1. Capital and Financial Market Hall and Lieberman, 3 rd edition, Thomson South-Western, Chapter 13

2. 2 Consider…  1626, Peter Minuit bought Manhattan from the Man- a-hat-a Indians for goods valued at $24  The 12800 acres are now valued at $627 million/acre or $8 trillion unimproved  This was a heck a deal for the Dutch Is this true?

3. 3 The Value of Future Dollars  Always preferable to receive a given sum of money earlier rather than later Because present dollars can earn interest and Because borrowing dollars requires payment of interest  $1 one year from now is not equal to $1 today Mechanism (r = rate of interest) Opportunity cost of spending $1 today = $(1 + r)*1 = $(1 + r) at r = 0.1; opportunity cost is $1.10 next period

4. 4 Future Value  Future Value: the value in dollars at a future point in time of a sum of money today.  Compounding: successive application of interest payments to generate future values. Period 0Period 1Period 2 $1(1+r)*$1$(1+r)*{(1+r)*$1} = (1+r) 2 *$1

5. 5 Future Value  Generally, $1 today is worth $(1+r) t t years from now At r = 0.1 Period 0: $1 Period 1: $(1+ 0.1) = $1.10 Period 2: $(1 + 0.1) 2 = $1.21 Period 3: $(1 + 0.1) 3 = $1.33 …… Period 40: $(1 + 0.1) 40 = $45.26

6. 6 Future Value: Man-a-hat-a Indians  How much is $24 in 1626 worth today if they just collected interest?  $1 in 1626 is worth $(1+r) T in 2006, T = 2006-1626 = 380 At r = 0.1; $24*(1+r) 380 = $1,286,564 trillion At r = 0.08; $24*(1+r) 380 = $120.6 trillion At r= 0.07; $24*(1+r) 380 = $35.2 trillion At r = 0.06; $24*(1+r) 380 = $99.2 billion At r = 0.05; $24*(1+r) 380 = $2.7 billion Breakeven r=7.23%

7. 7 Example: Investment for Retirement  Suppose you want to be a millionaire when you retire. How much should you start putting away FV = $1 million A = annual amount invested  How much would you have after T years?

8. 8 Example: Investment for Retirement  Suppose you want to be a millionaire when you retire. How much should you start putting away  FV = {[(1+r)T+1 – (1+r)]/r}A  Current age = 18; Millionaire by 40? 50? 60?

9. 9 Present Value  Present value (PV) of a future payment is the value of that future payment in today ’ s dollars  Value of any asset is sum of present values of all future benefits it generates  Discounting Converting a future value into its present-day equivalent  Discount rate Interest rate used in computing present values Period 0Period 1 $1 (1+r)*$1 $1/(1+r) $1

10. 10 Present Value  Suppose that the annual interest rate is r, PV of $Y to be received T years in the future is equal to  Present value of a future payment is smaller if Size of the payment is smaller Interest rate is larger Payment is received later

11. 11 Present Value  Generally  Period 0Period T $1 (1+r) T *$1 $1/(1+r) T $1  At r = 0.1; compute present value of $1 in Period X Period Present Value 1$1/(1+.1) = $0.91 2$1/(1 +.1) 2 = $0.83 3$1/(1 +.1) 3 = $0.75 40 $1/(1 +.1) 40 = $0.02

12. 12 Consider…  Furnace Advertisement Furnace costs $2,000 Energy Savings = $200/year Claim: The furnace will pay for itself in 10 years Is this true?

13. 13 Example : Furnace  $200 T periods in the future will be worth $200/(1+r) T now At r = 0.1; Year Present Value 1$200/(1+.1) = $181.82 2$200/(1 +.1) 2 = $165.29 3$200/(1 +.1) 3 = $150.26 … 10 $200/(1 +.1) 10 = $77.11 ADD UP THESE RETURNS Present Value = $1,429 It would take 24 years to break even at r = 0.1

14. 14 Conclusions Regarding Present & Future Value  General Formula PV : Present Value FV: Future Value FV T = (1+r) T * PV 0 (Compounding) PV 0 = FV T / (1+r) T (Discounting)

15. 15 Other Issues and Applications  Present Value can be used in making capital/equipment decisions.  Consider the problem of purchasing a piece of equipment with a MRP of $100/year and a lifespan of 10 years.  How would you compute the present value of this stream of returns?  Present value can be used to value returns that vary over time Modified to account for uncertainty

16. 16 Investment in Human Capital  Suppose you are an account for an entertainment company. You have to decide whether to take a specialized course in how to handle the books of entertainment companies.  Costs: $30,000 tuition + $25,000 foregone income  Benefits: Increase your income by $10,000 a year for the next eight years before you retire.  If interest rate=10%, what ’ s your decision?  What if interest rate=8%?

17. 17 Bonds  One of the methods to finance the production is selling bonds  Bond is a promise to pay a specific sum of money at some future date This amount of money is principal (face value)  Most common amount: $10,000 The date at which a bond ’ s principal will be paid to bond ’ s owner is Maturity Date

18. 18 Bonds  Principal:  The value of the bond at maturity  The face value on the bond  Future Value  Individuals buy bonds at the present value of the principal

19. 19 The Bond Market  Pure discount bond Promises no payments except for principal it pays at maturity  Coupon payments Series of periodic payments that a bond promises before maturity  Yield Rate of return a bond earns for its owner

20. 20 How Much is a Pure Discount Bond Worth?  Value of a bond with a face value of $10,000 which matures in exactly one year and has an interest rate of 10% is  Bond will sell for $9,091

21. 21 How Much Is A Coupon Payment Bond Worth?  Bond with a principal of $10,000, a five-year maturity and an annual coupon payment of $600 has a present value of  Total present value is what bond is worth Price at which it will trade  As long as buyers and sellers use the same discount rate of 10% in their calculations

22. 22 How To Calculate Yield?  Suppose bond matures in one period P BOND = PV = FV/(1+r) Yield is implied by (1+r) = FV/PV  If bond matures T periods from now P BOND = PV = FV/(1+r) T Annual yield is implied by (1+r) = ( FV/PV ) 1/T  The higher the price of any given bond the lower the yield on that bond

23. 23 Bond’s Yield: Example  Suppose FV = $10,000; P BOND = $9500; Maturity in one period Then, yield is (1+r) = FV/PV = (10,000/9,500) = 1.053 Implying that annual interest rate r = 0.053

24. 24 Why Do Bond Prices (and Bond Yields) Differ?  Each bond traded everyday has its own unique yield  Why doesn ’ t each bond sell at a price that makes its yield identical to the yield on any other bond? A bond — like any asset — is worth the total present value of its future payments

25. 25 Why Do Bond Prices (and Bond Yields) Differ?  To put a value on riskier bonds, markets participants use a higher discount rate than on safe bonds Leads to lower total present values and lower prices for riskier bonds With lower prices, riskier bonds have higher yields  Higher risk, higher yield, lower price

26. 26 Why Do Bond Prices (and Bond Yields) Differ?  Riskiness is only one reason that bond prices and bond yields differ Other reasons include  Differences in maturity dates  Differences in frequency of coupon payments  Because one bond is more widely traded (and therefore easier to sell on short notice) than another

27. 27 Rating on Bonds  According to the likelihood of default, bonds are rated in the following (Moody ’ s Investor ’ s Services estimate):  U.S. Treasury bond - the least risky  Aaa Corporate bond  Aa Corporate bond  A Corporate bond  Baa Corporate bond  Ba Corporate bond  B Corporate bond - higher risk

28. 28 Can you outguess the market? Suppose you expect that price of bond will fall tomorrow because the Federal Reserve Board of Governor ’ s is going to raise the reserve rate (the interest rate charged to banks by the Fed). What will you do? If everyone has the same information, all act similarly, what will happen?

29. 29 Fundamental value of stocks  Stock: share of ownership in the firm  Stockholder has a share of the future earnings of the firm  Stock price should be the present value of the stream of future earnings per share

30. 30 Fundamental value of stocks  Stock price should be the present value of the stream of future earnings per share (E)  PV = Price of stock = E + E/(1+r) + E/ (1+r) 2 + E/ (1+r) 3 + … = E/r  Price Earnings (PE) ratio: Price of stock/E = (1/r)  Very high PE ratios imply having to pay a lot per $ of expected earnings

31. 31 Valuing a Share of Stock  Important conclusions about factors that can affect a stock ’ s value An increase in current profits increases value of a share of stock An increase in anticipated growth rate of profits increases value of a share of stock A rise in interest rates — or even an anticipated rise in interest rates — decreases value of a share of stock An increase in perceived riskiness of future profits decreases value of a share of stock

32. 32 Gambling vs. Investing  Expected return P i = probability that outcome i happens R i = Return when outcome i happens C = investment costs N outcomes Probabilities add up to 1 Expected Return = Σ P i R i - C i=1 N

33. 33 Gambling vs. investing Fair bet: Expected return is zero Coin flip: Pay C = $1 to play Heads: Receive R 1 = $2, P 1 =.5 Tails: Receive R 2 = $0, P 2 =.5 Expected Return = P 1 R 1 + P 2 R 2 - C =.5*2 +.5*0 - 1 = 0

34. 34 Gambling  Unfair bet: Gambler: Expected return <0 Casino: Expected return >0  Example : slot machines pay 92 ¢ per $ bet Expected return for customer = -8 ¢ Expected return for Casino = 8 ¢  Lottery Expected return for customer = -50 ¢ /$ Expected return for Lottery = 50 ¢ /$

35. 35 Gambling  Cards, Horses  Gambler: Expected return depends on skill Casino: Expected return >0 on average or else they rent the space (poker)  Casinos will not offer games that have negative expected return to the Casino

36. 36 What proportion of ISU college students gamble? Overall 56% Males 61% Females49% Gamblers spent 64% < $20/month 18% $20-$60/month 18% > $60/month Average $33 per month T. Hira and K. Monson. “A social learning perspective of gambling among college students”

37. 37 Why do ISU students gamble? Entertainment 65% To win money 30% Women more likely to say “ for entertainment ” Men more likely to say “ to win ” T. Hira and K. Monson. “A social learning perspective of gambling among college students”

38. 38 Risk From Uncertainty  Future payment is not guaranteed sometimes There is uncertainty in your investment The higher the risk, the higher the payoff Goal: maximize the expected future return by choosing one or some among a bunch of financial assets, given the same risk  Or reduce the risk to the least given the same expected return

39. 39 The Higher the Risk, the Higher the payoff  Investment on A is less risky than investment on B, but has a lower expected return from investment tradeoff Probability 0.20.8 Expected Return 80 Payoff from A0100 Probability 0.80.2 Expected Return 120 Payoff from B0600

40. 40 Diversification - Portfolio  Holding several assets can lower risk without sacrificing return  The mixed portfolio yields higher utility—same expected return, lower variance Probability 0.20.30.5 Expected Return St Dev Return A300201611.14 B020 168.00 0.5A+0.5B151020164.36

41. 41 Diversification  How can you low the risk? 1. Mutual fund Financial intermediary holds a portfolio of stock. 2. Individual investors buy shares of the portfolio 3. Holding assets over a long period can lower risk - Higher average return wins out Warren Buffet: Asked when is the best time to sell stock ………… Never