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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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4B6005 Dr. Siri Chutikamoltham
Is maximizing stock price good for
employees, and customers?
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5B6005 Dr. Siri Chutikamoltham
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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9B6005 Dr. Siri Chutikamoltham
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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Financial Calculator Solution
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
Financial Calculator Solution
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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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77B6005 Dr. Siri Chutikamoltham
Three solution methods
1. Greatest future wealth: FV
2. Greatest wealth today: PV
3. Highest rate of return: Highest EFF%
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78B6005 Dr. Siri Chutikamoltham
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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79B6005 Dr. Siri Chutikamoltham
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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80B6005 Dr. Siri Chutikamoltham
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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81B6005 Dr. Siri Chutikamoltham
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.
Financial Calculator Solution
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82B6005 Dr. Siri Chutikamoltham
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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83B6005 Dr. Siri Chutikamoltham
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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84B6005 Dr. Siri Chutikamoltham
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.
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