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Learning Objectives
To learn how to use the Financial Calculator
Copyright by Diane Scott Docking 2015 2
3
TI BA II+ Calculator Setup—Follow This!!
Use one period per year: P/Y = 1
[P/Y] 1
Set decimal to 6 places: Format DEC=6
[FORMAT] 6
Set BGN register to “END”
Copyright by Diane Scott Docking 2015
2ND ENTER
2ND ENTER
4
Financial Calculators—TI BA II+
N
I/Y
PMT
FV
PV
Number of time periods
Interest rate (%)
Future Value
Present Value
Payment
Basic Calculator Keys
Copyright by Diane Scott Docking 2015
5
Financial Calculators—TI BA II+
Has embedded formulas
Five time value keys: N, I/Y, PV, PMT, FV• Use either four or five keys
• Interest rate (I/Y) is entered as a whole number, not a decimal (e.g. 7% is entered as 7)
• PV and FV must carry opposite signs (‘+’ or ‘-’)• PMT must carry the same sign as either the PV or the FV,
whichever is appropriate
Some calculators distinguish between inflows and outflows
Cash flow sign convention: If a PV is entered as negative the computed FV is positive
Copyright by Diane Scott Docking 2015
6
Time is Money
$100 in your hand today is worth more or less than $100 in one year?Money earns interest
• The higher the interest rate, the faster your money grows
Q: How much would $1,000 promised in one year be worth today if you could be earning 12% interest?
Copyright by Diane Scott Docking 2015
7
Time is Money
A: $1,000/(1.12)1 = $892.86
Copyright by Diane Scott Docking 2015
t0 t1
$1,000PV
So
Verify: $892.86 x .12 = $ 107.14 interest earned plus initial investment = $ 892.86
yields = $1,000.00
Financial Calculators & Cash Flow Sign Convention
Input $1,000 FV Input 12 I/Y Input 1 N Input 0 PMT Calculate PV (Cpt PV)
Is PV positive or negative? Why? What’s the deal?
Here are the key strokes:
1000 12 1 0
PV will be NEGATIVE. A -$892.86. But answer is $892.82.
By convention we put PV in as a negative number, so that FV will be positive.
Ignore the negative sign. The negative sign simply means you invested (had a cash outflow).
Copyright by Diane Scott Docking 2015 8
FV
I/Y
N
PMT
CPT PV
9
1. FV of a Lump Sum: What’s the FV of an initial $100 investment after 3 years if i = 10%?
FV = ?
0 1 2 310%
100
Copyright by Diane Scott Docking 2015
$100 x .10 = Interest $ 10 Principal $100 Balance $110 x .10 = interest $11
balance $110 Balance $121 x .10 = interest $ 12.10
balance $121.00 FV = $133.10
$100 x .10 = $10 x 3 yrs. = $30 in interest if withdraw interest each year.
Financial Calculator Input: FV of a Lump Sum
Input -$100 PV Input 10 I/Y Input 3 N Input 0 PMT Calculate FV (Cpt FV)
Is FV positive or negative? Why? What’s the deal?
Here are the key strokes:
100 10 3 0
FV will be a POSITIVE $133.10.
By convention we put PV in as a negative number, so that FV will be positive.
Copyright by Diane Scott Docking 2015 10
PV
I/Y
N
PMT
CPT FV
+│─
11
Another Example: FV of a Lump Sum
Mary invests $1,000 today for 20 years @ 8%. How much will she have in 20 years?
FVn = PV(1+i) n FV20 = $1,000 (1.08)20 = $4,660.96
Copyright by Diane Scott Docking 2015
Here are the key strokes: 1000 8 20 0
FV will be a POSITIVE $4,660.96
By convention we put PV in as a negative number, so that FV will be positive.
Input -$1000 PV Input 8 I/Y Input 20 N Input 0 PMT Calculate FV (Cpt FV)
+│─ PV
I/Y
N
PMT
CPT FV
12
2. PV of a Lump Sum: What’s the PV if i = 10% to end up with FV = $100 after 3 years?
FV = 100
0 1 2 310%
75.13
Copyright by Diane Scott Docking 2015
Verify:$75.13 x .10 = Interest $ 7.51
Principal $75.13 Balance $82.64 x .10 = interest $ 8.26
balance $82.64 Balance $90.90 x .10 = interest $ 9.09
balance $90.90 FV = $99.99 = $100
$100 /(1.10)3 = $75.13
Financial Calculator Input: PV of a Lump Sum
Input $100 FV Input 10 I/Y Input 3 N Input 0 PMT Calculate PV (Cpt PV)
Here are the key strokes:
100 10 3 0
PV will be a NEGATIVE $75.13.
Ignore negative sign. Answer is $75.13.
Copyright by Diane Scott Docking 2015 13
FV
I/Y
N
PMT
CPT PV
14
3. FV of an annuityExample 1: What is the FV of a 3-year
ordinary annuity of $100 at 10%?
$100 100100
0 1 2 310%
FV =
10% 10%
Copyright by Diane Scott Docking 2015
110121
100(1.10)=
100(1.10)2=
$331
Input $0 PV Input 10 I/Y Input 3 N Input $100 PMT Calculate FV (Cpt FV)
Here are the key strokes:
0 10 3 100
FV will be a NEGATIVE $331. Ignore negative sign. Answer: $331.
Cannot put 0 in as a negative.
Copyright by Diane Scott Docking 2015 15
PV
I/Y
N
PMT
CPT FV
Financial Calculator Input: FV of an ordinary annuity
16
Example 2: What’s the FV of a 3-year annuity due of $100 at 10%?
100$100 100
0 1 2 310%
FV = Copyright by Diane Scott Docking 2015
100(1.10)= 110100(1.10)2= 121
133.10100(1.10)3=
$364.10
Set calculator to BGN mode
Input $0 PV Input 10 I/Y Input 3 N Input $100 PMT Calculate FV (Cpt FV)
Here are the key strokes:
[BGN] [SET]
0 10 3 100
FV will be a NEGATIVE $364.10. Ignore negative sign. Answer: $364.10.
Cannot put 0 in as a negative.
Copyright by Diane Scott Docking 2015 17
PV
I/Y
N
PMT
CPT FV
Financial Calculator Input: FV of an annuity due
2ND 2ND
18
4. PV of an annuityExample 1: What’s the PV of an 3-year
ordinary annuity of $100 per year at 10%?
100 100100
0 1 2 310%
= PVCopyright by Diane Scott Docking 2015
=100/(1.10)1
90.91=100/(1.10)2
82.64
75.13
$248.68
=100/(1.10)3
Reset calculator to END mode
Input $0 FV Input 10 I/Y Input 3 N Input $100 PMT Calculate PV (Cpt PV)
Here are the key strokes:
[BGN] [SET]
0 10 3 100
PV will be a NEGATIVE $248.68. Ignore negative sign. Answer: $248.68.
Cannot put 0 in as a negative.
Copyright by Diane Scott Docking 2015 19
FV
I/Y
N
PMT
CPT PV
2ND 2ND
Financial Calculator Input: PV of an ordinary annuity
20
Example 2: What’s the PV of an 3-year annuity due of $100 per year at 10%?
100 100
0 1 2 3
10%
100
= PV
Copyright by Diane Scott Docking 2015
90.91=100/(1.10)
82.64=100/(1.10)2
273.55
Reset calculator back to BGN mode
Input $0 FV Input 10 I/Y Input 3 N Input $100 PMT Calculate PV (Cpt PV)
Here are the key strokes:
[BGN] [SET]
0 10 3 100
PV will be a NEGATIVE $273.55 Ignore negative sign. Answer: $273.55
Cannot put 0 in as a negative.
Copyright by Diane Scott Docking 2015 21
FV
I/Y
N
PMT
CPT PV
2ND 2ND
Financial Calculator Input: PV of an annuity due
22
Example: What is the FV of this uneven cash flow stream if rates are 10% and payment is made at end of the year?
0
100
1
300
2
300
310%
-50
4
Copyright by Diane Scott Docking 2015
300 x (1.10) =
300 x (1.10)2 =
100 x (1.10)3=
330363133.10
FV = $776.10
Using Calculator for Uneven CFs
Reset calculator to END mode
Input $0 CF0
Input $100 CF1
Input $300 CF2
Input $300 CF3
Input -$50 CF4
Input 10% interest Calculate FV
Here are the key strokes: [BGN] [SET]
0 , C01 appears,
100 ,F01 appears,1 ,C02 appears
300 ,F02 appears,1 ,C03 appears
300 ,F03 appears,1 ,C04 appears
50 ,F04 appears, 1 , C05 appears
, I= appears, 10 , NPV= appears,
NPV = 530.09 appears. This is the PV of the CFs.
Continued>>>>>>>>>>>
Copyright by Diane Scott Docking 2015
23
CF
CPT
NPV
2ND
ENTER ↓
2ND
ENTER ↓ ENTER ↓
ENTER ↓ ENTER ↓
+│─ ↓
ENTER ↓
ENTER ↓
ENTER ↓
↓ENTERENTER
Financial Calculator Input:FV of uneven cash flows
Input $530.09 PV Input 10 I/Y Input 4 N Input $0 PMT Calculate FV (Cpt FV)
Here are the key strokes:
530.09 10 4 0
FV will be a $776.10.
Copyright by Diane Scott Docking 2015 24
PV
I/Y
N
PMT
CPT FV
Financial Calculator Input:FV of uneven cash flows (continued)
+│─
25
Example: What is the PV of this uneven cash flow stream if rates are 10% and payment is made at the end of the year?
0
100
1
300
2
300
310%
-50
4
90.91
______
$530.08 = PVCopyright by Diane Scott Docking 2015
=100/(1.10)
=300/(1.10)2
=300/(1.10)3
=-50/(1.10)4
247.93
225.39
-34.15
Reset calculator to END mode
Input $0 CF0
Input $100 CF1
Input $300 CF2
Input $300 CF3
Input -$50 CF4
Input 10% interest Calculate PV
Here are the key strokes: [BGN] [SET]
0 , C01 appears,
100 ,F01 appears,1 ,C02 appears
300 ,F02 appears,1 ,C03 appears
300 ,F03 appears,1 ,C04 appears
50 ,F04 appears, 1 , C05 appears
, I= appears, 10 , NPV= appears,
NPV = 530.09 appears. This is the PV of the CFs.
Copyright by Diane Scott Docking 2015
26
CF
CPT
NPV
2ND
Financial Calculator Input:PV of uneven cash flows
ENTER ↓
2ND
ENTER ↓ ENTER ↓
ENTER ↓ ENTER ↓
+│─ ↓
ENTER ↓
ENTER ↓
ENTER ↓
↓ENTERENTER
27
Agree to make “step payments” on a contract as follows:
$1,000 per month for the first year
$1,300 per month for the second year
$2,000 per month for the third year
At 10% annual rate, what is the PV of these payments?
Example: PV of Monthly Uneven Cash Flow Stream
Copyright by Diane Scott Docking 2015
Make sure calculator is set to END mode
Input $0 CF0
Input $1000 CF1-12
Input $1300 CF13-24
Input $2000 CF25-36
Input 10%/12 =0.83333% interest
Calculate PV
Here are the key strokes: [CLR WORK] 0 , C01 appears,
1000 ,F01 appears, 12 ,C02 appears
1300 ,F02 appears,12 ,C03 appears
2000 ,F03 appears,12 ,C04 appears
, I= appears, 10 12 , I=0.833333 appears
, NPV= appears,
NPV = 43,400.52 appears. This is the PV of the CFs.
Copyright by Diane Scott Docking 2015
28
CF
CPT
NPV
ENTER ↓
ENTER ↓ ENTER ↓
ENTER ↓ ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
Financial Calculator Input: PV of Monthly Uneven Cash Flow Stream
=
2ND CF 2ND
÷
29
Recall the formula:
We can use the Financial Calculator to solve for EAR.
Calculating Effective Annual Rates with a Calculator
Copyright by Diane Scott Docking 2015
11
m
Nom
m
iEAR
Where: m is number of compounding periods per year.
30
Example: EAR% for a nominal rate of 8%, compounded quarterly? Daily?
Copyright by Diane Scott Docking 2015
TO PRESS DisplaySelect Interest Conversion [ICONV] NOM = 0
Enter nominal interest rate 8 NOM = 8.00
Enter # of compounding periods per year
4 C/Y = 4.00
Compute EAR EFF = 8.243%
Enter # of compounding periods per year
365 C/Y = 365.00
Compute EAR EFF = 8.3278%
2ND
ENTER
↓ ↓ ENTER
CPT↑
↑ ↑
↑ CPT
ENTER
31
Example: EAR% for a nominal rate of 10%, compounded semi-annually, quarterly, monthly, and daily?
Copyright by Diane Scott Docking 2015
TO PRESS DisplaySelect Interest Conversion [ICONV] NOM = 0
Enter nominal interest rate 10 NOM = 10.00
Enter # of compounding periods per year
2 C/Y = 2.00
Compute EAR EFF = 10.25%
Enter # of compounding periods per year
4 C/Y = 4.00
Compute EAR EFF = 10.381%
Enter # of compounding periods per year
12 C/Y = 12.00
Compute EAR EFF = 10.471%
Enter # of compounding periods per year
365 C/Y = 365.00
Compute EAR EFF = 10.516%
2ND
ENTER
↓ ↓ ENTER
CPT↑
↑ ↑
↑ CPT
↑ ↑
↑
↑ ↑
↑
CPT
CPT
ENTER
ENTER
ENTER
Finding “n” and “i” of a Lump Sum
It is EASY to find “n” and “i” using a Financial Calculator
FV & PV of a lump sum: Example 1: At what interest rate would you have to
invest $100 today to end up with $133.10 in 3 years?
Copyright by Diane Scott Docking 201532
Input - $100 PV Input $133.10 FV Input 3 N Input $0 PMT Calculate I/Y (Cpt I/Y)
Here are the key strokes:
100 133.10 3 0
I/Y = 10%
FV
I/Y
N
PMT
CPT
PV+│─
Finding “n” and “i” of a Lump Sum
FV & PV of a lump sum: Example 2: If you invest $100 today at 10%, how long
will it take to grow to $133.10?
Copyright by Diane Scott Docking 2015 33
Input - $100 PV Input $133.10 FV Input 10 1/Y Input $0 PMT Calculate N (Cpt N)
Here are the key strokes:
100 133.10 10 0
N = 3 years
FV
N
I/Y
PMT
CPT
PV+│─
Finding “n”, “i”, and “payment” of Annuities
It is EASY to find “n”, “i”, and “payments” using a financial calculator.
FV & PV of an ordinary annuity: Example 1: At what interest rate would you have to
invest $100 payments made annually (at end of year) to end up with $331 in 3 years?
Example 2: If you invest $100 annually (at end of year) at 10%, for how many years must you invest before your future value equals $331?
Example 3: How much must you invest annually (at end of year) at 10%, for 3 years to accumulate a future value of $331 at the end of 3 years?
Copyright by Diane Scott Docking 2015 34
Finding “n”, “i”, and “payment” of Annuities
Finding “i”
FV & PV of an ordinary annuity: Example 1: At what interest rate would you have to
invest $100 payments made annually (at end of year) to end up with $331 in 3 years?
Copyright by Diane Scott Docking 2015 35
Input $0 PV Input - $331 FV Input 3 N Input $100 PMT Calculate I/Y (Cpt I/Y) Need to make FV or payments negative.
Here are the key strokes:
0 331 3 100
I/Y = 10%
FV
I/Y
N
PMT
CPT
PV
+│─
Finding “n”, “i”, and “payment” of Annuities
Finding “n”
FV & PV of an ordinary annuity: Example 2: If you invest $100 annually (at end of year)
at 10%, for how many years must you invest before your future value equals $331?
Copyright by Diane Scott Docking 2015 36
Input $0 PV Input $331 FV Input 10 1/Y Input -$100 PMT Calculate N (Cpt N)
Here are the key strokes:
0 331 10 100
N = 3 years
FV
N
I/Y
PMT
CPT
PV
+│─
Finding “n”, “i”, and “payment” of Annuities
Finding “payment”
FV & PV of an ordinary annuity: Example 3: How much must you invest annually (at end
of year) at 10%, for 3 years to accumulate a future value of $331 at the end of 3 years?
Copyright by Diane Scott Docking 2015 37
Input $0 PV Input $331 FV Input 10 1/Y Input 3 N Calculate Pmt (Cpt Pmt)
Here are the key strokes:
0 331 10 3
Pmt = -$100
FV
N
I/Y
PMTCPT
PV
Finding “n”, “i”, and “payment” of Annuities
It is EASY to find “n”, “i”, and “payments” using a financial calculator.
FV & PV of an annuity due: Example 1: At what interest rate would you have to
invest $100 payments made annually (at beginning of year) to end up with $364.10 in 3 years?
Example 2: If you invest $100 annually (at beginning of year) at 10%, for how many years must you invest before your future value equals $364.10?
Example 3: How much must you invest annually (at beginning of year) at 10%, for 3 years to accumulate a future value of $364.10 at the end of 3 years?
Copyright by Diane Scott Docking 2015 38
Finding “n”, “i”, and “payment” of Annuities
Finding “i”
FV & PV of an annuity due: Example 1: At what interest rate would you have to
invest $100 payments made annually (at beginning of year) to end up with $364.10 in 3 years?
Copyright by Diane Scott Docking 201539
Set calculator to BGN mode
Input $0 PV Input -$364.10 FV Input 3 N Input $100 PMT Calculate I/Y (Cpt I/Y)
Here are the key strokes:
[BGN] [SET]
0 364.10 3 100 I/Y = 10%
PV
I/Y
N
PMT
CPT
FV
2ND 2ND
+│─
Finding “n”, “i”, and “payment” of Annuities
Finding “n”
FV & PV of an annuity due: Example 2: If you invest $100 annually (at beginning of
year) at 10%, for how many years must you invest before your future value equals $364.10?
Copyright by Diane Scott Docking 201540
Set calculator to BGN mode
Input $0 PV Input -$364.10 FV Input 10 I/Y Input $100 PMT Calculate N (Cpt N)
Here are the key strokes: Already at BGN
0 364.10 10 100 N = 3
PV
I/Y
N
PMT
CPT
FV+│─
Finding “n”, “i”, and “payment” of Annuities
Finding “payment”
FV & PV of an annuity due: Example 3: How much must you invest annually (at
beginning of year) at 10%, for 3 years to accumulate a future value of $364.10 at the end of 3 years?
Copyright by Diane Scott Docking 201541
Set calculator to BGN mode
Input $0 PV Input -$364.10 FV Input 10 I/Y Input 3 N Calculate Pmt (Cpt Pmt)
Here are the key strokes: Already at BGN
0 364.10 10 3 PMT = $100
PV
I/Y
N
PMTCPT
FV+│─
42
Constructing Amortization Schedules using the Financial Calculator
Construct an amortization schedulefor a $1,000, 10% annual rate loanwith 3 equal payments in arrears (paid at end of year).
Copyright by Diane Scott Docking 2015
43
Step 1: Find the required payments.
PMT PMTPMT
0 1 2 310%
-1,000
3 10 -1000 0
INPUTS
OUTPUT
N I/Y PV FVPMT
402.11
Amortization Schedule Using Calculator
Copyright by Diane Scott Docking 2015
44
2nd AMORT:
Amortization Schedule using Calculator
Copyright by Diane Scott Docking 2015
P1 = ___ P2 = ___
BAL = _______ PRN =______ INT =______
P1 = ___ P2 = ___
BAL = _______ PRN =______ INT =______
P1 = ___ P2 = ___
BAL = _______ PRN =______ INT =______
-697.89 302.11 100.00
enter
enter 1 1
2
Ignore negative sign
2
3 3
enter
enter
enter
enter
-365.56 332.33 69.79
365.56 0 36.56
45
BEG PRN ENDYR BAL PMT INT PMT BAL
1 $1,000 $402.11 $100 $302.11$697.89
2 697.89 402.11 69.79 332.33 365.56
3 365.56 402.12 36.56 365.56 0
TOT 1,206.34 206.35 1,000
Copyright by Diane Scott Docking 2015
Amortization Schedule using Calculator
46
Example: Amortization of a Real-World Mortgage (and why to stay home with mom and dad)
Buy a $300,000 house with 20% down Finance $240,000 at 6% over 30 years Questions:
What are your monthly mortgage payments?For the first year, how much did you pay in interest and
principal?What is the loan balance at the end of year 5?For the 12th monthly payment, how much did you pay in
interest and principal?How much total interest did you pay in years 1 through 5?
Copyright by Diane Scott Docking 2015
47
Example: Amortization of a Real-World Mortgage
Questions:What are your monthly mortgage payments?
Copyright by Diane Scott Docking 2015
N = 30 yrs x 12 = 360 paymentsI/Y = 6%/12 = 0.50%
INPUTS
OUTPUT 1,438.92
360 .50 -240,000 0
N PMTI/Y PV FV
48
Questions:For the first year, how much did you pay in interest and
principal? Keep payment information in calculator.
2nd AMORT:
Copyright by Diane Scott Docking 2015
P1 = ___ P2 = ___
BAL = ___________
PRN =___________
INT =____________
-237,052.77
2,947.23
14,319.83
enter
enter 1 12
Ignore negative sign
Example: Amortization of a Real-World Mortgage
49
Questions:What is the loan balance at the end of year 5?
Keeping everything the same in the calculator
Bring back up to P1 by hitting the ↑ two times.
Copyright by Diane Scott Docking 2015
P1 = ___ P2 = ___
BAL = ___________ -223,330.46
enter
enter 60 60
Ignore negative sign
Example: Amortization of a Real-World Mortgage
50
Questions:For the 12th monthly payment, how much did you pay in interest
and principal? Keeping everything the same in the calculator
Bring back up to P1 by hitting the ↑ four times.:
Copyright by Diane Scott Docking 2015
P1 = ___ P2 = ___
BAL = ___________
PRN =___________
INT =____________
-237,052.77
252.40
1,186.53
enter
enter 12 12
Ignore negative sign
Example: Amortization of a Real-World Mortgage
51
Questions:How much total interest did you pay in years 1 through 5?
Keeping everything the same in the calculator
Bring back up to P1 by hitting the ↑ four times.:
Copyright by Diane Scott Docking 2015
P1 = ___ P2 = ___
BAL = ___________
PRN =___________
INT = ____________
-223,330.46
16,669.54
enter
enter 1 60
Ignore negative sign
Example: Amortization of a Real-World Mortgage
69,665.73