SlideShare uma empresa Scribd logo
1 de 37
Baixar para ler offline
6-1
6-1
Time Value of Money
Value of Money = f(Time)
6-2
Chapter outline
• The concept of TVM
• Interest rate (Meaning, Components, Simple vs
Compound)
• Time lines (why important?)
• Present value, Future value
• Annuities (ordinary vs annuity due)
• Nominal/Quoted vs Effective Interest rates
• Amortization Schedule
6-3
Time Value of Money
Define
Indicates the purchasing power of money changes during time
being or the money in your hand now is not equal to the
money will be in future
Why matters
- Inflation/Deflation
- Uncertainty/Risk
- Opportunity costs
Applications
• planning for retirement,
• valuing stocks and bonds,
• setting up loan payment schedules, and making corporate
decisions regarding investing in new plant and equipment
6-4
Interest Rate
An interest rate is the percentage of principal
charged by the lender for the use of its money/fund
Components:
- Inflation
- Opportunity cost
- Risk
Simple vs Compound Interest Rate
6-5
Time lines
• Show the timing of cash flows.
• Tick marks occur at the end of periods, so Time
0 is today; Time 1 is the end of the first period
(year, month, etc.) or the beginning of the
second period.
CF0 CF1 CF3
CF2
0 1 2 3
i%
6-6
Drawing time lines:
$100 lump sum due in 2 years;
3-year $100 ordinary annuity
100 100
100
0 1 2 3
i%
3 year $100 ordinary annuity
100
0 1 2
i%
$100 lump sum due in 2 years
6-7
Drawing time lines:
Uneven cash flow stream; CF0 = -$50,
CF1 = $100, CF2 = $75, and CF3 = $50
100 50
75
0 1 2 3
i%
-50
Uneven cash flow stream
6-8
What is the future value (FV) of an initial $100
after 3 years, if i/YR = 10%?
• Finding the FV of a cash flow or series of cash
flows when compound interest is applied is
called compounding.
• FV can be solved by using the arithmetic,
financial calculator, and spreadsheet methods.
FV = ?
0 1 2 3
10%
100
6-9
Solving for FV:
The arithmetic method
• After 1 year:
FV1 = PV ( 1 + i ) = $100 (1.10)
= $110.00
• After 2 years:
FV2 = PV ( 1 + i )2 = $100 (1.10)2
=$121.00
• After 3 years:
FV3 = PV ( 1 + i )3 = $100 (1.10)3
=$133.10
• After n years (general case):
FVn = PV ( 1 + i )n
6-10
FV (some examples)
If Cash inflow and outflow one time:
- If you deposit $1000 for 10 years at 12% interest rate, how much will you
receive after 10 years? Calculate and show time lines.
- If your grand father deposited $5000 before 30 years at 10% interest rate
at a commercial bank, how much would you receive today. Show
calculations and time lines.
If there is more than one cash outflow and one cash
inflow:
- If you deposit $1000 now, $5000 after 1 year, $6000 after 2 year, and
$4000 after 3 years, how much will you receive after 4 years at 10%
interest rate. Show calculations and time lines.
- If your forefathers deposited $10000 before 50 years at 6% interest rate,
and more $10000 before 30 years at 8% interest rate. How much in total
you would receive today. Show calculations and time lines of each
scenario.
6-11
What is the present value (PV) of $100 due in
3 years, if i/YR = 10%?
• Finding the PV of a cash flow or series of cash
flows when compound interest is applied is
called discounting (the reverse of compounding).
• The PV shows the value of cash flows in terms of
today’s purchasing power.
PV = ? 100
0 1 2 3
10%
6-12
Solving for PV:
The arithmetic method
• Solve the general FV equation for PV:
PV = FVn / ( 1 + i )n
PV = FV3 / ( 1 + i )3
= $100 / ( 1.10 )3
= $75.13
6-13
What is the PV of this uneven cash flow
stream?
0
100
1
300
2
300
3
10%
-50
4
90.91
247.93
225.39
-34.15
530.08 = PV
6-14
Present value concept
© Dr. Sheikh Abu Taher
6-15
Solving for PV:
Uneven cash flow stream
• Input cash flows in the calculator’s “CFLO”
register:
– CF0 = 0
– CF1 = 100
– CF2 = 300
– CF3 = 300
– CF4 = -50
• Enter I/YR = 10, press NPV button to get NPV =
$530.09. (Here NPV = PV.)
6-16
Exercises (PV and FV)
• If you deposit $10000 for 5 years at 10% interest rate, how
much will you receive after 5 years?
• If you would like to receive $20000 after 5 years, how much
do you need to deposit today if the interest rate is 10%?
• If you deposit $3000 at year 1, 3500 at year 2, $0 at year 4 and
$4000 at year 5, how much will you receive after 5 years if the
interest rate is 10%? Show time lines.
• If you would like to receive $3000 at year 1, 3500 at year 2, $0
at year 4 and $4000 at year 5, how much do you need to
deposit today if the interest rate is 10%? Show time lines.
6-17
Discussion: Annuity
Annuity define: Series of equal payment or receipt/cash inflow
or outflow for number of periods (periods can be day, month,
quarter, year, etc)
Examples: EMI, home loan, automobile loan, Internet bill, house
rent, etc
i = 1, 2, …………………….n
Types:
1. Ordinary annuity
2. Annuity due
6-18
What is the difference between an ordinary
annuity and an annuity due?
Ordinary Annuity
PMT PMT
PMT
0 1 2 3
i%
PMT PMT
0 1 2 3
i%
PMT
Annuity Due
6-19
Future Value Annuity
6-20
Present Value Annuity
6-21
The Power of Compound Interest
A 20-year-old student wants to start saving for
retirement. She plans to save $3 a day. Every day, she
puts $3 in her drawer. At the end of the year, she
invests the accumulated savings ($1,095) in an online
stock account. The stock account has an expected
annual return of 12%.
How much money will she have when she is 65 years
old?
6-22
Classifications of interest rates
• Nominal rate (iNOM) – also called the quoted or
state rate. An annual rate that ignores
compounding effects.
– iNOM is stated in contracts. Periods must also be
given, e.g. 8% Quarterly or 8% Daily interest.
• Periodic rate (iPER) – amount of interest charged
each period, e.g. monthly or quarterly.
– iPER = iNOM / m, where m is the number of
compounding periods per year. m = 4 for quarterly
and m = 12 for monthly compounding.
6-23
Nominal vs Effective Annual Rate
Example: If nominal interest rate is 10%, what
will be the effective interest rate, if
1.If payment is made quarterly
2. If payment is made monthly
3. If payment is made daily
© Dr. Sheikh Abu Taher
6-24
Classifications of interest rates
• Effective (or equivalent) annual rate (EAR = EIR)–
the annual rate of interest actually being earned,
taking into account compounding.
for 10% semiannual investment
EAR/EIR = ( 1 + iNOM / m )m - 1
= ( 1 + 0.10 / 2 )2 – 1 = 10.25%
– An investor would be indifferent between an
investment offering a 10.25% annual return
and one offering a 10% annual return,
compounded semiannually.
Relationship between EIR and m is
6-25
Why is it important to consider effective rates of
return?
• An investment with monthly payments is different
from one with quarterly payments. Must put each
return on an % basis to compare rates of return.
Must use % for comparisons. See following values
of % rates at various compounding levels.
EARANNUAL 10.00%
EARQUARTERLY 10.38%
EARMONTHLY 10.47%
EARDAILY (365) 10.52%
➢ Estimate the above using the formula discussed and
find out the relationship between EAR and m.
6-26
Can the effective rate ever be equal to the
nominal rate?
• Yes, but only if annual compounding is
used, i.e., if m = 1.
• If m > 1, EFF% will always be greater than
the nominal rate.
6-27
When is each rate used?
• iNOM written into contracts, quoted by banks
and brokers. Not used in calculations or
shown on time lines.
• iPER Used in calculations and shown on time
lines. If m = 1, iNOM = iPER = EAR.
• EAR Used to compare returns on investments
with different payments per year. Used in
calculations when annuity payments don’t
match compounding periods.
6-28
What is the FV of $100 after 3 years under 10%
semiannual compounding? Quarterly
compounding?
$134.49
(1.025)
$100
FV
$134.01
(1.05)
$100
FV
)
2
0.10
1
(
$100
FV
)
m
i
1
(
PV
FV
12
3Q
6
3S
3
2
3S
n
m
NOM
n
=
=
=
=
+
=
+
=


6-29
What’s the FV of a 3-year $100 annuity, if the
quoted interest rate is 10%, compounded
semiannually?
• Payments occur annually, but compounding
occurs every 6 months.
• Cannot use normal annuity valuation techniques.
0 1
100
2 3
5%
4 5
100 100
6
1 2 3
6-30
Loan amortization
• Amortized Loan - A loan that is repaid in equal
payments over its life.
• Amortization tables are widely used for home
mortgages, auto loans, business loans,
retirement plans, etc.
• Financial calculators and spreadsheets are
great for setting up amortization tables.
• EXAMPLE: Construct an amortization schedule
for a $1,000, 10% annual rate loan with 3 equal
payments.
6-31
Step - 1
• Find how much do you need to pay equally in
each installment
You need to follow annuity formula here
6-32
Step 2:
Find the interest paid in Year 1
• The borrower will owe interest upon the initial
balance at the end of the first year. Interest to
be paid in the first year can be found by
multiplying the beginning balance by the
interest rate.
INTt = Beg balalancet (i)
INT1 = $1,000 (0.10) = $100
6-33
Step 3:
Find the principal repaid in Year 1
• If a payment of $402.11 was made at the end
of the first year and $100 was paid toward
interest, the remaining value must represent
the amount of principal repaid.
PRIN = PMT – INT
= $402.11 - $100 = $302.11
6-34
Step 4:
Find the ending balance after Year 1
• To find the balance at the end of the period,
subtract the amount paid toward principal
from the beginning balance.
END Balance= BEG Balance – PRIN
= $1,000 - $302.11
= $697.89
6-35
Constructing an amortization table:
Repeat steps 1 – 4 until end of loan
Year BEG BAL
(1)
PMT (2) INT (3) PRIN
(4)
END
BAL (6)
1 $1,000 $402 $100 $302 $698
2 698 402 70 332 366
3 366 402 37 366 0
TOTAL 1,206.34 206.34 1,000 -
• Interest paid declines with each payment as the
balance declines. What are the tax implications
of this?
6-36
Illustrating an amortized payment:
Where does the money go?
• Constant payments.
• Declining interest payments.
• Declining balance.
$
0 1 2 3
402.11
Interest
302.11
Principal Payments
6-37
Example
• Construct Loan Amortization Schedule,
$100,000 at 6% for 5 Years

Mais conteúdo relacionado

Semelhante a Time value Ch6.pdf

Bba 2204 fin mgt week 5 time value of money
Bba 2204 fin mgt week 5 time value of moneyBba 2204 fin mgt week 5 time value of money
Bba 2204 fin mgt week 5 time value of moneyStephen Ong
 
Time Value Of Money F F M
Time  Value Of  Money   F F MTime  Value Of  Money   F F M
Time Value Of Money F F MZoha Qureshi
 
L3 - With Answers.pdf
L3 - With Answers.pdfL3 - With Answers.pdf
L3 - With Answers.pdfnewton47
 
Understanding the time value of money (annuity)
Understanding the time value of money (annuity)Understanding the time value of money (annuity)
Understanding the time value of money (annuity)DIANN MOORMAN
 
4th Lecture- discounted cash flows (1).pptx
4th Lecture- discounted cash flows (1).pptx4th Lecture- discounted cash flows (1).pptx
4th Lecture- discounted cash flows (1).pptxabdelhameedibrahim4
 
Time value of money
Time value of moneyTime value of money
Time value of moneySewaleAbate1
 
ACCA F9 Investment appraisal-Discounted Cash Flow Techniques
ACCA F9 Investment appraisal-Discounted Cash Flow TechniquesACCA F9 Investment appraisal-Discounted Cash Flow Techniques
ACCA F9 Investment appraisal-Discounted Cash Flow TechniquesSaraf Academy
 
TIME VALUE OF MONEY
TIME VALUE OF MONEYTIME VALUE OF MONEY
TIME VALUE OF MONEYCHARAK RAY
 
Chapter 6: The Time Value of Money
Chapter 6: The Time Value of MoneyChapter 6: The Time Value of Money
Chapter 6: The Time Value of MoneyNada G.Youssef
 
Chapter 5 Time Value of Money.pptx
Chapter 5 Time Value of Money.pptxChapter 5 Time Value of Money.pptx
Chapter 5 Time Value of Money.pptxHazlina Hussein
 
PPT-1_SIMPLE-AND-GENERAL-ANNUITIES-1.pptx
PPT-1_SIMPLE-AND-GENERAL-ANNUITIES-1.pptxPPT-1_SIMPLE-AND-GENERAL-ANNUITIES-1.pptx
PPT-1_SIMPLE-AND-GENERAL-ANNUITIES-1.pptxMaryGraceBirao
 
A introdu ction to financial management topic time value of money
A introdu ction to financial management topic time value of moneyA introdu ction to financial management topic time value of money
A introdu ction to financial management topic time value of moneyVishalMotwani15
 
Cash Flow Statement
Cash Flow StatementCash Flow Statement
Cash Flow StatementKushPanchal8
 
Financial institutions and markets solutions
Financial institutions and markets solutionsFinancial institutions and markets solutions
Financial institutions and markets solutionsayesha shahid
 
Discounted Cash Flow
Discounted Cash FlowDiscounted Cash Flow
Discounted Cash FlowRod Medallon
 
time value of money
time value of moneytime value of money
time value of moneyashfaque75
 

Semelhante a Time value Ch6.pdf (20)

Bba 2204 fin mgt week 5 time value of money
Bba 2204 fin mgt week 5 time value of moneyBba 2204 fin mgt week 5 time value of money
Bba 2204 fin mgt week 5 time value of money
 
Time Value Of Money F F M
Time  Value Of  Money   F F MTime  Value Of  Money   F F M
Time Value Of Money F F M
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
Chapter 4.doc
Chapter 4.docChapter 4.doc
Chapter 4.doc
 
L3 - With Answers.pdf
L3 - With Answers.pdfL3 - With Answers.pdf
L3 - With Answers.pdf
 
Understanding the time value of money (annuity)
Understanding the time value of money (annuity)Understanding the time value of money (annuity)
Understanding the time value of money (annuity)
 
4th Lecture- discounted cash flows (1).pptx
4th Lecture- discounted cash flows (1).pptx4th Lecture- discounted cash flows (1).pptx
4th Lecture- discounted cash flows (1).pptx
 
Time value of money
Time value of moneyTime value of money
Time value of money
 
ACCA F9 Investment appraisal-Discounted Cash Flow Techniques
ACCA F9 Investment appraisal-Discounted Cash Flow TechniquesACCA F9 Investment appraisal-Discounted Cash Flow Techniques
ACCA F9 Investment appraisal-Discounted Cash Flow Techniques
 
TIME VALUE OF MONEY
TIME VALUE OF MONEYTIME VALUE OF MONEY
TIME VALUE OF MONEY
 
Chapter 6: The Time Value of Money
Chapter 6: The Time Value of MoneyChapter 6: The Time Value of Money
Chapter 6: The Time Value of Money
 
Chapter 5 Time Value of Money.pptx
Chapter 5 Time Value of Money.pptxChapter 5 Time Value of Money.pptx
Chapter 5 Time Value of Money.pptx
 
PPT-1_SIMPLE-AND-GENERAL-ANNUITIES-1.pptx
PPT-1_SIMPLE-AND-GENERAL-ANNUITIES-1.pptxPPT-1_SIMPLE-AND-GENERAL-ANNUITIES-1.pptx
PPT-1_SIMPLE-AND-GENERAL-ANNUITIES-1.pptx
 
A introdu ction to financial management topic time value of money
A introdu ction to financial management topic time value of moneyA introdu ction to financial management topic time value of money
A introdu ction to financial management topic time value of money
 
Timevalueofmoney
TimevalueofmoneyTimevalueofmoney
Timevalueofmoney
 
F.M - Chapter 5.pptx
F.M - Chapter 5.pptxF.M - Chapter 5.pptx
F.M - Chapter 5.pptx
 
Cash Flow Statement
Cash Flow StatementCash Flow Statement
Cash Flow Statement
 
Financial institutions and markets solutions
Financial institutions and markets solutionsFinancial institutions and markets solutions
Financial institutions and markets solutions
 
Discounted Cash Flow
Discounted Cash FlowDiscounted Cash Flow
Discounted Cash Flow
 
time value of money
time value of moneytime value of money
time value of money
 

Último

Olympus 38DL Plus Ultrasonic Thickness Gauge
Olympus 38DL Plus Ultrasonic Thickness GaugeOlympus 38DL Plus Ultrasonic Thickness Gauge
Olympus 38DL Plus Ultrasonic Thickness GaugeStephenKim86
 
unfinished legacy it is a clothing brand
unfinished legacy it is a clothing brandunfinished legacy it is a clothing brand
unfinished legacy it is a clothing brandakashm530190
 
Importance of Commercial Vehicle Insurance.pptx
Importance of Commercial Vehicle Insurance.pptxImportance of Commercial Vehicle Insurance.pptx
Importance of Commercial Vehicle Insurance.pptxBonano Insurance
 
Shopclues: Failure & Solutions in Business Model
Shopclues: Failure & Solutions in Business ModelShopclues: Failure & Solutions in Business Model
Shopclues: Failure & Solutions in Business ModelBhaviniSharma12
 
14 march 2024-capital-markets-update eni.pdf
14 march 2024-capital-markets-update eni.pdf14 march 2024-capital-markets-update eni.pdf
14 march 2024-capital-markets-update eni.pdfEni
 
Streamlining Your Accounting A Guide to QuickBooks Migration Tools.pptx
Streamlining Your Accounting A Guide to QuickBooks Migration Tools.pptxStreamlining Your Accounting A Guide to QuickBooks Migration Tools.pptx
Streamlining Your Accounting A Guide to QuickBooks Migration Tools.pptxPaulBryant58
 
The Smart Bridge Interview now Veranda Learning
The Smart Bridge Interview now Veranda LearningThe Smart Bridge Interview now Veranda Learning
The Smart Bridge Interview now Veranda LearningNaval Singh
 
Optimize Your CRM Customization and Beyond
Optimize Your CRM Customization and BeyondOptimize Your CRM Customization and Beyond
Optimize Your CRM Customization and BeyondBoundify
 
0311 National Accounts Online Giving Trends.pdf
0311 National Accounts Online Giving Trends.pdf0311 National Accounts Online Giving Trends.pdf
0311 National Accounts Online Giving Trends.pdfBloomerang
 
Reframing Requirements: A Strategic Approach to Requirement Definition, with ...
Reframing Requirements: A Strategic Approach to Requirement Definition, with ...Reframing Requirements: A Strategic Approach to Requirement Definition, with ...
Reframing Requirements: A Strategic Approach to Requirement Definition, with ...Jake Truemper
 
The Vietnam Believer_Newsletter_Vol.001_Mar12 2024
The Vietnam Believer_Newsletter_Vol.001_Mar12 2024The Vietnam Believer_Newsletter_Vol.001_Mar12 2024
The Vietnam Believer_Newsletter_Vol.001_Mar12 2024believeminhh
 
Wallet Pitch for startup fintech and loan
Wallet Pitch for startup fintech and loanWallet Pitch for startup fintech and loan
Wallet Pitch for startup fintech and loansujat8807
 
"InShorts: A Game-Changer in the Digital News Age"
"InShorts: A Game-Changer in the Digital News Age""InShorts: A Game-Changer in the Digital News Age"
"InShorts: A Game-Changer in the Digital News Age"Adharsh45
 
CORPORATE SOCIAL RESPONSIBILITY - FINAL REQUIREMENT.pdf
CORPORATE SOCIAL RESPONSIBILITY - FINAL REQUIREMENT.pdfCORPORATE SOCIAL RESPONSIBILITY - FINAL REQUIREMENT.pdf
CORPORATE SOCIAL RESPONSIBILITY - FINAL REQUIREMENT.pdfLouis Malaybalay
 
Pitch Deck Teardown: SuperScale's $5.4M Series A deck
Pitch Deck Teardown: SuperScale's $5.4M Series A deckPitch Deck Teardown: SuperScale's $5.4M Series A deck
Pitch Deck Teardown: SuperScale's $5.4M Series A deckHajeJanKamps
 
Bus Eth ch3 ppt.ppt business ethics and corporate social responsibilities ppt
Bus Eth ch3 ppt.ppt business ethics and corporate social responsibilities pptBus Eth ch3 ppt.ppt business ethics and corporate social responsibilities ppt
Bus Eth ch3 ppt.ppt business ethics and corporate social responsibilities pptendeworku
 
Strategic Resources Corporate Presentation - March 2024 Update
Strategic Resources Corporate Presentation - March 2024 UpdateStrategic Resources Corporate Presentation - March 2024 Update
Strategic Resources Corporate Presentation - March 2024 UpdateAdnet Communications
 
Young Woman Entrepreneur - Kaviya Cherian
Young Woman Entrepreneur - Kaviya CherianYoung Woman Entrepreneur - Kaviya Cherian
Young Woman Entrepreneur - Kaviya CherianCDEEPANVITA
 
A Comprehensive Case Study on the IL&FS Crisis (final).pptx
A Comprehensive Case Study on the IL&FS Crisis (final).pptxA Comprehensive Case Study on the IL&FS Crisis (final).pptx
A Comprehensive Case Study on the IL&FS Crisis (final).pptxShainaMaheshwari1
 
Mist Cooling & Fogging System Company in Saudi Arabia
Mist Cooling & Fogging System Company in Saudi ArabiaMist Cooling & Fogging System Company in Saudi Arabia
Mist Cooling & Fogging System Company in Saudi Arabiaopstechsanjanasingh
 

Último (20)

Olympus 38DL Plus Ultrasonic Thickness Gauge
Olympus 38DL Plus Ultrasonic Thickness GaugeOlympus 38DL Plus Ultrasonic Thickness Gauge
Olympus 38DL Plus Ultrasonic Thickness Gauge
 
unfinished legacy it is a clothing brand
unfinished legacy it is a clothing brandunfinished legacy it is a clothing brand
unfinished legacy it is a clothing brand
 
Importance of Commercial Vehicle Insurance.pptx
Importance of Commercial Vehicle Insurance.pptxImportance of Commercial Vehicle Insurance.pptx
Importance of Commercial Vehicle Insurance.pptx
 
Shopclues: Failure & Solutions in Business Model
Shopclues: Failure & Solutions in Business ModelShopclues: Failure & Solutions in Business Model
Shopclues: Failure & Solutions in Business Model
 
14 march 2024-capital-markets-update eni.pdf
14 march 2024-capital-markets-update eni.pdf14 march 2024-capital-markets-update eni.pdf
14 march 2024-capital-markets-update eni.pdf
 
Streamlining Your Accounting A Guide to QuickBooks Migration Tools.pptx
Streamlining Your Accounting A Guide to QuickBooks Migration Tools.pptxStreamlining Your Accounting A Guide to QuickBooks Migration Tools.pptx
Streamlining Your Accounting A Guide to QuickBooks Migration Tools.pptx
 
The Smart Bridge Interview now Veranda Learning
The Smart Bridge Interview now Veranda LearningThe Smart Bridge Interview now Veranda Learning
The Smart Bridge Interview now Veranda Learning
 
Optimize Your CRM Customization and Beyond
Optimize Your CRM Customization and BeyondOptimize Your CRM Customization and Beyond
Optimize Your CRM Customization and Beyond
 
0311 National Accounts Online Giving Trends.pdf
0311 National Accounts Online Giving Trends.pdf0311 National Accounts Online Giving Trends.pdf
0311 National Accounts Online Giving Trends.pdf
 
Reframing Requirements: A Strategic Approach to Requirement Definition, with ...
Reframing Requirements: A Strategic Approach to Requirement Definition, with ...Reframing Requirements: A Strategic Approach to Requirement Definition, with ...
Reframing Requirements: A Strategic Approach to Requirement Definition, with ...
 
The Vietnam Believer_Newsletter_Vol.001_Mar12 2024
The Vietnam Believer_Newsletter_Vol.001_Mar12 2024The Vietnam Believer_Newsletter_Vol.001_Mar12 2024
The Vietnam Believer_Newsletter_Vol.001_Mar12 2024
 
Wallet Pitch for startup fintech and loan
Wallet Pitch for startup fintech and loanWallet Pitch for startup fintech and loan
Wallet Pitch for startup fintech and loan
 
"InShorts: A Game-Changer in the Digital News Age"
"InShorts: A Game-Changer in the Digital News Age""InShorts: A Game-Changer in the Digital News Age"
"InShorts: A Game-Changer in the Digital News Age"
 
CORPORATE SOCIAL RESPONSIBILITY - FINAL REQUIREMENT.pdf
CORPORATE SOCIAL RESPONSIBILITY - FINAL REQUIREMENT.pdfCORPORATE SOCIAL RESPONSIBILITY - FINAL REQUIREMENT.pdf
CORPORATE SOCIAL RESPONSIBILITY - FINAL REQUIREMENT.pdf
 
Pitch Deck Teardown: SuperScale's $5.4M Series A deck
Pitch Deck Teardown: SuperScale's $5.4M Series A deckPitch Deck Teardown: SuperScale's $5.4M Series A deck
Pitch Deck Teardown: SuperScale's $5.4M Series A deck
 
Bus Eth ch3 ppt.ppt business ethics and corporate social responsibilities ppt
Bus Eth ch3 ppt.ppt business ethics and corporate social responsibilities pptBus Eth ch3 ppt.ppt business ethics and corporate social responsibilities ppt
Bus Eth ch3 ppt.ppt business ethics and corporate social responsibilities ppt
 
Strategic Resources Corporate Presentation - March 2024 Update
Strategic Resources Corporate Presentation - March 2024 UpdateStrategic Resources Corporate Presentation - March 2024 Update
Strategic Resources Corporate Presentation - March 2024 Update
 
Young Woman Entrepreneur - Kaviya Cherian
Young Woman Entrepreneur - Kaviya CherianYoung Woman Entrepreneur - Kaviya Cherian
Young Woman Entrepreneur - Kaviya Cherian
 
A Comprehensive Case Study on the IL&FS Crisis (final).pptx
A Comprehensive Case Study on the IL&FS Crisis (final).pptxA Comprehensive Case Study on the IL&FS Crisis (final).pptx
A Comprehensive Case Study on the IL&FS Crisis (final).pptx
 
Mist Cooling & Fogging System Company in Saudi Arabia
Mist Cooling & Fogging System Company in Saudi ArabiaMist Cooling & Fogging System Company in Saudi Arabia
Mist Cooling & Fogging System Company in Saudi Arabia
 

Time value Ch6.pdf

  • 1. 6-1 6-1 Time Value of Money Value of Money = f(Time)
  • 2. 6-2 Chapter outline • The concept of TVM • Interest rate (Meaning, Components, Simple vs Compound) • Time lines (why important?) • Present value, Future value • Annuities (ordinary vs annuity due) • Nominal/Quoted vs Effective Interest rates • Amortization Schedule
  • 3. 6-3 Time Value of Money Define Indicates the purchasing power of money changes during time being or the money in your hand now is not equal to the money will be in future Why matters - Inflation/Deflation - Uncertainty/Risk - Opportunity costs Applications • planning for retirement, • valuing stocks and bonds, • setting up loan payment schedules, and making corporate decisions regarding investing in new plant and equipment
  • 4. 6-4 Interest Rate An interest rate is the percentage of principal charged by the lender for the use of its money/fund Components: - Inflation - Opportunity cost - Risk Simple vs Compound Interest Rate
  • 5. 6-5 Time lines • Show the timing of cash flows. • Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period. CF0 CF1 CF3 CF2 0 1 2 3 i%
  • 6. 6-6 Drawing time lines: $100 lump sum due in 2 years; 3-year $100 ordinary annuity 100 100 100 0 1 2 3 i% 3 year $100 ordinary annuity 100 0 1 2 i% $100 lump sum due in 2 years
  • 7. 6-7 Drawing time lines: Uneven cash flow stream; CF0 = -$50, CF1 = $100, CF2 = $75, and CF3 = $50 100 50 75 0 1 2 3 i% -50 Uneven cash flow stream
  • 8. 6-8 What is the future value (FV) of an initial $100 after 3 years, if i/YR = 10%? • Finding the FV of a cash flow or series of cash flows when compound interest is applied is called compounding. • FV can be solved by using the arithmetic, financial calculator, and spreadsheet methods. FV = ? 0 1 2 3 10% 100
  • 9. 6-9 Solving for FV: The arithmetic method • After 1 year: FV1 = PV ( 1 + i ) = $100 (1.10) = $110.00 • After 2 years: FV2 = PV ( 1 + i )2 = $100 (1.10)2 =$121.00 • After 3 years: FV3 = PV ( 1 + i )3 = $100 (1.10)3 =$133.10 • After n years (general case): FVn = PV ( 1 + i )n
  • 10. 6-10 FV (some examples) If Cash inflow and outflow one time: - If you deposit $1000 for 10 years at 12% interest rate, how much will you receive after 10 years? Calculate and show time lines. - If your grand father deposited $5000 before 30 years at 10% interest rate at a commercial bank, how much would you receive today. Show calculations and time lines. If there is more than one cash outflow and one cash inflow: - If you deposit $1000 now, $5000 after 1 year, $6000 after 2 year, and $4000 after 3 years, how much will you receive after 4 years at 10% interest rate. Show calculations and time lines. - If your forefathers deposited $10000 before 50 years at 6% interest rate, and more $10000 before 30 years at 8% interest rate. How much in total you would receive today. Show calculations and time lines of each scenario.
  • 11. 6-11 What is the present value (PV) of $100 due in 3 years, if i/YR = 10%? • Finding the PV of a cash flow or series of cash flows when compound interest is applied is called discounting (the reverse of compounding). • The PV shows the value of cash flows in terms of today’s purchasing power. PV = ? 100 0 1 2 3 10%
  • 12. 6-12 Solving for PV: The arithmetic method • Solve the general FV equation for PV: PV = FVn / ( 1 + i )n PV = FV3 / ( 1 + i )3 = $100 / ( 1.10 )3 = $75.13
  • 13. 6-13 What is the PV of this uneven cash flow stream? 0 100 1 300 2 300 3 10% -50 4 90.91 247.93 225.39 -34.15 530.08 = PV
  • 14. 6-14 Present value concept © Dr. Sheikh Abu Taher
  • 15. 6-15 Solving for PV: Uneven cash flow stream • Input cash flows in the calculator’s “CFLO” register: – CF0 = 0 – CF1 = 100 – CF2 = 300 – CF3 = 300 – CF4 = -50 • Enter I/YR = 10, press NPV button to get NPV = $530.09. (Here NPV = PV.)
  • 16. 6-16 Exercises (PV and FV) • If you deposit $10000 for 5 years at 10% interest rate, how much will you receive after 5 years? • If you would like to receive $20000 after 5 years, how much do you need to deposit today if the interest rate is 10%? • If you deposit $3000 at year 1, 3500 at year 2, $0 at year 4 and $4000 at year 5, how much will you receive after 5 years if the interest rate is 10%? Show time lines. • If you would like to receive $3000 at year 1, 3500 at year 2, $0 at year 4 and $4000 at year 5, how much do you need to deposit today if the interest rate is 10%? Show time lines.
  • 17. 6-17 Discussion: Annuity Annuity define: Series of equal payment or receipt/cash inflow or outflow for number of periods (periods can be day, month, quarter, year, etc) Examples: EMI, home loan, automobile loan, Internet bill, house rent, etc i = 1, 2, …………………….n Types: 1. Ordinary annuity 2. Annuity due
  • 18. 6-18 What is the difference between an ordinary annuity and an annuity due? Ordinary Annuity PMT PMT PMT 0 1 2 3 i% PMT PMT 0 1 2 3 i% PMT Annuity Due
  • 21. 6-21 The Power of Compound Interest A 20-year-old student wants to start saving for retirement. She plans to save $3 a day. Every day, she puts $3 in her drawer. At the end of the year, she invests the accumulated savings ($1,095) in an online stock account. The stock account has an expected annual return of 12%. How much money will she have when she is 65 years old?
  • 22. 6-22 Classifications of interest rates • Nominal rate (iNOM) – also called the quoted or state rate. An annual rate that ignores compounding effects. – iNOM is stated in contracts. Periods must also be given, e.g. 8% Quarterly or 8% Daily interest. • Periodic rate (iPER) – amount of interest charged each period, e.g. monthly or quarterly. – iPER = iNOM / m, where m is the number of compounding periods per year. m = 4 for quarterly and m = 12 for monthly compounding.
  • 23. 6-23 Nominal vs Effective Annual Rate Example: If nominal interest rate is 10%, what will be the effective interest rate, if 1.If payment is made quarterly 2. If payment is made monthly 3. If payment is made daily © Dr. Sheikh Abu Taher
  • 24. 6-24 Classifications of interest rates • Effective (or equivalent) annual rate (EAR = EIR)– the annual rate of interest actually being earned, taking into account compounding. for 10% semiannual investment EAR/EIR = ( 1 + iNOM / m )m - 1 = ( 1 + 0.10 / 2 )2 – 1 = 10.25% – An investor would be indifferent between an investment offering a 10.25% annual return and one offering a 10% annual return, compounded semiannually. Relationship between EIR and m is
  • 25. 6-25 Why is it important to consider effective rates of return? • An investment with monthly payments is different from one with quarterly payments. Must put each return on an % basis to compare rates of return. Must use % for comparisons. See following values of % rates at various compounding levels. EARANNUAL 10.00% EARQUARTERLY 10.38% EARMONTHLY 10.47% EARDAILY (365) 10.52% ➢ Estimate the above using the formula discussed and find out the relationship between EAR and m.
  • 26. 6-26 Can the effective rate ever be equal to the nominal rate? • Yes, but only if annual compounding is used, i.e., if m = 1. • If m > 1, EFF% will always be greater than the nominal rate.
  • 27. 6-27 When is each rate used? • iNOM written into contracts, quoted by banks and brokers. Not used in calculations or shown on time lines. • iPER Used in calculations and shown on time lines. If m = 1, iNOM = iPER = EAR. • EAR Used to compare returns on investments with different payments per year. Used in calculations when annuity payments don’t match compounding periods.
  • 28. 6-28 What is the FV of $100 after 3 years under 10% semiannual compounding? Quarterly compounding? $134.49 (1.025) $100 FV $134.01 (1.05) $100 FV ) 2 0.10 1 ( $100 FV ) m i 1 ( PV FV 12 3Q 6 3S 3 2 3S n m NOM n = = = = + = + =  
  • 29. 6-29 What’s the FV of a 3-year $100 annuity, if the quoted interest rate is 10%, compounded semiannually? • Payments occur annually, but compounding occurs every 6 months. • Cannot use normal annuity valuation techniques. 0 1 100 2 3 5% 4 5 100 100 6 1 2 3
  • 30. 6-30 Loan amortization • Amortized Loan - A loan that is repaid in equal payments over its life. • Amortization tables are widely used for home mortgages, auto loans, business loans, retirement plans, etc. • Financial calculators and spreadsheets are great for setting up amortization tables. • EXAMPLE: Construct an amortization schedule for a $1,000, 10% annual rate loan with 3 equal payments.
  • 31. 6-31 Step - 1 • Find how much do you need to pay equally in each installment You need to follow annuity formula here
  • 32. 6-32 Step 2: Find the interest paid in Year 1 • The borrower will owe interest upon the initial balance at the end of the first year. Interest to be paid in the first year can be found by multiplying the beginning balance by the interest rate. INTt = Beg balalancet (i) INT1 = $1,000 (0.10) = $100
  • 33. 6-33 Step 3: Find the principal repaid in Year 1 • If a payment of $402.11 was made at the end of the first year and $100 was paid toward interest, the remaining value must represent the amount of principal repaid. PRIN = PMT – INT = $402.11 - $100 = $302.11
  • 34. 6-34 Step 4: Find the ending balance after Year 1 • To find the balance at the end of the period, subtract the amount paid toward principal from the beginning balance. END Balance= BEG Balance – PRIN = $1,000 - $302.11 = $697.89
  • 35. 6-35 Constructing an amortization table: Repeat steps 1 – 4 until end of loan Year BEG BAL (1) PMT (2) INT (3) PRIN (4) END BAL (6) 1 $1,000 $402 $100 $302 $698 2 698 402 70 332 366 3 366 402 37 366 0 TOTAL 1,206.34 206.34 1,000 - • Interest paid declines with each payment as the balance declines. What are the tax implications of this?
  • 36. 6-36 Illustrating an amortized payment: Where does the money go? • Constant payments. • Declining interest payments. • Declining balance. $ 0 1 2 3 402.11 Interest 302.11 Principal Payments
  • 37. 6-37 Example • Construct Loan Amortization Schedule, $100,000 at 6% for 5 Years