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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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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


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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