Slides for BAII+ Calculator
Training Videos
1
Slides for Lesson 1
There are no corresponding slides
for Lesson 1, “Introduction to the
Calculator”
2
Slides for Lesson 2
The following three (3) slides are
used in Lesson 2, “Introduction to
Time Value of Money” and are
referred to in the video as the slides
from Ch. 3, 6-8
3
Example: Investment Evaluation
(referred to as slide 6)
• Propose to buy an asset costing $350 million.
Assume the asset will sell for $520 million at the
end of 4 years.
• You could invest your money elsewhere for 10%,
where risk is similar to the risk of proposed asset.
• Should you buy the asset? Why or why not?
It is helpful to draw a timeline
IMPORTANT FINANCE PRINCIPLE
0
1
2
3
4
Assets with similar risk should have
-350*
similar return. Thus the appropriate rate to
use here is the 10% benchmark.
520
* By convention, cash OUTFLOWS are listed as negatives,
while cash INFLOWS are listed as positives.
4
Example Solution
(referred to as slide 7)
1. Calculate Present Value of the $520
520
PV 
.
4  35517
(1.10)
2. Calculate Future Value of the $350
FV  350  (110
. )  512.44
4
3. Calculate Rate of Return on Asset
1/ t
 FV 
r 
1

 PV 
 520 
r

 350 
1/4
Should Buy
intrinsic value
($355.17)
greater than
cost ($350)
Should Buy
Future
expected value
of not buying
($512.44) less
than value of
buying ($520)
Should Buy
expected return
of buying
(10.4%) Greater
than investing
elsewhere (10%)
 1 = 0.1040 = 10.40%
5
Example Solution – Calculator
(referred to as slide 8)
Clear TVM registers
Set P/Y=1
Calculate Present Value
N
I/Y
PV
PMT
FV
4
10
-355.17
0
520
Calculate Future Value
N
I/Y
PV
PMT
FV
4
10
-350
0
512.435
Calculate Interest Rate
N
I/Y
PV
PMT
FV
4
10.403
-350
0
520
6
Slides for Lesson 3
The following six (6) slides are
used in Lesson 3, “TVM –
Annuities and Periods other than
Annual” and are referred to in the
video as the slides from Ch. 3, 1719, 21, and 36
7
Example: Present Value of an Annuity
(referred to as slide 17)
• You need $25,000 a year for business school.
– 1st $25,000 at the end of 12 months
– 2nd $25,000 at the end of 24 months
• You can earn 8% per year in an investment
account.
• How much money do you need today?
8
Example Solution – Annuity Formula
(referred to as slide 18)
0
$?
1
$ 25,000
PMT
PV ( Annuity ) 
r
2
$ 25,000

1 
1  (1  r )t 


25, 000 
1 
PV 
1
 44,581.62

2
0.08  (1.08) 
9
Example Solution – Calculator and Excel
(referred to as slide 19)
On the calculator, input N, I/Y, PMT, and FV
N
2
I/Y
8
PV
-44581.62
PMT
25000
FV
0
In Excel, Use the PV Function
10
Example: Future Value of an Annuity
(referred to as slide 21)
• Suppose you plan to retire ten years from today. You
plan to invest $2,000 a year at the end of each of the
next ten years. You can earn 8% per year (compounded
annually) on your money. How much will your
investment be worth at the end of the tenth year?
PMT
t
(1+r) - 1
FV(Annuity) =
r


2,000
10
FV(Annuity ) =
(1.08) - 1  28,973.13
0.08
11
Example Solution – Calculator and Excel
(referred to as slide 21, continued)
On calculator, set P/Y=1, set payments to END, input N, I/Y, PV,
PMT and compute FV
N
I/Y
PV
10
8
0
PMT
FV
-2,000 28,973.13
In Excel, use the FV function
The zero indicates that the cash flows occur at the END of the year. If they
were at the beginning, we would enter a 1 here.
12
Present Value Example
(referred to as slide 36)
• Suppose you need $400 to buy textbooks in 2 quarters. Current
interest rates are 12% per year (compounded quarterly). How
much money do you need to deposit today? (Remember that t and
4* 1 4
r must match)
 0.12 
EPR  1 
 1  0.03
– Can use quarters

4 

FV
400
PV 

 377.04
t
2
(1  r ) (1.03)
– Is there another way? What if we use 6-month periods?
APR 

EPR = 1 +
m 

my
-1
 0.12 
EPR  1 
4 

4* 1 2
 1  0.0609
FV
400
PV 

 377.04
t
1
(1  r ) (1.0609)
13
Slides for Lesson 4
The following six (6) slides are
used in Lesson 4, “TVM –
Amortizing Loans” and are
referred to in the video as the slides
from Ch. 3, 39-44.
14
Amortizing Loans – Example
(referred to as slide 39)
• You have decided to buy a new SUV and finance
the purchase with a five year loan. The car costs
$36,000 and you are going to put $2,500 down.
Interest starts accruing when the loan is taken.
The first loan payment is one month after the
interest starts accruing. The interest rate on the
loan is 8.4% (APR) per year for the five year
period.
15
Amortizing Loans – Example
(referred to as slide 40)
– You know you will be paying an equal amount each
month for the next 60 months. What type of security
is this?
It is an annuity with t=60
– What is the present value of the loan? What is the
present value of the annuity?
36,000 – 2,500 = 33,500
– What is the effective monthly rate that you are paying
for your car? What is the EAR?
12* 1
0.084  12

EAR  1 +
- 1  0.007

12 

– How can you determine your monthly payment?
16
Determining Your Payment
(referred to as slide 41)
• Recall you are borrowing $33,500 at 8.4% APR for
60 months. Also recall:
C
1 
PV(Annuity ) = 1 t
r  (1 + r) 
• We know the present value, r, and t. Thus, we can
solve for C which is the payment
33,500  0.007
PV  r
C
 $685.69

1  

1
1 - (1 + r) t  1 60 

  (1 + 0.007) 
17
Determining Your Payment – Calculator
(referred to as slide 42)
• Recall you are borrowing $33,500 at 8.4% APR for
60 months.
• On BA II+
– Clear TVM
– Set payments per year to 12 (<2nd><I/Y>12<ENTER>)
N
I/Y
PV
PMT
FV
60
8.4
33,500
-685.69
0
18
Amortization Table
(referred to as slide 43)
$33,500 car loan at 8.4% APR for 60 months
Month Payment Interest Principal Balance
1
0.007 x 33,500
685.69
234.50
685.69 – 234.50 33,500 – 451.19
451.19
0.007 x 33,048.81 685.69 – 231.34
33,048.81
33,048.81 – 454.35
2
685.69
231.34
454.35
32,594.46
3
685.69
228.16
457.53
32,136.93
685.69 
1

Balance after 3 payments
PV 
1

57   32,136.92
0.007  (1007
. ) 
685.69 
1

PV 
1
. 19
Balance after 48 payments

12   7,86581
0.007  (1007
. ) 
What if ?
(referred to as slide 44)
• What if you wanted to know the balance
remaining after 2 years of payments?
• What if you wanted to know the total amount you
paid in principal during the first 2 years?
• What if you wanted to know the total amount paid
in interest during the first 2 years?
• What if you wanted to know the total amount of
interest paid during the third year?
20
Slides for Lesson 5
The following six (6) slides are
used in Lesson 4, “Bonds” and are
referred to in the video as the slides
from Ch. 5, 11-15.
21
Bond Pricing, Example
(Referred to as slide 11)
• Suppose IPC Co. Issues $1,000 bonds with 5 years to
maturity. The semi-annual coupon is $50. Suppose the
market quoted yield-to-maturity for similar bonds is 10%
(APR, compounded semiannually). What is the present
value (i.e. current market price) of the bond? What if the
YTM was 8%? What if the YTM was 12%?
IMPORTANT FINANCE PRINCIPLE
REMEMBER: Assets with similar risk
should have similar return. Thus the
appropriate rate to use here is 10%
• Steps to calculate bond price
– Calculate the present value of the Face amount
– Calculate the present value of the coupon payments
– Add the two components to get the price
22
IPC Example
(Referred to as slide 13)
 Face Value
C 
1
Price =
+
1 t 
YTM  (1 + YTM)  (1 + YTM) t
1. Price if similar bonds have a 10% yield-to-maturity:
Remember that payment, time, and rate ALL must match.
Since we have a semiannual payment we NEED a
semiannual rate. What is the effective semiannual rate?
2 1 2 
my
 APR 
EPR  1 
m 

 0.10 
 1 EPR  1 
2 

 1  0.05
Notice that 5 years means 10 semiannual periods.

50 
1
1,000
Price =
+
1 10 
0.05  (1 + 0.05)  (1 + .05)10
= 386.09  613.91  1,000
23
IPC Example
(Referred to as slide 13 and slide 14)
 Face Value
C 
1
Price =
+
1 t 
YTM  (1 + YTM)  (1 + YTM) t
2. Price if similar bonds have an 8% yield-to-maturity:

50 
1
1,000
Price =
+
1 10 
0.04  (1 + 0.04)  (1 + .04)10
= 405.55  675.56  1,081.11
3. Price if similar bonds have a 12% yield-to-maturity:

50 
1
1,000
Price =
+
1 10 
0.06  (1 + 0.06)  (1 + .06)10
Notice
the
impact
of
Change
in YTM
on Price
= 368.00  558.39  926.39
24
Easy Bond Pricing on your Calculator
(Referred to as slide 15)
Clear TVM registers
Set P/Y=2 (2 payments per year)
Price if YTM = 10%
N
10
I/Y
10
PV
-1,000
PMT
50
FV
1,000
Price if YTM = 8%
N
10
I/Y
8
PV
-1,081.11
PMT
50
FV
1,000
What is YTM if Price=$1,200?
N
10
I/Y
5.384
PV
-1,200
PMT
50
FV
1,000
25
Par, Discount, and Premium Bonds
Recall IPC Bond Example YTM = 10%, Price = $1000
• Par Bonds
– Price = Face Value
– YTM = Coupon Rate
– Current yield = Coupon rate
• Discount Bonds
– Price < Face Value
– YTM > Coupon Rate
– Current yield > Coupon rate
• Premium Bonds
– Price > Face Value
– YTM < Coupon Rate
– Current yield < Coupon rate
Coupon Rate
Current Yield
100
 10%
1000
100
 10%
1000
YTM = 12%, Price = $926.39
100
 10%
1000
100
Current Yield
 10.80%
926.39
Coupon Rate
YTM = 8%, Price = $1081.11
100
 10%
1000
100
Current Yield
 9.25%
26
1081.11
Coupon Rate
Slides for Lesson 6
The following six (6) slides are
used in Lesson 6, “Cash Flow
Worksheet – NPV and IRR” and
are referred to in the video as the
slides from Ch. 6, and Ch 5, slides
12-15.
27
NPV Example
(referred to as slide 6)
• Decide whether to open a new production plant.
The initial cost of the plant is $600 million. Over
the next four years, the plant is expected to
generate cash flows from assets of $200 mm,
$220 mm, $225 mm, and $210 mm. The risk of
the cashflows requires that the appropriate
discount rate is 20%.
• How do you compute cash flows from assets?
• Should we proceed with the project?
28
NPV Example
0
1
-600
200
2
3
220
225
4
210
Required Rate of
return on project is
20%
T
CFt
NPV  Cost  
t
(
1

r
)
t 1
200
220
225
210
NPV  600 



2
3
4
(1.20) (1.20) (1.20) (1.20)
NPV = -600 + 166.67 + 152.78 + 130.21 + 101.27 = -49.07
29
Internal Rate of Return (IRR)
• Thus, for our example:
T
CFt
0 = 
t
t = 0 (1 + IRR)
200
220
0= - 600 

1
2
(1  IRR)
(1  IRR)
225
210


3
4
(1  IRR)
(1  IRR)
The rate that makes this equation true is 15.67%.
Thus, IRR = 15.67%
30
Bond Pricing, Example
(Referred to as slide 12 in Ch. 5)
• Suppose IPC Co. Issues $1,000 bonds with 5 years to
maturity. The semi-annual coupon is $50. Suppose the
market quoted yield-to-maturity for similar bonds is 10%
(APR, compounded semiannually). What is the present
value (i.e. current market price) of the bond? What if the
YTM was 8%? What if the YTM was 12%?
IMPORTANT FINANCE PRINCIPLE
REMEMBER: Assets with similar risk
should have similar return. Thus the
appropriate rate to use here is 10%
• Steps to calculate bond price
– Calculate the present value of the Face amount
– Calculate the present value of the coupon payments
– Add the two components to get the price
31
IPC Example
(Referred to as slide 13 in Ch. 5)
 Face Value
C 
1
Price =
+
1 t 
YTM  (1 + YTM)  (1 + YTM) t
1. Price if similar bonds have a 10% yield-to-maturity:
Remember that payment, time, and rate ALL must match.
Since we have a semiannual payment we NEED a
semiannual rate. What is the effective semiannual rate?
2 1 2 
my
 APR 
EPR  1 
m 

 0.10 
 1 EPR  1 
2 

 1  0.05
Notice that 5 years means 10 semiannual periods.

50 
1
1,000
Price =
+
1 10 
0.05  (1 + 0.05)  (1 + .05)10
= 386.09  613.91  1,000
32
IPC Example
(Referred to as slide 13 and slide 14, in Ch. 5)
 Face Value
C 
1
Price =
+
1 t 
YTM  (1 + YTM)  (1 + YTM) t
2. Price if similar bonds have an 8% yield-to-maturity:

50 
1
1,000
Price =
+
1 10 
0.04  (1 + 0.04)  (1 + .04)10
= 405.55  675.56  1,081.11
3. Price if similar bonds have a 12% yield-to-maturity:

50 
1
1,000
Price =
+
1 10 
0.06  (1 + 0.06)  (1 + .06)10
Notice
the
impact
of
Change
in YTM
on Price
= 368.00  558.39  926.39
33
Easy Bond Pricing on your Calculator
(Referred to as slide 15, in Ch. 5)
Clear TVM registers
Set P/Y=2 (2 payments per year)
Price if YTM = 10%
N
10
I/Y
10
PV
-1,000
PMT
50
FV
1,000
Price if YTM = 8%
N
10
I/Y
8
PV
-1,081.11
PMT
50
FV
1,000
What is YTM if Price=$1,200?
N
10
I/Y
5.384
PV
-1,200
PMT
50
FV
1,000
34