1. 2007 Page 1 F. MICHAUX CORPORATE FINANCE

2. 2007 Page 2 F. MICHAUX GENERAL AGENDA Valuation and Discounted Cash Flow Method Valuing Bonds Valuing Stocks

3. 2007 Page 3 F. MICHAUX VALUATION AND DISCOUNTED CASH FLOW METHOD

4. 2007 Page 4 F. MICHAUX TIME VALUE OF MONEY BASIC PROBLEM FACED BY FINANCIAL MANAGER IS HOW TO VALUE FUTURE CASH FLOWS? I HAVE TO SPEND MONEY TODAY TO BUILD A PLANT WHICH WILL GENERATE CASH FLOWS IN THE FUTURE

5. 2007 Page 5 F. MICHAUX IF I HAD THE DOLLAR TODAY I COULD INVEST IT EARN INTEREST DURING THE YEAR SO THAT I’D HAVE MORE THAN A DOLLAR IN A YEAR’S TIME A DOLLAR TODAY IS WORTH MORE THAN A DOLLAR IN THE FUTURE

6. 2007 Page 6 F. MICHAUX INVESTING FOR ONE PERIOD I INVEST $100 TODAY AT r =.1 PER YEAR AT END OF YEAR, I RECEIVE $110 (FV) FV=100(1+r)

7. 2007 Page 7 F. MICHAUX PRESENT VALUE Present Value = PV PV = Discount Factor X C 1

8. 2007 Page 8 F. MICHAUX Discount Factor = DF = PV of $1 Discount Factors can be used to compute the present value of any cash flow. PRESENT VALUE

9. 2007 Page 9 F. MICHAUX Replacing “1” with “t” allows the formula to be used for cash flows that exist at any point in time. PRESENT VALUE

10. 2007 Page 10 F. MICHAUX PRESENT VALUES EXAMPLE: SAVING FOR A NEW COMPUTER You will need $3,000 in a year’s time to buy a computer You can earn interest at 8% per year How much do you need to set aside now? PV OF $3,000 = 3,000/1.08 = 3,000 x.926 = $2,777.77.926 is the 1-YEAR DISCOUNT FACTOR at the end of 1 year $2,777.77 grows to 2,777.77 x 1.08 = $3,000

11. 2007 Page 11 F. MICHAUX OFTEN CALLED DISCOUNT FACTOR CALCULATING DISCOUNTED CASH FLOWS r DISCOUNT RATE HURDLE RATE OPPORTUNITY COST OF CAPITAL

12. 2007 Page 12 F. MICHAUX WE HAVE ASSUMED THAT FUTURE CASH FLOWS ARE KNOWN WITH CERTAINTY IF FUTURE CASH FLOWS ARE NOT CERTAIN USE EXPECTED FUTURE CASH FLOWS USE HIGHER DISCOUNT RATE EXPECTED RATE OF RETURN ON OTHER INVESTMENTS OF COMPARABLE RISK WHICH IS NOT AVAILABLE TO US BECAUSE WE INVESTED IN THE PROJECT SAFE DOLLAR IS WORTH MORE THAN A RISKY DOLLAR

13. 2007 Page 13 F. MICHAUX INTEREST RATE DOES NOT HAVE TO BE FOR A YEAR INTEREST RATE per period WHERE THE PERIOD IS ALWAYS SPECIFIED THE EQUATION FV=PV(1+r) GIVES THE FV at the end of the period, WHEN I INVEST P AT AN INTEREST RATE OF r PER PERIOD

14. 2007 Page 14 F. MICHAUX EXAMPLE r =.02 PER QUARTER P=$100 HOW MUCH DO I HAVE AT THE END OF THE QUARTER? FV=PV(1+r)=100x1.02=102

15. 2007 Page 15 F. MICHAUX TWO RULES FOR ACCEPTING OR REJECTING PROJECTS 1. INVEST IN PROJECTS WITH POSITIVE NPV 2. INVEST IN PROJECTS OFFERING RETURN GREATER THAN OPPORTUNITY COST OF CAPITAL

16. 2007 Page 16 F. MICHAUX RATE OF RETURN RULE RETURN = PROFIT = 400 - 350 = 14.3% INVESTMENT 350 ACCEPT PROJECT BECAUSE RATE OF RETURN IS GREATER THAN THE OPPORTUNITY COST OF CAPITAL, 7%

17. 2007 Page 17 F. MICHAUX VALUING AN OFFICE BUILDING STEP 1: FORECAST CASH FLOWS Cost of building, C 0 = 350 Sale price in Year 1, C 1 = 400 STEP 2: ESTIMATE OPPORTUNITY COST OF CAPITAL If equally risky investments in the capital market offer a return of 7%, then cost of capital, r = 7% STEP 3: Discount future cash flows C 1 400 PV = = = 374 1 + r 1.07 STEP 4: Accept project if PV of payoff exceeds investment NPV = -350 + 374 = +24

18. 2007 Page 18 F. MICHAUX ONE-PERIOD PROJECT: RETURN UNCERTAIN INVEST $1,000 NOW. RECEIVE EXPECTED UNCERTAIN CASH FLOW AFTER 1 YEAR, WHOSE EXPECTED VALUE IS $1,300 INVESTORS CAN BUY EQUALLY RISKY SECURITIES WITH 35% EXPECTED RETURN. DECISION: 1. DON'T INVEST BECAUSE 30% PROJECT RETURN IS LESS THAN 35% OPPORTUNITY COST. 2. DON'T INVEST BECAUSE NET PRESENT VALUE IS NEGATIVE. 1,300 NET PRESENT VALUE = 1.35 - 1,000 = 963 - 1,000 = -37 VALUE OF FIRM WILL FALL BY $37 IF WE ACCEPT THE PROJECT

19. 2007 Page 19 F. MICHAUX INVESTING FOR MORE THAN ONE PERIOD I INVEST P=$100 FOR 2 YEARS AT r =.1 PER YEAR. AT END OF YEAR 1, I HAVE FV 1 =100X1.1=110 IN MY ACCOUNT, WHICH IS MY BEGINNING PRINCIPAL FOR YEAR 2. AT THE END OF YEAR 2, I WILL HAVE FV 2 =FV 1 (1+r) =P(1+r)(1+r) =P(1+r) 2 =121 I WILL EARN $10 INTEREST IN YEAR 1, $11 INTEREST IN YEAR 2, ALTHOUGH r =.1 IN BOTH YEARS. WHY?

20. 2007 Page 20 F. MICHAUX FUTURE VALUE OF $121 HAS FOUR PARTS FV 2 =P(1+r) 2 =P+2rP+Pr 2 P=100 RETURN OF PRINCIPAL 2rP=20 SIMPLE INTEREST ON PRINCIPAL FOR 2 YEARS AT 10% PER YEAR Pr 2 =1 INTEREST EARNED IN YEAR 2 ON $10 INTEREST PAID IN YEAR 1 AMOUNT OF SIMPLE INTEREST CONSTANT EACH YEAR AMOUNT OF COMPOUND INTEREST INCREASES EACH YEAR

21. 2007 Page 21 F. MICHAUX FV OF PRINCIPAL, P, AT END OF n YEARS IS FV n =PV(1+R) n

22. 2007 Page 22 F. MICHAUX COMPOUND INTEREST INTEREST EARNED ON PRINCIPAL AND REINVESTED INTEREST OF PRIOR PERIODS

23. 2007 Page 23 F. MICHAUX SIMPLE INTEREST INTEREST EARNED ON THE ORIGINAL PRINCIPAL ONLY

24. 2007 Page 24 F. MICHAUX Compound Interest i ii iii iv v Periods Interest Value Annually per per APR after compounded year period (i x ii) one year interest rate 1 6% 6% 1.06 6.000% 2 3 6 1.03 2 = 1.0609 6.090 4 1.5 6 1.015 4 = 1.06136 6.136 12.5 6 1.005 12 = 1.06168 6.168 52.1154 6 1.001154 52 = 1.06180 6.180 365.0164 6 1.000164 365 = 1.06183 6.183

25. 2007 Page 25 F. MICHAUX FUTURE VALUE Year 1 2 5 10 20 5% 1.050 1.103 1.276 1.629 2.653 10% 1.100 1.210 1.331 2.594 6.727 15% 1.150 1.323 2.011 4.046 16.37 0 2 4 6 8 10 12 14 16 1820 20 15 10 5 0 FUTURE VALUE OF $1 YEARS

26. 2007 Page 26 F. MICHAUX PRESENT VALUE PRESENT VALUE OF $1 r = 5% r = 10% r = 15% PRESENT VALUE Year 5%10%15% 1.952.909.870 2.907.826.756 5.784.621.497 10.614.386.247 20.377.149.061 YEARS

27. 2007 Page 27 F. MICHAUX FUTURE VALUE COMPOUND PRINCIPAL AMOUNT FORWARD INTO THE FUTURE PRESENT VALUE DISCOUNT A FUTURE VALUE BACK TO THE PRESENT

28. 2007 Page 28 F. MICHAUX BASIC RELATIONSHIP BETWEEN PV AND FV

29. 2007 Page 29 F. MICHAUX Present Values Example Assume that the cash flows from the construction and sale of an office building is as follows. Given a 7% required rate of return, create a present value worksheet and show the net present value.

30. 2007 Page 30 F. MICHAUX Present Values Example - continued Assume that the cash flows from the construction and sale of an office building is as follows. Given a 7% required rate of return, create a present value worksheet and show the net present value.

31. 2007 Page 31 F. MICHAUX = PV 0 = DISCOUNTED CASH FLOW (DCF) EQUATION

32. 2007 Page 32 F. MICHAUX  NPV = NET PRESENT VALUE OF A PROJECT WHERE THE SUMMATION IS OVER ALL THE CASH FLOWS GENERATED BY THE PROJECT, INCLUDING INITIAL NEGATIVE CASH FLOWS AT THE START OF THE PROJECT, C 0 ETC.

33. 2007 Page 33 F. MICHAUX EXAMPLE C 0 = -500, C 1 = +400, C 2 = +400 r 1 = r 2 =.12 NPV = -500 + + = -500 + 400 (.893) + 400 (.794) = -500 + 357.20 + 318.80 = +176 400 400 1.12 (1.12) 2

34. 2007 Page 34 F. MICHAUX PV =

35. 2007 Page 35 F. MICHAUX PERPETUITIES CASH FLOWS LAST FOREVER PV = AS n GETS VERY LARGE

36. 2007 Page 36 F. MICHAUX ALTERNATIVE WAY TO VALUE A PERPETUITY IF I LEAVE AN AMOUNT OF MONEY, P, IN THE BANK, I CAN EARN ANNUAL INTEREST OF C = rP FOREVER

37. 2007 Page 37 F. MICHAUX C r EXAMPLE: SUPPOSE YOU WANT TO ENDOW A CHAIR AT YOUR OLD UNIVERSITY, WHICH WILL PROVIDE $100,000 EACH YEAR FOREVER. THE INTEREST RATE IS 10% $100,000 PV = = $1,000,000.10 A DONATION OF $1,000,000 WILL PROVIDE AN ANNUAL INCOME OF.10 X $1,000,000 = $100,000 FOREVER. PV = VALUING PERPETUITIES

38. 2007 Page 38 F. MICHAUX PV GROWING PERPETUITIES

39. 2007 Page 39 F. MICHAUX GROWING PERPETUITIES SUPPOSE YOU WISH TO ENDOW A CHAIR AT YOUR OLD UNIVERSITY WHICH WILL PROVIDE $100,000 PER YEAR GROWING AT 4% PER YEAR TO TAKE INTO ACCOUNT INFLATION. THE INTEREST RATE IS 10% PER YEAR.

40. 2007 Page 40 F. MICHAUX PV = FOUR VARIABLES, PV, r, n, C IF WE KNOW ANY THREE, SOLVE FOR THE FOURTH

41. 2007 Page 41 F. MICHAUX Asset Year of payment Present Value 1 2.. t+1.. Perpetuity (first payment year 1) Perpetuity (first payment year t + 1) Annuity from year 1 to year t (1+r) 1 t ) C r ( - C r ) r C1 ( t C r PRICE AN ANNUITY AS EQUAL TO THE DIFFERENCE BETWEEN TWO PERPETUITIES

42. 2007 Page 42 F. MICHAUX CALCULATING PV WHEN I KNOW C, r, N OR HOW MUCH AM I PAYING FOR MY CAR? EXAMPLE:  I BUY A CAR WITH THREE END-OF-YEAR PAYMENTS OF $4,000  THE INTEREST RATE IS 10% A YEAR 1 1 PV = $4,000 x - = $4,000 x 2.487 = $9,947.41.10.10(1.10) 3 ANNUITY TABLE NUMBER INTEREST RATE OF YEARS 5% 8% 10% 1.952.926.909 2 1.859 1.783 1.736 3 2.723 2.577 2.487 5 4.329 3.993 3.791 10 7.722 6.710 6.145

43. 2007 Page 43 F. MICHAUX LOANS EXAMPLE: AMORTIZATION SCHEDULE FOR 5-YEAR, $5,000 LOAN, 9% INTEREST RATE, ANNUAL PAYMENTS IN ARREARS. SOLVE FOR PMT AS ORDINARY ANNUITY PMT=$1,285.46 WE KNOW THE TOTAL PAYMENT, WE CALCULATE THE INTEREST DUE IN EACH PERIOD AND BACK CALCULATE THE AMORTIZATION OF PRINCIPAL 1 1 PMT = $5,000 / - $5,000 / 3.889 = $1,285.46.09.09(1.09) 5

44. 2007 Page 44 F. MICHAUX AMORTIZATION SCHEDULE YEAR BEGINNING TOTAL INTEREST PRINCIPAL ENDING...............BALANCE PAYMENT PAID PAID BALANCE 15,000 1,285.46 450.00835.46 4,164.54 24,165 1,285.46 374.81910.653,253.88 33,254 1,285.46 292.85992.612,261.27 42,261 1,285.46 203.51 1,081.951,179.32 51,179 1,285.46 106.14 1,179.32 0 INTEREST DECLINES EACH PERIOD AMORTIZATION OF PRINCIPAL INCREASES OVER TIME

45. 2007 Page 45 F. MICHAUX AMORTIZING LOAN Year $ AMORTIZATION  INTEREST 30

46. 2007 Page 46 F. MICHAUX GENERAL RESULT = EAR = r IS THE QUOTED ANNUAL RATE, COMPOUNDED m TIMES PER YEAR EAR EQUIVALENT ANNUALLY COMPOUNDED RATE

47. 2007 Page 47 F. MICHAUX ANNUAL PERCENTAGE RATE (APR) EXAMPLE: CAR LOAN CHARGES INTEREST AT 1% PER MONTH APR OF 12% PER YEAR BUT EAR=(1+.01) 12 -1=12.6825% PER YEAR THIS IS THE RATE YOU ACTUALLY PAY

48. 2007 Page 48 F. MICHAUX 6% INTEREST RATE COMPOUNDING EAR APR FREQUENCY YEAR 1 6.000% 6.000% QUARTER 4 6.136% 6.000% MONTH 12 6.168% 6.000% DAY 365 6.183% 6.000% MINUTE 525,600 6.184% 6.000% CONTINUOUSLY - 6.184% 6.000%

49. 2007 Page 49 F. MICHAUX GENERAL RESULT EAR = = e r – 1 = e r – 1 AS m INCREASES WITHOUT LIMIT $1 INVESTED CONTINUOUSLY AT AN INTEREST RATE r FOR t YEARS BECOMES e rt -1

50. 2007 Page 50 F. MICHAUX 10% PER YEAR CONTINUOUSLY COMPOUNDED EAR = e.1 - 1 = 10.51709%

51. 2007 Page 51 F. MICHAUX NOMINAL AND REAL RATES OF INTEREST NOMINAL CASH FLOW FROM BANK IS $1,100 IF INFLATION IS 6% OVER THE YEAR, REAL CASH FLOW IS REAL CASH FLOW =

52. 2007 Page 52 F. MICHAUX NOMINAL AND REAL RATES OF INTEREST 20-YEAR $1,000 INVESTMENT 10% PER YEAR INTEREST RATE EXPECTED AVERAGE FUTURE INFLATION 6% / YEAR FUTURE NOMINAL CASH FLOW = $1,000x1.1 20 = $6,727.50 FUTURE REAL CASH FLOW

53. 2007 Page 53 F. MICHAUX NOMINAL RATE OF RETURN 10% REAL RATE OF RETURN FISHER EQUATION (1+ r nominal ) = (1+ r real )(1+EXPECTED INFLATION RATE) = 1 + r real + EXPECTED INFLATION RATE + r real (EXPECTED INFLATION RATE) APPROXIMATELY, r nominal = r real +EXPECTED INFLATION RATE

54. 2007 Page 54 F. MICHAUX Internal Rate of Return Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

55. 2007 Page 55 F. MICHAUX VALUING BONDS

56. 2007 Page 56 F. MICHAUX BONDS INTEREST ONLY LOANS, PRINCIPAL OR FACE VALUE OR PAR VALUE REPAID AT END OF LOAN STATED INTEREST RATE CALLED COUPON DENOMINATIONS (OR PAR VALUES) OF CORPORATE BONDS TYPICALLY $1,000. GOVERNMENT BONDS USUALLY HAVE GREATER PAR VALUES. BOND SELLING AT PAR IS SELLING “FLAT.” MATURITY SOMETIMES CASUALLY USED FOR REMAINING LIFE OF BOND OR CURRENT MATURITY MOST US BONDS PAY INTEREST SEMIANNUALLY PRICE OFTEN STATED AS PERCENTAGE OF PAR VALUE

57. 2007 Page 57 F. MICHAUX 6%, 5 year bonds CASH FLOWS AT END OF EACH YEAR (IGNORING SEMIANNUAL PAY) 1995 1996 1997 1998 1999 60 60 60 60 1,060 SIMILAR BONDS RETURN 6.9% BOND IS SELLING AT 96.3 (PERCENT OF PAR VALUE)

58. 2007 Page 58 F. MICHAUX AFTER BOND IS ISSUED, INTEREST RATES ON SIMILAR BONDS CHANGE BUT CASH FLOWS FROM BOND STAY SAME PRICE OF BOND WILL VARY BECAUSE THE PRICE IS THE PV OF THE REMAINING CASH FLOWS DISCOUNT RATES CHANGE WITH CHANGES IN YIELD TO MATURITY (YTM) OR YIELD ON SIMILAR BONDS!

59. 2007 Page 59 F. MICHAUX PV(BOND) = PV (COUPON PAYMENTS) + PV (FINAL PAYMENT) PV(COUPON PAYMENTS) IS THE PV OF AN ANNUITY = 246.67 + 716.33 = $963 PV(BOND)

60. 2007 Page 60 F. MICHAUX YTM TURN THE QUESTION AROUND ASK WHAT RETURN, r, DO INVESTORS EXPECT WHEN A 5-YEAR, 6% COUPON BOND IS PRICED AT 96.3? WE NEED TO FIND THE VALUE OF r THAT SATISFIES THE EQUATION r IS THE YIELD TO MATURITY (YTM) OR YIELD WE ASSUME A FLAT TERM STRUCTURE OF INTEREST RATES

61. 2007 Page 61 F. MICHAUX INTEREST RATE RISK WHEN MARKET INTEREST RATES RISE, BOND PRICES FALL. WHEN MARKET INTEREST RATES FALL, BOND PRICES RISE. BOND PRICE SENSITIVITY TO CHANGES IN INTEREST RATES GREATER 1. LONGER CURRENT MATURITY 2. LOWER THE COUPON RATE.

62. 2007 Page 62 F. MICHAUX WHY ARE LONGER MATURITY BONDS MORE SENSITIVE TO CHANGES IN MARKET INTEREST RATES? MORE OF THE PRICE OF THE BOND IS DERIVED FROM CASH FLOWS (INTEREST AND PRINCIPAL) THAT OCCUR LATER IN TIME AND THEREFORE HAVE TO BE DISCOUNTED MORE MORE SENSITIVE TO CHANGES IN INTEREST RATES

63. 2007 Page 63 F. MICHAUX EXAMPLE: IS MORE SENSITIVE TO CHANGES IN r THAN

64. 2007 Page 64 F. MICHAUX BONDS MAKE SEMI-ANNUAL COUPON PAYMENTS ANNUAL COUPON RATE IS QUOTED AS TWICE THE SEMIANNUAL COUPON RATE –6% COUPON BOND PAYS $30 TWICE A YEAR BOND YIELD IS QUOTED AS TWICE THE SEMIANNUAL BOND YIELD

65. 2007 Page 65 F. MICHAUX VALUE OF A BOND ANNUAL COUPON C, ANNUAL YIELD TO MATURITY r

66. 2007 Page 66 F. MICHAUX TERM STRUCTURE Spot Rate - The actual interest rate today (t=0) Forward Rate - The interest rate, fixed today, on a loan made in the future at a fixed time. Future Rate - The spot rate that is expected in the future. Yield To Maturity (YTM) - The IRR on an interest bearing instrument. YTM (r) Year 1981 1987 & present 1976 1 5 10 20 30

67. 2007 Page 67 F. MICHAUX TERM STRUCTURE WE DISCOUNT CASH FLOW AT TIME 1 BY r 1 RATE APPROPRIATE FOR 1-PERIOD LOAN RATE FIXED TODAY, 1-PERIOD SPOT RATE WE DISCOUNT CASH FLOW AT TIME 2 BY r 2 RATE APPROPRIATE FOR 2-PERIOD LOAN RATE FIXED TODAY, 2-PERIOD SPOT RATE TERM STRUCTURE OF INTEREST RATES DESCRIBED BY SERIES OF INTEREST RATES r 1 r 2 ETC

68. 2007 Page 68 F. MICHAUX YIELD TO MATURITY INSTEAD OF DISCOUNTING EACH PAYMENT AT DIFFERENT RATE OF INTEREST –FIND SINGLE RATE OF INTEREST, r WHICH GIVES SAME PV –YTM –REALLY IRR BOND TABLES SHOW BOND PRICES FOR DIFFERENT COUPONS AND YTM BOND PRICES QUOTED AS PERCENT OF FACE VALUE

69. 2007 Page 69 F. MICHAUX DURATION YearCFPV@YTM% of Total PV% x Year 110596.77.0900.090 210589.19.0830.164 310582.21.0760.227 410575.77.0700.279 5 1105734.88.6813.406 1078.821.004.166 Duration Example (Bond 1) Calculate the duration of our 10.5% bond @ 8.5% YTM

70. 2007 Page 70 F. MICHAUX YearCFPV@YTM% of Total PV% x Year 1 9082.95.0810.081 2 9076.45.0750.150 3 9070.46.0690.207 4 9064.94.0640.256 5 1090724.90.7113.555 1019.701.004.249 Duration Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? DURATION

71. 2007 Page 71 F. MICHAUX DURATION AND VOLATILITY DURATION MEASURES AVERAGE TIMING OF CASH FLOWS –DURATION =1 x [PV(C 1 )/V] + 2 x [PV(C 2 )/V] +... BONDS WITH LONGER DURATION ALSO HAVE GREATER VOLATILITY VOLATILITY(%) = DURATION/(1 + YIELD) VOLATILITY OF BOND(1) (%) = 4.166/1.085 = 3.84 VOLATILITY OF BOND(2) (%) = 4.249/1.085 = 3.92

72. 2007 Page 72 F. MICHAUX VALUING STOCKS

73. 2007 Page 73 F. MICHAUX WHY IS IT IMPORTANT TO HAVE A THEORY OF THE VALUATION OF COMMON STOCKS? MANAGERS SHOULD BE MAKING DECISIONS WHICH INCREASE SHARE PRICE –NEED TO UNDERSTAND HOW SHARE PRICE IS DETERMINED CASES WHERE WE CANNOT DIRECTLY OBSERVE STOCK PRICE –WE ARE TRYING TO VALUE A DIVISION OF A COMPANY PRIVATELY HELD FIRM FOR POSSIBLE SALE

74. 2007 Page 74 F. MICHAUX STOCKS & STOCK MARKET Common Stock - Ownership shares in a publicly held corporation. Secondary Market - market in which already issued securities are traded by investors. Dividend - Periodic cash distribution from the firm to the shareholders. P/E Ratio - Price per share divided by earnings per share.

75. 2007 Page 75 F. MICHAUX STOCKS & STOCK MARKET Book Value - Net worth of the firm according to the balance sheet. Liquidation Value - Net proceeds that would be realized by selling the firm’s assets and paying off its creditors. Market Value Balance Sheet - Financial statement that uses market value of assets and liabilities.

76. 2007 Page 76 F. MICHAUX IF I AM GOING TO HOLD A STOCK FOREVER PRICE OF THE STOCK =PV(EXPECTED FUTURE DIVIDENDS)

77. 2007 Page 77 F. MICHAUX VALUING COMMON STOCKS Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends. H - Time horizon for your investment.

78. 2007 Page 78 F. MICHAUX Example Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return? VALUING COMMON STOCKS

79. 2007 Page 79 F. MICHAUX Example Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return? VALUING COMMON STOCKS

80. 2007 Page 80 F. MICHAUX LET’S SEE HOW MUCH SOMEONE WILL PAY FOR THE STOCK TODAY HOW MUCH SHOULD THE PERSON WHO BUYS IT FROM ME PAY FOR THE STOCK NOW (P 0 ) IF SHE IS GOING TO RECEIVE A DIVIDEND AT THE END OF THE PERIOD (DIV 1 ) AND THEN SHE IS GOING TO SELL IT (AT A PRICE P 1 )?

81. 2007 Page 81 F. MICHAUX

82. 2007 Page 82 F. MICHAUX WE HAVE NOW SUCCEEDED IN RELATING TODAY’S PRICE TO: EXPECTED DIVIDENDS IN YEARS 1 AND 2, DIV1 AND DIV2 EXPECTED PRICE AT END OF YEAR 2, P2 WE CAN REPEAT THE PROCESS

83. 2007 Page 83 F. MICHAUX LET’S SEE HOW MUCH SOMEONE WILL PAY FOR THE STOCK IN TWO YEAR’S TIME HOW MUCH SHOULD THE PERSON PAY FOR THE STOCK IN TWO YEAR’S TIME (P2) IF SHE IS GOING TO RECEIVE A DIVIDEND AFTER ONE YEAR (DIV3) AND THEN SHE IS GOING TO SELL IT (AT A PRICE P3)?

84. 2007 Page 84 F. MICHAUX P0P0

85. 2007 Page 85 F. MICHAUX =   NOW THE PRICE OF THE STOCK IS OBVIOUSLY INDEPENDENT OF THE TIME HORIZON, H.  AS WE GO OUT FURTHER IN TIME, MORE OF THE PRICE IS ACCOUNTED FOR BY THE DIVIDEND TERMS, SO THAT THE PRESENT VALUE OF THE TERMINAL PRICE BECOMES LESS IMPORTANT.

86. 2007 Page 86 F. MICHAUX AS WE GO OUT FURTHER IN TIME, PRESENT VALUE OF THE DIVIDEND TERMS INCREASES AND THE PRESENT VALUE OF THE TERMINAL PRICE DECLINES Horizon period DIVIDENDS INCREASE BY 10% A YEAR CAPITALIZATION RATE IS 15% Present value of

87. 2007 Page 87 F. MICHAUX 1. BY CONSIDERING HOW MUCH A BUYER WILL PAY FOR THE STOCK WHEN IT IS REPEATEDLY SOLD, WE FIND THAT THE STOCK PRICE IS THE PV OF ALL FUTURE DIVIDENDS. 2. WE OBTAIN THE SAME RESULT INDEPENDENTLY OF THE ASSUMPTIONS WE MAKE ABOUT THE LENGTH OF SUCCESSIVE HOLDING PERIODS.

88. 2007 Page 88 F. MICHAUX VALUING COMMON STOCK If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY. Assumes all earnings are paid to shareholders.

89. 2007 Page 89 F. MICHAUX Constant Growth - A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model). VALUING COMMON STOCK

90. 2007 Page 90 F. MICHAUX Example- continued If the same stock is selling for $100 in the stock market, what might the market be assuming about the growth in dividends? Answer The market is assuming the dividend will grow at 9% per year, indefinitely. VALUING COMMON STOCK

91. 2007 Page 91 F. MICHAUX If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher. Payout Ratio - Fraction of earnings paid out as dividends Plowback Ratio - Fraction of earnings retained by the firm. VALUING COMMON STOCK

92. 2007 Page 92 F. MICHAUX Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations. g = return on equity X plowback ratio “g” can also be estimated from historical growth rates in: dividends eps (earnings per share) VALUING COMMON STOCK

93. 2007 Page 93 F. MICHAUX ESTIMATING THE CAPITALIZATION RATE OR REQUIRED RATE OF RETURN If dividends are expected to grow at a constant rate, g DIV 1 P 0 = r - g DIV 1 so that r = + g P 0 MARKET CAPITALIZATION RATE =DIVIDEND YIELD, (D 1 /P 0 ) + EXPECTED RATE OF GROWTH IN DIVIDENDS, g

94. 2007 Page 94 F. MICHAUX Example Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision? VALUING COMMON STOCK

95. 2007 Page 95 F. MICHAUX Example Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to blow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision? No GrowthWith Growth VALUING COMMON STOCK

96. 2007 Page 96 F. MICHAUX Example Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to blow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision? No Growth With Growth VALUING COMMON STOCK

97. 2007 Page 97 F. MICHAUX Example - continued If the company did not plowback some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00. The difference between these two numbers (75.00-41.67=33.33) is called the Present Value of Growth Opportunities (PVGO). VALUING COMMON STOCK

98. 2007 Page 98 F. MICHAUX Present Value of Growth Opportunities (PVGO) - Net present value of a firm’s future investments. Sustainable Growth Rate - Steady rate at which a firm can grow: plowback ratio X return on equity. VALUING COMMON STOCK

99. 2007 Page 99 F. MICHAUX SUPERNORMAL GROWTH FIRM MAY HAVE A CURRENT HIGH RATE OF GROWTH WHICH CANNOT BE SUSTAINED –SUPERNORMAL GROWTH DO NOT USE THE SUPERNORMAL GROWTH RATE IN CALCULATING –COST OF EQUITY – FAIR MARKET PRICE

100. 2007 Page 100 F. MICHAUX DIVIDEND DIV0 AT t=0 GROWING AT A SUPERNORMAL GROWTH RATE gS TO DIVt AT t, AND THEN GROWING AT A NORMAL GROWTH RATE gn WHAT IS THE PRICE OF THE STOCK TODAY? PRICE TODAY, P 0 = PV OF DIVIDENDS IN SUPERNORMAL GROWTH PERIOD + PV OF CONSTANT GROWTH DIVIDENDS SUPERNORMAL GROWTH

101. 2007 Page 101 F. MICHAUX SUPERNORMAL GROWTH

102. 2007 Page 102 F. MICHAUX INCOME V.S. GROWTH STOCKS Investors in utility stocks expect dividend income. Hence, a high payout ratio of about 40%-50% is normal. Technology stocks can have zero payout ratio.

103. 2007 Page 103 F. MICHAUX New Economy v.s. Old Economy Stocks New economy stocks have high P/E Old economy stocks have high Div/P (Autumn 1999) P/EDiv/P Admiral77.80.2 Lynx Group44.70.8 Cable & Wireless75.40.9 B.T.36.81.6 Power Gen8.78.6 UU7.37.1 Hyder Water3.719.8

104. 2007 Page 104 F. MICHAUX Problems with DGM Theoretical –Relationship between current and future dividends (M&M) and share price –Determinants of dividend growth Practical –Accounting information –Accounting earnings v.s. economic earnings –Economic Value Added, Cash flow Return on Equity

105. 2007 Page 105 F. MICHAUX DIVIDENDS IRRELEVANT? In 1950s 9/10 US companies paid dividends Today only 1/5 US company pays dividend Higher capital gains tax? Share buybacks? Fashion in bull market? Stock market still punishes companies trimming or suspending dividends by 6% and 25% drop in share price respectively.

106. 2007 Page 106 F. MICHAUX P/E ratio and DGM Divide each side of 2 nd equation by EPS 1

107. 2007 Page 107 F. MICHAUX FCF and PV Valuing a Business The value of a business is usually computed as the discounted value of FCF out to a valuation horizon (H). The valuation horizon is sometimes called the terminal value and is calculated like PVGO.

108. 2007 Page 108 F. MICHAUX FCF and PV Free Cash Flows (FCF) should be the theoretical basis for all PV calculations. FCF is a more accurate measurement of PV than either Div or EPS. The market price does not always reflect the PV of FCF. When valuing a business for purchase, always use FCF.

109. 2007 Page 109 F. MICHAUX FCF and PV Valuing a Business PV (free cash flows)PV (horizon value)

110. 2007 Page 110 F. MICHAUX FCF and PV Example Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6%

111. 2007 Page 111 F. MICHAUX FCF and PV Example - continued Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6%.

112. 2007 Page 112 F. MICHAUX FCF and PV Example - continued Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6%.

113. 2007 Page 113 F. MICHAUX Company Value Enterprise Value Equity Value Equity Value = Enterprise Value – Debt