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Business 2039 SDE Day 1 Introduction to Finance II

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

Finance II Spring 2010 Evaluation System

Attendance

- Not mandatory
- Highly recommended
- Archived lectures available asynchronously

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.

Quizzes

- Delivered through WebCT
- Attempt the sample
- 25 multiple choice questions
- 1 hour in duration

Brief Content

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.

Final Examination

- Proctored
- Tuesday, June 15, 2010
- 600 900 pm
- 35 of overall grade
- Comprehensive test of all of 2039

Business 2039 Finance II

- Foundational Concepts

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

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

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

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

Foundational Concepts What Does a Financial

Manager Do?

- Monitor Evaluate corporate performance
- Critically evaluate business alternatives
- Recommend corporate divestitures/acquisitions
- Evaluate expansion proposals

Agenda

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

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

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

Lets Take a Look at the Chapters in Your Text

- Business 2039

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

Needs of Savers and Borrowers

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

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

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

Foundational Concepts Chapter 3 Financial

Statements

- Accounting Principles
- Organizing a Firms Transactions
- Preparing Accounting Statements
- The Canadian Tax System
- Corporate Taxes
- Personal Taxes

Agenda

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

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

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

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

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

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

The Modern Corporation

- Separation of ownership and management
- Governance Challenges
- Executive Compensation

What is Profit?

Profit is measured over a period of time ( a

week, a month, a quarter, a year) in absolute

dollars.

How Can Profits be Maximized?

Increase Sales

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

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

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?

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 .

Risk and Return

Security Valuation

- market values are a function of
- magnitude
- timing
- riskiness
- of the expected (forecast) cashflows

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

Other Topics

- agency theory
- income taxation
- financial institutions and markets
- cost of capital
- capital budgeting

Key Terms and Definitions

- Corporation
- Agency costs
- Information asymmetry
- Profit-maximization
- Shareholder wealth maximization

Terms

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

Internet Links and On Line Resources

- ? Treasury Management Association of Canada
- ? Canadian Tire
- ? Air Canada
- ? Dominion Bond Rating Service
- ? Standard and Poors

Web Links

Time Value of Money Concepts

- Business 2039

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

Interest

- Time Value of Money Skills

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.

Interest

- Invest 10,000 _at_ 8 for one year
- Interest earned by the lender by the end of one

year - 1,000 .08 80

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

Simple Interest

- A General Formula (one year)
- Future Value (1,000 .08) 1,000 FV

1,080 - FV 1,000 (1r)
- FV C (1r)

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.

Compounding

- Time Value of Money Skills

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.

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

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,)

Compound Interest

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

Compound Interest Formula (For a single cash flow)

- FVtC(1r)t
- (1r)t is known as the future value interest

factor FVIFr,t

FVIFr,t (For a single cash flow)

- Tables of future value interest factors can be

created

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.

FVIFr,t (For a single cash flow)

- How long does it take to double or triple your

investment? At 5...at 10?

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!

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.

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.

Types of Problems in Compounding

- Time Value of Money Skills

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)

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

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

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

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

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

Annuities

- Time Value of Money Concepts - 2039

Annuity

- An annuity is a finite series of equal and

periodic cash flows.

Annuities - example

- You save an equal amount each month over a given

period of time.

Annuity

An annuity is a finite series of equal and

periodic cash flows where C1C2C3Ct

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.

Future Value of An Annuity

- The formula for the Future Value of an annuity

(FVAt) is

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

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

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.

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!!!

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.

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

Discounting Cash Flows

- Time Value of Money

What is Discounting?

- Discounting is the inverse of compounding.

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

PVIFr,t (For a single cash flow)

- Tables of present value interest factors can be

created

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.

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!!!!

The Reinvestment Rate

- Business 2039

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...

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

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.

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...

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...

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.

FV of an Annuity Demonstrated

FV of an Annuity Demonstrated

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.

PV of an Annuity Demonstrated

Bond Valuation

- 2019 Review

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

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

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

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.

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.

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

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?

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

Using the Approximation Formula to Solve for

Yield to Maturity

- Bond Valuation and Interest Rates

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.

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

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

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.

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.

Yield to Maturity

Yield to Maturity ...

Yield to Maturity ...

Yield to Maturity ...

Yield to Maturity ...

Now instead of earning 9.2 she will only earn

8.478 because of the poor reinvestment rate

opportunities.

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.

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)

Bond Pricing Theorums

- Malkiel Theorums

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).

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.

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.

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.)

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.

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.

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.

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.

Theorum Implications

- 3 It is not necessary to buy the longest term to

get large price fluctuations.

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.

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.

How a change in interest rates affects market

prices for bonds of varying lengths of maturity.

Internal Rate of Return and MIRR

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!!!!

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.

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.

Yield to Maturity The Approximation Approach

- Business 2039

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

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

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.

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.

Loan Amortization Schedules

- Business 2039

K. Hartviksen

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

Blended Interest and Principal Loan Payments -

example

Where Pmt unknown t 20 years r 8

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.

Loan Amortization Tables

- It is often useful to break down the loan payment

into its constituent parts.

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

Loan Amortization Tables

K. Hartviksen

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

Net Present Value and Other Investment Criteria

- Business 2039

1

K. Hartviksen

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

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.

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.

Payback Example

Discounted Payback Example

Discounted Payback Graphed

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)

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.

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

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.

NPV Example

NPV Example

NPV Example

NPV Example

NPV Example

NPV Example

NPV Example

NPV Profile

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.

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.

IRR Example

IRR Example

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

NPV Profile

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.

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.

THE END!