B6005 Lecture 1 Overview and TVM Handout

8/2/2019 B6005 Lecture 1 Overview and TVM Handout

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B6005

Financial Management

Lecture 1

Time Value of Money


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2B6005 Dr. Siri Chutikamoltham

What is Finance?

Applications of financial and economic principles to

maximize shareholder value.

Main goals of a finance manager:

To maximize shareholder value = Max stock price

To ensure the company does not run out of cash

To max shareholder value, should firms behave

ethically?

Do firms have any responsibilities to society at large?


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Is maximizing stock price good for society?,


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Is maximizing stock price good for

employees, and customers?


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The Three Basic Business Decisions

Investment Financing

Operations


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The Process of Value Creation

Selecting and makingsound resourcecommitments

Selecting and sourcingprudent funding options

Operating resources ina competitive, cost-

effective manner


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Economic and Competitive Environment

Data Sources

Analytical framework and tools

Overall Results and Value

Creation

InvestmentEffectiveness

FinancingEffectiveness

OperationalEffectiveness


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8MBA 6230Dr. Siri Chuikamoltham

Returns Net incremental CFs + Side effects

Discount Rate WACC Kd YTM Ke CAPM

ToolsNPV

IRR

PBMod PB

PIMod IRR

Investment Decision + NPV projects IRR > discount rate

Financing DecisionUse D/E that maximizesproject value and matchesthe assets being financed

Financing Mix Debt interest tax

shield, fin. distress IPO Seasoned equity Derivatives

Financing Type Liabilities match assets Duration Currency Interest Rate Business Risk

MaximizeShareholder

Value

Dividend DecisionReturn cash to shareholdersif there are not enough + NPVprojects

How Much? Residual cash Shareholder preferences Signaling

What Form? Cash dividends Stock repurchase

What will this course teach you

to max shareholder value?


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What determines a firms fundamental, or

intrinsic, value?

Intrinsic value is the sum of all the future expectedfree cash flows when converted into todays dollars.

FCF = Free Cash Flows, WACC = weighted average

cost of capital

Value =FCF1 FCF2 FCF

(1 + WACC)1 (1 + WACC)(1 + WACC)2

+ +


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Free Cash Flows (FCF)

Free cash flows are the cash flows that are available (or

free) for distribution to all investors (stockholders and

creditors).

FCF = (sales revenues - operating costs - operatingtaxes ) - required investments in operating capital.

FCF = NOPATrequired investments in net operating

capital.

NOPAT = net operating profit after tax


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Weighted Average Cost of Capital

(WACC)

WACC = wdkd(1 - T) + wpskps + weke

debt: cost = kd preferred stock: cost = kps

equity: cost = ke Corporate tax rate = T

Weight of debt = wd Weight of preferred stock = wps

Weight of equity= we


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Time Value of Money

Important Concepts

Time line

Lump sum

Annuity Uneven cash flows (CF)

Present Value

Future

Net present value (NPV)

Compounding

Discounting

Nominal rate Periodic rate

Effective rate

Amortization


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Principle of Time Value of Money

A dollar received today is worth more than

a dollar received tomorrow.Why?


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CF0 CF1 CF3CF2

0 1 2 3i%

Tick marks at end of periods, so Time 0 is today; Time1 is the end of Period 1; or the beginning of Period 2.

+CF = Cash inflow -CF = Cash outflow

Time lines show timing of cash flows.


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Time line for a $100 lump sum due at the

end of Year 2

100

0 1 2 Yeari%


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100 100100

0 1 2 3i%

Time line for an ordinary annuity of $100

for 3 years


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Ordinary Annuity

PMT PMTPMT

0 1 2 3i%

PMT PMT

0 1 2 3i%

PMT

Annuity Due

PV FV

Ordinary Annuity v.s. Annuity Due


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100 5075

0 1 2 326.8%

-150

Time line for uneven CFs-$50 now and $100, $75, and $50 at the end of

Years 1 through 3, at interest rate of 26.8% per

year


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FV = ?

0 1 2 3

10%

Finding FVs (moving to the right on a time line) is called

compounding.

100

Future value of a lump sumWhats the FV of an initial $100 after 3 years at

10% interest rate?


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After 1 year:

FV1 = PV + INT1 = PV + PV (i)

= PV(1 + i)

= $100(1.10)= $110.00.

After 2 years:

FV2 = PV(1 + i)2

= $100(1.10)2

= $121.00.

Whats the FV of an initial $100 after 3

years at 10% interest rate?


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After 3 years:

FV3 = PV(1 + i)3

= $100(1.10)3= $133.10.

In general,

FVn = PV(1 + i)n

Whats the FV of an initial $100 after 3

years at 10% interest rate?


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Four Ways to Find FVs

Solve the equation with a regular calculator

Use a financial calculator.

Use a spreadsheet. Use a compounding/discounting table.


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Solve this equation:

There are 4 variables. If 3 are known, the

calculator will solve for the 4th.

FV PV in n 1 .

Equation and Regular Calculator Solution


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3 10 -100 0N I/YR PV PMT FV

133.10

Heres the setup to find FV:

Clearing automatically sets everything to 0, but for safetyenter PMT = 0.

Set: P/YR = 1, END.

INPUTS

OUTPUT

Financial Calculator Solution


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Spreadsheet Solution for FV

Insert Function Financial FV OK0.10Rate

Nper

Pmt

PV

Type

3

-100

(must be % or decimal)

(leave blank)

(0 = end of period (default);1 = beginning of period)

FV 133.10


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Tabular Approach

Table: Future Value of $1 at the End of n

Periods

Source: Web/CD Extensions, Student Resource Disk, Chapter 2


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Example: Tabular Approach

FV = PV x compounding factor

Compounding factor: Period 3, Interest rate 10% =

1.331

FV = 100 x 1.331 = $133.10

$0.00

$1.00

$2.00

$3.00

$4.00

$5.00

0 2 4 6 8 10 12

FutureV

alue

of$1

Periods

Relationships among Future Value, Growth,Interest Rate, and Time


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Example 1

Find FV of an initial bank deposit of $1000, at an interest rate of5%, the money remaining in the account for 10 years.

What is the FV if the interest rate increases to 7%?

What is the FV if the time increases to 12 years @interest 5%?


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Relationship between FV, Interest rate and

Time

The longer the time, the .FV

The higher the interest rate, the .FV


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20%

2

0 1 2 ?

-1 FV = PV(1 + i)n$2 = $1(1 + 0.20)n

(1.2)n = $2/$1 = 2

nLN(1.2) = LN(2)n = LN(2)/LN(1.2)n = 0.693/0.182 = 3.8.

Rough estimate:rule of 72

N = 72/i

A Common FV Application

Finding the Time to Double


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10%

Present Value of a lump sumWhats the PV of $100 due in 3 years if i = 10%?

Finding PVs is discounting, the reverse of compounding.

100

0 1 2 3

PV = ?


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Whats the PV of $100 due in 3 years if i = 10%?

Equation Approach

Solve FVn = PV(1 + i )n for PV

PV = FV1+ i = FV 11+ in n nn

PV = $100 11.10=$100

0.7513 = $75.13.

3


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3 10 0 100

N I/YR PV PMT FV-75.13

Either PV or FV must be negative. Here PV = -75.13.Put in $75.13 today, take out $100 after 3 years.

INPUTS

OUTPUT


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Tabular ApproachUse Present Value Table to solve the

previous question

Spread Sheet Approach

Same as finding FV, but indicatePV instead


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20 -1 0 2

N I/YR PV PMT FV3.8

INPUTS

OUTPUT

Financial Calculator


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FV of an ordinary annuity

Whats the FV of a 3-year ordinary annuity of

$100 at 10%?

100 100100

0 1 2 310%

110

121FV = 331


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3 10 0 -100

331.00

N I/YR PV PMT FV

Have payments but no lump sum PV, so enter 0 forpresent value.

INPUTS

OUTPUT



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Example 2

You invest $3,000 in a tax-exempt retirement accountevery year for the next 35 years, with your first deposit

occurring 1 year from today. How much will you have

in the account if the annual return is 8%?

How much will you have in 10 years?


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PV of an ordinary annuity

Whats the PV of this ordinary annuity?

100 100100

0 1 2 310%

90.91

82.6475.13

248.69 = PV


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Have payments but no lump sum FV, so enter 0 for

future value.

3 10 100 0N I/YR PV PMT FV

-248.69

INPUTS

OUTPUT

Whats the PV of this ordinary annuity?


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A B C D

1 0 1 2 32 100 100 100

3 248.69

Excel Formula in cell A3:

=NPV (10%,B2:D2)

Spreadsheet Solution


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Special Function for Annuities

For ordinary annuities, this formula in cell A3 gives248.96:

=PV(10%,3,-100)

A similar function gives the future value of 331.00:

=FV(10%,3,-100)


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FV and PV of an annuity due

100 100

0 1 2 310%

100


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3 10 100 0

-273.55

N I/YR PV PMT FV

Switch from End to Begin.Then enter variables to find PVA3 = $273.55.

Then enter PV = 0 and press FV to findFV = $364.10.

INPUTS

OUTPUT

Find the FV and PV if the

annuity were an annuity due.


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Excel Function for Annuities Due

Change the formula to:

=PV(10%,3,-100,0,1)

The fourth term, 0, tells the function there are no othercash flows. The fifth term tells the function that it is anannuity due. A similar function gives the future value ofan annuity due:

=FV(10%,3,-100,0,1)


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PV of an uneven cashflowWhat is the PV of this uneven cash

flow stream?

0

100

1

300

2

300

310%

-50

4

90.91

247.93

225.39-34.15

530.08 = PV


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What is the PV of this uneven cash

flow stream?

Input in CFLO register:

CF0 = 0

CF1

= 100

CF2 = 300

CF3 = 300

CF4 = -50 Enter I = 10%, then press NPV button to get NPV = 530.09.

(Here NPV = PV.)


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Excel Formula in cell A3:

=NPV(10%,B2:E2)

A B C D E

1 0 1 2 3 42 100 300 300 -50

3 530.09

Spreadsheet Solution


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Relationship between PV, Interest rate and

Time

The longer the time, the .. PV

The higher the interest rate, the PV

Implications:


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0 1 2 310%

0 1 2 3

5%

4 5 6

134.01

100 133.10

1 2 30

100

Annually: FV3 = $100(1.10)3 = $133.10.

Semiannually: FV6 = $100(1.05)6 = $134.01.

Will the FV of a lump sum be larger or smaller if

the compounding more often, at a constant

interest rate?

C di I t t


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3 different rates:

iNom = nominal, or stated, or quoted, rate per year, the frequency

of compounding is usually given.

Examples:

8%; Quarterly

8%, Daily interest (365 days)

iPer = periodic rate = iNom/m

m is number of compounding periods per year( m = 4 for

quarterly, 12 for monthly, and 360 or 365 for daily compounding.

Examples: 2% per quarter

8%/365 = 0.022 % per day

Must use EAR= EFF% = effective annual rate to compare.

Compounding Interest


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Effective Annual Rate (EAR or EFF%)

The annual rate which causes PV to grow to the same

FV as under multi-period compounding.

Example: EFF% for 10%, semiannual:

FV = (1 + iNom/m)m= (1.05)2 = 1.1025.

EFF%= 10.25% because (1.1025)1 = 1.1025.

Any PV would grow to same FV at 10.25% annually or 10%

semiannually.

Used to compare returns on investments with different paymentsper year


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Or use a financial calculator.

EFF% = - 1(1 + )iNommm

= - 1.0(1 + )0.102

2

= (1.05)2

- 1.0= 0.1025 = 10.25%.

How to find EFF% for a nominal rate of 10%,

compounded semiannually?


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EAR = EFF% of 10%

EARAnnual =

EARQ = (1 + 0.10/4)4 - 1 =

EARM = (1 + 0.10/12)12 - 1 =

EARD(360) = (1 + 0.10/360)360 - 1 =


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Self test: Example 3

A credit card balance, with interest calculated

monthly, at an annual rate of 18%. What is the

effective annual rate (EAR)?

EAR = (1 + inom/12 )12 - 1


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Example 4

FV of $100 after 3 years under 10% semiannual

compounding? Quarterly compounding?

= $100(1.05)6 = $134.01.

FV3Q = $100(1.025)12 = $134.49.

FV = PV 1 .+i

m

nNom

mn FV = $100 1 +

0.10

23S

2x3


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Example 5

FV at the end of Year 3 of the following CFstream if the quoted interest rate is 10%,compounded semiannually?

0 1

100

2 35%

4 5 6 6-mos.periods

100 100


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Payments occur annually, but compoundingoccurs each 6 months.

So we cant use normal annuity valuation

techniques.

Example 5 (cont)

FV at the end of Year 3 of the following CF

stream if the quoted interest rate is 10%,compounded semiannually?


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1st Method: Compound each CF using

periodic rate

0 1

100

2 35%

4 5 6

100 100.00110.25121.55331.80

FVA3 = $100(1.05)4 + $100(1.05)2 + $100

= $331.80.


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2nd Method: Treat as an Annuity and

compound with EAR

1. Find the EAR for the quoted rate:

EAR = (1 + ) - 1 = 10.25%.0.1022


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3 10.25 0 -100INPUTS

OUTPUT

N I/YR PV FVPMT

331.80

2. Use EAR = 10.25% for the annual rate in your

calculator:

2nd Method: Treat as an Annuity


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Self Test: Example 6

Fractional Time Periods

On January 1 you deposit $100 in an account that pays

a nominal interest rate of 11.33463%, with daily

compounding (365 days).

How much will you have on October 1, or after 9months (273 days)? (Days given.)


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IPER= 11.33463%/365

= 0.031054% per day.

FV=?

0 1 2 273

0.031054%

-100

Convert interest to daily rate


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FV = $100 1.00031054= $100 1.08846 = $108.85.273 273

Find FV using formula

FVn

= PV(1 + i)n


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273 -100 0

108.85

INPUTS

OUTPUT

N I/YR PV FVPMT

IPer = iNOM/M

= 11.33463/365= 0.031054% per day.

Calculator Solution


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Amortized Loan

An amortized loan is a loan that is paid off in

equal installments over a specified period of

time.

Amortization tables are widely used--for home

mortgages, auto loans, business loans,

retirement plans, and so on. They are very

important!


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Amortization

Construct an amortization schedule for a

$1,000, 10% annual rate loan with 3 equalpayments.


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Step 1: Find the required payments.

PMT PMTPMT

0 1 2 310%

-1,000

3 10 -1000 0INPUTS

OUTPUTN I/YR PV FVPMT

402.11


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Step 2: Find interest charge for Year 1.

INTt = Beg balt (i)INT1 = $1,000(0.10) = $100.

Step 3: Find repayment of principal in

Year 1.

Repmt = PMT - INT= $402.11 - $100= $302.11.


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Step 4: Find ending balance after

Year 1.

End bal = Beg bal - Repmt

= $1,000 - $302.11 = $697.89.

Repeat these steps for Years 2 and 3

to complete the amortization table.


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Interest portion declines as the loan gets closer to maturity.

BEG PRIN ENDYR BAL PMT INT PMT BAL

1 $1,000 $402 $100 $302 $6982 698 402 70 332 366

3 366 402 37 366 0

TOT 1,206.34 206.34 1,000

Step 4: Calculation


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$

0 1 2 3

402.11 Interest

302.11

Level payments. Interest declines because outstandingbalance declines. Lender earns 10% on loan outstanding,which is falling.

Principal Payments

Step 4: Calculation


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Example 7

You plan to buy a $400,000 flat. If you put20% down, you can get a 30-year mortgage at

6%. What is your monthly mortgage payment?

If the mortgage is for 15 year?

Example 8


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p

A. You want to have $2M when you retire 35 yearsfrom now. You estimate that your investment in your

retirement account will give you a 12% average rate ofreturn. How much do you need to save a year for yourretirement?

B. Now you feel that the stock market is too risky. Youwant to shift your retirement account into a safer bondfund that gives a return of 5% per year. How much doyou need to save a year?


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Self Test: Example 9

Comparing Investments

You are offered a note which pays $1,000 in 15 months(or 456 days) for $850. You have $850 in a bank whichpays a 6.76649% nominal rate, with 365 dailycompounding, which is a daily rate of 0.018538% andan EAR of 7.0%. You plan to leave the money in the

bank if you dont buy the note. The note is riskless.

Should you buy it?


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IPER

= 0.018538% per day.

1,000

0 365 456 days

-850

Daily time line


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Three solution methods

1. Greatest future wealth: FV

2. Greatest wealth today: PV

3. Highest rate of return: Highest EFF%


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1. Greatest Future Wealth

Find FV of $850 left in bank for15 months and compare withnotes FV = $1,000.

FVBank = $850(1.00018538)456

= $924.97 in bank.

Buy the note: $1,000 > $924.97.


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456 -850 0

924.97

INPUTS

OUTPUT

N I/YR PV FVPMT

IPER = iNOM/M

= 6.76649%/365

= 0.018538% per day.

Calculator Solution to FV


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Find PV of note, and compare

with its $850 cost:

PV = $1,000/(1.00018538)456= $918.95.

2. Greatest Present Wealth


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456 .018538 0 1000

-918.95

INPUTS

OUTPUT

N I/YR PV FVPMT

6.76649/365 =

PV of note is greater than its $850 cost, so buythe note. Raises your wealth.



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Find the EFF% on note and compare

with 7.0% bank pays, which is your

opportunity cost of capital:FVN = PV(1 + I)

N

$1,000 = $850(1 + i)456

Now we must solve for I.

3. Rate of Return


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456 -850 0 1000

0.035646%per day

INPUTS

OUTPUT

N I/YR PV FVPMT

Convert % to decimal:Decimal = 0.035646/100 = 0.00035646.

EAR = EFF% = (1.00035646)365 - 1

= 13.89%.

Calculator Solution


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P/YR = 365

NOM% = 0.035646(365) = 13.01

EFF% = 13.89Since 13.89% > 7.0% opportunity cost,

buy the note.

Using interest conversion

S


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Summary

Time value of money is one of the mostimportant concepts in Finance.

Must know how to calculate FV, FVA, PV,

PVA, NPV, PMT, I, N, amortization schedule.

Must know the difference between APR and

EAR

Setting up cash flows is vital.

There are several approaches to solve time

value of money problems.

Documents

B6005 Lecture 1 Overview and TVM Handout