CALCULATOR GUIDE
Calculator Guide
Contents
Calculator Guide
Calculator Guide BAII+
Features for the CFA® Exam
1
Page
Intro
Setting up the calculator
Memory functions
Effective and nominal interest
Time Value of Money
Capital budgeting
Statistics (standard deviation)
Linear regression and covariance
Probabilities (factorial, combination,
permutation)
Deprecation
2
2
4
5
7
22
30
35
42
45
2
Calculator Guide BAII+
Calculator Guide
Calculator Guide
Introduction
Setting up the BAII+
Only 2 calculators are allowed in the CFA®
examinations:
1. Texas Instruments BAII+ and BAII+
Professional
2. Hewlett Packard 12C and HP12C Platinum
Changing the decimal points:
Most students prefer to use up to 9 decimal points
(this will remove the extra zeros from the screen).
We recommend the BAII+ Professional as we
believe it is easier to use and has more
functionality for the exam
There is a calculator video tutorial on the
Schweser website for those with either Essential or
Premium packages
2nd
·
DEC =
9
ENTER
With decimals set to “9” you will always have the
maximum accuracy in your answer, and can round
it to the number of places that will suit the problem.
3
4
Calculator Guide
Calculator Guide
Setting up the BAII+
Setting up the BAII+
Changing from Chn to AOS
Most students prefer to use the calculator in AOS
mode however the calculator default is Chn
Changing from Chn to AOS
What Does this mean?
Perform the following calculation: 3 + 5 x 4 =
·
2nd
ENTER
Switches from Chn to AOS and
visa versa
Checking the periods
You calculator should be set up for 1 period per
year P/Y=1. To check:
If your calculator is set to Chain (“Chn”), the
answer will be 32 (= 8 x 4)
If your calculator is set to “AOS,” the answer
will be 23 (= 3 + 20)
2nd
I/Y
P/Y = 1
If anything other than P/Y =
1 is displayed then:
5
CFA® 2010 Level I
Keep pressing the ↓ until
you see either AOS or Chn
↓
2nd
1
1
ENTER
6
CALCULATOR GUIDE
Calculator Guide
Using the Memory Functions
Calculator Guide
The BA II+ allows you to store up to 10 items in the
memory at any one time. This can massively speed up
calculations in the exam!
To store an item in the memory
When you have the number on screen to store it
simply press:
You can store data on any
STO
0-9
numerical button from 0 to 9
Memory Functions
To recall an item in the memory
Just press RCL and then the
RCL
0-9
numerical button you stored the
data on
7
Calculator Guide BAII+
8
Calculator Guide
Clearing the Memory/Resetting the
Calculator
Calculator Guide
You can review any data stored in the memory by:
2nd
0
↑
Nominal and Effective
Interest Rates
(BEY and EAY)
↓
Deleting the memory
You don’t really need to. If you store new data on a
numerical key the calculator simply overwrites what
was previously stored
Resetting the Calculator
Be warned this clears the memories but also resets
Chn and decimal points
2nd
+/-
10
ENTER
9
Calculator Guide BAII+
Calculator Guide
Calculator Guide
Nominal vs. Effective Rates
Effective Annual Rate
Nominal rate (stated rate) represents the
contractual rate (think APR). This is the
quoted interest rate.
Assume the stated annual rate is 12%
Semi Annual Compounding (this can be done for any
numer of compounding periods per year
2nd
Effective rate represents the rate of return
actually being earned.
Effective rate = (1 + periodic rate)m – 1
2nd
CE/C
NOM =
12
EFF =
Access interest conversion
Delete previously stored data
Leave Blank
ENTER
2
↓
↓
Enter No
C/Y =
Compounding periods
11
CFA® 2010 Level I
2
2
ENTER
12
CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Effective Annual Rate (cont)
Now get EFF back on the
screen by either:
↓
↓
or
Time Value of Money
↑
EFF =
CPT
= 12.36%
Note that this function can also be used to calculate a
nominal rate give an effective interest rate
Applications
Converting between Nominal from Effective (Quants)
Converting between BEY and EAY (Debt)
14
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Calculator Guide BAII+
Calculator Guide
Calculator Guide
FV of Single Sum
Time Value and Your Calculator
What is the future value of $200 invested today for
four years when the interest rate is 10%
Calculator notation:
– N = number of years or number of
payments
– I/Y = interest rate per period
– PV = present value
– FV = future value
– PMT = payments (for annuities)
T0
T1
T2
T3
T4
i = 10%
$200
?
FV n = PV (1 + r )
or use TVM buttons
n
15
16
Calculator Guide
Calculator Guide
PV of Single Sum
FV of Single Solution
2nd
FV
-$200
PV
4
N
10
I/Y
CPT
FV
What is the present value of $200 to be received
in four years when the interest rate is 10%
Clears data stored on TVM keys
T0
The order the data is
entered does not matter
T1
?
= $292.82
NB Present Value (PV) is always entered as a negative
on the calculator and future cash flows as positives.
You are willing to payout $200 today to receive an inflow
of $292.82 in the future
CFA® 2010 Level I
T2
T3
T4
i = 10%
PV =
17
$200
FV n
(1 + r )n
or use TVM buttons and adjust
for non-annual compounding if
needed
18
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CALCULATOR GUIDE
Calculator Guide
Calculator Guide
PV of Single Sum
2nd
FV
$200
FV
4
N
10
I/Y
CPT
PV
PV of an Ordinary Annuity
Clears data stored on TVM keys
T0
T1
T2
T3
T4
?
$200
$200
$200
$200
i = 10%
The order the data is
entered does not matter
= -$136.60
Ordinary annuity: A stream of equal CFs at equal
intervals paid at end of each period
For the above problem we keep the calculator in
END mode indicating that the cash flows arise at
the end of periods
19
20
Calculator Guide
Calculator Guide
PV of an Ordinary Annuity
2nd
FV
$200
PMT
4
N
10
I/Y
CPT
PV
FV of an Ordinary Annuity
Clears data stored on TVM keys
T0
T1
T2
T3
T4
$200
$200
$200
$200
?
i = 10%
The order the data is
entered does not matter
= -$633.97
21
22
Calculator Guide
Calculator Guide
PV of an Annuity Due
FV of an Ordinary Annuity
2nd
FV
-$200
PMT
4
N
10
I/Y
CPT
FV
Clears data stored on TVM keys
T1
T2
T3
$200
$200
$200
$200
?
The order the data is
entered does not matter
Annuity Due: CFs at the beginning of each period therefore
we will need the calculator in BGN mode.
Note that T1 is a point in time and represents the end of the
first period or the beginning of the second
= $928.20
23
CFA® 2010 Level I
T0
i = 10%
24
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CALCULATOR GUIDE
Calculator Guide
Calculator Guide
FV of an Annuity Due
PV of an Annuity Due
2nd
PMT
2nd
ENTER
2nd
FV
$200
PMT
4
N
10
I/Y
CPT
PV
T0
Displays END or BGN
T1
T2
T3
T4
$200
$200
$200
?
i = 10%
Switches from END to
BGN and visa versa in this
example we need BGN
Clears data stored on TVM keys
CE/C
$200
Again the cash flows are at the start of each period
requiring us to use BGN mode
The order the data is
entered does not matter
Always switch back
to END mode after
finishing calculation25
= -$697.37
26
Calculator Guide
Calculator Guide
FV of an Annuity Due
2nd
PMT
2nd
ENTER
2nd
FV
-$200
PMT
4
N
10
I/Y
CPT
FV
Calculating I/Y and N – Problems
Displays END or BGN
Elmer has won his state lottery and has been
offered 20 annual payments of $200,000 each
beginning today or a single payment of
$2,267,000. What is the annual discount rate
used to calculate the lump-sum payout
amount?
Switches from END to
BGN and visa versa in this
example we need BGN
Clears data stored on TVM keys
CE/C
The order the data is
entered does not matter
= $1,021.02
Always switch back
to END mode after
finishing calculation
Note because the first payment is immediate
we need to use BGN mode.
27
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Calculator Guide
Calculator Guide
Calculating I/Y and N – Problems
T0
T1
T2
T3
Calculating I/Y and N – Problems
T19
$200,000
$200,000 $200,000 $200,000 $200,000 $200,000
20
PMT
N
The order the data is
entered does not matter
($2,267,000)
-$2,267,000
2nd
PMT
Displays END or BGN
2nd
ENTER
CE/C
2nd
FV
CPT
Switches from END to
BGN and visa versa in this
example we need BGN
PV
I/Y
= 7%
Always switch back
to END mode after
finishing calculation
NB Present Value (PV) is always entered as a negative on the
calculator and future cash flows as positives.
Clears data stored on TVM keys
29
CFA® 2010 Level I
30
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CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Calculating I/Y and N – Problems
Calculating I/Y and N – Problems
T0
If Elmer can choose the amount of his annual
payout, based on the same discount rate used
above, how many payments of $232,631 could
Elmer receive if his first payment were today?
T1
T?
T3
T2
$232,631 $232,631 $232,631 $232,631 $232,631
($2,267,000)
Note because the first payment is immediate
we need to use BGN mode.
2nd
PMT
Displays END or BGN
2nd
ENTER
CE/C
2nd
FV
Switches from END to
BGN and visa versa in this
example we need BGN
Clears data stored on TVM keys
31
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Calculator Guide
Calculator Guide
Valuing a Semi Annual Coupon Bond
Calculating I/Y and N – Problems
$232,631
7
-$2,267,000
CPT
Buzacky LTD issued a bond some years ago.
The bond has 3 complete years outstanding and
pays a 8% semi annual coupon. Bond of
equivalent risk have BEYs of 10% in the market.
What is the current price?
PMT
I/Y
The order the data is
entered does not matter
PV
N
= 15
Always switch back
to END mode after
finishing calculation
Number of periods 3 x 2 = 6
Periodic coupon = $80/2 = $40
Discount rate = 10%/2 = 5%
Redemption value = $1,000
NB Present Value (PV) is always entered as a negative on the
calculator and future cash flows as positives.
33
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Calculator Guide
Calculator Guide
Calculating YTM
Valuing a Semi Annual Coupon Bond
2nd
$40
$1,000
FV
Buzacky Ltd issued a bond some years ago. The
bond has 3 complete years outstanding and pays
a 8% semi annual coupon. The bond is currently
trading at $895 in the market. What is the yield
on the bond?
Clears data stored on TVM keys
PMT
FV
6
N
5
I/Y
CPT
PV
The order the data is
entered does not matter
Number of periods 3 x 2 = 6
Periodic coupon = $80/2 = $40
Redemption value = $1,000
= $949.24
35
CFA® 2010 Level I
36
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CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Valuing a Semi Annual Coupon Bond
2nd
FV
PV of Uneven Cash Flows
Clears data stored on TVM keys
FV
$1,000
6
N
-$895
PV
CPT
I/Y
T1
T2
T3
?
$300
$600
$200
i = 10%
PMT
$40
T0
The order the data is
entered does not matter
Note that the cash flows are at the end of the
period so ensure you are in END mode
= 6.15% (semi annual YTM)
BEY = 6.15% x 2 = 12.30%
37
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Calculator Guide
Calculator Guide
PV of Uneven Cash Flows
PV of Uneven Cash Flows (cont)
Enters cash flow mode
CF
2nd
C03=
CE/C
Clears data stored in memory
CFO=
↓
This example has no T0 cash flow
C01=
300
F01=
↓
NPV
C02=
600
F02=
↓
ENTER
I=
↓
ENTER
Enters Net Present Value mode
10
ENTER
NPV=
↓
CPT
= $918.86
Net Present Value
39
40
Calculator Guide
Calculator Guide
FV of Uneven Cash Flows
T0
↓
Enter discount rate
You will not need to change
frequency
ENTER
200
T1
T2
T3
$300
$600
$200
FV of Uneven Cash Flows
CF
Enters cash flow mode
i = 10%
2nd
?
Note that the cash flows are at the end of the
period so ensure you are in END mode
41
CFA® 2010 Level I
7
CE/C
Clears data stored in memory
CFO=
↓
This example has no T0 cash flow
C01=
300
F01=
↓
C02=
600
F02=
↓
ENTER
↓
You will not need to change
frequency
ENTER
↓
42
CALCULATOR GUIDE
Calculator Guide
Calculator Guide
FV of Uneven Cash Flows (cont)
C03
200
NPV
ENTER
Enters Net Present Value mode
I=
10
ENTER
Capital Budgeting
↓
Enter discount rate
NPV=
↓
NFV=
CPT
Used for calculating present
value
= $1,223
44
Net Future Value (BAII+ Professional only)
43
Calculator Guide BAII+
Calculator Guide
Calculator Guide
Net Present Value (NPV)
Net Present Value (NPV)
Example using a 10% discount rate
The sum of the present values of a series of cash flows
NPV = CF0 +
T0
CF1
CF2
CFn
+
+ ... +
1
2
(1 + k) (1 + k)
(1 + k)n
T1
T2
T3
T4
$25
$100
$75
$50
i = 10%
-$175
Discount rate (k): cost of capital to the firm doing that project
NPV is very useful for assessing feasibility of projects.
NPV ≥ 0 ACCEPT PROJECT!
NPV < 0 REJECT PROJECT!
NPV is the change in wealth in present value
terms from a series of cash flows
45
46
Calculator Guide
Calculator Guide
Net Present Value (NPV)
CF
Enters cash flow mode
2nd
CE/C
CFO=
-$175
C01=
$25
F01=
Net Present Value (NPV)
Clears data stored in memory
↓
C02=
$100
F02=
↓
CFA® 2010 Level I
ENTER
↓
ENTER
↓
$75
F03=
↓
C04=
$50
NPV
You will not need to change
frequency
ENTER
C03=
I=
↓
ENTER
↓
ENTER
Enters Net Present Value mode
10
ENTER
↓
Enter discount rate
NPV=
47
8
CPT
= $20.87
48
CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Internal Rate of Return (IRR)
Internal Rate of Return (IRR)
IRR is the discount rate that equates the PV of a
series of cash flows to their cost
T0
The IRR is the discount rate that makes the NPV
=0
-$175
NPV = 0 = CF0 +
T1
T2
T3
T4
$25
$100
$75
$50
CF1
CF2
CFn
+
+ ... +
(1 + IRR)1 (1 + IRR)2
(1 + IRR)n
49
50
Calculator Guide
Calculator Guide
Internal Rate of Return (IRR)
CF
Internal Rate of Return (IRR)
Enters cash flow mode
2nd
CE/C
CFO=
-$175
C01=
$25
F01=
↓
C02=
$100
F02=
↓
Clears data stored in memory
ENTER
↓
ENTER
↓
$75
F03=
↓
C04=
$50
IRR
You will not need to change
frequency
ENTER
C03=
IRR=
ENTER
↓
ENTER
Enters Internal Rate of Return Mode
CPT
= 15.067%
↓
51
52
Calculator Guide
Calculator Guide
Payback Period & Discounted
Payback
Payback Period & Discounted
Payback
Primarily a measure of liquidity
Asses how long it take to recover the initial
investment on a project
Projects with payback periods longer than an arbitrary
number of years are rejected
Limitations
Not a measure of value
Ignores time value of money (solved by using
discounted payback)
Ignores CFs beyond the payback period
T0
T1
T2
T3
T4
$25
$100
$75
$50
i = 10%
-$175
Calculate the payback period and discounted
payback period
NB This functionality is only available on the
BAII+ Professional
53
CFA® 2010 Level I
54
9
CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Payback Period & Discounted
Payback
CF
Payback Period & Discounted
Payback
Enters cash flow mode
2nd
CE/C
CFO=
-$175
ENTER
↓
C01=
$25
ENTER
↓
F01=
↓
C02=
$100
F02=
↓
C03=
$75
F03=
↓
C04=
$50
ENTER
↓
Clears data stored in memory
NPV
You will not need to change
frequency
ENTER
I=
↓
ENTER
Enters Net Present Value mode
10
ENTER
↓
Enter discount rate
55
56
Calculator Guide
Calculator Guide
Payback Period & Discounted
Payback
NPV=
↓
NFV=
↓
PB=
CPT
= 2.67 Years
DPB=
CPT
= 3.39 Years
Breakeven Quantity of Sales
Breakeven quantity is the level of sales
at which a firm’s EBIT is zero.
QBE =
Total Fixed Costs
Price − Var. Cost per unit
↓
Example: If P = $85; V = $60; F =
$500,000;
What is the firm’s breakeven point?
57
58
Calculator Guide
Calculator Guide
Breakeven Quantity of Sales
2nd
6
2nd
CE/C
FC=
Enters break even mode
Clears data stored in memory
$500,000
ENTER
Statistical Concepts and
Market Returns
↓
VC=
$60
ENTER
↓
P=
$85
ENTER
↓
PFT=
↓
Q=
CPT
Break even is the quantity at which 0
profit is made so leave blank
60
= 20,000 units
59
CFA® 2010 Level I
Calculator Guide BAII+
10
CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Population and Sample Means
Measures of Central Tendency:
Population and Sample Means
Over the last 3 years Cerny Plc’s stock returns have been
as follows:
Population and sample means have different
symbols but are both arithmetic means
N
∑X
i
Population Mean : µ =
i=1
Year
% Return
1
6
2
8
3
4
May be entered
as decimals or
whole numbers
N
Calculate the mean return
n
∑X
i
Sample Mean : X =
i=1
n
61
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Calculator Guide
Calculator Guide
Population and Sample Means
2nd
7
2nd
CE/C
X01=
Population and Sample Means (cont)
Enters data entry mode
X03=
4
Clears data stored in memory
2nd
8
ENTER
6
↓
2nd
This is used for entering the
probability of the X variable
occurring as we are using historic
data this can be left blank
Y01=
↓
X02=
8
Y02=
↓
ENTER
ENTER
ENTER
Enters statistics mode
Keep pressing until 1-V appears
1-V = 1 Variable
↓
↓
Pressing the down arrow
repeatedly now allows you to
review the statistic for the data
you entered
X=6
63
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Calculator Guide
Calculator Guide
Population Mean with Probabilities
Population and Sample Means
Over the last 3 years Cerny Plc’s stock returns have been
as follows:
May be entered
as decimals or
whole numbers
% Return
Probability
6
0.3
8
0.2
4
0.5
Must be
entered as
whole
numbers
2nd
7
2nd
CE/C
Enters data entry mode
Clears data stored in memory
X01=
6
ENTER
↓
Y01=
30
ENTER
↓
The calculator requires the probability to be entered
as a whole number not a decimal
Calculate the mean return
65
CFA® 2010 Level I
↓
11
X02=
8
ENTER
↓
Y02=
20
ENTER
↓
66
CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Population and Sample Means (cont)
X03=
4
Y03=
50
2nd
2nd
ENTER
Sample Variance (s2) and Sample
Standard Deviation (s)
↓
n
8
Enters statistics mode
ENTER
s2 =
X = 5.4
s=
n −1
i=1
n −1
Key difference between calculation of σ2 and s2 is
that the sum of the squared deviations for s2 is
divided by n – 1 instead of n
Pressing the down arrow
repeatedly now allows you to
review the statistic for the data
you entered
67
68
Calculator Guide
Calculator Guide
Sample Variance (Sx2)
Sample Variance (Sx2) Solution
Over the last 3 years Cerny Plc’s stock returns have
been as follows:
Year
% Return
1
6
2
8
3
4
7
2nd
CE/C
X01=
May be entered
as decimals or
whole numbers
Clears data stored in memory
ENTER
6
Y01=
↓
With this data it is more likely that sample standard
deviation will be of use as it appears we only have a
sample of three years
X02=
8
Y02=
↓
69
Enters data entry mode
2nd
Calculate the sample standard deviation and
variance.
ENTER
2nd
8
2nd
ENTER
ENTER
↓
70
Calculator Guide
Sample Variance (Sx2) Solution
4
↓
This is used for entering the
probability of the X variable
occurring as we are using historic
data this can be left blank
Calculator Guide
X03=
2
i
i=1
Keep pressing until 1-V appears
∑ ( X − X)
n
2
i
1-V = 1 Variable
↓
∑ ( X − X)
Population Variance and
Standard Deviation
↓
Variance is the average
of the squared deviations
from the mean
Enters statistics mode
Keep pressing until 1-V appears
Standard deviation is
the square root of
variance
1-V = 1 Variable
↓
N
∑ (X
Pressing the down arrow repeatedly now
allows you to review the statistic for the data
you entered
Sx= 2
Sx = Sample Standard Deviation
Sx2 = 4
σX = Population Standard Deviation
CFA® 2010 Level I
σ2 =
71
i
i=1
N
− µ)
2
σ =
σ2
72
12
CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Expected Population Variance (σx2)
Population Variance (σx2)
Over the last 3 years Cerny Plc’s stock returns have
been as follows:
% Return Probability
May be entered
as decimals or
whole numbers
6
0.3
8
0.2
4
0.5
Must be
entered as
whole
numbers
Calculate the population standard deviation and
variance.
With this data it is more likely that population
standard deviation will be of use as the probabilities
sum to one indicating we have the full range of
possible outcomes
2nd
7
2nd
CE/C
Enters data entry mode
Clears data stored in memory
X01=
6
ENTER
↓
Y01=
30
ENTER
↓
The calculator requires the probability to be entered
as a whole number not a decimal
X02=
8
ENTER
↓
Y02=
20
ENTER
↓
73
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Calculator Guide
Calculator Guide
Population Variance (σx2)
X03=
4
Y03=
50
2nd
8
2nd
ENTER
ENTER
↓
Linear Regression
Covariance/Correlation
Enters statistics mode
Keep pressing until 1-V appears
1-V = 1 Variable
↓
Pressing the down arrow repeatedly
now allows you to review the statistic for
the data you entered
σx = 1.56
σx2 = 2.44
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Calculator Guide BAII+
Calculator Guide
Calculator Guide
Covariance of Rates of Return
Covariance
cov1,2 =
t =1
n −1
Example: Calculate the covariance between
the return on the two stocks indicated below:
For each observation, multiply each probability
times the product of the two random variables
deviations from their means and sum them
77
CFA® 2010 Level I
∑ (Rt,1 − R1 )( Rt,2 − R2 ) 
n
Covariance: A measure of how two variables move
together
Values range from minus infinity to positive infinity
Units of covariance difficult to interpret
Covariance positive when the two variables tend to
be above (below) their expected values at the
same time
Year
Stock 1
Stock 2
1
+0.05
+0.07
2
–0.02
–0.04
3
+0.12
+0.18
May be entered
as decimals or
whole numbers
78
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CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Covariance of Rates of Return
2nd
7
2nd
CE/C
Covariance of Rates of Return
Enters data entry mode
2nd
Clears data stored in memory
X01=
5
ENTER
↓
Y01=
7
ENTER
↓
X02=
-2
ENTER
↓
Y02=
-4
ENTER
↓
X03=
12
ENTER
↓
Y03=
18
8
2nd
ENTER
Enters statistics mode
Keep pressing until LIN appears
LIN = Linear Regression
Pressing the down arrow
repeatedly now allows you to
review the statistic for the data
you entered
↓
n=
79
No of paired observations (3 in this example)
x=
Mean value of “x” variable
Sx=
Sample standard deviation of “x” variable
Calculator Guide
Calculator Guide
Covariance of Rates of Return
σx=
Population standard deviation of “x” variable
y=
Mean value of “y” variable
Sy=
Sample standard deviation of “y” variable
σy=
Population standard deviation of “y” variable
a=
Intercept of regression line
b=
Gradient of regression line
r=
Sample correlation coefficient
80
Covariance of Rates of Return
Sx=
7
STO
1
Sy=
11
STO
2
r=
1
STO
3
Covariance = Sx x Sy x r
RCL
1
x
RCL
2
x
RCL
3
=
Cov = 77 or as a
decimal 0.0077
81
82
Calculator Guide
Calculator Guide
Joint Probability Function
Returns
RB = 40% RB = 20% RB = 0% E(RB) = 18%
RA = 20%
RA = 15%
0.15
Probabilities
Probability Concepts
0.60
RA = 4%
0.25
E(RA) = 13%
Unfortunately the calculator can’t do this as there
are two variables and probabilities and the
calculator only has X and Y inputs (see quants for
manual working)
CFA® 2010 Level I
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Calculator Guide BAII+
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CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Choosing r Objects from n Objects
Multiplication Rule of Counting
Without Replacement
When order does not matter and with just two
possible labels, we can use the combination
formula (binomial formula).
n factorial = n! = n(n - 1)(n - 2)(n - 3) . . . . 1
Example: You want to assign four security
analysts to cover four different industries. In how
many ways can the assignments be made?
4
2nd
x
n
Cr =
n!
(n − r )! r !
= 24
85
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Calculator Guide
Calculator Guide
Choosing r Objects From n Objects
Choosing r Objects from n Objects
When order does
matter, we use the
permutation formula:
Example: You have 5 stocks and want to place
orders to sell 3 of them. How many different
combinations of 3 stocks are there?
5
2nd
+
3
nPr =
N!
(n − r)!
Example: You have 5 stocks and want to sell 3,
one at a time. The order of the stock sales matters.
How many ways are there to choose the 3 stocks to
sell in order?
=
= 10
5
2nd
-
3
=
= 60
87
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Calculator Guide
Calculator Guide
Straight Line Method
Example
A new piece of equipment cost $4,000 on 1
January 20x0 and is likely to last for 3 years with
an estimated residual value of $1,000 at the end
of the period.
Depreciation
depreciation expense =
original cost - salvage value
depreciable life
89
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Calculator Guide BAII+
CFA® 2010 Level I
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CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Straight Line Method
2nd
CE/C
Clears data stored in memory
Straight line depreciation
Cycles between all the
ENTER
depreciation methods
SL
2nd
Once you have SL on screen
4
LIF =
↓
M01 =
Enters depreciation mode
4
2nd
Straight Line Method
↓
ENTER
CST=
$4,000
ENTER
↓
SAL=
$1,000
ENTER
↓
YR=
↓
This is used to tell the calculator
if the asset was purchased
partway through a month or year
i.e. 4.5 would be halfway through
month 4 (you will not need this in
the exam)
You can now choose the year
you want (lets say year 2)
2
91
ENTER
Calculator Guide
Double Declining Balance Method
Accelerated Methods – Allocation of cost is
greatest in early years
to review the data
↓
92
Calculator Guide
Straight Line Method
Now just press
↓
DEP= Annual depreciation expense
Example
A new piece of equipment cost $4,000 on 1 January
20x0 and is likely to last for 3 years with an
estimated residual value of $1,000 at the end of the
period.
= 750
RBV= Reduced book value (the equivalent of NBV)
i.e. cost – accumulated depreciation
= 2,500
DDB = (Cost-Acc Depn) X (2/Useful Economic Life)
RDV= Remaining depreciable value i.e. the remaining
amount of depreciation to be charged through
the Income Statement in subsequent years
= 1,500
Be careful not to depreciate
below residual value!
NBV
93
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Calculator Guide
Calculator Guide
Double Declining Balance Method
2nd
2nd
DB= 200
2nd
4
CE/C
M01 =
Enters depreciation mode
↓
Clears data stored in memory
Straight line depreciation
Cycles between all the
ENTER
depreciation methods
Once you have DB = 200 on screen
LIF =
Double Declining Balance Method
4
ENTER
CST=
SAL=
↓
YR=
↓
$4,000
ENTER
↓
$1,000
ENTER
↓
You can now choose the year
you want (lets say year 2)
2
95
CFA® 2010 Level I
This is used to tell the calculator
if the asset was purchased
partway through a month or year
i.e. 4.5 would be halfway through
month 4 (you will not need this in
the exam)
ENTER
↓
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CALCULATOR GUIDE
Calculator Guide
Calculator Guide
Double Declining Balance Method
Now just press
↓
to review the data
DEP= Annual depreciation expense
= 1,000
RBV= Reduced book value (the equivalent of NBV)
i.e. cost – accumulated depreciation
= 1,000
RDV= Remaining depreciable value i.e. the remaining
amount of depreciation to be charged through
the Income Statement in subsequent years
=0
97
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Calculator Guide
Calculator Guide
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CFA® 2010 Level I
100
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