FM12 Ch 01 Show
Transcript of FM12 Ch 01 Show
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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.
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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
Financial Calculator Solution
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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
Financial Calculator Solution
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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
Financial Calculator Solution
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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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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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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
Financial Calculator Solution
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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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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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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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Financial calculator: HP10BII
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).
Financial calculator: HP10BII
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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).
Financial calculator: HP10BII
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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.
When is each rate used?
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IPER: Used in calculations, shown ontime lines.
If INOM has annual compounding,then IPER = INOM/1 = INOM.
(Continued)
When is each rate used?
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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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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
Financial Calculator Solution
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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.
Financial Calculator Solution
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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