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CHAPTER 1

Overview of Financial

Management and the FinancialEnvironment

Prof. Steve Lebischak

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Topics in Chapter Forms of business organization

Objective of the firm: Maximize wealth

Determinants of fundamental value

Financial securities, markets andinstitutions

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Why is corporate finance

important to all managers? Corporate finance provides the skills

managers need to:

Identify and select the corporate strategiesand individual projects that add value totheir firm.

Forecast the funding requirements of theircompany, and devise strategies foracquiring those funds.

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Business Organization from Start-

up to a Major Corporation

Sole proprietorship

Partnership Corporation

(More . .)

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Starting as a ProprietorshipAdvantages:

Ease of formation

Subject to few regulations

No corporate income taxes

Disadvantages:

Limited life Unlimited liability

Difficult to raise capital to support growth

80% of businesses, 13% of sales

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Starting as or Growing into a

PartnershipA partnership has roughly the same

advantages and disadvantages as a soleproprietorship.

Limited Partner, GP, LLC

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Becoming a CorporationA corporation is a legal entity separate

from its owners and managers.

File papers of incorporation with state.

Charter

Bylaws

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Advantages and Disadvantages of

a CorporationAdvantages:

Unlimited life

Easy transfer of ownership

Limited liability

Ease of raising capital limited liability forinvestors

Disadvantages: Double taxation

Cost of set-up and report filingVirginia 3 to 10 days to set up, $5000

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Becoming a Public Corporation

and Growing Afterwards Initial Public Offering (IPO) of Stock

Raises cash

Allows founders and pre-IPO investors toharvest some of their wealth

Secondary Market

Subsequent issues of debt and equity

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Agency Problems and

Corporate Governance Agency problem: managers may act in their

own interests and not on behalf of owners

(stockholders) Corporate governance is the set of rules that

control a companys behavior towards itsdirectors, managers, employees,

shareholders, creditors, customers,competitors, and community.

Corporate governance can help controlagency problems.

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What should be managements

primary objective?

The primary objective should beshareholder wealth maximization, whichtranslates to maximizing thefundamental stock price.

Should firms behave ethically?

Do firms have any responsibilities tosociety at large? Shareholders are alsomembers of society.

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Thek Social Responsibility ofBusiness isto Increase Profits Milton Friedman

If a corporate executive spends in adifferent way than owners would he isimposing a tax.

Stockholders, customers, employeescan spend their own money on aparticular action.

12

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Is maximizing stock price good for

society, employees, and customers?

Employment growth is higher in firmsthat try to maximize stock price. Onaverage, employment goes up in:

firms that make managers into owners(such as LBO firms)

firms that were owned by the governmentbut that have been sold to privateinvestors

(Continued)

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What three aspects of cash flows

affect an investments value?

Any asset is valuable to extent itgenerates cash flows. Amount ofexpected cash flows (bigger is better)

Timing of the cash flow stream (sooneris better)

Risk of the cash flows (less risk isbetter)

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Free Cash Flows (FCF) Free cash flows are the cash flows that

are available (or free) for distribution toall investors (stockholders andcreditors). Excess over what is requiredto run the business

FCF = sales revenues - operating costs- operating taxes - required investmentsin operating capital.

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What is the weighted average

cost of capital (WACC)? WACC is the average rate of return required

by all of the companys investors.

WACC is affected by: Capital structure (the firms relative amounts of

debt and equity)

Interest rates

Risk of the firm

Investors overall attitude toward risk

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What determines a firms

fundamental, or intrinsic, value?

Intrinsic value (education) is the sum

of all the future expected free cashflows when converted into todaysdollars:

Value =FCF1 FCF2 FCF

(1 + WACC)1 (1 + WACC)(1 + WACC)2

+ +

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Who are the providers (savers)

and users (borrowers) of capital?

Households: Net savers

Non-financial corporations: Net users(borrowers)

Governments: Net borrowers

Financial corporations: Slightly netborrowers, but almost breakeven

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Transfer of Capital from

Savers to Borrowers Direct transfer (e.g., corporation issues

commercial paper to insurance company)

Through an investment banking house (e.g.,IPO, seasoned equity offering, or debtplacement)

Through a financial intermediary (e.g.,individual deposits money in bank, bankmakes commercial loan to a company)

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Cost of Money What do we call the price, or cost, of

debt capital?

The interest rate

What do we call the price, or cost, ofequity capital?

Cost of equity = Required return =dividend yield + capital gain

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What four factors affect the

cost of money? Production opportunities what is the

benefit gained from the capital

Time preferences for consumption saver vs borrower

Risk

Expected inflation

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What economic conditions

affect the cost of money? Federal Reserve policies increasing money

supply lowers interest rates, leads to inflation

Budget deficits/surpluses deficit govtborrows or prints money both lead to inflation

Level of business activity (recession or boom) recession slows business activity andreduces interest

International trade deficits/surpluses deficitmust be supported by borrowing, borrowing

drives up interest rate

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What international conditions

affect the cost of money? Country risk. Depends on the countrys

economic, political, and social environment.

Exchange rate risk. Non-dollar denominatedinvestments value depends on what happensto exchange rate. Exchange rates affectedby:

International trade deficits/surpluses

Relative inflation and interest rates

Country risk

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What two factors lead to exchange

rate fluctuations?

Changes in relative inflation will lead to

changes in exchange rates.An increase in country risk will also cause

that countrys currency to fall.

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Financial Securities

Debt Equity Derivatives

Money

Market

T-Bills

CDs

Eurodollars

Fed Funds

Options

Futures

Forward

contract

Capital

Market

T-Bonds

Agency bonds

Municipals

Corporate bonds

Common

stock

Preferred stock

LEAPS

Swaps

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Typical Rates (Continued)Instrument Rate (April 2006)

U.S. T-notes and T-bonds 5.04%

Mortgages 6.15

Municipal bonds 4.66

Corporate (AAA) bonds 5.93

Preferred stocks 6 to 9%

Common stocks (expected) 9 to 15%

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What are some financial

institutions? Commercial banks

Investment banks

Savings & Loans, mutual savings banks, andcredit unions

Life insurance companies

Mutual funds Exchanged Traded Funds (ETFs)

Hedge funds

Pension funds

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What are some types of

markets?A market is a method of exchanging

one asset (usually cash) for another

asset.

Physical assets vs. financial assets

Spot versus future markets

Money versus capital markets

Primary versus secondary markets

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Primary vs. Secondary

Security Sales Primary

New issue (IPO or seasoned)

Key factor: issuer receives the proceedsfrom the sale.

Secondary

Existing owner sells to another party. Issuing firm doesnt receive proceeds and

is not directly involved.

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How are secondary markets

organized? By location

Physical location exchanges

Computer/telephone networks

By the way that orders from buyers andsellers are matched

Open outcry auction

Dealers (i.e., market makers)

Electronic communications networks (ECNs)

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Physical Location vs.

Computer/telephone Networks Physical location exchanges: e.g.,

NYSE, AMEX, CBOT, Tokyo Stock

Exchange

Computer/telephone: e.g., Nasdaq,government bond markets, foreign

exchange markets

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Types of Orders Instructions on how a transaction is to

be completed

Market Order Transact as quickly aspossible at current price

Limit Order Transact only if specific

situation occurs. For example, buy if pricedrops to $50 or below during the next twohours.

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Auction Markets Participants have a seat on the exchange,

meet face-to-face, and place orders for

themselves or for their clients; e.g., CBOT. NYSE and AMEX are the two largest auction

markets for stocks.

NYSE is a modified auction, with aspecialist.

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Dealer Markets Dealers keep an inventory of the stock (or

other financial asset) and place bid and askadvertisements, which are prices at whichthey are willing to buy and sell.

Often many dealers for each stock Computerized quotation system keeps track

of bid and ask prices, but does not

automatically match buyers and sellers. Examples: Nasdaq National Market, Nasdaq

SmallCap Market, London SEAQ, GermanNeuer Markt.

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Electronic Communications

Networks (ECNs) ECNs:

Computerized system matches orders from

buyers and sellers and automaticallyexecutes transaction.

Low cost to transact

Examples: Instinet (US, stocks, owned by

Nasdaq); Archipelago (US, stocks, ownedby NYSE); Eurex (Swiss-German, futurescontracts); SETS (London, stocks).

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Over the Counter (OTC)

Markets In the old days, securities were kept in a safe

behind the counter, and passed over the

counter when they were sold. Now the OTC market is the equivalent of a

computer bulletin board (e.g., Nasdaq PinkSheets), which allows potential buyers and

sellers to post an offer. No dealers

Very poor liquidity

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Chapter 1Web Extension 1A

A Closer Look at Markets:

Securitization and SocialWelfare

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Topics in Web Extension The home mortgage industry

Securitization in the mortgage industry

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Home Mortgages Before S&Ls The problems if an individual investor tried to

lend money to an aspiring homeowner:

Individual investor might not have enough moneyto fund an entire home

Individual investor might not be in a good positionto evaluate the risk of the potential homeowner

Individual investor might have difficulty collecting

mortgage payments S&Ls raised funds by taking deposits and used

proceeds to make home loans

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S&Ls Before Securitization Savings and loan associations (S&Ls)

solved the problems faced by individual

investors S&Ls pooled deposits from many investors

S&Ls developed expertise in evaluating the

risk of borrowers S&Ls had legal resources to collect

payments from borrowers

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Problems faced by S&Ls

Before Securitization S&Ls were limited in the amount of mortages

they could fund by the amount of deposits

they could raise S&Ls were raising money through short-term

floating-rate deposits, but making loans in theform of long-term fixed-rate mortgages

When interest rates increased, S&Ls facedcrisis because they had to pay more to

depositors than they collected frommortgagees

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Taxpayers to the Rescue Many S&Ls went bankrupt when

interest rates rose in the 1980s.

Because deposits are insured, taxpayersended up paying hundreds of billions ofdollars.

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Securitzation in the Home

Mortgage IndustryAfter crisis in 1980s, S&Ls now put their

mortages into pools and sell the pools

to other organizations, such as FannieMae.

After selling a pool, the S&Ls have

funds to make new home loans Risk is shifted to Fannie Mae

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Fannie Mae Shifts Risk to Its

Investors Risk hasnt disappeared, it has been shifted to Fannie

Mae.

But Fannie Mae doesnt keep the mortgages: Puts mortgages in pools, sells shares of these pools to

investors

Risk is shifted to investors.

But investors get a rate of return close to the mortgage rate,which is higher than the rate S&Ls pay their depositor.

Investors have more risk, but more return This is called securitization, since new securities have

been created based on original securities (mortgagesin this example)

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Collateralized Mortgage

Obligations (CMOs) Fannie Mae and others can also split

mortgage pools into special securities

Some securities might pay investors only themortage interest, others might pay only themortgage principle.

Some securities might mature quickly, othersmight mature later

Risk of basic mortgage is parceled out tothose investors who want that type of risk(and the potential return that goes with it).

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Other Assets Can be

Securitized Car loans

Student loans

Credit card balances

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Chapter 1Web Extension 1B

An Overview of Derivatives

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Topics in Web Extension Overview of derivatives

Forward contracts

Futures contracts

Options

Swaps

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Forward Contracts 2 parties to contract, each with a basic position:

One party is long (buy). Obligates party to buy theunderlying asset at some fixed price at a specified date in

the future. One party is short (sell). Obligates party to sell the

underlying asset at some fixed price at a specified date inthe future.

Terms

Forward price Delivery date (expiration date)

Forward contracts are common for currencies.

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Hedging Risk with Forward

Contracts US wine importer might plan on purchasing French

wine with euros in the fall. Could lock in thecurrency exchange rate for the fall by taking a long

position in a euro currency forward contract. US computer manufacturer might plan on selling

computers to German company in fall, with thepayment in euros. Could lock in exchange rate bytaking a short position in euro forward contract.

Both parties have reduced risk by locking in theexchange rate.

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Problems with Forward

Contracts Forward contracts are made directly

between two parties, so there is the

possibility of default. Forward contracts are often designed

for a specific need, so there is not astandardized contract, which makes itdifficult to have a secondary market.

Futures contract solve these problems.

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Futures Contracts Similar to forwards, except:

Marking-to-market

Many more assets- agriculture, livestock,metals, indexes, currencies, interest rates,energy

Standardized contracts that trade onexchanges, such as CBOT

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Options Basic Positions

Call / Put

Long / Short (writer) Terms

Exercise Price

Expiration Date (can let expire unexercised)

Assets- Stocks, indexes, currency, and futures

CBOE

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Chapter 1Web Extension 1C

A Closer Look at the Stock

Markets

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Topics inW

eb Extension Stock indexes

Regulation

Overview of investment banking

Stock trading

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Stock Indexes Stock indexes try to measure some

aspect of the market

The differ with respect to:

Composition (types of stock in the index)

Weighting (how the individual stocks are

aggregated into an index)

(More . .)

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Index Composition Replicate a particular exchange

Measure a countrys most importantstocks

Measure a particular business sector

Measure a particular investment style

Measure an international region

(More . .)

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Composition by Exchange NYSE Composite

Nasdaq Composite

(More . .)

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Composition by Style Two important investment styles are by the

size of the firm and by its growth prospects.

Growth is measure by high-expected salesgrowth and high price-book ratios (valuestocks have lower growth and lower price-book ratios)

Examples: Russell 1000 Growth

Russell Midcap Value

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Composition by International

Region Morgan Stanley Capital International

(MSCI)

EAFE (Europe, Asia, Far East) Index

Emerging Markets Index

Pacific Index

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StockW

eighting in Indexes Price weighted

DJIA

Market-value weighted S&P500

Nasdaq Composite

Equally weightedValue Line Index

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Regulation of Securities

Markets Government Regulation such as SEC.

Insider trading oversight (SEC)

Margin oversight (Federal Reserve)

Self-regulation such as NASD.

CircuitBreakers automatic halt in tradingif stock prices have exceptional changes.

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Public vs. Private Offerings Public offerings: registered with the SEC and

sale is made to the investing public. Shelf registration (Rule 415, since 1982) allows firms to

register an offering and sell parts of the offering over time.

Private offering: Sale to a limited number ofsophisticated investors not requiring the protection ofregistration.- Dominated by institutions.

- Very active market for debt securities.

- Not active for stock offerings.

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InvestmentBanking and

Security Offerings Underwritten vs. Best Efforts

Underwritten: firm commitment on proceeds to

the issuing firm. Best Efforts: no firm commitment.

Negotiated vs. Competitive Bid

Negotiated: issuing firm negotiates terms with

investment banker. Usually a 7% spread. Competitive bid: issuer structures the offering

and secures bids.

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Initial Public Offerings Initial Public Offerings (IPOs)

UnderpricingAverage increase is 14% on

first day.

Performance Underperforms similar stockduring three years after IPO.

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Costs of Trading Commission: fee paid to broker for making

the transaction Spread: cost of trading with dealer

Bid: price dealer will buy from you Ask: price dealer will sell to you Spread: ask - bid

Price Impact Large sales or purchase

might cause prices to change. Payment for Order Flow Exchange will pay

brokers to direct orders to them.

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The Specialist at the NYSE Handles around 10-20 stocks (one per

specialist) Stock trade at the specialists post Makes a market by matching buyers/seller

and by buying/selling from own inventory Goal is to maintain a fair and orderly

market so that price changes are smooth Specialist loses money when smoothing the

market, but makes it back during normalconditions

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Trading Away from Exchanges Third Market trading listed stocks but

not through exchange

Institutional market: to facilitate trades oflarger blocks of securities.

Involves services of dealers and brokers

Fourth Market institutions trading withinstitutions

No middleman involved in the transaction

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Margin Trading Investor uses only a portion of own

capital for an investment.

Borrows remaining component.

Margin arrangements differ for stocksand futures.

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Short Sales Mechanics Opening a short position:

Borrow stock through a dealer.

Sell it Deposit proceeds and margin in account.

Closing out the position: Buy the stock

Return to the party from which it wasborrowed.

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Chapter 2

Time Value of Money

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Time Value Topics Future value

Present value

Rates of return

Amortization

Ti li h i i f h

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Time lines show timing of cash

flows.

CF0 CF1 CF3CF2

0 1 2 3

I%

Tick marks at ends of periods, so Time 0is today; Time 1 is the end of Period 1; orthe beginning of Period 2.

Ti li f $100 l

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Time line for a $100 lump sum

due at the end of Year2.

100

0 1 2 Year I%

Ti li f di

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Time line for an ordinary

annuity of $100 for3

years

100 100100

0 1 2 3I%

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Time line for uneven CFs

100 5075

0 1 2 3I%

-50

FV f i iti l $100 ft

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FV of an initial $100 after3

years (i = 10%)

FV = ?

0 1 2 3

10%

Finding FVs (moving to the righton a time line) is called compounding.

100

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After 1 year

FV1 = PV + INT1 = PV + PV (I)= PV(1 + I)= $100(1.10)

= $110.00.

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After2

years

FV2 = FV1(1+I) = PV(1 + I)(1+I)= PV(1+I)2

= $100(1.10)2

= $121.00.

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After3

years

FV3 = FV2(1+I)=PV(1 + I)2(1+I)

= PV(1+I)3

= $100(1.10)3

= $133.10

In general,FVN = PV(1 + I)

N.

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ThreeW

ays to Find FVs Solve the equation with a regular

calculator.

Use a financial calculator.

Use a spreadsheet.

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Financial calculator: HP10BII

Adjust display brightness: hold downON and push + or -.

Set number of decimal places todisplay: Orange Shift key, then DISPkey (in orange), then desired decimal

places (e.g., 3). To temporarily show all digits, hit

Orange Shift key, then DISP, then =

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HP10BII (Continued)

To permanently show all digits, hitORANGE shift, then DISP, then . (period

key) Set decimal mode: Hit ORANGE shift,

then ./, key. Note: many non-US

countries reverse the US use ofdecimals and commas when writing anumber.

HP10BII Set Time Value

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HP10BII: Set Time Value

Parameters To set END (for cash flows occurring at

the end of the year), hit ORANGE shift

key, then BEG/END. To set 1 payment per period, hit 1, then

ORANGE shift key, then P/YR

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Financial calculators solve thisequation:

FVN + PV (1+I)N = 0.

There are 4 variables. If3 areknown, the calculator will solve forthe 4th.

Financial Calculator Solution

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3 10 -100 0

N I/YR PV PMT FV133.10

Clearing automatically sets everything to 0,but for safety enter PMT = 0.

Set: P/YR = 1, END for problems in this book.

INPUTS

OUTPUT

Heres the setup to find FV

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Whats the PV of $100 due in

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10%

What s the PV of $100 due in3

years if i = 10%?

Finding PVs is discounting, and its thereverse of compounding.

100

0 1 2 3

PV = ?

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1.10

Solve FVN = PV(1 + I )

N

for PV

PV =FVN

(1+I)N= FVN

1

1 + I

N

PV = $1001

= $100(0.7513) = $75.13

3

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3 10 0 100N I/YR PV PMT FV

-75.13

Either PV or FV must be negative. HerePV = -75.13. Put in $75.13 today, takeout $100 after 3 years.

INPUTS

OUTPUT


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Time to Double (Continued)

$2 = $1(1 + 0.20)N(1.2)N = $2/$1 = 2

N LN(1.2) = LN(2)N = LN(2)/LN(1.2)N = 0.693/0.182 = 3.8.

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20 -1 0 2

N I/YR PV PMT FV

3.8

INPUTS

OUTPUT


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Spreadsheet Solution Use the NPER function: see spreadsheet

in FM12 Ch 02 Mini Case.xls

= NPER(I, PMT, PV, FV)

= NPER(0.10, 0, -1, 2) = 3.8

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?%

2

0 1 2 3

-1FV = PV(1 + I)N

$2 = $1(1 + I)3

(2)(1/3) = (1 + I)1.2599 = (1 + I)

I = 0.2599 = 25.99%.

Finding the Interest Rate

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3 -1 0 2

N I/YR PV PMT FV

25.99

INPUTS

OUTPUT

Financial Calculator

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Ordinary Annuity

PMT PMTPMT

0 1 2 3I%

PMT PMT

0 1 2 3I%

PMT

Annuity Due

Ordinary Annuity vs. Annuity DueConstant & Fixed PMT

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FV Annuity Formula The future value of an annuity with N

periods and an interest rate of I can befound with the following formula:

= PMT(1+I)N-1

I

= 100(1+0.10)3-1

0.10= 331

Financial Calculator Formula

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Financial Calculator Formulafor Annuities

Financial calculators solve this equation:

FVN + PV(1+I)N + PMT (1+I)

N-1

I= 0.

There are 5 variables. If4 are known,the calculator will solve for the 5th.

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3 10 0 -100

331.00

N I/YR PV PMT FV

Have payments but no lump sum PV, soenter 0 for present value.

INPUTS

OUTPUT


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Spreadsheet Solution

Use the FV function: see spreadsheet.

= FV(I, N, PMT, PV)

= FV(0.10, 3, -100, 0) = 331.00

Whats the PV of this ordinary

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111

What s the PV of this ordinaryannuity?

100 100100

0 1 2 3

10%

90.91

82.64

75.13

248.69 = PV 100/(1+0.10)^3 = 75.13

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PV Annuity Formula

The present value of an annuity with Nperiods and an interest rate of I can be

found with the following formula:

= PMT 1

I

1

I (1+I)N

= 100 1

0.1

1

0.1(1+0.1)3= 248.69

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113

Have payments but no lump sum FV, soenter 0 for future value.

3 10 100 0N I/YR PV PMT FV

-248.69

INPUTS

OUTPUT


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Spreadsheet Solution

Use the PV function: see spreadsheet.

= PV(I, N, PMT, FV)

= PV(0.10, 3, 100, 0) = -248.69

Find the FV and PV if the

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115

Find the FV and PV if theannuity were an annuity due.

100 100

0 1 2 310%

100

PV and FV of Annuity Due

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PV and FV of Annuity Duevs. Ordinary Annuity

PV of annuity due:

= (PV of ordinary annuity) (1+I)

= (248.69) (1+ 0.10) = 273.56

FV of annuity due:

= (FV of ordinary annuity) (1+I)

= (331.00) (1+ 0.10) = 364.1

PV of Annuity Due: Switch

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3 10 100 0

-273.55

N I/YR PV PMT FV

INPUTS

OUTPUT

PV of Annuity Due: Switchfrom End to Begin

FV of Annuity Due: Switch

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3 10 0 100

-364.1

N I/YR PV PMT FV

INPUTS

OUTPUT

FV of Annuity Due: Switchfrom End to Begin

Excel Function for Annuities

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Excel Function for AnnuitiesDue

Change the formula to:

=PV(10%,3,-100,0,1)

The fourth term, 0, tells the function there are no

other cash flows. The fifth term tells the function

that it is an annuity due. A similar function gives the

future value of an annuity due:

=FV(10%,3,-100,0,1)

What is the PV of this

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120

What is the PV of thisuneven cash flow stream?

0

100

1

300

2

300

310%

-50

4

90.91

247.93

225.39

-34.15

530.08 = PV

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Clear all: Orange Shift key, then C Allkey (in orange).

Enter number, then hit the CFj key. Repeat for all cash flows, in order.

To find NPV: Enter interest rate (I/YR).

Then Orange Shift key, then NPV key(in orange).


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Financial calculator HP10BII(more)

To see current cash flow in list, hit RCLCFj CFj

To see previous CF, hit RCL CFj To see subsequent CF, hit RCL CFj +

To see CF 0-9, hit RCL CFj 1 (to see CF

1). To see CF 10-14, hit RCL CFj .(period) 1 (to see CF 11).


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Input in CFLO register:

CF0 = 0

CF1 = 100 CF2 = 300

CF3 = 300

CF4 = -50 Enter I = 10%, then press NPV button

to get NPV = 530.09. (Here NPV = PV.)

a a a u a o 0(more)

Excel Formula in cell A3:

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=NPV(10%,B2:E2)

NFV = NPV (1 + I )^N

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Nominal rate (INOM

)

Stated in contracts, and quoted bybanks and brokers.

Not used in calculations or shown ontime lines

Periods per year (M) must be given.

Examples: 8%; Quarterly

8%, Daily interest (365 days)

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Periodic rate (IPER

)

IPER = INOM/M, where M is number of compounding

periods per year. M = 4 for quarterly, 12 for monthly,

and 360 or 365 for daily compounding.

Used in calculations, shown on time lines.

Examples:

8% quarterly: IPER = 8%/4 = 2%.

8% daily (365): IPER = 8%/365 = 0.021918%.

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The Impact of Compounding

Will the FV of a lump sum be larger orsmaller if we compound more often,

holding the stated I% constant? Why?

The Impact of Compounding

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p p g(Answer)

LARGER

If compounding is more frequent thanonce a year--for example, semiannually,quarterly, or daily--interest is earned on

interest more often.

FV Formula with Different

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Compounding Periods

INOMFVN = PV 1 +M

M N

$100 at a 12% nominal rate with

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$100 at a 12% nominal rate with

semiannual compounding for 5 years

= $100(1.06)10 = $179.08

INOMFVN = PV 1 +

M

M N

0.12FV5S = $100 1 +

2

2x5

FV of $100 at a 12% nominal rate for

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FV of $100 at a 12% nominal rate for5 years with different compounding

FV(Ann.) = $100(1.12)5 = $176.23

FV(Semi.) = $100(1.06)10 = $179.08FV(Quar.) = $100(1.03)20 = $180.61

FV(Mon.) = $100(1.01)60 = $181.67

FV(Daily) = $100(1+(0.12/

365))

(5x365)

= $182.19

Effective Annual Rate (EAR =

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(EFF%)

The EAR is the annual rate whichcauses PV to grow to the same FV as

under multi-period compounding.

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Effective Annual Rate Example

Example: Invest $1 for one year at 12%,semiannual:

FV = PV(1 + INOM/M)M N

FV = $1 (1.06)^2 = 1.1236.

EFF% = 12.36%, because $1 invested forone year at 12% semiannual compounding

would grow to the same value as $1 investedfor one year at 12.36% annual compounding.

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Comparing Rates

An investment with monthly paymentsis different from one with quarterly

payments. Must put on EFF% basis tocompare rates of return. Use EFF%only for comparisons.

Banks say interest paid daily. Sameas compounded daily.

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A source of confusion

136

Show an annual rate of 9.5323% compounded daily

=

A daily rate of 0.0261%

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Finding EFF with HP10BII

Type in nominal rate, then Orange Shiftkey, then NOM% key (in orange).

Type in number of periods, then OrangeShift key, then P/YR key (in orange).

To find effective rate, hit Orange Shift

key, then EFF% key (in orange).

EAR (or EFF%) for a Nominal

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Rate of of 12%

EARAnnual = 12%.

EARQ = (1 + 0.12/4)4 - 1 = 12.55%.

EARM = (1 + 0.12/12)12 - 1 = 12.68%.

EARD(365) = (1 + 0.12/365)365 - 1= 12.75%.

Can the effective rate ever be

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equal to the nominal rate?

Yes, but only if annual compounding isused, i.e., if M = 1.

If M > 1, EFF% will always be greaterthan the nominal rate.

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When is each rate used?

INOM:

Written into contracts, quotedby banks and brokers. Not usedin calculations or shown

on time lines.


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IPER: Used in calculations, shown ontime lines.

If INOM has annual compounding,then IPER = INOM/1 = INOM.

(Continued)


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(Continued)

EAR (or EFF%): Used to comparereturns on investments with different

payments per year. Used for calculations if and only if

dealing with annuities where payments

dont match interest compoundingperiods.

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Amortization

Construct an amortization schedule fora $1,000, 10% annual rate loan with 3

equal payments.

Step 1: Find the required

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payments.

PMT PMTPMT

0 1 2 310%

-1,000

3 10 -1000 0INPUTS

OUTPUT

N I/YR PV FVPMT

402.11

Step 2: Find interest charge

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for Year 1.

INTt = Beg balt(I)

INT1 = $1,000(0.10) = $100.

Step 3: Find repayment of

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Repmt = PMT - INT

= $402.11 - $100= $302.11.

principal in Year 1.

Step 4: Find ending balance

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after Year 1.

End bal = Beg bal - Repmt

= $1,000 - $302.11 = $697.89.

Repeat these steps for Years 2 and 3to complete the amortization table.

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Amortization Table

YEARBEGBAL PMT INT

PRINPMT

ENDBAL

1 $1,000 $402 $100 $302 $698

2 698 402 70 332 366

3 366 402 37 366 0

TOT 1,206.34 206.34 1,000

Interest declines becausedi b l d li

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outstanding balance declines.

$0$50

$100

$150

$200

$250$300

$350

$400

$450

PMT 1 PMT 2 PMT 3

Interest

Principal

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150

Amortization tables are widelyused--for home mortgages, auto

loans, business loans, retirementplans, and more. They are veryimportant!

Financial calculators (andspreadsheets) are great for settingup amortization tables.

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Fractional Time Periods

On January 1 you deposit $100 in anaccount that pays a nominal interest

rate of 11.33463%, with dailycompounding (365 days).

How much will you have on October 1,or after 9 months (273 days)? (Daysgiven.)

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IPER = 11.33463%/365= 0.031054% per day.

FV=?

0 1 2 273

0.031054%

-100

Convert interest to daily rate

Fi d FV

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FV273= $100 (1.00031054)273

= $100 (1.08846) = $108.85

Find FV

C l l t S l ti

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273 -100 0

108.85

INPUTS

OUTPUT

N I/YR PV FVPMT

IPER = iNOM/M= 11.33463/365= 0.031054% per day.

Calculator Solution

hi d i d

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Non-matching rates and periods

Whats the value at the end of Year 3 ofthe following CF stream if the quoted

interest rate is 10%, compoundedsemiannually?

Time line for non-matchingt d i d

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rates and periods

0 1

100

2 35%

4 5 6 6-mos.periods

100 100

N t hi t d i d

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Non-matching rates and periods

Payments occur annually, butcompounding occurs each 6 months.

So we cant use normal annuityvaluation techniques.

1 t M th d C d E h CF

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1st Method: Compound Each CF

0 1

100

2 35%

4 5 6

100 100.00110.25121.55

331.80FVA3 = $100(1.05)

4 + $100(1.05)2 + $100= $331.80.

2nd Method: Treat as anit fi i l l l t

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annuity, use financial calculator

Find the EFF% (EAR) for the quoted rate:

EFF% = 1 + 1 = 10.25%0.10

2

2

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Daily time line

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IPER = 0.018538% per day.

1,000

0 365 456 days

-850

Daily time line

Th l ti th d

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Three solution methods

1. Greatest future wealth: FV

2. Greatest wealth today: PV

3. Highest rate of return: EFF%

1 G eatest F t e Wealth

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1. Greatest Future Wealth

Find FV of $850 left in bank for15 months and compare with

notes FV = $1,000.

FVBank = $850(1.00018538)456

= $924.97 in bank.

Buy the note: $1,000 > $924.97.

Calculator Solution to FV

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456 -850 0

924.97

INPUTS

OUTPUT

N I/YR PV FVPMT

IPER = INOM/M

= 6.76649%/365= 0.018538% per day.

Calculator Solution to FV

2 Greatest Present Wealth

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Find PV of note, and comparewith its $850 cost:

PV = $1,000/(1.00018538)456

= $918.95.

2. Greatest PresentWealth


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456 .018538 0 1000

-918.95

INPUTS

OUTPUT

N I/YR PV FVPMT

6.76649/365 =

PV of note is greater than its $850cost, so buy the note. Raises yourwealth.


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Calculator Solution

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456 -850 0 1000

0.035646%per day

INPUTS

OUTPUT

N I/YR PV FVPMT

Convert % to decimal:Decimal = 0.035646/100 = 0.00035646.EAR = EFF% = (1.00035646)365 - 1

= 13.89%.

Calculator Solution

Using interest conversion

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P/YR =365NOM% =0.035646(365) = 13.01EFF% =13.89

Since 13.89% > 7.0% opportunity cost,buy the note

Using interest conversion

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