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Business 2039 SDE Day 1 Introduction to Finance II

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Title: Business 2039 SDE Day 1 Introduction to Finance II


1
Business 2039 SDE Day 1 Introduction to Finance II
2
First Day - Learning Goals
  • Introduce you to Finance II and expectations
  • Reinforce understanding of the key concepts
    including
  • What does a financial manager do?
  • What skills and knowledge does a financial
    manager require?
  • Normative goal of the financial manager role as
    an agent and trustee for the shareholder
  • Focus of finance on cash flow
  • The need to utilize financial information
    prepared by accountants but understand the
    limitations inherent in those financial
    statements
  • Time value of money skills
  • Valuation skills
  • Project evaluation tools
  • Create awareness of the assumptions underlying
    analytical formula and the resultant need to
    understand algorithms.

Learning Goals
3
Finance II Spring 2010 Evaluation System
4
Attendance
  • Not mandatory
  • Highly recommended
  • Archived lectures available asynchronously

5
Participation
  • Graded 4 observations during the class (every 3
    lectures)
  • Probably easiest to earn during class
  • Outside of class time with key questions
  • Discussion groups be a resource to others.

6
Quizzes
  • Delivered through WebCT
  • Attempt the sample
  • 25 multiple choice questions
  • 1 hour in duration

7
Brief Content
8
Individual Hand-in Assignment
  • Opportunity to apply theory and skills to
    practical problems/situations
  • Follow instructions in the course outline closely
  • Be sure to submit both hard copy and electronic
    version before due date and time (note electronic
    file-naming conventions)
  • You must credit your sources of information.

9
Final Examination
  • Proctored
  • Tuesday, June 15, 2010
  • 600 900 pm
  • 35 of overall grade
  • Comprehensive test of all of 2039

10
Business 2039 Finance II
  • Foundational Concepts

11
Foundational Concepts What Does a Financial
Manager Do?
  • Raise capital to finance operations
  • Manage cash flow
  • Monitor Evaluate corporate performance
  • Critically evaluate business alternatives

Agenda
12
Foundational Concepts What Does a Financial
Manager Do?
  • Raise capital to finance operations
  • Negotiate bank financing (loans, leases, lines of
    credit, letters of credit)
  • Raise capital in the markets
  • Sell commercial paper to investors in the money
    market
  • Sell bonds to investors in the bond market, or
    negotiate private placements
  • Sell new equity to investors in the stock market
  • Decide to retain operating earnings to grow the
    business
  • Sell assets to generate cash
  • Invest surplus funds to generate investment income

Agenda
13
Foundational Concepts What Does a Financial
Manager Do?
  • Manage cash flow
  • Forecast cash inflows and outflows in order to
    predict daily cash balances (cash budgets)
  • Set and evaluate policies credit policies
    (extended to customers)
  • Ensure fixed contractual obligations are
    honoured.

Agenda
14
Foundational Concepts What Does a Financial
Manager Do?
  • Monitor Evaluate corporate performance
  • Forecast budgets for the coming year(s)
  • Compare actual results with budget noting
    variance and taking action as appropriate
  • Ensure economic value-added
  • Risk assessment and management strategies
  • Insurance (manage exposure to pure risk)
  • Derivatives (exchange-rate risk for example)
  • Recommend appropriate risk management policies
  • Employee training/orientation
  • Employee protection policies
  • Internal controls
  • Take corrective action as required

Agenda
15
Foundational Concepts What Does a Financial
Manager Do?
  • Monitor Evaluate corporate performance
  • Critically evaluate business alternatives
  • Recommend corporate divestitures/acquisitions
  • Evaluate expansion proposals

Agenda
16
Foundational Concepts Controllable and
Non-controllable Issues for the Financial Manager
  • Uncontrollable
  • Tax policy
  • Monetary Fiscal Policy of the Government
  • Interest rates
  • Market prices for stock and bonds
  • Exchange rates
  • Inflation
  • Actions of competitors
  • Things Influenced
  • Financial policies practices
  • Investment/divestment decisions
  • Amount of debt undertaken
  • Rate of growth of the firm
  • Risk undertaken by the firm

These are just some simple examples. The point,
however, is that while the financial manager may
not control some thingsshe must still understand
those uncontrollable variables and manage in the
context of them.
Agenda
17
Foundational Concepts What Does a Financial
Manager Need to Know?
  • The financial manager will need knowledge of
  • Insurance
  • Risk management
  • Financial markets
  • Financial Institutions
  • Taxation
  • Law (corporate, contract, securities)
  • Accounting/budgeting/financial statements/auditing
  • Employee Benefits Pensions actuarial sciences
  • Economics (interest rates, markets, inflation)
  • Finance (time value of money, valuation of
    stocks, bonds and money-market instruments, cost
    of capital, capital structure, capital budgeting)

Agenda
18
Foundational Concepts What Skills Does a
Financial Manager Need to Possess?
  • The financial manager will need the following
    skills
  • Soft skills
  • Listening
  • Negotiation
  • Communication (oral and written)
  • Hard skills
  • Financial analysis
  • Budgeting variance analysis
  • Statistical and mathematical skills
  • Spreadsheet modeling

Agenda
19
Lets Take a Look at the Chapters in Your Text
  • Business 2039

20
Foundational Concepts Chapter 1 Introduction to
Finance
  • Introduction to Finance
  • Real Versus Financial Assets
  • The Financial System
  • Financial Instruments and Markets
  • The Global Financial Markets

Agenda
21
Needs of Savers and Borrowers
22
How Do DTIs Meet the Needs of Both Savers and
Borrowers?
  • Pooling of deposits maintaining adequate
    liquidity reserves
  • Expertise in financial contracting
  • Expertise in risk assessment and contract pricing
  • Expertise in contract monitoring
  • Expertise in portfolio management

23
Financial Institutions Types Functions
  • Deposit-Taking Institutions (Banks, Trusts,
    Credit Unions)
  • Lending (consumer and commercial loans
    mortgages)
  • Transaction services (deposits, GICs/Term
    Deposits, savings, chequing accounts,
    money-orders, currency exchange)
  • Insurance Companies (risk offlay and
    intergenerational transfers)
  • Property Casualty Insurers home auto
  • Life Insurance mortalility and morbidity
    (health) products (life insurance, disability
    insurance, accidental death dismemberment,
    critical illness, etc.)
  • Pooled Investment Funds (denomination
    intermediation)
  • Mutual funds ETFs
  • Pension/endowment fund management (Investment
    counsel)
  • Investment Dealers
  • Underwriting
  • Brokerage and wealth management
  • Finance Companies
  • Leasing/lending services

24
Foundational Concepts Chapter 2 Business
(Corporate) Finance
  • Types of Business Organizations
  • Sole Proprietorships
  • Partnerships
  • Trusts
  • Corporations
  • The Goals of the Corporation
  • The Role of Management and Agency Issues
  • Corporate Finance
  • Finance Careers and the Organization of the
    Finance Function

Agenda
25
Foundational Concepts Chapter 3 Financial
Statements
  • Accounting Principles
  • Organizing a Firms Transactions
  • Preparing Accounting Statements
  • The Canadian Tax System
  • Corporate Taxes
  • Personal Taxes

Agenda
26
Foundational Concepts Chapter 4 Financial
Statement Analysis and Forecasting
  • Consistent Financial Analysis
  • A Framework for Financial Analysis
  • Leverage Ratios
  • Efficiency Ratios
  • Productivity Ratios
  • Liquidity
  • Valuation Ratios
  • Financial Forecasting

Agenda
27
Foundational Concepts Chapter 5 The Time Value
of Money
  • Opportunity cost
  • Simple and compound interest
  • The assumptions
  • The formula
  • The implications
  • Using formula, calculations, spreadsheets, tables
  • Compounding and Discounting
  • Finding a future sum
  • Finding a present value
  • Solving for a rate
  • Finding the number of periods
  • Annuities and perpetuities
  • Nominal versus Effective Rates
  • Loan or Mortgage Arrangements

Agenda
28
Foundational Concepts Chapter 6 Bond Valuation
and Interest Rates
  • The Basic Structure of Bonds
  • Bond Valuation
  • Bond Yields
  • Interest Rate Determinants
  • Other Types of Bonds/Debt Instruments

Agenda
29
Foundational Concepts Chapter 7 Equity Valuation
  • Equity Securities
  • Valuation of Equity Securities
  • Preferred Share Valuation
  • Common Share Valuation by Using the DDM
  • Using Multiples to Value Shares The
    Price-Earnings ratio

Agenda
30
Foundational Concepts Chapter 13 Capital
Budgeting, Risk Considerations
  • Project Analysis Tools
  • Net Present Value
  • Payback
  • Discounted payback
  • Internal rate of return
  • Problems with IRR the reinvestment rate
    assumption
  • Where the problem becomes critical
    mutually-exclusive investment proposals where the
    firms cost of capital is less than the crossover
    discount rate
  • Profitability Index
  • Problems with the profitability index
  • How managers use these tools
  • Capital rationing
  • Appropriate discount rate

Agenda
31
Foundational Concepts Chapter 14 Cash Flow
Estimation and Capital Budgeting Decisions
  • General Guidelines
  • Estimating and Discounting Cash Flows
  • Sensitivity to Inputs
  • Replacement Decisions
  • Inflation and Capital Budgeting Decisions

Agenda
32
The Modern Corporation
  • Separation of ownership and management
  • Governance Challenges
  • Executive Compensation

33
What is Profit?
Profit is measured over a period of time ( a
week, a month, a quarter, a year) in absolute
dollars.
34
How Can Profits be Maximized?
Increase Sales
35
What is appropriate Profit?
Depends on amount invested.
If the firm earns 28,220 in annual profit using
2m in assets, the rate of return 1.4
If you earned this profit using 20,000 in
assets, the rate of return 141
36
Appropriate Profit Depends on other Investment
Returns Available AND the risk of the investment!
9 - 9 FIGURE
Security Market Line
Expected Return
M
ERM 8
RF2
ßM 1
ß risk
37
Is Profit Maximization Always in the Best
Interests of the Shareholder?
  • Profits are for one period what about the
    future?
  • What risks have been undertaken in order to
    generate those profits?
  • What are the profits in relation to the capital
    invested?

38
Shareholder Wealth Maximization
  • The value of a stock today is a function of the
    timing, magnitude and riskiness of future cash
    flows.

Value of the stock today
0 1 2 3 4 5 .
39
Risk and Return
40
Security Valuation
  • market values are a function of
  • magnitude
  • timing
  • riskiness
  • of the expected (forecast) cashflows

41
Securities
  • Money market securities
  • Commercial paper/bankers acceptances/treasury
    bills
  • Bonds (long-term debt)
  • preferred stock
  • common stock
  • derivatives
  • rights/warrants/convertibles
  • exchange-traded options

42
Other Topics
  • agency theory
  • income taxation
  • financial institutions and markets
  • cost of capital
  • capital budgeting

43
Key Terms and Definitions
  • Corporation
  • Agency costs
  • Information asymmetry
  • Profit-maximization
  • Shareholder wealth maximization

Terms
44
In summary you have
  • Refreshed your knowledge of the key underlying
    concepts and skills of finance.
  • learned that profit-maximization is not an
    appropriate long-term goal for a financial
    manager
  • learned that shareholder wealth maximization
    takes into account the timing, magnitude and
    riskiness of all net cash flow benefits the
    shareholder might expect to receive from their
    investment.
  • learned that finance focuses on cash flow.
  • Learned that the time value of money concept
    should be applied in any longer term financial
    decision.

Summary
45
Internet Links and On Line Resources
  • ? Treasury Management Association of Canada
  • ? Canadian Tire
  • ? Air Canada
  • ? Dominion Bond Rating Service
  • ? Standard and Poors

Web Links
46
Time Value of Money Concepts
  • Business 2039

47
Concepts and Terms
  • Simple interest
  • Compound interest
  • Compounding
  • Annuity
  • Discounting a single cash flow
  • Discounting an annuity
  • Discounting a growing annuity
  • Loan amortization tables
  • More frequent compounding
  • Calculating
  • Time
  • Rate
  • Present value
  • Ex ante
  • Ex post

48
Interest
  • Time Value of Money Skills

49
Interest
  • The charge for the privilege of borrowing money
  • Usually expressed as an annual percentage rate.
  • Lenders charge interest for the use of their
    moneyborrowers pay the lend for the privilege.

50
Interest
  • Invest 10,000 _at_ 8 for one year
  • Interest earned by the lender by the end of one
    year
  • 1,000 .08 80

51
Simple Interest
  • Invest 10,000 _at_ 8 for one year
  • Interest and principle forecast at end of one
    year
  • (1,000 .08) 1,000 1,080
  • 1,000 (1 .08) 1,080

52
Simple Interest
  • A General Formula (one year)
  • Future Value (1,000 .08) 1,000 FV
    1,080
  • FV 1,000 (1r)
  • FV C (1r)

53
Simple Interest
  • Simple interest assumes that when interest is
    received at the end of the investment period, the
    interest is removed from the investmentand only
    the original principle is invested in the next
    period.

54
Compounding
  • Time Value of Money Skills

55
Compound Interest
  • Compound interest assumes that when interest is
    received at the end of the investment period, the
    interest is reinvested together with the original
    principle.
  • This means that in each successive period,
    interest is earned on both the original principal
    as well as the accumulated interest of prior
    periods.

56
Compound Interest
  • How much will you have in (at the end of) two
    years?
  • Future Value2 1,000 (1r1) (1r2)
  • FV2 1,000 (1.08)(1.08)
  • FV2 1,000 (1.08)2
  • FV2C(1r)t

57
Compound Interest
  • Notice the compound interest assumptions that are
    embodied in the basic formula
  • Future Value2 1,000 (1r1) (1r2)
  • FVt C (1r)t
  • Assumptions
  • The rate of interest does not change over the
    periods of compound interest
  • Interest is earned and reinvested at the end of
    each period
  • The principal remains invested over the life of
    the investment
  • The investment is started at time 0 (now) and we
    are determining the compound value of the whole
    investment at the end of some time period (t
    1, 2, 3, 4,)

58
Compound Interest
59
Compound Interest Formula (For a single cash flow)
  • FVtC(1r)t
  • Where
  • FVt the future value (sum of both interest and
    principal) of the investment at some time in the
    future
  • C the original principal invested
  • r the rate of return earned on the investment
  • t the time or number of periods the investment
    is allowed to grow

60
Compound Interest Formula (For a single cash flow)
  • FVtC(1r)t
  • (1r)t is known as the future value interest
    factor FVIFr,t

61
FVIFr,t (For a single cash flow)
  • Tables of future value interest factors can be
    created

62
FVIFr,t (For a single cash flow)
  • The table shows that the longer you investthe
    greater the amount of money you will accumulate.
  • It also shows that you are better off investing
    at higher rates of return.

63
FVIFr,t (For a single cash flow)
  • How long does it take to double or triple your
    investment? At 5...at 10?

64
The Rule of 72
  • If you dont have access to time value of money
    tables or a financial calculator but want to know
    how long it takes for your money to doubleuse
    the rule of 72!

65
FVIFr,t (For a single cash flow)
  • Let us predict what happens with an investment if
    it is invested at 5 show the accumulated value
    after t1, t2, t3, etc.

66
FVIFr,t (For a single cash flow)
  • Let us predict what happens with an investment if
    it is invested at 5 and 10 show the
    accumulated value after t1, t2, t3, etc.

Notice compound interest creates an exponential
curve and there will be a substantial difference
over the long term when you can earn higher rates
of return.
67
Types of Problems in Compounding
  • Time Value of Money Skills

68
Types of Compounding Problems
  • There are really only four different things you
    can be asked to find using this basic equation
  • FVtC(1r)t
  • Find the initial amount of money to invest (C)
  • Find the Future value (FVt)
  • Find the rate (r)
  • Find the time (t)

69
Types of Compounding Problem Finding the amount
of money to invest
  • You hope to save for a down payment on a home.
    You hope to have 40,000 in four years time
    determine the amount you need to invest now at 6
  • FVtC(1r)t
  • 40,000 C (1.1)4
  • 40,000/1.464127,320.53

70
Types of Compounding Problem Finding the rate
  • Your have asked your father for a loan of 10,000
    to get you started in a business. You promise to
    repay him 20,000 in five years time.
  • What compound rate of return are you offering to
    pay?
  • FVtC(1r)t
  • 20,000 10,000 (1r)5
  • 2(1r)5
  • 21/51r
  • 1.148691r
  • r 14.869

71
Types of Compounding Problem Finding the time
  • You have 150,000 in your RRSP (Registered
    Retirement Savings Plan). Assuming a rate of 8,
    how long will it take to have the plan grow to a
    value of 300,000?
  • FVtC(1r)t
  • 300,000 150,000 (1.08)t
  • 2(1.08)t
  • ln 2 ln 1.08 t
  • 0.69314 .07696 t
  • t 0.69314 / .076961041 9.006375057 years

72
Types of Compounding Problem Finding the time
using logarithms
  • You have 150,000 in your RRSP (Registered
    Retirement Savings Plan). Assuming a rate of 8,
    how long will it take to have the plan grow to a
    value of 300,000?
  • FVtC(1r)t
  • 300,000 150,000 (1.08)t
  • 2(1.08)t
  • log 2 log 1.08 t
  • 0.301029995 0.033423755 t
  • t 9.006468453 years

73
Types of Compounding Problem Finding the future
value
  • You have 650,000 in your pension plan today.
    Because you have retired, you and your employer
    will not make any further contributions to the
    plan. However, you dont plan to retire for five
    more years so the principal will continue to
    grow.
  • Assuming a rate of 8, forecast the value of your
    pension plan in 5 years.
  • FVtC(1r)t
  • FV5 650,000 (1.08)5
  • FV5 650,000 1.469328077
  • FV5 955,063.25

74
Annuities
  • Time Value of Money Concepts - 2039

75
Annuity
  • An annuity is a finite series of equal and
    periodic cash flows.

76
Annuities - example
  • You save an equal amount each month over a given
    period of time.

77
Annuity
An annuity is a finite series of equal and
periodic cash flows where C1C2C3Ct
78
Future Value of An Annuity
  • An example of a compound annuity would be where
    you save an equal sum of money in each period
    over a period of time to accumulate a future sum.

79
Future Value of An Annuity
  • The formula for the Future Value of an annuity
    (FVAt) is

80
Future Value of An Annuity
Example How much will you have at the end of
three years if you save 1,000 each year for
three years at a rate of 10? FVA3 1,000
(1.1)3 - 1.1 1,000 3.31 3,310
81
Future Value of An Annuity
Example How much will you have at the end of
three years if you save 1,000 each year for
three years at a rate of 10? FVA3 1,000
(1.1)3 - 1 / .1 1,000 3.31
3,310 What does the formula assume? 1,0001
(1.1) (1.1) 1,210 1,0002 (1.1)
1,100 1,0003
1,000 Sum 3,310
82
Future Value of An Annuity Assumptions
FVA3 1,000 (1.1)3 - 1.1 1,000 3.31
3,310 What does the formula assume?
1,0001 (1.1) (1.1) 1,210 1,0002
(1.1) 1,100 1,0003
1,000 Sum
3,310 The FVIFA assumes that time zero (t0)
(today) you decide to invest, but you dont make
the first investment until one year from today.
The Future Value you forecast is the value of the
entire fund (a series of investments together
with the accumulated interest) at the end of some
year t 1 or t 2 in this case t 3. NOTE
the rate of interest is assumed to remain
unchanged throughout the forecast period.
If these assumptions dont holdyou cant use the
formula.
83
Adjusting your solution to the circumstances of
the problem
  • The time value of money formula can be applied to
    any situationwhat you need to do is to
    understand the assumptions underlying the
    formulathen adjust your approach to match the
    problem you are trying to solve.
  • In the foregoing problemít isnt too logical to
    start a savings programand then not make the
    first investment until one year later!!!

84
Example of Adjustment (An annuity due)
  • You plan to invest 1,000 today, 1,000 one year
    from today and 1,000 two years from today.
  • What sum of money will you accumulate if your
    money is assumed to earn 10.
  • This is known as an annuity due rather than a
    regular annuity.

85
Example of Adjustment (An annuity due)
  • You plan to invest 1,000 today, 1,000 one year
    from today and 1,000 two years from today.
  • What sum of money will you accumulate if your
    money is assumed to earn 10.
  • You should know that there is a simple way of
    adjusting a normal annuity to become an annuity
    duejust multiply the normal annuity result by
    (1r) and you will convert to an annuity due!
  • FVA3 (Annuity due) 1,000 (1.1)3 - 1.1
    (1 r) 1,000 3.31 1.1 3,310 1.1
    3,641

1,0001 (1.1) (1.1) (1.1) 1,331
1,0002 (1.1) (1.1) 1,210
1,0003 (1.1) 1,100 Sum
3,641
86
Discounting Cash Flows
  • Time Value of Money

87
What is Discounting?
  • Discounting is the inverse of compounding.

88
Example of Discounting
  • You will receive 10,000 one year from today.
    If you had the money today, you could earn 8 on
    it.
  • What is the present value of 10,000 today at 8?
  • PV0FV1 PVIFr,t 10,000 (1/ 1.081)
  • PV0 10,000 0.9259 9,259.26
  • NOTICE A present value is always less than the
    absolute value of the cash flow unless there is
    no time value of money. If there is no rate of
    interest then PV FV

89
PVIFr,t (For a single cash flow)
  • Tables of present value interest factors can be
    created

90
PVIFr,t (For a single cash flow)
  • Notice the farther away the receipt of the cash
    flow from todaythe lower the present value
  • Notice the higher the rate of interestthe
    lower the present value.

91
PVIFr,t (For a single cash flow)
  • If someone offers to pay you a sum 50 or 60 years
    hencethat promise is pretty-much worthless!!!

The present value of 10 million promised 100
years from today at a 10 discount rate is
10,000,000 0.0001 1,000!!!!
92
The Reinvestment Rate
  • Business 2039

93
The Nature of Compound Interest
  • When we assume compound interest, we are
    implicitly assuming that any credited interest is
    reinvested in the next period, hence, the growth
    of the fund is a function of interest on the
    principal, and a growing interest upon interest
    stream.
  • This principal is demonstrated when we invest
    10,000 at 8 per annum over a period of say 4
    yearsthe terminal value of this investment can
    be decomposed as follows...

94
FV4 of 10,000 _at_ 8
Of course we can find the answer using the
formula FV4 10,000(1.08)4 10,000(1.36048896
) 13,604.89
95
Annuity Assumptions
  • When using the unadjusted formula or table values
    for annuities (whether future value or present
    value) we always assume
  • the focal point is time 0
  • the first cash flow occurs at time 1
  • intermediate cash flows are reinvested at the
    rate of interest for the remaining time period
  • the interest rate is unchanging over the period
    of the analysis.

96
FV of an Annuity Demonstrated
When determining the Future Value of an
Annuitywe assume we are standing at time zero,
the first cash flow will occur at the end of the
year and we are trying to determine the
accumulated future value of a series of five
equal and periodic payments as demonstrated in
the following time line...
97
FV of an Annuity Demonstrated
We could be trying find out how much we would
accumulate in a savings fundif we saved 2,000
per year for five yearsbut we wont make the
first deposit in the fund for one year...
98
FV of an Annuity Demonstrated
The time value of money formula assumes that each
payment will be invested at the going rate of
interest for the remaining time to maturity.
99
FV of an Annuity Demonstrated
100
FV of an Annuity Demonstrated
101
FV of an Annuity Demonstrated
  • In summary the assumptions are
  • focal point is time zero
  • we assume the cash flows occur at the end of
    every year
  • we assume the interest rate does not change
    during the forecast period
  • the interest received is reinvested at that same
    rate of interest for the remaining time until
    maturity.

102
PV of an Annuity Demonstrated
103
Bond Valuation
  • 2019 Review

104
Bond Value General Formula
Where I interest (or coupon ) payments kb
the bond discount rate (or market rate) n the
term to maturity F Face (or par) value of the
bond
105
Bond Valuation Example
  • What is the market price of a ten year, 1,000
    bond with a 5 coupon, if the bonds
    yield-to-maturity is 6?

Calculator Approach 1,000 FV 50 PMT 10 N I/Y
6 CPT PV 926.40
106
Bond Valuation Semi-Annual Coupons
  • For example, suppose you want to value a 5 year,
    10,000 Government of Canada bond with a 4
    coupon, paid twice a year, given a YTM of 6.

Calculator Approach 10,000 FV 400 2 PMT 5
x 2 N 6 2 I/Y CPT PV 926.40
107
Bond Yield to Maturity
  • The yield to maturity is that discount rate that
    causes the sum of the present value of promised
    cash flows to equal the current bond price.

108
Solving for YTM
  • To solve for YTM, solve for YTM in the following
    formula
  • There is a Problem
  • You cant solve for YTM algebraically therefore,
    must either use a financial calculator, Excel,
    trial error or approximation formula.

109
Solving for YTM
  • Example What is the YTM on a 10 year, 5 coupon
    bond (annual pay coupons) that is selling for
    980?
  • Financial Calculator
  • 1,000 FV
  • 980 /- PV
  • PMT
  • N
  • I/Y 5.26

110
Solving for YTM Semi-annual Coupons
  • When solving for YTM with a semi-annual pay
    coupon, the yield obtained must be multiplied by
    two to obtain the annual YTM
  • Example What is the YTM for a 20 year, 1,000
    bond with a 6 coupon, paid semi-annually, given
    a current market price of 1,030?

111
Solving for YTM Semi-annual Coupons
What is the YTM for a 20 year, 1,000 bond with a
6 coupon, paid semi-annually, given a current
market price of 1,030?
Financial Calculator 1,000 FV 1,030 /- PV 30
PMT 40 N I/Y 2.87 x
2 5.746
112
Using the Approximation Formula to Solve for
Yield to Maturity
  • Bond Valuation and Interest Rates

113
The Approximation Formula
  • This formula gives you a quick estimate of the
    yield to maturity
  • It is an estimate because it is based on a linear
    approximation (again you will remember the
    exponential nature of compound interest)
  • Should you be concerned with the error
    inherent in the approximated YTM?
  • NO
  • Remember a YTM is an ex ante calculation as a
    forecast, it is based on assumptions which may or
    may not hold in this case, therefore as a
    forecast or estimate, the approximation approach
    should be fine.

114
The Approximation Formula
  • F Face Value Par Value 1,000
  • B Bond Price
  • I the semi annual coupon interest
  • N number of semi-annual periods left to
    maturity

115
Example
  • Find the yield-to-maturity of a 5 year 6 coupon
    bond that is currently priced at 850. (Always
    assume the coupon interest is paid
    semi-annually.)
  • Therefore there is coupon interest of 30 paid
    semi-annually
  • There are 10 semi-annual periods left until
    maturity

116
Example with Solution
  • Find the yield-to-maturity of a 5 year 6 coupon
    bond that is currently priced at 850. (Always
    assume the coupon interest is paid semi-annually.)

The actual answer is 9.87...so of course, the
approximation approach only gives us an
approximate answerbut that is just fine for
tests and exams.
117
The Logic of the Equation Approximation Formula
for YTM
  • The numerator simply represents the average
    semi-annual returns on the investmentit is made
    up of two components
  • The first component is the average capital gain
    (if it is a discount bond) or capital loss (if it
    is a premium priced bond) per semi-annual period.
  • The second component is the semi-annual coupon
    interest received.
  • The denominator represents the average price of
    the bond.
  • Therefore the formula is basically, average
    semi-annual return on average investment.
  • Of course, we annualize the semi-annual return so
    that we can compare this return to other returns
    on other investments for comparison purposes.

118
Yield to Maturity
119
Yield to Maturity ...
120
Yield to Maturity ...
121
Yield to Maturity ...
122
Yield to Maturity ...
Now instead of earning 9.2 she will only earn
8.478 because of the poor reinvestment rate
opportunities.
123
The Reinvestment Rate Assumption
  • It is crucial to understand the reinvestment rate
    assumption that is built-in to the time value of
    money.
  • Obviously, when we forecast, we must make
    assumptionshowever, if that assumption not
    realisticit is important that we take it into
    account.
  • This reinvestment rate assumption in particular,
    is important in the yield-to-maturity
    calculations in bondsand in the Internal Rate of
    Return (IRR) calculation in capital budgeting.

124
Bond Applications
  • Bonds are typically purchased by life insurance
    companies.
  • These firms plan to buy and hold the bonds until
    they mature.
  • These firms require a given return in order to
    accumulate a terminal value 20, 25 or 30 years
    out into the future.however, they are acutely
    aware that the reinvestment of the coupon
    interest can dramatically affect their realized
    return (making it different than the
    yield-to-maturity.)\
  • They have some alternativeschoose zero coupon
    bonds, or immunize themselves from interest rate
    fluctuations (using duration matching strategies)

125
Bond Pricing Theorums
  • Malkiel Theorums

126
Theorums about Bond Prices
  • 1. Bond prices move inversely to bond yields.
  • 2. For any given difference between the coupon
    rate and the yield to maturity, the accompanying
    price change will be greater, the longer the term
    to maturity (long-term bond prices are more
    sensitive to interest rates changes than
    short-term bond prices).

127
Theorums about Bond Prices
  • 3. The percentage change described in theorum 2
    increases at a diminishing rate as n increases.
  • 4.For any given maturity, a decrease in yields
    causes a capital gain which is larger than the
    capital loss resulting from an equal increase in
    yields.

128
Theorums about Bond Prices
  • 5. The higher the coupon rate on a bond, the
    smaller will be the percentage change for any
    given change in yields.

129
Theorum Implications
  • 1. It is best to buy into the bond market at the
    peak of an interest rate cycle.
  • Because
  • as interest rates fall, bond prices will rise
    and the investor will receive capital gain (this
    is important for investors with investment time
    horizons that are shorter than the term remaining
    to maturity of the bond.)

130
Theorum Implications
  • 1. It is best to buy into the bond market at the
    peak of an interest rate cycle.
  • Because
  • the bond will be priced to offer a high yield to
    maturity. If your investment time horizon
    matches the term to maturity for the bond, then
    holding the bond till it matures should offer you
    a high rate of return. (If it is a high coupon
    bond, though, you will have to reinvest those
    coupons when received a the going rate of
    interest. If it is a stripped bond, then there
    would be no interest rate risk and the ex ante
    yield to maturity will equal the ex post yield.

131
Theorum Implications
  • 1. When you expect a rise in interest rates,
    sell short/leave the market/move to bonds with
    fewer years to maturity.
  • Because if rates rise, then you will experience
    capital losses on the bond. Of course, paper
    capital losses may not be particularly relevant
    if your investment time horizon equals the term
    to maturity because, as the maturity date
    approaches, the bond price will approach its par
    value regardless of prevailing interest rates.

132
Theorum Implications
  • 2. If interest rates go up your capital losses
    will be smaller if you are in the short end of
    the market.
  • So your choice of investing in bonds with short
    or long-terms to maturity should be influenced by
    your expectations for changes in interest rates.
    If you think rates will rise (and bond prices
    fall) invest short term. If you think rates will
    fall (and bond prices rise) then invest in
    long-term bonds. (The foregoing assumes that you
    are not interested in purely immunizing your
    position.

133
Theorum Implications
  • 2. If you are at the peak of the short-term
    interest rate cycle, buying into the long end of
    the market will bring you the greatest returns.

134
Theorum Implications
  • 3 It is not necessary to buy the longest term to
    get large price fluctuations.

135
Theorum Implications
  • 4 For a given change in interest rates an
    investor will receive a greater capital gain when
    rates fall and he/she is in a long position, than
    if he/she is short and interest rates rise.

136
Theorum Implications
  • 5 Bonds with low coupon rates have more price
    volatility (bond price elasticity) than bonds
    with high coupon rates, other things being equal.
  • It follows, that stripped bonds have the
    greatest interest rate elasticity.

137
How a change in interest rates affects market
prices for bonds of varying lengths of maturity.
138
Internal Rate of Return and MIRR
139
The Modified IRR
  • Since the IRR result can inappropriately bias
    decision-makers when using the IRR approach, the
    MIRR has been developed.
  • Under the MIRR, the intermediate cashflows are
    compounded to the end of the useful life of the
    project at the firms weighted average cost of
    capital (a realistic, and generally achievable
    rate) and then the initial cost of the project is
    equated with the total accumulated terminal
    value, solving for the rate of return that make
    the two equalthat is the MIRR.
  • The MIRR avoids the exaggerated reinvestment rate
    assumption that underlys the IRR approachand
    instead assumes a reinvestment rate assumption
    that is conservative and achievablethe WACC.
  • Remember, decision makers like to use rates of
    returnmost dont understand the meaning of an
    NPV 100,000!!!!

140
The Modified IRR an example
Let us assume a capital project with an initial
cost of 1,000,000 and annual net incremental
after tax cash flow benefits of 300,000 and a
useful life of 5 years. If the firms WACC is 10
what is the projects MIRR?
Step one is to forecast the total accumulated
value of the ATCF benefits of the project.
141
The Modified IRR an example
The second step is to equate the cost of the
project with the accumulated future value of the
projectand solve for the discount rate that
equates the two. The discount rate is your MIRR.
142
Yield to Maturity The Approximation Approach
  • Business 2039

143
The Approximation Formula
  • F Face Value Par Value 1,000
  • P Bond Price
  • C the semi annual coupon interest
  • N number of semi-annual periods left to
    maturity

144
Example
  • Find the yield-to-maturity of a 5 year 6 coupon
    bond that is currently priced at 850. (Always
    assume the coupon interest is paid
    semi-annually.)
  • Therefore there is coupon interest of 30 paid
    semi-annually
  • There are 10 semi-annual periods left until
    maturity

145
Example with solution
  • Find the yield-to-maturity of a 5 year 6 coupon
    bond that is currently priced at 850. (Always
    assume the coupon interest is paid semi-annually.)

The actual answer is 9.87...so of course, the
approximation approach only gives us an
approximate answerbut that is just fine for
tests and exams.
146
The logic of the equation
  • The numerator simply represents the average
    semi-annual returns on the investmentit is made
    up of two components
  • The first component is the average capital gain
    (if it is a discount bond) or capital loss (if it
    is a premium priced bond) per semi-annual period.
  • The second component is the semi-annual coupon
    interest received.
  • The denominator represents the average price of
    the bond.
  • Therefore the formula is basically, average
    semi-annual return on average investment.
  • Of course, we annualize the semi-annual return so
    that we can compare this return to other returns
    on other investments for comparison purposes.

147
Loan Amortization Schedules
  • Business 2039

K. Hartviksen
148
Blended Interest and Principal Loan Payments -
formula
Where Pmt the fixed periodic payment t the
amortization period of the loan r the rate of
interest on the loan
149
Blended Interest and Principal Loan Payments -
example
Where Pmt unknown t 20 years r 8
150
Blended Interest and Principal Loan Payments -
example
Where Pmt unknown t 20 years r 8
This assumes you make annual payments on this
loanmost financial institutions want to see
monthly payments.
151
Loan Amortization Tables
  • It is often useful to break down the loan payment
    into its constituent parts.

152
How are Loan Amortization Tables Used?
  • To separate the loan repayments into their
    constituent components.
  • Each level payment is made of interest plus a
    repayment of principal outstanding on the loan.
  • This is important to do when the loan has been
    taken out for the purposes of earning taxable
    incomeas a result, the interest is a
    tax-deductible expense.

K. Hartviksen
153
Loan Amortization Tables
K. Hartviksen
154
Loan Amortization Example
In the third year, 800 of interest is paid.
Total interest over the life of the loan 2,400
1,600 800 4,800
155
Net Present Value and Other Investment Criteria
  • Business 2039

1
K. Hartviksen
156
This Chapter - Topics
  • Net Present Value
  • Payback Period
  • Discounted Payback
  • Average Accounting Return
  • Internal Rate of Return
  • Multiple IRRs
  • Mutually Exclusive Investments (NPV vs. IRR)
  • Profitability Index
  • capital rationing

2
K. Hartviksen
157
Long-Term Investments
  • When a firm considers a new project, corporate
    acquisition, plant expansion or asset acquisition
    that will produce income over the course of many
    yearsthis is called capital budgeting.
  • It is imperative that in the analysis of such
    projects that we consider the timing, riskiness
    and magnitude of the incremental, after-tax
    cashflows that the project is expected to
    generate for the firm.

158
Payback Method
  • This is a simple approach to capital budgeting
    that is designed to tell you how many years it
    will take to recover the initial investment.
  • It is often used by financial managers as one of
    a set of investment screens, because it gives the
    manager an intuitive sense of the projects risk.

159
Payback Example
160
Discounted Payback Example
161
Discounted Payback Graphed
162
Discounted Payback
  • Overcomes the lack of consideration of the time
    value of money
  • can help us see the pattern of cashflows beyond
    the payback point.
  • If carried to the end of the projects useful
    lifewill tell us the projects NPV (if you are
    using the firms WACC)

163
Average Accounting Return
  • ARR Average Accounting Profit
  • Average Accounting Value
  • This flawed approachis presented only to alter
    you to its disadvantages and have you avoid its
    use in practice.

164
Net Present Value
  • NPV -PV of initial cost PV of incremental
    after-tax benefits
  • if greater than 0 - accept
  • if equal to 0 - indifferent
  • if less than 0 - reject

165
Firms Cost of Capital
  • At this point in the course, you will be given
    the firms cost of capital
  • the firms cost of capital determines the minimum
    rate of return that would be acceptable for a
    capital project.
  • The weighted average cost of capital (WACC) is
    the relevant discount rate for NPV analysis.

166
NPV Example
167
NPV Example
168
NPV Example
169
NPV Example
170
NPV Example
171
NPV Example
172
NPV Example
173
NPV Profile
174
NPV Profiles
  • The slope of the NPV profile depends on the
    timing and magnitude of cashflows.
  • Projects with cashflows that occur late in the
    projects life will have an NPV that is more
    sensitive to discount rate changes.

175
IRR
  • The internal rate of return (IRR) is that
    discount rate that causes the NPV of the project
    to equal zero.
  • If IRR gt WACC, then the project is acceptable
    because it will return a rate of return on
    invested capital that is likely to be greater
    than the cost of funds used to invest in the
    project.

176
IRR Example
177
IRR Example
178
IRR vs. NPV
  • Both methods use the same basic decision inputs.
  • The only difference is the assumed discount rate.
  • The IRR assumes intermediate cashflows are
    reinvested at IRRNPV assumes they are reinvested
    at WACC

179
NPV Profile
180
Profitability Index
  • Uses exactly the same decision inputs as NPV
  • simply expresses the relative profitability of
    the projects incremental after-tax cashflow
    benefits as a ratio to the projects initial
    cost.
  • PI PV of incremental ATCF benefits
  • PV of initial cost of project
  • If PIgt1, then we accept because the PV of
    benefits exceeds the PV of costs.

181
Capital Rationing
  • The corporate practice of limiting the amount of
    funds dedicated to capital investments in any one
    year.
  • Is academically illogical.
  • In the long-run could threaten a firms
    continuing existence through erosion of its
    competitive position.

182
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