1. © 2003 McGraw-Hill Ryerson Limited 10 Chapter Valuation and Rates of Return Valuation and Rates of Return McGraw-Hill Ryerson©2003 McGraw-Hill Ryerson Limited Based on: Terry Fegarty Carol Edwards, Lawrence J. Gitman April 12, 2005

2. © 2003 McGraw-Hill Ryerson Limited Chapter 10 - Outline  Valuation Concepts  Importance of Valuation  Basic Valuation Model  3 Factors that Influence the Required Rate of Return  Valuation of Bonds  Relationship Between Bond Prices and Yields  Valuation Preferred Stock  Valuation of Common Stock  Valuation Using the Price-Earnings Ratio  Summary and Conclusions PPT 10-2

3. © 2003 McGraw-Hill Ryerson Limited Valuation Concepts  The value or price of a stock or bond is based upon the present value of future expected cash flows to the investor  Key inputs to the valuation process include:  Cash Flows (returns),  Timing, and  Required Return (risk).  Greater risk can be incorporated into an analysis by using a higher required return or discount rate. PPT 10-4

4. © 2003 McGraw-Hill Ryerson Limited Valuation Concepts - Importance of Asset Valuation  Valuation is important to any firm for at least 2 reasons: 1. A firm must continually assess its market value if it satisfies its goal of share price maximization. 2. It must accurately determine the worth or value of its business when selling securities to raise long-term funds.  Firms (Issuers) will lose money if they undervalue their businesses  Would-be investors would not want to pay more than what the businesses are worth, so firms must not overvalue their businesses.

5. © 2003 McGraw-Hill Ryerson Limited Valuation Concepts - Basic Valuation Model  The VALUE of any asset is the Present Value of all future cash flows it is expected to provide over the relevant time period. V 0 = value of the asset at time zero CF t = cash flow expected at the end of year t k = appropriate required rate of return (discount rate) n = relevant time period

6. © 2003 McGraw-Hill Ryerson Limited  Definitions - Bonds  Firms borrow money from lenders for the long term by issuing securities which are called bonds:  Firms collect the money when they issue the bond, or sell it to the public.  The money they collect is the amount of the loan.  The amount of the loan may be known as the par value, face value, maturity value, or the principal.  The date on which the loan will be paid off is the maturity date. For many bonds, its life or maturity could be for a term of 20 to 30 years. Valuation of Bonds - Bond Characteristics

7. © 2003 McGraw-Hill Ryerson Limited Valuation of Bonds - Bond Characteristics  Definitions - Coupon Rate  The issuer (firm) promises to make specified fixed income payments (interest) each year(or semi-annually) to the bondholders (lenders).  These payments are known as the coupon (or interest) and are based on the coupon rate stated in the issued bonds. Interest payment is usually made semi-annually.  The coupon rate is the annual interest payment divided by the face value of the bond.  This coupon rate on a bond is set at the time of issue and does not change for the life of the bond.  This coupon rate is based on the Government of Canada Bonds rate with the same maturity date plus a premium for risk.

8. © 2003 McGraw-Hill Ryerson Limited Valuation of Bonds - Bond Characteristics  Definitions - Coupon Rate vs Yield to Maturity (YTM)  After a bond is issued, two major factors can occur:  Economic conditions can change  A firm’s risk can change  These changes will be reflected on the issued bond in its interest rate (also known discount rate, rate of return) and more specifically, Yield to Maturity (YTM).  While the interest and principal payment will remain unchanged if the bond is re-issued, the price of the bond will change if the coupon rate deviates from the YTM.  Yield to Maturity is the rate of return investors earn if they buy the bond at the new price and hold it until maturity.  This is also the interest rate (or discount rate) at which the cash flows from the bond are discounted to determine its present value (New Price).

9. © 2003 McGraw-Hill Ryerson Limited 3 Factors that Influence the YTM (Required Rate of Return) 1. Real Rate of Return:  represents the interest cost of the investment  in the early 1990’s, 5-7%, but now about 3-4% 2. Inflation Premium:  a premium to compensate for the effects of inflation  lately, 2% 3. Risk Premium:  a premium associated with business and financial risk  typically, 2-6% So, the Required Rate of Return equals: Real Rate of Return + Inflation Premium + Risk Premium

10. © 2003 McGraw-Hill Ryerson Limited Relationship Between Bond Prices and YTM Bond prices are inversely related to YTM (Bond Yields), that is, they move in opposite directions As interest rates in the economy change, the price or value of a bond changes:  if the required rate of return increases, the price of the bond will decrease  if the required rate of return decreases, the price of the bond will increase

11. © 2003 McGraw-Hill Ryerson Limited Table 10-1 Bond price table PPT 10-7

12. © 2003 McGraw-Hill Ryerson Limited 0........$1,000.00$1,000.00 1........ 1,018.52982.14 5........1,079.85927.90 10........1,134.20887.00 15........1,171.19863.78 20........1,196.36850.61 25........1,213.50843.14 30........1,225.16838.90 Time Period Bond Price withBond Price with in Years 8 Percent Yield 12 Percent Yield (of 10 percent bond) to Maturity to Maturity PPT 10-9 Table 10-2 Impact of time to maturity on bond prices

13. © 2003 McGraw-Hill Ryerson Limited 1,300 1,200 1,100 1,000 900 800 700 Bond Price ($) 30 2515 Number of years to maturity * The relationship in the graph is not symmetrical in nature. 10% bond, $1,000 par value Assumes 12% yield to maturity 5 0 Assumes 8% yield to maturity PPT 10-10 Figure 10-2 Relationship between time to maturity and bond price*

14. © 2003 McGraw-Hill Ryerson Limited Company Name Coupon (interest rate %) Maturity Date (April 8, 2022) Price (Last transaction price = $138.50/ $100 of face value) Yield (Annual interest Market price) Change(Closing price up $1.12/ $100 from previous day) PPT 10-11 Reading Bond Quotations

15. © 2003 McGraw-Hill Ryerson Limited Valuation of Bonds – Bond Example  par value = $1000  coupon = 6.5% of par value per year, paid semi- annually.  Interest Payment = $65 per year/2 = $32.50 every 6 months.  maturity = 24 years (matures in 2029) x 2 = 48 periods.  issued by AT&T. 0 1 2 34 5 ….. 48 $32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000

16. © 2003 McGraw-Hill Ryerson Limited Valuation of Bond Formula Where: P b = Price of the bond n = total number of periods I t = Interest Payments Y = Yield to maturity (required rate of return) P n = Principal payment at maturity t = number corresponding to a period; running from 1 to n

17. © 2003 McGraw-Hill Ryerson Limited Bond Example Problem  Suppose a firm decides to issue 20-year bonds with a par value of $1,000 and annual coupon payments. The return on other corporate bonds of similar risk is currently 12%, so we decide to offer a 12% coupon interest rate.  What would be a fair price for these bonds? 0 1 2 3...20 1000 P b =? 120 120 120... 120

18. © 2003 McGraw-Hill Ryerson Limited Bond Example Problem N = 20 I/YR = 12 FV = 1,000 PMT = 120 Solve PV = -$1,000 Note: If the coupon rate = YTM (rate of return, discount rate) the bond will sell at par value.

19. © 2003 McGraw-Hill Ryerson Limited Bond Example Problem  Mathematical Solution:  P b = I (PVIFA Y, n ) + P n (PVIF Y, n ) = 120 (PVIFA.12, 20 ) + 1000 (PVIF.12, 20 ) = $1,000

20. © 2003 McGraw-Hill Ryerson Limited Bond Example Problem  Suppose interest rates fall immediately after we issue the bonds. The YTM (required return) on bonds of similar risk drops to 10%. What would happen to the bond’s price? N = 20 I/YR = 10 FV = 1,000 PMT = 120 Solve PV = -$1,170.27 Note: If the coupon rate > YTM, the bond will sell at a premium.

21. © 2003 McGraw-Hill Ryerson Limited Bond Example Problem  Mathematical Solution:  P b = I (PVIFA Y, n ) + P n (PVIF Y, n ) = 120 (PVIFA.10, 20 ) + 1000 (PVIF.10, 20 ) = $1,170.27

22. © 2003 McGraw-Hill Ryerson Limited Bond Example Problem  Suppose interest rates rise immediately after we issue the bonds. The YTM (required return) on bonds of similar risk rises to 14%. What would happen to the bond’s price? N = 20 I/YR = 14 FV = 1,000 PMT = 120 Solve PV = -$867.54 Note: If the coupon rate < YTM, the bond will sell at a discount.

23. © 2003 McGraw-Hill Ryerson Limited Bond Example Problem  Mathematical Solution:  P b = I (PVIFA Y, n ) + P n (PVIF Y, n ) = 120 (PVIFA.14, 20 ) + 1000 (PVIF.14, 20 ) = $867.54

24. © 2003 McGraw-Hill Ryerson Limited Valuation of Bonds The value of a bond is made up of 2 parts:  PV of the interest payments (an annuity)  PV of the principal payment (a lump sum) The principal payment at maturity:  can also be called the par value or face value  is usually $1,000 The interest rate used:  is the yield to maturity (discount rate)  also called the required rate of return PPT 10-5

25. © 2003 McGraw-Hill Ryerson Limited Semiannual Coupon Payments and Bond Values  The procedure to value bonds paying semiannual interest involved compounding interest more frequently than annually:  Convert annual interest (coupon), I, to semiannual by dividing I by 2.  Convert number of years to maturity to number of 6-month periods to maturity by multiplying n by 2.  Convert Yield to Maturity (required rate of return) from annual to semiannual by dividing Y by 2.

26. © 2003 McGraw-Hill Ryerson Limited Valuation of Preferred Stock - Characteristics  Firms can also raise long term money by issuing and selling securities which are called preferred stocks or shares.  Investors who purchase these shares are called preferred shareholders  Preferred Stock is a hybrid security:  it’s like common stock - no fixed maturity (perpetuity).  technically, it’s part of equity capital.  it’s like debt - preferred dividends are fixed.  Usually sold for $25, $50, or $100 per share.  Dividends are fixed either as a dollar amount or as a percentage of par value.

27. © 2003 McGraw-Hill Ryerson Limited Valuation of Preferred Stock - Characteristics  Example: In 1988, Xerox issued $75 million of 8.25% preferred stock at $50 per share.  $4.125 is the fixed, annual dividend per share.  Is valued without any principal payment since it has no ending life.  Price is based upon PV of future dividends.  Creditors have prior claim on earnings; interest on debt must be paid before preferred stockholders can receive anything.  Once creditor claims have been met, preferred stock has priority over common stockholders in terms of claims on assets in liquidation, that is,dividends must be paid before common stockholders receive any payment.

28. © 2003 McGraw-Hill Ryerson Limited Valuation of Preferred Stock  Failure to pay preferred dividend does not result in bankruptcy.  To value a Preferred Stock, we use the following formula: Where : Pp= Price of Preferred Stock Dp= Annual Dividend for Preferred Stock Kp= Required Rate of Return or Discount Rate

29. © 2003 McGraw-Hill Ryerson Limited Valuation of Preferred Stock-Example  Xerox preferred pays an 8.25% dividend on a $50 par value.  Suppose our required rate of return on Xerox preferred is 9.5%.

30. © 2003 McGraw-Hill Ryerson Limited Valuation of Common Stock - Characteristics  Common stock represents equity or ownership; includes voting rights.  Limited liability: liability is limited to the amount of owners’ investment.  Claims Priority: lower than debt and preferred.  Unlike preferred stock, there is no pre-set dividend rate. Instead, dividends are paid at the discretion of the firm’s board of directors.  Common Stock is a variable-income security.  dividends may be increased or decreased, depending on earnings.

31. © 2003 McGraw-Hill Ryerson Limited Valuation of Common Stock - Characteristics  The value of common shares is equal to the present value of all future dividends the company is expected to pay over an infinite time horizon.  There are 3 possible cases:  No growth in dividends (valued like preferred stock)  Constant growth in dividends  Variable growth in dividends  Required rate of return reflects the dividend yield on the stock and the expected growth rate in the dividend

32. © 2003 McGraw-Hill Ryerson Limited Valuation of Common Stock- No Growth Model  Under the no growth circumstance, the formula is similar to preferred stock: Where : Po= Price of Common Stock today D 0 = Current Annual Common Dividend (constant value) K e = Required Rate of Return on Common Stock

33. © 2003 McGraw-Hill Ryerson Limited Valuation of Common Stock- Constant Growth Model  Under the Constant Growth Model, the formula is: Where : Po= Price of Common Stock today D 1 = Dividend at the end of the 1 st year K e = Required Rate of Return on Common Stock g = constant growth rate in dividends

34. © 2003 McGraw-Hill Ryerson Limited Valuation Using the Price-Earnings Ratio  The Price-Earnings (P/E) ratio can also be used to value common stocks  The P/E ratio is influenced by many factors:  the earnings and sales growth of the firm  the risk (or volatility in performance)  the debt-equity structure  the dividend policy  the quality of management  a number of other factors  The average P/E ratio for TSX Composite, excluding Nortel and JDS Uniphase, in early 2002 was 33 to 1 PPT 10-14

35. © 2003 McGraw-Hill Ryerson Limited High vs. Low P/Es A stock with a high P/E ratio:  indicates positive expectations for the future of the company  means the stock is more expensive relative to earnings  typically represents a successful and fast-growing company  is called a growth stock A stock with a low P/E ratio:  indicates negative expectations for the future of the company  may suggest that the stock is a better value or buy  is called a value stock PPT 10-15

36. © 2003 McGraw-Hill Ryerson Limited Table 10-4 An example of stock quotations from the Globe and Mail PPT 10-16 Source: ILX Systems, a division of Thomson Information Services Inc.

37. © 2003 McGraw-Hill Ryerson Limited Your Daily Paper CompanyVolumeHighLowCloseChange Inco 3760 29.15028.50028.600-.400 Stock Volume (Total number of shares traded (100s) Close (Last price paid at close of trading) High (Highest price paid per share for the day was $29.15) Low (Lowest price paid per share for the day was $28.50) Change (Difference between today’s price and previous day’s. A.40 decrease) PPT 10-17 Reading Stock Quotations

38. © 2003 McGraw-Hill Ryerson Limited Summary and Conclusions  The price of a bond reflects the present value of future payments of interest and principal, discounted at current market bond yields  The price of a preferred or common stock reflects the present value of future dividends, discounted at current market dividend yields  An alternative for valuing common stock is the price-earnings ratio PPT 10-20  The value of securities is based upon the present value of expected future cash flows from the investment, discounted at the rate of return required by investors  The required rate of return includes premiums for expected inflation and the perceived risk of the investment