1. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-0 Corporate Finance Ross  Westerfield  Jaffe Sixth Edition 5 Chapter Five How to Value Bonds and Stocks Prepared by Gady Jacoby University of Manitoba and Sebouh Aintablian American University of Beirut

2. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-1 Chapter Outline 5.1Definition and Example of a Bond 5.2How to Value Bonds 5.3Bond Concepts 5.4The Present Value of Common Stocks 5.5Estimates of Parameters in the Dividend- Discount Model 5.6Growth Opportunities 5.7The Dividend Growth Model and the NPVGO Model (Advanced) 5.8Price Earnings Ratio 5.9Stock Market Reporting 5.10 Summary and Conclusions

3. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-2 Valuation of Bonds and Stock First Principles: –Value of financial securities = PV of expected future cash flows To value bonds and stocks we need to: – Estimate future cash flows: Size (how much) and Timing (when) – Discount future cash flows at an appropriate rate: The rate should be appropriate to the risk presented by the security.

4. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-3 5.1Definition and Example of a Bond A bond is a legally binding agreement between a borrower (bond issuer) and a lender (bondholder): –Specifies the principal amount of the loan. –Specifies the size and timing of the cash flows: In dollar terms (fixed-rate borrowing) As a formula (adjustable-rate borrowing)

5. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-4 5.1Definition and Example of a Bond Consider a Government of Canada bond listed as 6.375 of December 2009. –The Par Value of the bond is $1,000. –Coupon payments are made semi-annually (June 30 and December 31 for this particular bond). –Since the coupon rate is 6.375 the payment is $31.875. –On January 1, 2002 the size and timing of cash flows are:

6. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-5 5.2How to Value Bonds Identify the size and timing of cash flows. Discount at the correct discount rate. –If you know the price of a bond and the size and timing of cash flows, the yield to maturity is the discount rate.

7. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-6 Pure Discount Bonds Information needed for valuing pure discount bonds: –Time to maturity (T) = Maturity date - today’s date –Face value (F) –Discount rate (r) Present value of a pure discount bond at time 0:

8. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-7 Pure Discount Bonds: Example Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.

9. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-8 Level-Coupon Bonds Information needed to value level-coupon bonds: –Coupon payment dates and time to maturity (T) –Coupon payment (C) per period and Face value (F) –Discount rate Value of a Level-coupon bond = PV of coupon payment annuity + PV of face value

10. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-9 Level-Coupon Bonds: Example Find the present value (as of January 1, 2002), of a 6.375 coupon Government of Canada bond with semi-annual payments, and a maturity date of December 31, 2009 if the YTM is 5-percent. –On January 1, 2002 the size and timing of cash flows are:

11. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-10 Bond Market Reporting The Government of Canada issued this bond The bond pays an annual coupon rate of 6.375% The bond matures on December 31, 2009 The bond is selling at 108.98% of the face value of $1,000 The bond’s quoted annual yield to maturity is 5%

12. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-11 5.3Bond Concepts 1.Bond prices and market interest rates move in opposite directions. 2.When coupon rate = YTM, price = par value. When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond) 3.A bond with longer maturity has higher relative (%) price change than one with shorter maturity when interest rate (YTM) changes. All other features are identical. 4. A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical.

13. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-12 YTM and Bond Value 800 1000 1100 1200 1300 $1400 00.010.020.030.040.050.060.070.080.090.1 Discount Rate Bond Value 6 3/8 When the YTM < coupon, the bond trades at a premium. When the YTM = coupon, the bond trades at par. When the YTM > coupon, the bond trades at a discount.

14. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-13 Maturity and Bond Price Volatility C Consider two otherwise identical bonds. The long-maturity bond will have much more volatility with respect to changes in the discount rate Discount Rate Bond Value Par Short Maturity Bond Long Maturity Bond

15. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-14 Coupon Rate and Bond Price Volatility Consider two otherwise identical bonds. The low-coupon bond will have much more volatility with respect to changes in the discount rate Discount Rate Bond Value High Coupon Bond Low Coupon Bond

16. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-15 Holding Period Return Suppose that on January 1, 2002, you bought the above 6.375 coupon Government of Canada bond with semi-annual payments, and a maturity date of December 31, 2009. At that time the YTM was 5-percent, and you paid $1,089.75 (the PV of the bond). Six months later (July 1, 2002), You sold the bond when the YTM was 4-percent. The size and timing of cash flows (as of July 1, 2002 ) were:

17. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-16 Your holding period return was: This annualizes to an effective rate of: Given that the YTM at that time was 4-percent, you sold the bond for: Holding Period Return (continued)

18. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-17 5.4The Present Value of Common Stocks Dividends versus Capital Gains Valuation of Different Types of Stocks –Zero Growth –Constant Growth –Differential Growth

19. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-18 Case 1: Zero Growth Assume that dividends will remain at the same level forever  Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:

20. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-19 P 0 = Div 1 / r = 0.75/0.12 = $6.25 ABC Corp. is expected to pay $0.75 dividend per annum, starting a year from now, in perpetuity. If stocks of similar risk earn 12% annual return, what is the price of a share of ABC stock? The stock price is given by the present value of the perpetual stream of dividends: A Zero Growth Example 01234 $0.75 …

21. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-20 Case 2: Constant Growth Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity: Assume that dividends will grow at a constant rate, g, forever. i.e....

22. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-21 A Constant Growth Example XYZ Corp. has a common stock that paid its annual dividend this morning. It is expected to pay a $3.60 dividend one year from now, and following dividends are expected to grow at a rate of 4% per year forever. If stocks of similar risk earn 16% effective annual return, what is the price of a share of XYZ stock?

23. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-22 A Constant Growth Example (continued) The stock price is given by the the present value of the perpetual stream of growing dividends: $3.60$3.60  1.04 $3.60  1.04 2 $3.60  1.04 3 P 0 = Div 1 / (r-g) = 3.60/(0.16-0.04) = $30.00 01234 …

24. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-23 Case 3: Differential Growth Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter. To value a Differential Growth Stock, we need to: –Estimate future dividends in the foreseeable future. –Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2). –Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.

25. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-24 Case 3: Differential Growth  Assume that dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter......

26. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-25 Case 3: Differential Growth  Dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter … 0 1 2 … NN +1 …

27. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-26 Case 3: Differential Growth We can value this as the sum of: an N-year annuity growing at rate g 1 plus the discounted value of a perpetuity growing at rate g 2 that starts in year N+1

28. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-27 Case 3: Differential Growth To value a Differential Growth Stock, we can use  Or we can cash flow it out.

29. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-28 A Differential Growth Example A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. If stocks of similar risk earn 12% effective annual return, what is the stock worth?

30. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-29 With the Formula

31. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-30 A Differential Growth Example (continued) … 0 1 234 0 1 2 3 The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.

32. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-31 5.5 Estimates of Parameters in the Dividend-Discount Model The value of a firm depends upon its growth rate, g, and its discount rate, r. –Where does g come from? –Where does r come from?

33. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-32 Where does g come from? Formula for Firm’s Growth Rate (g): The firm will experience earnings growth if its net investment (total investment-depreciation) is positive. To grow, the firm must retain some of its earnings. This leads to: Earnings next Year Earnings this Year Retained earnings this Year Return on retained earnings =+ 

34. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-33 This leads to the formula for the firm’s growth rate: g = Retention ratio × Return on retained earnings The return on retained earnings can be estimated using the firm’s historical return on equity (ROE) Where does g come from? Dividing both sides by this year’s earnings, we get: Earnings this Year Earnings next Year 1 Retained earnings this Year Return on retained earnings =+  Earnings this Year 1 + gRetention ratio

35. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-34 Where does g come from? An Example Ontario Book Publishers (OBP) just reported earnings of $1.6 million, and it plans to retain 28- percent of its earnings. If OBP’s historical ROE was 12-percent, what is the expected growth rate for OBP’s earnings? With the above formula: g = 0.28 × 0.12 = 0.0336 = 3.36% Or: Total earnings Change in earnings = $1.6 million (0.28×$1.6 million)×0.12 =0.0336

36. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-35 In practice, there is a great deal of estimation error involved in estimating r. The discount rate can be broken into two parts. –The dividend yield –The growth rate (in dividends) From the constant growth cas, we can write: Where does r come from?

37. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-36 Where does r come from? An Example Manitoba Shipping Co. (MSC) is expected to pay a dividend next year of $8.06 per share. Future Dividends for MSC are expected to grow at a rate of 2% per year indefinitely. If an investor is currently willing to pay $62.00 per one MSC share, what is her required return for this investment? With the above formula: r = (8.06/62) + 0.02 = 0.15 = 15%

38. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-37 5.6Growth Opportunities Growth opportunities are opportunities to invest in positive NPV projects. The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100-percent of its earnings as dividends and the net present value of the growth opportunities.

39. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-38 5.7The Dividend Growth Model and the NPVGO Model (Advanced) We have two ways to value a stock: –The dividend discount model. –The price of a share of stock can be calculated as the sum of its price as a cash cow plus the per- share value of its growth opportunities.

40. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-39 The Dividend Growth Model and the NPVGO Model Consider a firm that has EPS of $5 at the end of the first year, a dividend-payout ratio of 30-percent, a discount rate of 16-percent, and a return on retained earnings of 20-percent. The dividend at year one will be $5 ×.30 = $1.50 per share. The retention ratio is.70 ( = 1 -.30) implying a growth rate in dividends of 14% =.70 × 20% From the dividend growth model, the price of a share is:

41. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-40 The NPVGO Model First, we must calculate the value of the firm as a cash cow. Second, we must calculate the value of the growth opportunities. Finally,

42. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-41 5.8Price Earnings Ratio Many analysts frequently relate earnings per share to price. The price earnings ratio is a.k.a the multiple –Calculated as current stock price divided by annual EPS –The National Post uses last 4 quarters’ earnings Firms whose shares are “in fashion” sell at high multiples. Growth stocks for example. Firms whose shares are out of favour sell at low multiples. Value stocks for example.

43. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-42 Other Price Ratio Analysis Many analysts frequently relate earnings per share to variables other than price, e.g.: –Price/Cash Flow Ratio cash flow = net income + depreciation = cash flow from operations or operating cash flow –Price/Sales current stock price divided by annual sales per share –Price/Book (a.k.a. Market to Book Ratio) price divided by book value of equity, which is measured as assets - liabilities

44. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-43 5.9Stock Market Reporting BCE has been as high as $42.10 in the last year. BCE has been as low as $32.25 in the last year. Given the current price, the dividend yield is 3½ % Given the current price, the P/E ratio is 11.8 times earnings 1,921,000 shares traded hands in the last day’s trading BCE ended trading at $34.50, down $0.47 from yesterday’s close BCE pays a dividend of 1.2 dollars/share

45. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-44 5.9Stock Market Reporting BCE Incorporated is having a tough year, trading near their 52- week low. Imagine how you would feel if within the past year you had paid $42.10 for a share of BCE and now had a share worth $34.50! That $1.20 dividend wouldn’t go very far in making amends. Yesterday, BCE had another rough day in a rough year. BCE “opened the day down” beginning trading at $34.59, which was down from the previous close of $34.97 = $34.50 + $0.47

46. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-45 5.10Summary and Conclusions In this chapter, we used the time value of money formulae from previous chapters to value bonds and stocks. 1.The value of a zero-coupon bond is 2.The value of a perpetuity is

47. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-46 5.10Summary and Conclusions (continued) 3.The value of a coupon bond is the sum of the PV of the annuity of coupon payments plus the PV of the par value at maturity. 4.The yield to maturity (YTM) of a bond is that single rate that discounts the payments on the bond to the purchase price.

48. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-47 5.10Summary and Conclusions (continued) 5.A stock can be valued by discounting its dividends. There are three cases: 1.Zero growth in dividends 2.Constant growth in dividends 3.Differential growth in dividends

49. McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 5-48 5.10Summary and Conclusions (continued) 6.The growth rate can be estimated as: g = Retention ratio × Return on retained earnings 7.An alternative method of valuing a stock was presented. The NPVGO values a stock as the sum of its “cash cow” value plus the present value of growth opportunities.