Simple Evolution of a Business Sole proprietorship owned

Simple Evolution of a Business • Sole proprietorship (owned by single individual) – Joe does well making snowboards in his garage – Demand rises, Joe wants to expand Raise funds for expansion External Internal Reinvest profits Retained Earnings Borrow from Bank Borrow from friends

No Such Thing as a Free Lunch • Joe likes the sole proprietorship legal status, – Gives him control over the business • No layers of management to worry about – But, he recognizes two disadvantages: • Limited ability to raise funds • Unlimited personal liability – No legal distinction between personal assets & business assets

Alternative Legal Structures • Partnership – jointly owned firm with two or more partners – Advantages: • Shares work with partners • Shares risks with partners – Disadvantages: • Unlimited liability • Limited ability to raise funds

Alternative Legal Structures • Corporation – legal “person” separate from owners – Advantages: • Limited personal liability • Greater ability to raise funds – Disadvantages: • Costly to organize • Double taxation of profits • Separation of ownership and control

√ √ Invest

Alternatives • Bonds – Government Bonds – Corporate Bonds – Municipal Bonds s Cash Equivalents Ÿ Money Market Funds Ÿ Treasury Bills (T-bills) Ÿ Certificates of Deposit – International Bonds • Stocks – Large Company Stocks • large-cap – Small Company Stocks • small-cap – International Stocks s Real Assets Ÿ Real Estate Ÿ Commodities Ÿ Gold & silver Bonds & Stocks are the two main types of financial securities.

Joe’s Snowboard Co. – a Corporation • Joe finds 9 people to invest money in his business. • In exchange for investing money they will receive a share of the profits – Joe plus 9 each invest $10, 000; • now there are 10 stockholders, • each with 10% ownership of Joe’s Snowboard Co.

Expansion Financing Alternatives • Joe’s Snowboard Co. – The corporation wants to expand Raise funds for expansion Internal Reinvest profits External Borrow from Bank Financial Markets Retained Earnings Bonds Stock

A Key Role of Stock Markets • Provide liquidity – investors more likely to purchase stocks if • they know selling them will not be terribly difficult • limited liability – most can lose is the purchase price – easier for companies to raise funds for investment • promotes long-run economic growth

What Is Stock & Where’s the Return? • Share of stock = share of ownership of company – Own part of company – Stockholder has a piece of equity • stocks often called equities • Return from owning stock? – Share in profits: • dividends • stock price appreciation – capital gain

Bonds • World’s largest investment sector • Debt – promises to repay fixed amount of funds – corporate bonds (30 -year maturity common) – government debt • • U. S. Savings bonds U. S. Treasury bills (3 and 6 mo. ; one year) U. S. Treasury notes (2, 5, 10 year) U. S. Treasury bonds (over 10 year) – for more info: http: //www. treasurydirect. gov/

Characteristics of Bonds • Bond is an IOU from issuer – maturity date – repayment of principal – face value – amount to be paid upon maturity – coupon rate – interest rate paid periodically on face value until maturity – Primary issue: • When initially issued, the buyer is loaning funds to the issuer (U. S. Treasury, corporation, state/local government) – Secondary market: • Bonds are bought and sold repeatedly before maturity

U. S. Treasury issued after 9 -11 Not liquid

Treasury Bills • T-bills – short term • one year or less maturity – minimum denomination = $1, 000 – sold at discount (“zero-coupon bond”) • government pays face value at maturity – For example: – purchase T-Bill with 1 -year maturity for $950 » i = (face value – price paid)/(price paid) = ($1, 000 - 950) / (950) = 5. 3%

If U. S. Considered Safe Haven • Demand for T-Bills increases – (D-curve shift rightward) P rises • As P $1, 000 effective yield (i) 0%

3 -Month Treasury Bills Secondary Market Double-digit inflation

If U. S. Considered Credit Risk • Demand for T-Bills falls – (shift D leftward) P of T-bills falls – As P falls i rises e. g. , Greek bond rates have VERY high risk spread over Euro bonds

Treasury Notes & Bonds • Face value – suppose $1, 000 • Coupon rate • interest rate paid on the face value of bond • usually pay semiannually, • but we’ll assume annual • Maturity date

E 2 + S + I 2 = F 2 I: Time to Invest Your Money • Suppose you receive a high-school graduation gift from your uncle – $10, 000 • In 10 years you plan to purchase your first home and you need a down-payment • Go stand on the investment of your choice …

Investment Choices – Savings account – Bonds – Stocks Concepts that arise in this discussion? Risk Liquidity Ø Return

Problem: How to Invest My Savings Alternatives Risk Criteria Return Liquidity Income Bonds Stock Savings Acct What criteria (factors) are important to you in making this decision?

Understanding Rates of Return

The Magic of Compounding • When you save, you earn interest. – spend it and it stops growing • But if you leave the interest in so it can grow. . . – you start to get interest on the interest you earned • Interest on interest is money you didn’t work for – your money is making money for you! • Over time, interest on interest is large! – but only if you leave the interest to grow.

POWER OF COMPOUNDING • Compound Interest is Exponential Growth Pn = P( 1 + i )n

Compound Interest & the Rule of 72 • How many years does it take to double your investment? • You will be given a jar with 100 beans

How Long Does It Take to Double Your Investment? • Using the interest rate given to you – add the “interest” in beans to your original 100. – count how many years it takes you to reach the top of the blue tape. Be sure to use “compounding!” How long did it take?

Fill in the Added Amount after Each Year Amount to add 9 10 11 12 13 14 15 17 New total: 109 119 130 142 155 169 184 201

Compounding & the Bean Counters • Rule of 72: – 72/i = # of years to double • In this case, i = % growth • For example, – If you earn 9% per year, • takes about 8 years to double your money – If population growth rate is 2% per year • takes 36 years to double

Teaching Compounding to Students? • Observe power of compounding – the chessboard game • The King’s Chessboard

The Chessboard of Financial Life • What would you rather have: – $10, 000 in cold cash, – or, the amount of money on the last square (i. e. , the 64 th) of a chessboard if: • 1 penny on first square • 2 pennies on 2 nd square • 4 pennies on 3 rd square • 8 pennies on 4 th square • so on, doubling with each subsequent square • Well. . . ? ?

The Power of Compounding! • How solve the problem? • General formula? Pn = P( 1 + i )n • Pn = ($0. 01)(1 + 1)63 – r = 100% (or 1. 0) – with n = 63 squares after 1 st – Pn = $92, 233, 720, 368, 600, 000 • slightly over $10, 000! • a no-brainer!

Which Would You Rather Have? • Combined current fortune of the 400 richest Americans, or • The wealth you would receive from being paid weekly • • 1 cent the first week 2 cents the second week 4 cents the third week and so on for the year • P 52 = ($0. 01)(1 + 1)51

And the Answer Is. . . • 400 richest? – about $1 trillion • One cent, doubled each week for one year? • P 52 = ($0. 01)(1 + 1)51 • = $22, 517, 998, 136, 900, or $21. 5 trillion, – just for final week of pay! – all weeks, $45 trillion! • “Yo Dad, no problem about my $1 per week allowance. • How about just doubling the weekly amount for the next six months and I’ll just take the resulting total. ” • ($16. 8 M)

Background: Stock Indices

Examples of Stock Indexes - Domestic • Dow Jones Industrial Average • Standard & Poor’s 500 • NASDAQ Composite • NYSE Composite • Wilshire 5000

Dow Jones Industrial Average (DJIA) • Large, “blue chip” corporations – 1896: included 12 stocks – 1928: included 30 stocks • Only 1 of the 30 stocks in the 1928 DJIA is still included: • General Electric – General Motors dropped off in 2009

Dow Jones Industrial Average (30 stocks) Alcoa Chevron American Express Kraft Foods Boeing Caterpillar Travelers Cos. (replace Citigp) Coca-Cola Du. Pont Pfizer Exxon Mobil General Electric Cisco Systems (replaced GM) Hewlett-Packard Home Depot IBM Intel Verizon Johnson & Johnson Mc. Donald’s Merck Microsoft 3 M J. P. Morgan Chase Bank of America Proctor & Gamble AT&T United Technologies Wal-Mart Walt Disney

Standard & Poor’s 500 • 500 large & popular companies – e. g. , Pepsi, Xerox, Reebok, Fedex Berkshire Hathaway • includes all of 30 DJIA • Broader base (500 versus 30) – Preferred over DJIA

Capitalization • Market value of company (P x Q) – P = per share price – Q = quantity of shares outstanding – Large cap: PQ > $10 B e. g. , Exxon, MS, Wal-Mart, GE – Mid cap: – Small cap: $2 B < PQ < $10 B $300 M < PQ < $2 B

Construction of Indices • Stock indices are weighted averages • How are stocks weighted? – Price weighted (DJIA) • equal number of shares of each stock • higher-priced stock have greater weight – Market-value weighted (S&P 500, NASDAQ) • in proportion to outstanding capitalization • larger companies have greater impact

Pn = (1 + i)n P 0 • Three applications: – Know P 0, i, and n • Calculate Pn

The Concept of Present Value • Flip coin to the other side of the compound growth formula – Which would you prefer: • $50 today, or • $50 ten years from today? – Money today is more valuable than the same amount of money in the future.

Time Value of Money • Which would you prefer – $ 50 today, or – $150 in 10 years? • Need way to compare sums of money at different times. Concept: Present value The PV of any future sum: - amount of money needed today to produce future sum (at some interest rate, i ).

Example • Your uncle says, – I promise to give you $10, 000 when you complete college in 4 years. – Two equivalent ways to think about this: • How much does your uncle have to have invested today, at some rate i, to end up with $10, 000 in 4 years? • What is the present value of $10, 000 four years from today, at interest rate, i?

Solve for Present Value • P 0 = Pn / (1+i)n (let’s assume i = 5%) = 10, 000/(1+. 05)4 = $8, 227 That is, the present value (of the promise from your uncle) is $8, 227. Verify? $8, 227(1. 05)4 ≈ $10, 000

A Generous Uncle! • Your uncle then adds on to his promise: – I promise to give you another $10, 000 when you reach age 30 (you are presently 18). – What is the present value of $10, 000 received 12 years from today? (i = 5%) – P 0 = Pn / (1+ i)n = 10, 000/(1+. 05)12 = $5, 568

Even More Generous • I promise to give you another $10, 000 when you reach age 40. – P 0 = Pn / (1+ i)n = 10, 000/(1+. 05)22 = $3, 419

Now, What is the Total Present Value of Uncle’s Promises? • Sum of the PV of all three. . . Nominal sum of the three gifts = $30, 000.

Put Differently. . . § If Uncle had $17, 214 now and earned 5% per year interest, he could withdraw: § $10, 000 at end of year 4, § $10, 000 at end of year 12, and § $10, 000 at end of year 22. § He would then have nothing left.

Applications of Present Value (Examples) • Suppose you win the $1, 000 lottery – $100 per year for 10 years • What is the present value of your winnings? – ignore taxes; assume i = 10%

Treasury Notes & Bonds • Face value – suppose $1, 000 • Coupon rate • interest rate paid on the face value of bond • usually pay semiannually • we assume annual • Maturity date

Face Value: $1, 000 Coupon rate: 1. 75% Time to Maturity: 10 years • Rate 1. 75 Treasury Bond Maturity Mo/Yr Price 5/15/22 Year 1 Year 2 $17. 50 101. 88 $1, 018. 80. . WSJ, July 6, 2012 Secondary Bond Market Yld 1. 544 Year 10 $17. 50 + $1, 000 How Much Is Such a Promise Worth Today?

The Power of Compound Interest • Upon his death in 1791, Benjamin Franklin left $5, 000 to each of his favorite cities – Boston and Philadelphia. • He stipulated that the money should be invested and not paid out for 100 - 200 years. – at 100 years, each city could withdraw $500, 000. – after 200 years, they could withdraw the remainder.

Power of Compounding • Actual result: – In 1891: Each city withdrew $500, 000 & • invested the remainder. – In 1991: Each city withdrew approximately: • $20, 000. • Calculate the geometric return (CAGR) – Assume $5, 000 grows to $20, 000 million in 200 years – $5, 000 (1 + i)200 = $20, 000 CAGR = 4. 23%

Real vs. Nominal • Nominal: – growth rate of money • Real: – growth rate of actual purchasing power – Inflation-adjusted rate of return

Warren Buffet on Gold • Today, the world’s gold stock is about 170, 000 metric tons. If all of this gold were melded together, it would form a cube of about 68 feet per side. (Picture it fitting comfortably within a baseball infield. ) At $1, 750 per ounce – gold’s price as I write this – its value would be $9. 6 trillion. Call this cube pile A. • Let’s now create a pile B costing an equal amount. For that, we could buy all U. S. cropland (400 million acres with output of about $200 billion annually), plus 16 Exxon Mobils (the world’s most profitable company, one earning more than $40 billion annually). After these purchases, we would have about $1 trillion left over for walking-around money (no sense feeling strapped after this buying binge). Can you imagine an investor with $9. 6 trillion selecting pile A over pile B?

• A century from now the 400 million acres of farmland will have produced staggering amounts of corn, wheat, cotton, and other crops – and will continue to produce that valuable bounty, whatever the currency may be. • Exxon Mobil will probably have delivered trillions of dollars in dividends to its owners and will also hold assets worth many more trillions (and, remember, you get 16 Exxons). The 170, 000 tons of gold will be unchanged in size and still incapable of producing anything. You can fondle the cube, but it will not respond. • Admittedly, when people a century from now are fearful, it’s likely many will still rush to gold. I’m confident, however, that the $9. 6 trillion current valuation of pile A will compound over the century at a rate far inferior to that achieved by pile B.