foundations of finance

Foundations of Finance

Week 1 – Overview of Financial Markets

2

Why do Financial Markets exist?

Overview of Financial Markets

People with Ideas/Opportunities

People with excess capital

↵↵Gains from trade !

3

Most (all ?) transactions fit into this framework

Demand for capital Supply of capital


Entrepreneurs Students Some countries Firms

Households (bank accounts)

Pension plans Some other countries

Provides for1. Consumption

smoothing 2. Optimal use of capital

4

Core concepts


TODAY: A bird’s eye perspective

Financial Markets

The role of markets in our economy and how they function

6

A Closer Look


Question: How does a firm obtain financing?

Part of the answer: It must issue financial assets

CONSUMERS OF CAPITAL

CAPITAL MARKETS

SUPPLIERS OF CAPITAL

7

What is a Financial Asset?


Real Assets are used to produce goods and services: land, equipment, buildings, knowledge Financial Assets are claims on real assets or the income generated by them

Large Firm

Start-up

CLAIM

FINANCIAL ASSETS

REAL ASSETSINVESTORS

CLAIM

8

Financial and Real Assets


Financial Assets One parties asset is another’s liability Thus the value of all financial assets in the

economy sums to zero Real Assets

The value of all real assets determines the true value of the economy


9

Real and Financial AssetsLiabilities AssetsMortgage - $2 MBank Loan - $1M

Shares of Stock - $5MBank Deposit – $3 M House - $3 M

Liabilities AssetsDeposits – $3 MEquity - $1M

Mortgage - $2 M Loans – $2 M

Liabilities Assets Equity - $4 MBank Debt – $1 M

Human Capital - $3MComputers - $ 1M Patents $1 M

Households

Banks

Firms

Common Types of Financial Assets

Features of Debt and Equity claims


11

Basic Financial Assets

Debt Bank Loan Corporate Bond Treasuries Pensions

Equity (Ownership) Stocks


12

A (hopefully) intuitive example You want to start a lemonade stand

You anticipate that it will earn $20 You have $10, but you need $15 Your parents lend you $5

How is this “firm” financed?

You make $12 in revenues how do you split the proceeds?

13

Debt vs. Equity


Seniority Debt holders paid first Equity holders paid once debt holders have

received all claims Cash Flows

Debt holders receive a fixed amount Equity holders have a claim on firm value which

exceeds liabilities to debt holders

What does this structure imply for the relative riskiness (variance) of these payoffs?


14

Debt vs. Equity - Graphically

What if the firm can’t pay back debt holders? Renegotiation Bankruptcy

0 5 10 15 20

02468

101214161820

Value of EquityValue of DebtFirm Value

15

Fixed Income Securities


Some examples: Treasury Bills/Bonds Municipal bonds Mortgages Credit card debt Student loans

Two types of cash flows Interest payments Principal payments


16

Fixed Income Cash Flows: An Example Loan with FV $ 20M, Semi-Annual Coupons &

5% Interest rate

Initial Capital Injection

Semi-Annual Coupon Payments

PrincipalPayment

17

Features of a Debt Contract


Maturity – length of loan term Interest Rate – e.g. fixed or floating Face value – The value of the principal owed at

maturity Payment Schedule

Frequency of coupon payments (Potentially no coupon payments)

Optionality – e.g. prepayment options If interest rates fall, borrowers may have the option of

paying off their existing loans and issuing new debt at the lower interest rate

Covenants Provisions which give the lender control rights in particular

scenarios


18

Revisiting the lemonade stand What were the features of the loan your

parents made to you? Interest rate?

Optionality?

Maturity?

Payment schedule? (e.g. coupons)


19

Market Value of Debt vs. Face Value Firm has debt of face value 10M Tomorrow the firm will either be worth

What is the market value of the firm’s debt?

Market value of debt: Market value of equity:

Firm Value 20M 15M 0MValue of Debt

Value of equity

€

20150

⎧ ⎨ ⎪

⎩ ⎪

w /w /w /

prob = 1 3prob = 1 3prob = 1 3


20

Equity Financing

An equity claim contains Cash-flow rights: the right to the firms cash

flows once debt-holders are paid off An infinite stream of dividends

Voting rights Cash flows rights

Dividends Should capital gains count?

21

Debt vs. Equity


SeatGeek.com is financed through debt and equity: Current value of equity: 6M Current value of debt: 9M, assume the face value of debt is also 9M

Presented with an investment opportunity which costs $11M and has payoffs given by:

Payoff =

What is the expected value of this project?

What is the firms value if it decides to undertake the project? €

30120

⎧ ⎨ ⎪

⎩ ⎪

w /w /w /

prob = 1 3prob = 1 3prob = 1 3

22

Debt vs. Equity


Goal: find the new value of debt and the new value of equity

Value of debt: Value of equity: Should management invest in the project?

Case 1: Case 2: Case 3: Project Payoff

30M 12M 0M

Firm ValueDebt PayoffEquity Payoff

23 Overview of Financial Markets

Any questions on Debt and/or Equity?


24

Or what about a hybrid? – Preferred Equity

Attributes of both debt and equity Bond-like

No voting power Priority over common stock Rated by credit-rating agencies

Stock-like Subordinate to debt Cash-flows are in the form of dividend payments


25

One clever type of preferred stock: Poison pills (This is an example of a potential “current

event” topic)

- Financial Times

26

Some background: What is a Poison Pill?

Marty Lipton


“In connection with the adoption of the Shareholder Rights Plan, the Board of Directors declared a dividend distribution of one preferred stock purchase right for each outstanding share of Tegal’s common stock to shareholders of record as of the close of business… Under the Plan, the rights generally will become exercisable if a person becomes an `acquiring person’ by acquiring 15% or more of the common stock of Tegal… If a person becomes an ‘acquiring person,’ each holder of a right (other than the acquiring person) would be entitled to purchase, at the then-current exercise price, such number of shares of preferred stock which are equivalent to shares of Tegal’s common stock having a value of twice the exercise price of the right.”

-Tegal press release – April 13, 2011

http://vimeo.com/18125037

27

How does it work


Hostile take-over triggers the right to exercise the option

2-for-1 exchange means any shares not exercised have been diluted to half their value

Acquirer cannot exercise Is this “rights plan” actually good for

shareholders ?

28

Back go Airgas versus Air Products


29

How should a firm finance it’s investments?


Some possible considerations Accessibility of debt versus equity Management incentives Asymmetric information Bankruptcy costs Tax advantages Reporting costs

You can learn more about capital structure in corporate finance

30

Financing the Firm – The Role of Limited Liability


Limited Liability – The concept whereby a person’s financial liability is limited to a fixed sum (typically the value of the person’s financial investment)

Can you think of howthis would be importantin a firm’s ability to gain

financing? What are some costs?

31

Back to the (fictional) story of SeatGeek.com


2000 2002 2003 2006

Two college grads have a great business idea. Personal loan from friends & family

Must hire employees to increase website functionality

VC funding (equity)

Expand operations by entering ticket brokering business

Issue corporate debt

Enter agreement with AMEX to purchase concierge services businessIssue public equity (IPO)

32

How will SeatGeek.com do an IPO?


The role of investment banks Determine size & features of offering “Place shares” Legal issues Pricing issues

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

0

40

80

120

160

200

0246810121416

Number of IPOS 1st Day Return


33

A Closer Look

How are these financialAssets traded?

CONSUMERS OF CAPTIAL CAPITAL

MARKETSSUPPLIERS OF CAPITAL

Market Mechanics

The primary and secondary markets for financial assets

35

Primary Market


SeatGeek works with an investment bank to structure an IPO

The company is now owned by multiple classes of investors

DEBT

EQUITY

Debt Holders

Equity Holders


36

Primary and Secondary Market

After new issues occur through the primary market

Later some investors may want to change their holdings

Secondary market allows investors to trade securities


37

An Interesting Aside: Relative Sizes of Secondary Markets Total value of US bond market – $31 trillion Total value of US stock market - $22 trillion Value of average daily dollar trade volume in

some secondary markets? US Stock Market ?

US Bond Market ?

Foreign Exchange ?

38

How are trades completed? Not this way


In a “direct search market” buyers and sellers transact without an intermediary

Seller

Buyer

39

Brokered Market


Sellers and buyers transact through brokers

Seller

Buyer

Broker Broker

Broker

Broker

40

Dealer Market


Dealers specialize in particular securities They absorb supply and demand shocks

through their own books

Seller

Buyer

Broker Broker

Broker

Dealer

Dealer

Broker


41

Broker

Broker

Auction Market Transactions occur centralized through an

auction

Seller

Buyer

Broker

Broker

Broker

BrokerBroker

Broker

Exchange

42

Secondary Markets


Auction Market (NYSE, AMEX) Call Auction Continuous Auction:

Floor Trading (open outcry system) Limit Order Book

Dealer (Market Maker) Market (NASDAQ) Electronic Communication Network

What determines the price?

43

Call Auction


All orders are aggregated into demand and supply schedules

Transactions are conducted at a specified time

A single price is determined such that supply equals demand

44

Call Auction – Building the Supply & Demand Curves


Buy 1,500 shares at $102


Buy 500 shares at $103











$102

$100

$101

$103

$104

1,000 2,000 3,000 4,000 5,000

Sell 2,000 shares at $104

Sell 500 shares at $102

Sell 1,500 shares at $101


45

Continuous Auction Continuous Auction or Dealer Market: Bid

and Ask Prices Bid Price = Price at which a seller can sell

an asset Ask Price = Price at which a buyer can buy

an asset Which Price should be higher? Why?


46

Continuous Action – Limit Order Book - 11:05

Time Trade ? Buyer Seller Quantity Price Post Bid

Post Ask

11:0111:0311:0411:0711:08

Sue: ASK 500 @ 20

11:00

11:05

Jim: ASK 2000 @ 19

Anne: ASK 2000 @ 18

Bill: BID 500 @ 17

Jane: BID 2000 @ 21

Rob: BID 1500 @ 18


47

The Role of the Dealer (a.k.a. Market Maker)

Dealer Holds inventory and quotes bid and ask prices

Provides a service of liquidity in exchange for the bid-ask spread

Bears risk of holding inventory

Bid-ask spread compensates dealer for risk and liquidity services

48

The Dealers Inventory: Some Thought Questions


What happens to the value of inventory if the stock price goes up? Down?

What happens to the size of the dealer’s inventory if bid-ask spread moves up? Down?

How does volume of trade affect inventory risk?

How does competition affect the spread?


49

US Equity Markets Today: Future of the NYSE

http://video.cnbc.com/gallery/?video=3000020578


50

Types of Trading Orders Market Order Buy or sell orders to be executed

immediately at the market price Limit Order (Our dealer book

example) Order to sell (buy) shares at or above (below)

a specified price Stop Orders

Order to sell (buy) if prices falls below (rises above) a specified level


51

Short Sales Speculator: Buy Low, Sell High How can we profit if we believe the

price is going to go down?


52

Short Sales in Practice

Legal Issues Naked short selling Occasional restrictions on shorting certain securities

Securities lending An industry allows for shorting in the presence of

naked short restrictions Which securities can be lent? Transparency issues in the securities lending market

(This is my research area – email me if you want to know more about shorting or sec lending.)


53

A Closer Look

CONSUMERS OF CAPITAL

CAPITAL MARKETS

SUPPLIERS OF CAPITAL

•How do investors decide what assets to invest in?


54

The Investment Management Industry

Difficult for individual investors to access certain financial opportunities Can you think of what features make some

assets more inaccessible than others? Economies of scale

Trading costs Ability to net trades

Governance Issues


55

Investment Management Vehicles

Money Market Funds Pension Funds Mutual Funds

Passive vs. Active Hedge Funds Other funds

VC/PE Funds Fund of Funds


56

How can Investors choose the best Investment opportunity

Important considerations for an Investor Investment Horizon Risk tolerance Level of Sophistication Fees

Tools to evaluate these concepts: The time value of money Time-adjusted return measures

Returns and Return Measures

A framework for evaluating investment opportunities

58

Time Value of Money



59

Time Value of Money Main axiom of finance:

Money in the future is worth less than the same amount of money is worth today

Why is this true? What if you KNOW you don’t need money until

tomorrow? What if there is absolutely no default risk?

60

Time Value of Money


Which cash flow would you prefer?

What about: Today 1 Year Later

$20$10

Today 1 Year Later

$20$10

Today 1 Year Later

$20$10

Today 1 Year Later

$20$10

61

Time Value of Money


Which of these cash flows would you prefer?

Need a concept that allows us to evaluate these options systematically

Today 1 Year Later

$20$10

Today 1 Year Later

$20$10


62

Time Value of Money & Financial Assets

Financial assets we have discussed thus characterized by exchanging some capital today for claims on future cash flows

Equity Purchase a part of an investment opportunity

today with the prospect of making money on the investment in the future

Bonds Lend money today in exchange for receiving your

investment back with interest


63

Time Value of Money

We will ask: Future value: How much is $1 invested today

worth in 1 year Present Value: How much is $1 received in 1 year

worth today

Note: Knowing the answer to one of the above questions implies the answer to the other Why is this?


64

Understanding interest rates Poll: I need $100 today – how much would you

want me to promise to pay you in 1 year to make the loan to me? 102? 105? 108? 112?

The answer to this question determines the interest rate

For this class, we will take the interest rate as given If you want to learn more about the determinates of

interest rates, consider taking macroeconomics or forecasting debt instruments


65

Future Value Suppose Interest Rate is 10% Then investors are indifferent between these two

cash flows:

So they are indifferent between making this investment and keeping their $100

Today 1 Year Later

$110$100


66

Future Value Interest rate is still 10% How much money would an investor need in

two years to lend $110 in 1 year

Answer: $110*(1.1) = $121 Today 1 Year Later

2 Years Later

?$110$100


67

Future Value Interest rate is still 10% What if you were lending $100 today and

receiving $X in 2 years? What should X be?

Answer: $100*(1.1)2 = $121 Today 1 Year Later

2 Years Later

?

$100

68

Future Value


In general: FV = PV*(1+r)T

In the previous 3 slides we could have used this formula to calculate the future value using: 1: PV = 100, r = 10%, T = 1 2: PV = 110, r = 10%, T = 1 3: PV = 100, r = 10%, T = 2

You get a $250 present from your family as a graduation present. If you invest it today, what will it be worth in 5 years?

69

Future Value of $1


20% 15% 10% 5% T/ R

1.2000 1.1500 1.1000 1.0500 1

1.4400 1.3225 1.2100 1.1025 2

1.7280 1.5209 1.3310 1.1576 3

2.0736 1.7490 1.4641 1.2155 4

2.4883 2.0114 1.6105 1.2763 5


70

Present Value – just the converse: You need $1000 in 1 year to pay for a

vacation. How much should you invest today at an interest rate of 5%?

We can use the same formula: PV = FV/(1+r)T Today

5 Years Later

1000

?


71

Present Value of $1

20% 15% 10% 5% T/ R

0.8333 0.8696 0.9091 0.9524 1

0.6944 0.7561 0.8264 0.9070 2

0.5787 0.6575 0.7513 0.8638 3

0.4823 0.5718 0.6830 0.8227 4

0.4019 0.4972 0.6209 0.7835 5


72

Single Cash Flow

The formula relates: Present Value Future Value Interest rate Time (number of periods)

FV=PV*(1+r)T


73

PV, FV, r, t are tied together

If you know any 3, you can find the 4th

Interest rate: r You know PV and FV at a given future

time t, how do you figure out the interest rate?

Investment Period: t You know PV, you know the interest rate,

and the FV. For how many periods do you need to invest?


74

Example I – Single Cash Flow Your grandmother promised you $5,000

upon your graduation (two years from now).

However, you want to use the money now. How much can you borrow today against this future $5,000, if the interest rate is 8% ?

Assume that grandmother is fully reliable


75

Example II – Single Cash Flow Suppose you open a savings account today

with $100 Suppose that the interest rate is 5% per year. How long will it take for you to become a

millionaire?


76

Multiple PeriodsOne

PeriodMultiple Periods

Future Value

Present Value

$ ?$ $$ ??$

r

? $ $? $$? $

AnnuitiesPerpetuities

Coupon BondZero

Coupon Bond

Multiple Payments

Pricing Real Securities

Developing Valuation Tool

r r r

r r rr r r

r r r

r


77

Valuing Zero-Coupon Bonds Makes one cash flow at maturity Consider a T-Bill issued by the government that

pays $1000 in one year; the interest rate is 10% What is the price of the bond?

Today 1 Year Later

1000

?


78

Valuing Coupon Bonds A coupon bond makes pays back only the

principal at the maturity but makes intermittent interest payments

Consider a T-Bill issued by the government that pays $1000 in 5 years and $10 in every prior year

What is the price of the bond? 1000

50

Today 5 Years Later


79

Multiple PeriodsOne


Future Value

Present Value

$ ?$ $$ ??$

r

? $ $? $$? $


Coupon BondZero

Coupon Bond

Multiple Payments



r r r

r r rr r r

r r r

r


80

FV of Multiple Cash Flows

Consider the following investment plan: You deposit $7,000 today You deposit $4,000 at the end of each of the

next 3 years Assuming the interest rate is 8%, how much

will you have in 4 years?

Time Line:

$7,000 $4,000 $4,000 $4,000

t0 t1 t2 t3 t4

?

81

$7,560 $12,484.8 $17,803.58



$7,000 $4,000 $4,000.0 $4,000.00

t0 t1 t2 t3 t4

23,547.87

$11,560 $21,803.58$16,484.8x1.08 x1.0

8

x1.08x1.0

8

Method 1: Rolling over cash-flows


82


$7,000 $4,000 $4,000.0 $4,000.00

x1.08

x(1.08)2

x(1.08)3

x(1.08)4

$4,320.00

$4,665.60

$5,038.85

$9,523.42

$23,547.87

t0 t1 t2 t3 t4

Method 2: Calculate the future value of each cash flow


83

$CF(4)/(1+r)4

PV of multiple cash flows Pricing a stream of cash flows

Get $CF(1) G

t0 t1 t2 t3 t4

/(1+r)

/(1+r)2

/(1+r)3

/(1+r)4

$CF(1)/(1+r)$CF(2)/(1+r)2

Get $CF(2) Get $CF(3) Get $CF(4)

$CF(3)/(1+r)3

4

1 )1()(

ttrtCFP


84

Pricing Coupon Bonds Bond w/ $100 FV, maturity of 4 years, $5 annual

coupon, discounted at 10% interest rate

$105/(1+.10)4

Get $5

t0 t1 t2 t3 t4

/(1+.10)/(1+.10)2/

(1+.10)3

/(1+.10)4

$5/(1+.10)

$5/(1+.10)2

Get $5 Get $5 Get $105

$5/(1+.10)3

15.84)1()(4

1

t

trtCFP


85

Multiple PeriodsOne


Future Value

Present Value

$ ?$ $$ ??$

r

? $ $? $$? $


Coupon BondZero

Coupon Bond

Multiple Payments



r r r

r r rr r r

r r r

r


Perpetuity Security that pays a fixed cash flow, C, every

period, forever. The interest rate is r.

…Pay $P

t=0

Get $C

t=1

Get $C

t=2

Get $C

t=3

86

€

P=C

1+ r+C

(1+ r)2 +C

(1+ r)3 +..

=C

(1+ r)tt=1

∞

∑


87

Deriving the perpetuity formula

€

P=C

1+ r+C

(1+ r)2 +C

(1+ r)3 +...

⇒ P(1+ r)=C +C

1+ r+

C(1+ r)2 + ...

⇒ P(1+ r) − P =C

⇒ P =Cr

Eq1:

Eq2 = Eq1*(1+r):

Subtract Eq1 from Eq2:

Extra credit: prove using a Taylor expansion. Due next class.

€

C(1+ r)tt=1

∞

∑ =Cr


88

Example III- Perpetuity Paying Forever:

Suppose that maintenance of a grave costs $100 every year, forever.

The interest rate is 5% per year. How much should you leave the trustee of a

grave?

89

Annuity


Security that pays a fixed cash flow, C, for T periods. The interest rate is r.

How can we relate this to our perpetuity formula?

Pay $P

t=0 t=T

Get $C

t=1

Get $C

t=2

Get $C

t=3 …

Get $C

€

P =C

(1+ r)tt=1

T

∑ =Cr⋅ 1 −

1(1+ r)T

⎡ ⎣ ⎢

⎤ ⎦ ⎥


90

Example IV - Annuity

What value car can you afford? You have no cash now You can afford to pay $632 per month The interest rate is 1% per month You want to have paid the loan in full in 48 months

€

P =C

(1+ r)tt=1

T

∑ =Cr⋅ 1−

1(1+ r)T

⎡ ⎣ ⎢

⎤ ⎦ ⎥

91

Multiple PeriodsOne


Future Value

Present Value

$ ?$ $$ ??$

r

? $ $? $$? $


Coupon BondZero

Coupon Bond

Multiple Payments




r r r

r r rr r r

r r r

r

RWJ 4, 5.1-5.2

H1_1H1_2H1_4


92

Putting it all together – Single vs. Multiple Cash Flow

You win the New York State Lottery, Jackpot is $3.0 million

You have a choice: $1.5 million today $150,000 annual payments for 20 years

The interest rate available to you is 5% a year Which option do you prefer?


93

Putting it all together – Single vs. Multiple Cash Flow

Time 0 1 Year 2 Years

3 Years

4 Years

5 Years

Time 0 1 Year 2 Years

3 Years

4 Years …20 Years

$1.5m

$150,000

$150,000

$150,000

$150,000

$150,000


94

Adding Risk

What changes if the cash flows are risk? How much a 50% chance of getting $100 in

1 month worth? Is it worth more or less than a 60% chance

of $100 in a month Is it worth more or less than a 100% chance

of getting $50 in one month?

Return Measures


96

Return Measures

Price: amount paid for an asset

Return: measure of profits earned on the investment

Return = Realized Payoff/Price


97

Outline: Return Measures Fixed Income Returns (Interest Rates)

Quoted rate (= Annual Percentage Rate) Effective Annual Rate Continuous Compounding

Stock Returns Single-period return:

Holding Period Return Multiple-period returns:

Arithmetic average Geometric average Internal Rate of Return


98

Compounding Up to now: annual compounding Suppose you can invest $100 in an account

that compounds every six months (pays 5% every six months)

How much do you have in six months? In one year?

Is this the same as 10% compounded annually?

Is this the same as 10.25% compounded annually?

This rate is quoted as “10% per year with semi-annual compounding” (this is the convention)


99

Quoted Interest Rates and EAR

FORMULA: Quoted interest rates are in the following format:“[quoted rate] compounded [period]”• For example: “10% compounded semi

annually” means that the investment is compounded twice a year at a periodic rate of 5%.

RESULT OF FORMULA: Effective Annual Rate (EAR) in this case is 10.25% year

100

Quoted Interest Rates


Quoted rate: 10% , compounded semi-annually

1 - 2%

10% 12

EAR

$105x(1+.05)$100 $110.25x(1+.05)

1\1\2008

7\1\2008

1\1\2009

x(1+.1025)

101

Quoted Interest Rates


The relationship between quoted rates and EAR (M is number of compounding periods):

1 - M

ratequoted 1M

EAR

$105x(1+q/M)$100 $110.25x(1+q/M)

1\1\2008

7\1\2008

1\1\2009

x(1+EAR)


102

Quoted Interest Rates Which loan would you prefer?

Bank A :15% compounded monthly Bank B: 15.1% compounded quarterly Bank C: 15.2% compounded annually


103

Continuous Compounding Consider increasingly frequent

compounding: annually, quarterly, daily, every second,…

What happens to the EAR? When Compounding happens “all the time”,

it is called continuous compounding EAR = exp(quoted rate) – 1 In our example: EAR = 10.52

1 1-Mq 1lim

M

r

MeEAR

Period M EAR

Year 1 10.000000%

QRT 4 10.381290%

Month 12 10.471310%

Day 365 10.515580%

Minute 525,600 10.517090%

Quoted Rate = 10%


104

APR Lenders are required by law to report the

Annual Percentage Rate, APR. APR is the Quoted Rate we discussed: APR =

periodic rate * #periods per year The APR represents simple interest and

therefore is the incorrect way to measure annual returns

Nonetheless, credit cards and others making loans to consumers are often required to report it


105

Example - APR

Your credit card has the following terms: Quoted Rate = 18%, compounded

monthly Periodic Rate = 1.5% per month APR = 12*1.5% = 18% per year

You missed a payment of $1 today, how much will the credit card company charge you in a year?19.56% 1 -

120.18 1

12

EAR


106

Outline: Return Measures Fixed Income (Interest Rates)

Quoted rate (= Annual Percentage Rate) Effective Annual Rate Continuous Compounding





107

Holding Period Return (HPR) - Example Holding Period Return – general definition:

Holding Period Return for stock:

Annualized HPR for holding period of T years:1)1( Annualized /1 THPRHPR

1AssetOfValueBeginningAssetOfValueEndingHPR

1price beginning

dividendcash price ending

HPR

108

Firm

Investor A

1y 2y 3y 4y 5y

Holding Period Return (HPR) – Stock Example


Investor B

Dividend of $1.60

Investor A buys a stock for $86

After 4 years, she gets a dividend of $1.60 and sells the stock for $99

$86

$99

%4117.1

%17186

1.60 99

41

AHPR

HPR


109

Stock Examples – Holding Period Return (HPR)

You bought Coca-Cola shares for $47.99 on 1/1/09 and sold them six months later on 6/1/09 for $49.02. Suppose there was no dividend payment in these six months. What is the HPR and the annualized HPR?

You bought Nike shares on 6/1/07 at $56.70 and sold the shares 2 years later at $57.05. Suppose the only dividend is $1.50 paid at the end of year 2. What is the HPR? What is the annualized HPR?


110

Outline: Return Measures Fixed Income (Interest Rates)

Quoted rate (= Annual Percentage Rate)

Effective Annual Rate Continuous Compounding





111

Multiple-Period Return – Arithmetic Average

Simple Average Return (Arithmetic Return) definition:

Not equivalent per-period return because it neglects compounding

Useful for forecasting the return next period

)...(1321 TA rrrr

Tr


112

Multiple-Period Return – Geometric Average Geometric Return definition:

Gives the equivalent per-period return

1)]1)...(1)(1[( /121 T

Tg rrrr


113

Hedge Fund Example – Multiple-Period Return

Suppose an Emerging Markets hedge fund has the following returns: Year 1: r1 = -50% Year 2: r2 = 100%

What is the forecasted return for year 3? What is the return if:

1st year profits are reinvested? 1st year profits are held as cash?


114

Hedge Fund Example – Multiple-Period Return

Suppose an Emerging Markets hedge fund has the following returns: Year 1: r1 = 100% Year 2: r2 = -50%

What is the forecasted return for year 3?

What is the return if: 1st year profits are reinvested? 1st year profits are held as cash?


115

Net Present Value NPV: The difference between an

investment’s present value and its cost NPV = PV(cash flows) – initial costs If NPV > 0, value is created, undertake

investment Is it really that simple? What information

do we need to calculate NPV?


116

Discount Rates and Rates of Return

FV=PV*(1+r)T

HPR = FV/PV - 1 = (1+r)T - 1


117

Internal Rate of Return (IRR) IRR is the return that sets the present value of

future cash flows equal to the initial cost

Used to evaluate projects

C(1) C(2) C(3)

T

ttIRR

tCPVP1 )1(

)()0(P(0)


118

Project Valuation Example: Internal Rate of Return (IRR)

Pfizer wants to compute the opportunities in a potential project

The Business plan projects the following cash flows: Initial investment: $100k Sales in year 1: $50k Sales in year 2: $50k Sales in year 3: $30k

What is the IRR?


119

Outline: Return Measures

Quoted rate (= APR) Effective Annual Rate Continuous Compounding Single-period return:



H1_3

H1_6

H1_5

RWJ 5.3

BKM 5.1


120

Next

Reading: Today: Review concept questions after

chapter 4 and chapter 5 of RWJ Required reading for next class:

BKM: 5.1, 5.2, 5.3, 5.5 Investment Game 1 – due class Tuesday,

May 31 Problem Set 1 – Due Tuesday, May 31

121

Outline – Week 1


Course Overview Financial Markets

Why they exist How they work

How do borrowers access markets How do capital markets work How do investors access markets?

Returns Time value of money

Single cash flow Multiple cash flows Perpetuities/annuities

Measures Compounding Equity cash flows

foundations of finance

Documents

knowledge financial

real assets matter

real assets firm equipment

real assetsover

households real estate

themlarge firm

excess capital gains

primary capital market