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Time Value Analysis. Corporate Finance. Dr. A. DeMaskey. Learning Objectives. Questions to be answered: What is time value of money? What is compounding? Discounting? How are the principles of time value analysis applied to the various types of cash flows?

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Presentation Transcript
time value analysis

Time Value Analysis

Corporate Finance

Dr. A. DeMaskey

learning objectives
Learning Objectives
  • Questions to be answered:
    • What is time value of money?
    • What is compounding? Discounting?
    • How are the principles of time value analysis applied to the various types of cash flows?
    • What different types of interest rates are used in finance?
basic concepts
Basic Concepts
  • Why time value of money?
  • Evaluating financial transactions
    • Expected cash flows
    • Risk
time lines
Time Lines

0

1

2

3

i%

CF0

CF1

CF2

CF3

Tick marksat ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2.

single cash flow
Single Cash Flow

0

1

2 Year

i%

100

Time line for a $100 lump sum due at the end of Year 2.

even cash flows annuity
Even Cash Flows: Annuity

0

1

2

3

i%

100

100

100

Time line for an ordinary annuity of $100 for 3 years.

uneven cash flows
Uneven Cash Flows

0

1

2

3

i%

-50

100

75

50

compounding
Compounding

0

1

2

3

10%

100

FV = ?

Finding FVs (moving to the right

on a time line) is called compounding.

discounting
Discounting

Finding PVs is discounting, and it’s the reverse of compounding.

0

1

2

3

10%

100

PV = ?

three ways to solve tvm problems
Three Ways to Solve TVM Problems
  • Solve the equation with a regular calculator.
  • Use a financial calculator.
  • Use a spreadsheet.
time value of a lump sum
Time Value of A Lump Sum
  • Future Value
  • Present Value
time value of a series of even cash flows
Time Value of a Series of Even Cash Flows
  • Types of Annuities
    • Ordinary annuity
    • Annuity due
    • Perpetual annuity
  • Future Value
  • Present Value
future value of an ordinary annuity
Future Value of an Ordinary Annuity

0

1

2

3

10%

100

100

100

110

121

FV = 331

present value of an ordinary annuity
Present Value of an Ordinary Annuity

0

1

2

3

10%

100

100

100

90.91

82.64

75.13

248.69 = PV

slide15

Difference Between an OrdinaryAnnuity and an AnnuityDue

Ordinary Annuity

0

1

2

3

i%

PMT

PMT

PMT

Annuity Due

0

1

2

3

i%

PMT

PMT

PMT

PV

FV

time value of uneven cash flows
Time Value of Uneven Cash Flows
  • Present Value
    • Sum of PVs of individual cash flow components
  • Future Value
    • Sum of FVs of individual cash flow components
compounding periods
Compounding Periods
  • Periodic Rate
    • iPer = iNom/m
  • Annual Percentage Rate (APR)
    • iNom = iPerx m
  • Effective Annual Rate (EAR)
    • EFF% = (1 + iNom/m)m – 1.0
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