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MBAMFM 253 Enhancing Firm Value

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Title: MBAMFM 253 Enhancing Firm Value


1
MBA/MFM 253 Enhancing Firm Value
2
The Big Picture
  • The Goal of Corporate Financial Management
  • Maximizing the Value of the Firm

3
Measuring Firm Value
  • The firm has many stakeholders we will focus on
    four Shareholders, bondholders, financial
    markets, and society.
  • Does an increase in stock price signal an
    increase in firm value?

4
What Determines Firm Value?
  • Firm and Project Risk
  • Input Costs
  • Industry
  • Economic Environment
  • Financing mix (Debt vs Equity)
  • Other?
  • How do you calculate value?

5
Goal of Financial Management
  • Maximize the value of the firm as determined by
    the present value of its expected cash flows,
    discounted back at a rate that reflects both the
    riskiness of the firms projects and the financing
    mix used to fund the projects.

6
Firm Value and Stock Prices
  • Is maximizing the value of the firm the same as
    maximizing the stock price?
  • Only if maximizing stock price does not have a
    negative impact on other stakeholders in the firm.

7
The Classical Objective Function
STOCKHOLDERS
BONDHOLDERS
SOCIETY
Managers
FINANCIAL MARKETS
8
Management and Stockholders
  • The Principal / Agent Problem
  • Whenever owners (principals) hire managers
    (agents) to operate the firm there is a potential
    conflict of interest. The managers have an
    incentive to act in their own best interest
    instead of the shareholders.

9
Management and StockholdersOther Problems
  • Lack of monitoring by shareholders
  • Individual shareholders often due not take the
    time monitor the firm
  • Lack of independence and expertise on the board.
  • Small ownership stake of directors
  • Take over defenses and acquisitions
  • Greenmail, Golden Parachutes, and Poison Pills.
    Overvaluing synergy.

10
Reducing Agency Problems
  • One way to reduce agency problems is to make
    management think more like a stockholder.
  • Offer managers Options and Warrants
  • Problems
  • May increase incentive to mislead markets
  • May increase incentive to take on extra risk

11
Reducing Agency Problems
  • More Effective Board of Directors
  • Boards have become smaller
  • Fewer insiders on the board
  • Increased compensation with options
  • Nominating committee instead of Chosen by CEO
  • Sarbanes Oxley and transparency
  • More active participation by large stockholders
    institutional ownership

12
Empirical Evidence on Governance
  • Gompers, Ishii, and Metrick (2003)
  • Developed corporate governance index based on
    best practices.
  • Buying stock in firms with high scores for
    governance and selling those with low scores
    resulted in large excess returns.

13
Disney Example
  • Reaction to decline in share price and captive
    board
  • Required executive sessions without CEO
  • New definition of director independence that must
    be met by a majority of the board
  • Reduction in committee size and rotation of
    committee chairs
  • New provisions for succession planning
  • Education and training for board members

14
Management and StockholdersBest Case
  • Best Case
  • Managers focus on stock price maximization and
    therefore the shareholders best interest.
  • Shareholders are not powerless do a good job of
    monitoring the firm. They make informed
    decisions about the board of directors and
    exercise their voting powers. The board acts
    independent of the CEO.

15
The Classical Objective Function
STOCKHOLDERS
Monitor the firm Hire fire Managers / Board
Maximize stockholder wealth
BONDHOLDERS
SOCIETY
Managers
FINANCIAL MARKETS
16
Conflicts Between Stockholders and Bondholders
  • Stock Price maximization may increase risk of
    default.
  • Risky projects that increase shareholder returns
    and increase chance of default
  • Funding projects with increased debt increasing
    chance of default.
  • Paying high dividend, decreasing cash available
    for interest payments

17
Bond Covenants and Other Solutions
  • Examples of Covenants
  • Restrictions on Investment policy
  • Restrictions on Dividend Policy
  • Restrictions on Additional Leverage
  • Problems
  • May force firm to pass up profitable projects
  • Bond Innovations
  • Puttable bonds and convertible bonds

18
Conflicts Between Stockholders and Bondholders
  • Best Case
  • Lenders are protected via covenants in
  • the debt contracts and management
  • considers both bond and stockholders
  • in decision making.
  • Lenders supply capital to the firm and receive a
    return based on risk

19
The Classical Objective Function
STOCKHOLDERS
Monitor the firm Hire fire Managers / Board
Maximize stockholder wealth
Bond Covenants
BONDHOLDERS
SOCIETY
Managers
Lend Money
FINANCIAL MARKETS
20
Managers and Financial Markets
  • The Information Problem
  • Firms may intentionally mislead financial
    markets. Both Public and Private information
    impact firm value
  • The Market Problem
  • Even if information is correct, the markets may
    not react properly
  • Market overreaction
  • Insider influence
  • Are Markets too focused on the short term?
  • Markets and expectations

21
Improving Transparency
  • Increased information sharing by independent
    analysts
  • Market Efficiencies
  • Low transaction costs
  • Free and wide access to information
  • Complete markets (short selling, insider
    trading?)

22
Managers and Financial Markets
  • Best Case
  • Management does not intentionally mislead the
    Financial markets
  • The markets interpret information correctly

23
The Classical Objective Function
STOCKHOLDERS
Monitor the firm Hire fire Managers / Board
Maximize stockholder wealth
Bond Covenants Protect Lenders
BONDHOLDERS
SOCIETY
Managers
Lend Money
Mangers do not use info to mislead markets
Fin Markets interpret info correctly
FINANCIAL MARKETS
24
Firms and Society
  • Management decisions often have social costs
    (intentional and non intentional)
  • pollution, Johns Manville and Asbestos
  • A problem exists if the firm is not accountable
    for the spillover costs that results from its
    operations.

25
Firms and Society
  • What responsibility do firms have in respect to
    the communities in which they operate and the
    well being of their customers?
  • One definition Sustainability meeting the
    needs of the present without compromising the
    ability of future generations to meet their own
    needs
  • Others?

26
Corporate Social Responsibility
  • Firms respond to financial incentives
  • Part of social responsibility depends on
    shareholders responding to poor decisions
    relating to social responsibility. (US
    Universities divesting in tobacco firms, customer
    boycotts etc.)
  • Should the firm pursue socially responsible
    actions if it decreases shareholder returns
    (decreases the value of the firm)??

27
Social Welfare
  • Assuming that all shareholders are protected
  • Does firm value maximization benefit society?

The owners of the firms stock are society
Stock price maximization promotes efficiency in
the allocation of resources
Promotes economic growth and employment
28
Firms and Society
  • Best Case
  • Management decisions have little or no social
    costs.
  • Management acts in the best interest of society,
    and attempts to be a good corporate citizen.
  • Any social costs can be traced back to the firm.

29
The Classical Objective Function
STOCKHOLDERS
Monitor the firm Hire fire Managers / Board
Maximize stockholder wealth
Bond Covenants Protect Lenders
Costs are traced to the firm
BONDHOLDERS
SOCIETY
Managers
Lend Money
No Social Costs
Mangers do not use info to mislead markets
Fin Markets interpret info correctly
FINANCIAL MARKETS
30
Our Assumption
  • In class we will assume that management attempts
    to act in the best interest of all stakeholders.
  • Therefore, stock price maximization and firm
    value maximization are basically the same thing.
  • However, we know that in the real world there
    cases where stakeholders incur costs associated
    with share price maximization.

31
Other Systems
  • Germany and Japan
  • Industrial groups where businesses invest in each
    other, and make decisions in the best interest of
    the group.
  • Potential Problems?
  • Less risk taking?
  • Contagion effects within the group
  • Conflicts of interest

32
Other Objectives?
  • Should firm value / stock maximization be
    replaced by other objectives?
  • Maximize Market Share
  • Observable does not require efficient markets
  • Based on assumption that market share increases
    pricing power and earnings (increasing firm
    value)
  • Profit Maximization
  • Consistent with Firm Value Max, creates problems
    with Accounting
  • Empire Building

33
Quick Outline of Class
  • Part 1 Review of basic tools and concepts
  • Time Value of Money
  • Measuring Risk and Return
  • Part 2 Applying and extending the basic tools to
    financial decision making

34
Financial Decision Making
  • The Investment Decision
  • Invest in assets that earn a return greater than
    the minimum acceptable hurdle rate
  • The Financial Decision
  • Find the right kind of debt for your firm and
    the right mix of debt and equity
  • The Dividend Decision
  • If you cannot find investments that make your
    minimum acceptable rate, return cash to owners of
    your business

35
Quick Outline of Class - Part 2
  • Investment Decision
  • Estimating Hurdle Rate Chapter 3, 4
  • Returns on projects Chapter 5
  • Financial Decision (Capital Structure)
  • Does an optimal mix exist? Chapters 6, 7, 8
  • Matching financing and projects Chapter 9
  • Dividend Decision
  • How much cash is available? Chapter 10
  • How do you return the cash? Chapter 11
  • Introduction to Valuation Chapter 12

36
Goal of Financial Management
  • Maximize the value of the firm as determined by
    the present value of its expected cash flows,
    discounted back at a rate that reflects both the
    riskiness of the firms projects and the financing
    mix used to fund the projects.

37
A Simple Example
  • You deposit 100 today in an account that earns
    5 interest annually for one year.
  • How much will you have in one year?
  • Value in one year Current value interest
    earned
  • 100 100(.05)
  • 100(1.05) 105
  • The 105 next year has a present value of 100 or
  • The 100 today has a future value of 105

38
Calculations
  • 105 100(1.05)
  • or
  • FV PV(1r)
  • Rearranging
  • PV FV/(1r)

39
Present Value and Returns
  • The 105 is discounted to its current value using
    the present value interest factor 1/(1r)
  • The interest rate represents the return you
    receive from waiting for one period to receive
    the 105.
  • The return also represents an amount of risk that
    is associated with the certainty of receiving
    105 in the future.

40
Risk and Return
  • Assume that you have 100 to invest and there are
    two options
  • You can invest it in a savings account that pays
    5 interest (the future return is known with
    certainty)
  • You can loan it to a friend starting a new
    business, if the business fails you get nothing,
    if the business succeeds you get 105
  • Which option would you choose?

41
Risk and Return
  • Consider two other options
  • You can invest it in a savings account that pays
    5 interest (the future return is known with
    certainty)
  • You can loan it to a friend starting a new
    business, if the business fails you get nothing,
    if the business succeeds you get 110
  • Which option would you choose?

42
Rules of Thumb
  • Generally, accepting extra risk is compensated
    with a higher expected return.
  • Most individuals (and financial managers) are
    risk averse They avoid risk, choosing the least
    risky of two alternatives with an equal return.
    However they may be willing to accept extra risk
    if compensated by extra return.

43
Cost of Capital
  • The return represents the return the investor
    expects to earn in return for giving up the 100
    today.
  • The investor is choosing to forego other
    investments
  • For the firm, this represents a cost, the cost of
    borrowing the 100 today and repaying an amount
    in the future.

44
Goal of Financial Management
  • Maximize the value of the firm as determined by
    the present value of its expected cash flows,
    discounted back at a rate that reflects both the
    riskiness of the firms projects and the financing
    mix used to fund the projects.

45
Outline of Class - Part 2Applications of the
Tools

The Investment Decision Allocating scarce
resources among possible projects under certainty
and uncertainty. (estimating future cash flows
and discounting them) The Financing Decision
What mix of Debt and Equity should be used? (the
financing mix) The Dividend Decision How much,
if any should be returned to the shareholders?
46
The Investment Decision
  • The total value of the firm is an aggregate of
    the value of its individual projects.
  • Choosing which projects to undertake will be
    based upon the concepts of present value.

47
The Investment Decision
  • Assume that you know that you can receive a 5
    risk free return by investing in a security.
  • Alternatively, you have a buyer willing to agree
    to pay you 105 at the end of a year for a
    product that you produce. To produce the product
    you need to invest 95 today. Would you be
    willing to pay 95 today to receive the 105?

48
The Investment Decision
  • The decision to invest depends upon the amount it
    would cost you to undertake the project and the
    opportunity cost of capital.
  • Assume for now, that you are certain that the
    buyer will purchase the product, in other words
    the project is risk free.
  • You can also receive a 5 return on a risk free
    security (5 is your opportunity cost of capital)

49
Accepting the project
  • It costs you 95 to undertake the project, if the
    project is undertaken, does firm value increase
    by 10 105 - 95?
  • No, The present value of the project is only 100

50
Net Present Value
  • The Net Present Value represents the increase in
    present value.
  • In this case the NPV is
  • The 5 return represents the opportunity cost of
    capital (the return forgone by investing in the
    project instead of the security)

51
The Investment Decision Again
  • Assume that you again know that you can receive a
    risk free 5 return. Would you be willing to pay
    102 to produce the project today to receive 105
    in one year?
  • No, you just learned that given a 5 return, the
    PV of 105 is 100. The example above is asking
    you to pay 102 for an investment worth 100.

52
Net Present Value
  • The Net Present Value represents the increase in
    present value.
  • In this case the NPV is
  • You would be better off investing in the
    security, with the same risk characteristics that
    pays a 5 return.

53
Net Present Value
  • In the first case you are paying 95 for an
    investment worth 100, you have increased value
    by 5.
  • In the second case you are paying 102 for an
    investment that is worth 100, you have decreased
    value by 2.

54
Net Present Value Rule
  • Accept investments that have a positive net
    present value and reject projects that have a
    negative net present value.

55
Rate of Return Rule
  • The rate of return on the project is based upon
    the investment and the final payoff
  • Accept projects with a Rate of Return greater
    than the opportunity cost of capital

56
Complications
  • Cash flows received from a project usually extend
    for more than one period.
  • How do you measure risk and the appropriate level
    of return?
  • Generally the future cash flows are not known
    with certainty.
  • The return (and riskiness) depends upon the type
    of financing used by the firm.

57
The Investment Decision
  • Assume that still can receive a 5 risk free
    return by investing in a security.
  • Alternatively, you can invest 100 to produce a
    product that will sell for 105 in one year if
    the economy grows at an average pace. If there
    is a recession you will only receive 100. If
    there is fast expansion you will generate 110.

58
Expected Return
  • The expected (or average) return from the project
    is 105 assuming each outcome is equally likely.
  • The 5 return no longer represents the
    opportunity cost of capital. The 5 is a risk
    free return, whether you invest in the project
    should depend upon the initial cost and the
    opportunity cost of capital

59
The Opportunity Cost of Capital
  • Assume that you find a stock selling for 96.33
    with the same outcomes (an expected price of 105
    in normal conditions, 100 in a recession and
    110 in a boom)
  • The expected rate of return on the stock is
  • This is also the Opportunity Cost of Capital

60
The Investment Decision
  • To decide if you want to invest, you need to find
    the NPV of the project.

61
The Investment Decision
  • Assume that the last problem still holds, but the
    risk free rate of interest is 3. A banker
    approaches you and based upon your past history
    offers to loan you 100 at a 4 rate of interest
    to finance the project.
  • The rate of interest is greater than the risk
    free rate (compensating for the risk) Should the
    project be undertaken?

62
Wrong Assumptions
  • Using the 4 as the cost of capital, the NPV of
    the project would be
  • Should the project be accepted?
  • No The opportunity cost of capital is 9, you
    can accept the same risk and have an expected
    return of 9

63
Whats next?
  • More detailed review of time value of money
  • More detailed review of the relationship between
    risk and return

64
Time Value of Money
  • A dollar received (or paid) today is not worth
    the same amount as a dollar to be received (or
    paid) in the future WHY?

You can receive interest on the current dollar
65
A Simple Example Revisited
  • You deposit 100 today in an account that earns
    5 interest annually for one year.
  • How much will you have in one year?
  • Value in one year Current value interest
    earned
  • 100 100(.05)
  • 100(1.05) 105
  • The 105 next year has a present value of 100 or
  • The 100 today has a future value of 105

66
Using a Time Line
  • An easy way to represent this is on a time line
  • Time 0 1 year
  • 5
  • 100 105

Beginning of First Year
End of First year
67
What would the 100 be worth in 2 years?
  • You would receive interest on the interest you
    received in the first year (the interest
    compounds)
  • Value in 2 years Value in 1 year interest
  • 105 105(.05) 105(1.05) 110.25
  • Or substituting 100(1.05) for 105
  • 100(1.05)(1.05)
  • 100(1.05)2 110.25

68
On the time line
  • Time 0 1 2
  • Cash -100 105 110.25
  • Flow

Beginning of year 1
End of Year 1 Beginning of Year 2
End of Year 2
69
Generalizing the Formula
  • 110.25 (100)(1.05)2
  • This can be written more generally
  • Let t The number of periods 2
  • r The interest rate per period .05
  • PV The Present Value 100
  • FV The Future Value 110.25
  • FV PV(1r)t
  • (110.25) (100)(1 0.05)2
  • This works for any combination of t, r, and PV

70
Future Value Interest Factor
  • FV PV(1r)t (1r)t is called the
  • Future Value Interest Factor (FVIFr,t)
  • It can be found using the yx key on your
    calculator

OR (1.05)2 1.1025 Either way original
equation can be rewritten FV PV(1r)t
PV(FVIFr,t) FV100(1.1025) 110.25
71
Calculation MethodsFV PV(1r)t
  • Regular Calculator
  • Financial Calculator
  • Spreadsheet

72
Using a Regular Calculator
  • Calculate the FVIF using the yx key
  • (1.05)21.1025
  • Proceed as Before
  • Plugging it into our equation
  • FV PV(FVIFrr,t)
  • FV 100(1.1025) 110.25

73
Financial Calculator
  • Financial Calculators have 5 TVM keys
  • N Number of Periods 2
  • I interest rate per period 5
  • PV Present Value 100
  • PMT Payment per period 0
  • FV Future Value ?
  • After entering the portions of the problem that
    you know, the calculator will provide the answer

74
Financial Calculator Example
  • On an HP-10B calculator you would enter
  • 2 N 5 I -100 PV 0 PMT FV
  • and the screen shows 110.25

75
Spreadsheet Example
  • Excel has a FV command
  • FV(rate,nper,pmt,pv,type)
  • FV(0.05,2,0,100,0)
  • 110.25
  • note Type refers to whether the payment is at
    the beginning (type 1) or end (type0) of the
    year

76
Calculating Present Value
  • We just showed that FVPV(1r)t
  • This can be rearranged to find PV given FV, r and
    t.
  • Divide both sides by (1r)t
  • which leaves PV FV/(1r)t

77
Example
  • If you wanted to have 110.25 at the end of two
    years and could earn 5 interest on any deposits,
    how much would you need to deposit today?
  • PV FV/(1r)t
  • PV 110.25/(10.05)2 100.00

78
Present Value Interest Factor
  • PV FV/(1r)t 1/(1r)t is called the
  • Present Value Interest Factor (PVIFr,t)
  • PVIFs can be calculated with your calculator

1/(1.05)2 0.907029 The original equation can
be rewritten PV FV/(1r)t FV(PVIFr,t) PV
110.25(.907029) 100
79
Calculating PV of a Single Sum
  • Regular calculator -Calculate PVIF
  • PVIF 1/ (1r)t PV 110.25(0.9070) 100.00
  • Financial Calculator
  • 2 N 5 I - 110.25 FV 0 PMT PV 100.00
  • Spreadsheet
  • Excel command PV(rate,nper,pmt,fv,type)
  • Excel command PV(.05,2,0,110.25,0)100.00

80
Example
  • Assume you want to have 1,000,000 saved for
    retirement when you are 65 and you believe that
    you can earn 10 each year.
  • How much would you need in the bank today if you
    were 25?
  • PV 1,000,000/(1.10)4022,094.93

81
What if you are currently 35? Or 45?
  • If you are 35 you would need
  • PV 1,000,000/(1.10)30 57,308.55
  • If you are 45 you would need
  • PV 1,000,000/(1.10)20 148,643.63
  • This process is called discounting (it is the
    opposite of compounding)

82
Annuities
  • Annuity A series of equal payments made over a
    fixed amount of time. An ordinary annuity makes
    a payment at the end of each period.
  • Example A 4 year annuity that makes 100 payments
    at the end of each year.
  • Time 0 1 2 3 4
  • CFs 100 100 100 100

83
Future Value of an Annuity
  • The FV of the annuity is the sum of the FV of
    each of its payments. Assume 6 a year
  • Time 0 1 2 3 4
  • 100 100 100 100 FV of CF

100(1.06)0100.00
100(1.06)1106.00
100(1.06)2112.36
100(1.06)3119.10
FV 437.4616
84
FV of An Annuity
  • This could also be written
  • FV100(1.06)0 100(1.06)1 100(1.06)2
    100(1.06)3
  • FV100(1.06)0 (1.06)1 (1.06)2(1.06)3
  • or for any n, r, payment, and t

85
FVIF of an Annuity (FVIFAr,t)
  • Just like for the FV of a single sum there is a
    future value interest factor of an annuity
  • This is the FVIFAr,t

86
Calculation Methods
  • Regular calculator -Approximate FVIFA
  • FVIFA (1r)t-1/r FV 100(4.374616)
    437.4616
  • Financial Calculator
  • 4 N 6 I 0 PV -100 PMT FV 437.4616
  • Spreadsheet
  • Excel command FV(rate,nper,pmt,pv,type)
  • Excel command FV(.06,4,100,0,0)437.4616

87
Present Value of an Annuity
  • The PV of the annuity is the sum of the PV of
    each of its payments
  • Time 0 1 2 3 4
  • 100 100 100 100

100/(1.06)194.3396
100/(1.06)288.9996
100/(1.06)383.9619
100/(1.06)479.2094
PV 346.5105
88
PV of An Annuity
  • This could also be written
  • PV100/(1.06)1100/(1.06)2100/(1.06)3100/(1.
    06)4
  • PV1001/(1.06)11/(1.06)21/(1.06)31/(1.06)4
  • or for any r, payment, and t

89
PVIF of an Annuity PVIFAr,t
  • Just like for the PV of a single sum there is a
    future value interest factor of an annuity

This is the PVIFAr,t
90
Calculation Methods
  • Regular calculator -Approximate FVIFA
  • PVIFA (1-1/(1r)t)/r FV 100(3.465105)
    346.5105
  • Financial Calculator
  • 4 N 6 I 0 FV -100 PMT PV 346.5105
  • Spreadsheet
  • Excel command PV(rate,nper,pmt,fv,type)
  • Excel command PV(.06,4,100,0,0)346.5105

91
Annuity Due
  • The payment comes at the beginning of the period
    instead of the end of the period.
  • Time 0 1 2 3 4
  • CFs Annuity 100 100 100 100
  • CFs Annuity Due 100 100 100 100
  • How does this change the calculation methods?

92
FV an PV of Annuity Due
  • FVAnnuity Due There is one more period of
    compounding for each payment, Therefore
  • FVAnnuity Due FVAnnuity(1r)
  • PVAnnuity Due There is one less period of
    discounting for each payment, Therefore
  • PVAnnuity Due PVAnnuity(1r)

93
Uneven Cash Flow Streams
  • What if you receive a stream of payments that are
    not constant? For example
  • Time 0 1 2 3 4
  • 100 100 200 200 FV of CF
  • 200(1.06)0200.00
  • 200(1.06)1212.00
  • 100(1.06)2112.36
  • 100(1.06)3119.10
  • FV 643.4616

94
FV of An Uneven CF Stream
  • The FV is calculated the same way as we did for
    an annuity, however we cannot factor out the
    payment since it differs for each period.

95
PV of an Uneven CF Streams
  • Similar to the FV of a series of uneven cash
    flows, the PV is the sum of the PV of each cash
    flow. Again this is the same as the first step
    in calculating the PV of an annuity the final
    formula is therefore

96
Quick Review
  • FV of a Single Sum FV PV(1r)t
  • PV of a Single Sum PV FV/(1r)t
  • FV and PV of annuities and uneven cash flows are
    just repeated applications of the above two
    equations

97
Perpetuity
  • Cash flows continue forever instead of over a
    finite period of time.

98
Growing Perpetuity
  • What if the cash flows are not constant, but
    instead grow at a constant rate?
  • The PV would first apply the PV of an uneven cash
    flow stream

99
Growing Perpetuity
  • However, in this case the cash flows grow at a
    constant rate which implies
  • CF1 CF0(1g)
  • CF2 CF1(1g) CF0(1g)(1g)
  • CF3 CF2(1g) CF0(1g)3
  • CFt CF0(1g)t

100
Growing Perpetuity
  • The PV is then Given as

101
Semiannual Compounding
  • Often interest compounds at a different rate than
    the periodic rate.
  • For example
  • 6 yearly compounded semiannual
  • This implies that you receive 3 interest each
    six months
  • This increases the FV compared to just 6 yearly

102
Semiannual CompoundingAn Example
  • You deposit 100 in an account that pays a 6
    annual rate (the periodic rate) and interest
    compounds semiannually
  • Time 0 1/2 1 3 3
  • -100 106.09
  • FV100(1.03)(1.03)100(1.03)2106.09

103
Effective Annual Rate
  • The effective Annual Rate is the annual rate that
    would provide the same annual return as the more
    often compounding
  • EAR (1inom/m)m-1
  • m of times compounding per period
  • Our example
  • EAR (1.06/2)2-11.032-1.0609

104
Real and Nominal Rates of Interest
  • The real rate of interest represents the change
    in purchasing power. It is equal to the nominal
    rate of interest adjusted for inflation.
  • 1rnomial(1rreal)(1inflation)
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