memory 0 (M0) by the displayed value. D < 0
Divide the value in memory 5 (M5) by the displayed value.
D 6 5
Raise the value in memory 4 (M4) to the power of the
D ; 4
displayed value.
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
& U
3
Display
Clear the calculator.
0.00
3
Enter the value for the first calculation.
Enter the operation and a constant value.
< 8
8
Store the operation and value, and then
calculate.
& ` N
24.00
7 N
56.00
Calculate 7 Q 8.
45 N
360.00
Compute 45 Q 8.
Overview of Calculator Operations
13
Keystrokes for Constant Calculations
This table shows how to create a constant for various operations.
To*
Press**
Add c to each subsequent entry
Subtract c from each subsequent entry
Multiply each subsequent entry by c
Divide each subsequent entry by c
Raise each subsequent entry to the power of c
Add c% of each subsequent entry to that entry
n H & ` c N
n B & ` c N
n < & ` c N
n 6 & ` c N
n ; & ` c N
n H & ` c 2 N
n B & ` c 2 N
Subtract c% of each subsequent entry from the
entry
*The letter c denotes the constant value.
**Repeat constant calculations with n N.
Last Answer Feature
Use the Last Answer (ANS) feature with problems that call
repeatedly for the same value or to copy a value:
•
•
•
•
From one place to another within the same worksheet
From one worksheet to another
From a worksheet to the standard-calculator mode
From the standard-calculator mode to a worksheet
To display the last answer computed, press & x.
Note: The calculator changes the value of the last answer whenever it
calculates a value automatically or whenever you:
•
•
•
Press ! to enter a value.
Press % to compute a value.
Press N to complete a calculation.
Example: Using the Last Answer in a Calculation
To
Press
Display
Key in and complete a calculation
3 H 1 N
4.00
14
Overview of Calculator Operations
To
Press
2 ;
Display
Key in a new calculation
Recall the last answer
Complete the calculation
2.00
4.00
& x
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.
Except for TVM variables, accessed in the standard-
calculator mode, all variables are prompted.
For example, to assign values to amortization variables, you
must first press & \ to access the Amortization
worksheet.
Each worksheet is independent of the others: operations in a worksheet
do not affect variables in other worksheets. When you exit a worksheet
or turn off the calculator, the calculator retains all worksheet data.
To select
Function
Press
TVM worksheet
(Chapter 2)
Analyzes equal cash flows, for ,, -, .,
example, annuities, loans, /, 0, or
mortgages, leases, and savings & [
Amortization worksheet Performs amortization & \
(Chapter 2)
calculations and generates an
amortization schedule
Cash Flow worksheet
(Chapter 3)
Analyzes unequal cash flows by & '
calculating net present value
and internal rate of return
Bond worksheet
(Chapter 4)
Computes bond price and yield & l
to maturity or call
Depreciation worksheet Generates a depreciation
& p
(Chapter 5)
schedule using one of six
depreciation methods
Overview of Calculator Operations
15
To select
Function
Press
Statistics worksheet
(Chapter 6)
Analyzes statistics on one- or
two-variable data using four
regression analysis options
& k
Percent
Computes percent change,
compound interest, and cost-
sell markup
& q
Change/Compound
Interest worksheet
(Chapter 7)
Interest Conversion
worksheet
(Chapter 7)
Converts interest rates
between nominal rate (or
annual percentage rate) and
annual effective rate
& v
& u
Date worksheet
(Chapter 7)
Computes number of days
between two dates, or
date/day of the week a
specified number of days is
from a given date
Profit Margin worksheet Computes cost, selling price,
& w
(Chapter 7)
and profit margin
Breakeven worksheet
(Chapter 7)
Analyzes relationship between & r
fixed cost, variable cost, price,
profit, and quantity
Memory worksheet
(Chapter 7)
Accesses storage area for up to & {
10 values
Accessing the TVM Worksheet Variables
•
To assign values to the TVM worksheet variables, use
the five TVM keys (,, -, ., /, 0).
•
To access other TVM worksheet functions, press the &
key, and then press a TVM function key (xP/Y, P/Y,
BGN). (See “TVM and Amortization Worksheet
Variables” on page 22.)
Note: You can assign values to TVM variables while in a
prompted worksheet, but you must return to the
standard-calculator mode to calculate TVM values or
clear the TVM worksheet.
16
Overview of Calculator Operations
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.)
To return to the standard-calculator mode, press & U.
Types of Worksheet Variables
•
•
•
•
•
Enter-only
Compute-only
Automatic-compute
Enter-or-compute
Settings
Note: The = sign displayed between the variable label and value
indicates that the variable is assigned the value.
Enter-Only Variables
Values for enter-only variables must be entered, cannot be computed,
and are often limited to a specified range, for example, P/Y and C/Y. The
value for an enter-only variable can be:
•
•
•
•
Entered directly from the keyboard.
The result of a math calculation.
Recalled from memory.
Obtained from another worksheet using the last answer feature.
When you access an enter-only variable, the calculator displays the
variable label and ENTER indicator. The ENTER indicator reminds you to
press ! after keying in a value to assign the value to the variable.
After you press !, the indicator confirms that the value is assigned.
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 %. The calculator computes and
displays the value based on the values of other variables.
Overview of Calculator Operations
17
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 %.
Enter-or-Compute Variables in the TVM Worksheet
You can either enter or compute values for the TVM worksheet variables
(N, I/Y, PV, PMT, and FV).
Note: Although you do not have to be in the standard-calculator mode
to assign values to these variables, you must be in the standard-calculator
mode to compute their values.
•
To assign the value of a TVM variable, key in a number and press a
variable key.
•
To compute the value of a TVM variable, press %, and then press the
variable key. The calculator computes and displays the value based
on the values of other variables.
Enter-or-Compute Variables in Prompted Worksheets
You can either enter or compute values for some prompted worksheet
variables (for example, the Bond worksheet YLD and PRI variables).
When you select an enter-or-compute variable, the calculator displays
the variable label with the ENTER and COMPUTE indicators.
•
The ENTER indicator prompts you to press ! to assign the keyed-
in value to the displayed variable.
•
The COMPUTE indicator prompts you to press % to compute a
value for the variable.
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.
18
Overview of Calculator Operations
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.
Overview of Calculator Operations
19
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).
To access the prompted Amortization worksheet, press & \.
Time-Value-of-Money and Amortization Worksheets
21
TVM and Amortization Worksheet Variables
Variable
Key
,
Display Type of Variable
N
Number of periods
Interest rate per year
Present value
Payment
Enter-or-compute
Enter-or-compute
Enter-or-compute
Enter-or-compute
Enter-or-compute
Enter-only
I/Y
PV
PMT
FV
-
.
/
0
Future value
P/Y
C/Y
Number of payments per year & [
Number of compounding
periods per year
#
Enter-only
END
BGN
End-of-period payments
& ]
& V
Setting
Setting
Beginning-of-period
payments
P1
Starting payment
Ending payment
Balance
& \
Enter-only
P2
#
#
#
#
Enter-only
BAL
PRN
INT
Auto-compute
Auto-compute
Auto-compute
Principal paid
Interest paid
Note: This guidebook categorizes calculator variables by the method of
entry. (See “Types of Worksheet Variables” on page 17.)
Using the TVM and Amortization Variables
Because the calculator stores values assigned to the TVM variables until
you clear or change them, you should not have to perform all steps each
time you work a problem.
•
To assign a value to a TVM variable, key in a number and press a TVM
key (,, -, ., /, 0).
•
To change the number of payments (P/Y), press & [, key in a
number, and press !. To change the compounding periods (C/Y),
press & [ #, key in a number, and press !.
•
•
To change the payment period (END/BGN), press & ], and then
press & V.
To compute a value for the unknown variable, press %, and then
press the key for the unknown variable.
22
Time-Value-of-Money and Amortization Worksheets
•
To generate an amortization schedule, press & \, enter the
first and last payment number in the range (P1 and P2), and press "
or # to compute values for each variable (BAL, PRN, and INT).
Resetting the TVM and Amortization Worksheet Variables
•
To reset all calculator variables and formats to default values
(including TVM and amortization variables), press & } !:
Variable
N
Default
Variable
END/BGN
P1
Default
END
0
0
0
0
0
1
1
I/Y
1
1
0
0
0
PV
P2
PMT
FV
BAL
PRN
P/Y
INT
C/Y
•
To reset only the TVM variables (N, I/Y, PV, PMT, FV) to default values,
press & ^.
•
•
To reset P/Y and C/Y to default values, press & [ & z.
To reset the Amortization worksheet variables (P1, P2, BAL, PRN,
INT) to default values, press & z while in the Amortization
worksheet.
•
To reset END/BGN to the default value, press & ] & z.
Clearing the Unused Variable
For problems using only four of the five TVM variables, enter a value of
zero for the unused variable.
For example, to determine the present value (PV) of a known future
value (FV) with a known interest rate (I/Y) and no payments, enter 0 and
press PMT.
Entering Positive and Negative Values for Outflows and
Inflows
Enter negative values for outflows (cash paid out) and positive values for
inflows (cash received).
Note: To enter a negative value, press S after entering the number. To
change a negative value to positive, press S.
Time-Value-of-Money and Amortization Worksheets
23
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. (This category includes most loans.)
•
Set BGN for annuities due, in which payments occur at the beginning
of each payment period. (This category includes most leases.)
Note: When you select beginning-of-period payments, the BGN indicator
appears. (No indicator appears for END payments.)
Updating P1 and P2
To update P1 and P2 for a next range of payments, press % with P1 or
P2 displayed.
Different Values for BAL and FV
The computed value for BAL following a specified number of payments
might be different than the computed value for FV following the same
number of payments.
•
When solving for BAL, PRN, and INT, the calculator uses the PMT
value rounded to the number of decimal places specified by the
decimal format.
•
When solving for FV, the calculator uses the unrounded value for
PMT.
Entering, Recalling, and Computing TVM Values
•
To enter a TVM value, key in the value and store it by pressing a TVM
key (,, -, ., /, 0).
•
To display a stored TVM value, press J and a TVM key.
You can enter or recall a value for any of the five TVM variables (N, I/Y,
PV, PMT, or FV) in either the standard calculator mode or a worksheet
mode. The information displayed depends on which mode is selected.
•
In standard calculator mode, the calculator displays the variable
label, the = sign, and the value entered or recalled.
24
Time-Value-of-Money and Amortization Worksheets
•
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. The total number of payments appears.
2. To assign the displayed value to N for a TVM calculation, press ,.
Entering Cash Inflows and Outflows
The calculator treats cash received (inflows) as a positive value and cash
invested (outflows) as a negative value.
•
You must enter cash inflows as positive values and cash outflows as
negative values.
•
The calculator displays computed inflows as positive values and
computed outflows as negative values.
Generating an Amortization Schedule
The Amortization worksheet uses TVM values to compute an
amortization schedule either manually or automatically.
Generating an Amortization Schedule Manually
1. Press & \. The current P1 value appears.
2. To specify the first in a range of payments, key in a value for P1 and
press !.
3. Press #. The current P2 value appears.
4. To specify the last payment in the range, key in a value for P2 and
press !.
5. Press # to display each of the automatically computed values:
•
•
•
BAL— the remaining balance after payment P2
PRN— the principal
INT— the interest paid over the specified range
Time-Value-of-Money and Amortization Worksheets
25
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.
The calculator computes the next range of payments using the same
number of periods used with the previous range of payments. For
example, if the previous range was 1 through 12 (12 payments),
pressing % updates the range to 13 through 24 (12 payments).
3. Press # to display P2.
•
If you press % with P1 displayed, a new value for P2 will be
displayed automatically. (You can still enter a new value for P2.)
•
If you did not press % with P1 displayed, you can press %
with P2 displayed to enter values for both P1 and P2 in the next
range of payments.
4. Press # to display each of the automatically computed values for
BAL, PRN, and INT in the next range of payments.
5. Repeat steps 1 through 4 until the schedule is complete.
Example: Computing Basic Loan Interest
If you make a monthly payment of $425.84 on a 30-year mortgage for
$75,000, what is the interest rate on your mortgage?
To
Press
Display
12.00
P/Y=
N=
Set payments per year to 12. & [ 12 !
0.00
Return to standard-calculator & U
mode.
Enter number of payments
using the payment multiplier.
30 & Z ,
360.00
26
Time-Value-of-Money and Amortization Worksheets
To
Press
Display
75,000.00õ
-425.84
5.50
PV=
Enter loan amount.
Enter payment amount.
Compute interest rate.
75000 .
425.84 S /
% -
PMT=
I/Y=
Answer: The interest rate is 5.5% per year.
Examples: Computing Basic Loan Payments
These examples show you how to compute basic loan payments on a
$75,000 mortgage at 5.5% for 30 years.
Note: After you complete the first example, you should not have to re-
enter the values for loan amount and interest rate. The calculator saves
the values you enter for later use.
Computing Monthly Payments
To
Press
Display
12.00
P/Y=
N=
Set payments per year to 12. & [ 12 !
0.00
Return to standard-calculator & U
mode.
Enter number of payments
using payment multiplier.
30 & Z ,
360.00
I/Y=
Enter interest rate.
Enter loan amount.
Compute payment.
5.5 -
5.50
75,000.00õ
-425.84
PV=
75000 .
% /
PMT=
Answer: The monthly payments are $425.84.
Computing Quarterly Payments
Note: The calculator automatically sets the number of compounding
periods (C/Y) to equal the number of payment periods (P/Y).
To
Press
Display
4.00
P/Y=
N=
Set payments per year to 4.
& [ 4 !
0.00
Return to standard-calculator & U
mode.
Enter number of payments
using payment multiplier.
30 & Z ,
120.00
Time-Value-of-Money and Amortization Worksheets
27
To
Press
Display
PMT=
Compute payment.
% /
-1,279.82
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
RST
0.00
Set all variables to defaults.
& }
!
N=
Enter number of payments.
Enter interest rate.
20 ,
20.00
I/Y=
PV=
FV=
.5 -
0.50
Enter beginning balance.
Compute future value.
5000 S .
% 0
-5,000.00
5,524.48
Answer: The account will be worth $5,524.48 after 20 years.
Computing Present Value
Example: How much money must you deposit to have $10,000 in 20
years?
To
Press
Display
FV=
PV=
Enter final balance.
Compute present value.
10000 0
% .
10,000.00
-9,050.63
Answer: You must deposit $9,050.63.
28
Time-Value-of-Money and Amortization Worksheets
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
Display
0.00
Set all variables to defaults.
Enter number of payments.
& } !
10 ,
RST
N=
10.00
Enter interest rate per
payment period.
10 -
10.00
I/Y=
Enter payment.
20000 S /
-20,000.00
PMT=
Time-Value-of-Money and Amortization Worksheets
29
To
Press
Display
Compute present value
(ordinary annuity).
% .
122,891.34
PV=
Set beginning-of-period
payments.
& ] & V
BGN
Return to calculator mode.
& U
% .
0.00
Compute present value
(annuity due).
135,180.48
PV=
Answer: The present value of the savings is $122,891.34 with an ordinary
annuity and $135,180.48 with an annuity due.
Example: Computing Perpetual Annuities
To replace bricks in their highway system, the Land of Oz has issued
perpetual bonds paying $110 per $1000 bond. What price should you pay
for the bonds to earn 15% annually?
To
Press
Display
733.33
Calculate the present value for a
perpetual ordinary annuity.
110 6 15 2 N
843.33
Calculate the present value for a
perpetual annuity due.
H 110 N
Answer: You should pay $733.33 for a perpetual ordinary annuity and
$843.33 for a perpetual annuity due.
A perpetual annuity can be an ordinary annuity or an annuity due
consisting of equal payments continuing indefinitely (for example, a
preferred stock yielding a constant dollar dividend).
Perpetual ordinary annuity
30
Time-Value-of-Money and Amortization Worksheets
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:
1
2
3
4
Year
$5000
$7000
$8000
$10000
Amount
Time-Value-of-Money and Amortization Worksheets
31
Given a 10% discount rate, does the present value of the cash flows
exceed the original cost of $23,000?
To
Press
Display
0.00
RST
I/Y=
Set all variables to defaults.
& }
!
Enter interest rate per cash flow
period.
10 -
10.00
FV=
N=
Enter 1st cash flow.
5000 S 0
-5,000.00
1.00
Enter 1st cash flow period.
1 ,
PV=
Compute present value of 1st cash % .
4,545.45
flow.
4,545.45
-7,000.00
2.00
Store in M1.
D 1
FV=
N=
Enter 2nd cash flow.
Enter 2nd cash flow period.
7000 S 0
2 ,
PV=
Compute present value of 2nd
cash flow.
% .
5,785.12
5,785.12
-8,000.00
3.00
Sum to memory.
D H 1
8000 S 0
3 ,
FV=
N=
Enter 3rd cash flow.
Enter period number.
PV=
6,010.52
Compute present value of 3rd
cash flow.
% .
6,010.52
-10,000.00
4.00
Sum to memory.
D H 1
10000 S 0
4 ,
FV=
N=
Enter 4th cash flow.
Enter period number.
32
Time-Value-of-Money and Amortization Worksheets
To
Press
Display
6,830.13
PV=
Compute present value of 4th
cash flow.
% .
6,830.13
23,171.23
171.23
Sum to memory.
D H 1
J 1
Recall total present value.
Subtract original cost.
B 23000 N
Answer: The present value of the cash flows is $23,171.23, which exceeds
the machine’s cost by $171.23. This is a profitable investment.
Note: Although variable cash flow payments are not equal (unlike
annuity payments), you can solve for the present value by treating the
cash flows as a series of compound interest payments.
The present value of variable cash flows is the value of cash flows
occurring at the end of each payment period discounted back to the
beginning of the first cash flow period (time zero).
Example: Computing Present Value of a Lease
With Residual Value
The Peach Bright Company wants to purchase a machine currently leased
from your company. You offer to sell it for the present value of the lease
discounted at an annual interest rate of 22% compounded monthly. The
machine has a residual value of $6500 with 46 monthly payments of
$1200 remaining on the lease. If the payments are due at the beginning
of each month, how much should you charge for the machine?
Time-Value-of-Money and Amortization Worksheets
33
The total value of the machine is the present value of the residual value
plus the present value of the lease payments.
To
Press
Display
0.00
RST
Set all variables to defaults.
& } !
& ] & V
BGN
Set beginning-of-period
payments.
Return to standard-calculator
mode.
& U
0.00
N=
Enter number of payments.
46 ,
46.00
I/Y=
Calculate and enter periodic
interest rate.
22 6 12 N -
1.83
FV=
Enter residual value of asset.
6500 S 0
-6,500.00
2,818.22
-1,200.00
40,573.18
PV=
Compute residual present value. % .
PMT=
PV=
Enter lease payment amount.
1200 S /
Compute present value of lease % .
payments.
Answer: Peach Bright should pay your company $40,573.18 for the
machine.
Example: Computing Other Monthly Payments
If you finance the purchase of a new desk and chair for $525 at 20% APR
compounded monthly for two years, how much is the monthly payment?
To
Press
Display
0.00
12.00
RST
Set all variables to defaults.
Set payments per year to 12.
& } !
& [ 12 !
P/Y=
34
Time-Value-of-Money and Amortization Worksheets
To
Press
Display
0.00
Return to standard-calculator
mode
& U
N=
Enter number of payments using 2 & Z ,
24.00
payment multiplier.
I/Y=
Enter interest rate.
Enter loan amount.
Compute payment.
20 -
20.00
525.00
-26.72
PV=
525 .
% /
PMT=
Answer: Your monthly payment is $26.72.
Example: Saving With Monthly Deposits
Note: Accounts with payments made at the beginning of the period are
referred to as annuity due accounts. Interest begins accumulating earlier
and produces slightly higher yields.
You invest $200 at the beginning of each month in a retirement plan.
What will the account balance be at the end of 20 years, if the fund earns
an annual interest of 7.5 % compounded monthly, assuming beginning-
of-period payments?
To
Press
Display
0.00
RST
Set all variables to defaults.
Set payments per year to 12.
& } !
& [ 12 !
& ] & V
P/Y=
BGN
12.00
Set beginning-of-period
payments.
0.00
Return to standard-calculator
mode.
& U
Time-Value-of-Money and Amortization Worksheets
35
To
Press
Display
240.00
N=
Enter number of payments
using payment multiplier.
20 & Z ,
I/Y=
Enter interest rate.
7.5 -
7.50
-200.00
PMT=
FV=
Enter amount of payment.
Compute future value.
200 S /
% 0
111,438.31
Answer: Depositing $200 at the beginning of each month for 20 years
results in a future amount of $111,438.31.
Example: Computing Amount to Borrow and
Down Payment
You consider buying a car for $15,100. The finance company charges
7.5% APR compounded monthly on a 48-month loan. If you can afford a
monthly payment of $325, how much can you borrow? How much do
you need for a down payment?
To
Press
Display
0.00
Set all variables to defaults.
Set payments per year to 12.
& } !
RST
& [ 12
!
12.00
P/Y=
0.00
Return to standard-calculator
mode
& U
Enter number of payments using 4 & Z ,
payment multiplier.
48.00
N=
Enter interest rate.
Enter payment.
7.5 -
7.50
I/Y=
325 S /
-325.00
PMT=
36
Time-Value-of-Money and Amortization Worksheets
To
Press
Display
Compute loan amount.
Compute down payment
% .
13,441.47
-1,658.53
PV=
H 15,100 S N
Answer: You can borrow $13,441.47 with a down payment of $1,658.53.
Example: Computing Regular Deposits for a
Specified Future Amount
You plan to open a savings account and deposit the same amount of
money at the beginning of each month. In 10 years, you want to have
$25,000 in the account.
How much should you deposit if the annual interest rate is 0.5% with
quarterly compounding?
Note: Because C/Y (compounding periods per year) is automatically set
to equal P/Y (payments per year), you must change the C/Y value.
To
Press
Display
0.00
RST
Set all variables to defaults.
Set payments per year to 12.
& } !
& [ 12 !
P/Y=
C/Y=
BGN
12.00
Set compounding periods to 4. # 4 !
4.00
Set beginning-of-period
payments.
& ] & V
0.00
Return to standard-calculator
mode.
& U
N=
Enter number of deposits using 10 & Z ,
120.00
payment multiplier.
I/Y=
Enter interest rate.
.5 -
0.50
25,000.00
-203.13
FV=
Enter future value.
25,000 0
% /
PMT=
Compute deposit amount.
Answer: You must make monthly deposits of $203.13.
Time-Value-of-Money and Amortization Worksheets
37
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
0.00
RST
Set all variables to defaults.
& } !
P/Y=
Set payments per year to 12. & [ 12 !
12.00
0.00
Return to standard-calculator & U
mode.
N=
Enter number of payments
using payment multiplier.
30 & Z ,
360.00
I/Y=
Enter interest rate.
Enter loan amount.
Compute payment.
6.125 -
120000 .
% /
6.13
120,000.00
-729.13*
PV=
PMT=
Answer: The computed monthly payment, or outflow, is $729.13.
Generating an Amortization Schedule
Generate an amortization schedule for the first three years of the loan. If
the first payment is in April, the first year has nine payment periods.
(Following years have 12 payment periods each.)
To
Press
Display
P1=
P1=
P2=
0
Select the Amortization worksheet.
Set beginning period to 1.
Set ending period to 9.
Display 1st year amortization data.
& \
1 !
1.00
# 9 !
9.00
BAL=
PRN=
INT=
#
#
#
118,928.63*
-1071.37*
-5,490.80*
P1=
P2=
Change beginning period to 10.
Change ending period to 21.
# 10 !
10.00
# 21 !
21.00
38
Time-Value-of-Money and Amortization Worksheets
To
Press
Display
BAL=
PRN=
INT=
Display 2nd year amortization data.
#
#
#
117,421.60*
_-1,507.03*
-7,242.53*
P1=
Move to P1 and press % to enter
# %
22.00
next range of payments.
P2=
Display P2.
#
33.00
BAL=
PRN=
INT=
Display 3rd year amortization data.
#
#
#
115,819.62*
-1601.98*
-7,147.58*
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
0.00
RST
Set all variables to defaults.
Set payments per year to 12.
& } !
& [ 12 !
& U
P/Y=
12.00
Return to standard-calculator
mode.
0.00
N=
Enter number of payments
using payment multiplier.
30 & Z ,
360.00
I/Y=
Enter interest rate.
Enter loan amount.
Compute payment.
7 -
7.00
82,000.00
-545.55
PV=
82000 .
% /
PMT=
Time-Value-of-Money and Amortization Worksheets
39
Generating an Amortization Schedule for Interest and
Balloon Payment
To
Press
Display
1.00
P1=
Select Amortization worksheet. & \
P2=
Enter end period (five years).
# 5 & Z !
60.00
BAL=
View balance due after five
years (balloon payment).
#
77,187.72
INT=
View interest paid after five
years.
# #
-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: $77,187.72
40
Time-Value-of-Money and Amortization Worksheets
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.
•
To compute net present value (NPV), net future value
(NFV), payback (PB), and discounted payback (DPB),
press # or " and % for each variable.
•
•
To compute the internal rate of return (IRR), press ).
To compute the modified internal rate of return
(MOD), press # to access the reinvestment rate (RI)
variable, key in a value, and press #.
Cash Flow Worksheet Variables
Variable
Key
Display Variable
Type**
CFo
Initial cash flow
'
#
Enter-only
Enter-only
th
Cnn*
Amount of n cash flow
th
#
Fnn*
Enter-only
Frequency of n cash flow
I
Discount rate
(
Enter-only
NPV
Net present value
# %
Compute-only
Cash Flow Worksheet
41
Variable
Key
Display Variable
Type**
NFV
PB
Net future value
# %
# %
# %
)%
#
Compute-only
Compute-only
Compute-only
Compute-only
Enter-only
Payback
DPB
IRR
RI
Discounted payback
Internal rate of return
Reinvestment rate
Modified Internal rate of return
MOD
#
Auto
Compute
*
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.)
Resetting Variables
•
•
•
•
To reset CFo, Cnn, and Fnn to default values, press ' and then
& z.
To reset NPV, NFV, PB, and DPB to default values to the default
value, press ( and then & z.
To reset IRR, RI, and MOD to default values 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 32 additional cash flows (C01–C32). Each cash flow can have a
unique value.
•
Enter positive values for cash inflows (cash received) and negative
values for cash outflows (cash paid out). To enter a negative value,
key in a number and press S.
Inserting and Deleting Cash Flows
The calculator displays INS or DEL to confirm that you can press & X
or & W to insert or delete cash flows.
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Cash Flow Worksheet
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.
Although you must enter unequal cash flows separately, you can enter
groups of consecutive, equal cash flows simultaneously using the Fnn
variable.
Entering Cash Flows
Cash flows consist of an initial cash flow (CFo) and up to 32 additional
cash flows (C01-C32), each of which can have a unique value. You must
enter the number of occurrences (up to 9,999), or frequency (F), for each
additional cash flow (C01-C32).
•
The calculator displays positive values for inflows (cash received) and
negative values for outflows (cash paid out).
•
To clear the Cash Flow worksheet, press & z.
To enter cash flows:
1. Press '. The initial cash-flow value (CFo) appears.
2. Key in a value for CFo and press !.
3. To select an additional cash-flow variable, press #. The C01 value
appears.
4. To change C01, key in a value and press !.
Cash Flow Worksheet
43
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.
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 32.
Note: The INS indicator confirms that you can insert a cash flow.
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Cash Flow Worksheet
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.
•
•
Net future value (NFV) is the total future value of all cash flows. A
positive NFV value also indicates a profitable investment.
Payback (PB) is the time required to recover the initial cost of an
investment, disregarding the present value of the cash inflows (time
value of money).
•
Discounted payback (DPB) is the time required to recover the initial
cost of an investment using the present value of the cash inflows
(time value of money).
•
•
Internal rate of return (IRR) is the interest rate at which the net
present value of the cash flows is equal to 0.
Modified internal rate of return (MOD) considers the reinvestment
of cash when solving for IRR.
Computing NPV, NFV, PB, and DPB
1. Press ( to display the current discount rate (I).
2. Key in a value and press !.
3. Press # to display the current net present value (NPV).
4. To compute the net present value for the series of cash flows
entered, press %.
5. To compute the net future value (NFV), press #. The NFV value
appears.
6. To compute payback (PB), press #. The PB value appears.
7. To compute the payback discounted over time (DBP), press #. The
DBP value appears.
Cash Flow Worksheet
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