1

Slides for BAII+ Calculator Training Videos

2

Slides for Lesson 1

There are no corresponding slides for Lesson 1, “Introduction to the Calculator”

3

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

4

• 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?

Example: Investment Evaluation (referred to as slide 6)

0 1 2 3 4

-350* 520

* By convention, cash OUTFLOWS are listed as negatives, while cash INFLOWS are listed as positives.

It is helpful to draw a timeline IMPORTANT FINANCE PRINCIPLE

Assets with similar risk should have similar return. Thus the appropriate rate

to use here is the 10% benchmark.

5

Example Solution (referred to as slide 7)

FV 3 5 0 1 1 0 5 1 2 4 44( . ) .

2. Calculate Future Value of the $350

1. Calculate Present Value of the $520

P V5 2 0

(1 .1 0 ) 4 3 5 5 1 7.

3. Calculate Rate of Return on Asset

rF V

P V1

1/ t

r5 2 0

3 5 01 = 0 .1 0 4 0 = 1 0 .4 0 %

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%)

6

Example Solution – Calculator (referred to as slide 8)

N I/Y PV PMT FV

N I/Y PV PMT FV

N I/Y PV PMT FV

Calculate Present Value

Calculate Future Value

Calculate Interest Rate

4 10 0 520-355.17

512.4354 10 0-350

10.403 5204 0-350

Clear TVM registers Set P/Y=1

7

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, 17-19, 21, and 36

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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?

9

Example Solution – Annuity Formula (referred to as slide 18)

1( ) 1

(1 )tPMT

PV Annuityr r

$ ?

0 1 2

$ 25,000 $ 25,000

2

25,000 11 44,581.62

0.08 (1.08)PV

10

Example Solution – Calculator and Excel (referred to as slide 19)

In Excel, Use the PV Function

N I/Y PV PMT FV

2 8 -44581.62 25000 0

On the calculator, input N, I/Y, PMT, and FV

11

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?

tPMTFV(Annuity) = (1+r) - 1

r

13.973,281 - (1.08)0.08

2,000 = )FV(Annuity 10

12

Example Solution – Calculator and Excel (referred to as slide 21, continued)

N I/Y PV PMT FV

10 8 0 -2,000 28,973.13

On calculator, set P/Y=1, set payments to END, input N, I/Y, PV, PMT and compute FV

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.

13

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 r must match)

– Can use quarters

– Is there another way? What if we use 6-month periods?

144*

0.121 1 0.03

4EPR

2

400377.04

(1 ) (1.03)t

FVPV

r

1

400377.04

(1 ) (1.0609)t

FVPV

r

myAPR

EPR = 1 + - 1m

124*

0.121 1 0.0609

4EPR

14

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.

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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.

16

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?

– What is the present value of the loan? What is the present value of the annuity?

– What is the effective monthly rate that you are paying for your car? What is the EAR?

– How can you determine your monthly payment?

112* 120.084EAR 1 + - 1 0.007

12

It is an annuity with t=60

36,000 – 2,500 = 33,500

17

Determining Your Payment (referred to as slide 41)

• Recall you are borrowing $33,500 at 8.4% APR for 60 months. Also recall:

• We know the present value, r, and t. Thus, we can solve for C which is the payment

tr)+(1

1 - 1

r

C = )PV(Annuity

tr)+(11

- 1

rPVC 69.685$

0.007)+(1

1 - 1

007.033,500

60

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Determining Your Payment – Calculator (referred to as slide 42)

N I/Y PV PMT FV

• 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>)

60 8.4 33,500 -685.69 0

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Amortization Table (referred to as slide 43)

$33,500 car loan at 8.4% APR for 60 monthsMonth Payment Interest Principal Balance

1

2

3

685.69

685.69

685.69

0.007 x 33,500

234.50685.69 – 234.50

451.1933,500 – 451.19

33,048.810.007 x 33,048.81

231.34685.69 – 231.34

454.35 32,594.4633,048.81 – 454.35

228.16 457.53 32,136.93

PV

6 8 5 6 9

0 0 0 71

1

1 0 0 73 2 1 3 6 9 25 7

.

. ( . ), . Balance after 3 payments

PV

6 8 5 6 9

0 0 0 71

1

1 0 0 77 8 6 5 8 11 2

.

. ( . ), .Balance after 48 payments

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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?

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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.

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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%?

• 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

IMPORTANT FINANCE PRINCIPLE

REMEMBER: Assets with similar risk should have similar return. Thus the appropriate rate to use here is 10%

23

IPC Example(Referred to as slide 13)

tt YTM)+(1

Value Face +

YTM)+(1

1 - 1

YTM

C = Price

1010 .05)+(1

1,000 +

0.05)+(1

1 - 1

0.05

50 = Price

1,000613.91 386.09 =

1. Price if similar bonds have a 10% yield-to-maturity:

1 1my

APREPR

m

122

0.101 1 0.05

2EPR

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?

Notice that 5 years means 10 semiannual periods.

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IPC Example(Referred to as slide 13 and slide 14)

tt YTM)+(1

Value Face +

YTM)+(1

1 - 1

YTM

C = Price

1010 .04)+(1

1,000 +

0.04)+(1

1 - 1

0.04

50 = Price

2. Price if similar bonds have an 8% yield-to-maturity:

1,081.11675.56 405.55 =

1010 .06)+(1

1,000 +

0.06)+(1

1 - 1

0.06

50 = Price

39.269558.39 368.00 =

3. Price if similar bonds have a 12% yield-to-maturity:Notice

the impact

of Change in YTM on Price

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N I/Y PV PMT FV

10 10 -1,000 50 1,000

Easy Bond Pricing on your Calculator(Referred to as slide 15)

N I/Y PV PMT FV

10 8 -1,081.11 50 1,000

N I/Y PV PMT FV

10 5.384 -1,200 50 1,000

Price if YTM = 10%

Price if YTM = 8%

What is YTM if Price=$1,200?

Clear TVM registers Set P/Y=2 (2 payments per year)

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Par, Discount, and Premium Bonds

• 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

YTM = 10%, Price = $10001 0 0

1 0 0 01 0 %Coupon Rate

Current Yield1 0 0

1 0 0 01 0 %

Recall IPC Bond Example

YTM = 12%, Price = $926.39

Coupon Rate

Current Yield %80.1039.926

100

%101000

100

YTM = 8%, Price = $1081.11

Coupon Rate

Current Yield %25.911.1081

100

%101000

100

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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.

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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?

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NPV Example

432 )20.1(

210

)20.1(

225

)20.1(

220

)20.1(

200600NPV

T

1tt

t

)r1(

CFCostNPV

0 1 2 3 4

-600 200 220 225 210

Required Rate of return on project is 20%

NPV = -600 + 166.67 + 152.78 + 130.21 + 101.27 = -49.07

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Internal Rate of Return (IRR)

• Thus, for our example:

T

0=tt

t

IRR)+(1

CF =0

43

21

IRR)(1

210

IRR)(1

225

IRR)(1

220

IRR)(1

200600- =0

The rate that makes this equation true is 15.67%. Thus, IRR = 15.67%

31

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%?

• 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

IMPORTANT FINANCE PRINCIPLE

REMEMBER: Assets with similar risk should have similar return. Thus the appropriate rate to use here is 10%

32

IPC Example(Referred to as slide 13 in Ch. 5)

tt YTM)+(1

Value Face +

YTM)+(1

1 - 1

YTM

C = Price

1010 .05)+(1

1,000 +

0.05)+(1

1 - 1

0.05

50 = Price

1,000613.91 386.09 =

1. Price if similar bonds have a 10% yield-to-maturity:

1 1my

APREPR

m

122

0.101 1 0.05

2EPR

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?

Notice that 5 years means 10 semiannual periods.

33

IPC Example(Referred to as slide 13 and slide 14, in Ch. 5)

tt YTM)+(1

Value Face +

YTM)+(1

1 - 1

YTM

C = Price

1010 .04)+(1

1,000 +

0.04)+(1

1 - 1

0.04

50 = Price

2. Price if similar bonds have an 8% yield-to-maturity:

1,081.11675.56 405.55 =

1010 .06)+(1

1,000 +

0.06)+(1

1 - 1

0.06

50 = Price

39.269558.39 368.00 =

3. Price if similar bonds have a 12% yield-to-maturity:Notice

the impact

of Change in YTM on Price

34

N I/Y PV PMT FV

10 10 -1,000 50 1,000

Easy Bond Pricing on your Calculator(Referred to as slide 15, in Ch. 5)

N I/Y PV PMT FV

10 8 -1,081.11 50 1,000

N I/Y PV PMT FV

10 5.384 -1,200 50 1,000

Price if YTM = 10%

Price if YTM = 8%

What is YTM if Price=$1,200?

Clear TVM registers Set P/Y=2 (2 payments per year)