1. T8.1 Chapter Outline Chapter 8 Stock Valuation Chapter Organization 8.1Common Stock Valuation 8.2Common Stock Features 8.3Preferred Stock Features 8.3Stock Market Reporting 8.4Summary and Conclusions CLICK MOUSE OR HIT SPACEBAR TO ADVANCE Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd.

2. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 2 Common Stock Valuation - the theory Investment theorists argue that the best measure of going - concern value for a common stock is the present value of expected future dividends The basic approach is to :  estimate the future earnings of the company  make a judgment on the proportion of earnings that would be paid out as dividends  discount the future dividend stream at the appropriate discount rate

3. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 3 Common Stock Cash Flows and the Fundamental Theory of Valuation In 1938, John Burr Williams postulated what has become the fundamental theory of valuation: The value today of any financial asset equals the present value of all of its future cash flows. For common stocks, this implies the following: D 1 P 1 D 2 P 2 P 0 = +and P 1 = + (1 + R) 1 (1 + R) 1 (1 + R) 1 (1 + R) 1 substituting for P 1 gives D 1 D 2 P 2 P 0 = + +. Continuing to substitute, we obtain (1 + R) 1 (1 + R) 2 (1 + R) 2 D 1 D 2 D 3 D 4 P 0 = + + + + … (1 + R) 1 (1 + R) 2 (1 + R) 3 (1 + R) 4

4. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 4 Common Stock Valuation - the theory We ultimately lose the future value of the stock price in the equation given that it is assumed to be in the distant future and the present value of this distant price is essentially zero this allows us to focus solely on the future dividend stream as the driver of the stock’s value What happens if the firm does not pay dividends - does this mean the stock does not have any value?  The issue here is one of expectations of future dividends or some form of liquidating dividend  according to the theory - rational investors would never place a value on a stock that was never going to pay a dividend

5. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 5 Common Stock Valuation - the theory 3 situations where the model can be applied  Zero Growth Case - no growth assumed for the dividends over time -  Constant Growth - steady growth in dividends is assumed - constant or even  Non-constant Growth - after a certain period of time dividends are assumed to grow at a constant pace - but at some point in the future

6. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 6 Common Stock Valuation: The Zero Growth Case According to the fundamental theory of value, the value of a financial asset at any point in time equals the present value of all future dividends. If all future dividends are the same, the present value of the dividend stream constitutes a perpetuity. The present value of a perpetuity is equal to C/r or, in this case, D 1 /R. example:Cooper, Inc. common stock currently pays a $1.00 dividend, which is expected to remain constant forever. If the required return on Cooper stock is 10%, what should the stock sell for today? P 0 = $1/.10 = $10. Given no change in the variables, what will the stock be worth in one year?

7. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 7 Common Stock Valuation: The Zero Growth Case (concluded) One year from now, the value of the stock, P 1, must be equal to the present value of all remaining future dividends. Since the dividend is constant, D 2 = D 1, and P 1 = D 2 /R = $1/.10 = $10. In other words, in the absence of any changes in expected cash flows (and given a constant discount rate), the price of a no-growth stock will never change. Put another way, there is no reason to expect capital gains income from this stock.

8. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 8 Common Stock Valuation: The Constant Growth Case In reality, investors generally expect the firm (and the dividends it pays) to grow over time. How do we value a stock when each dividend differs from the one preceding it? As long as the rate of change from one period to the next, g, is constant, we can apply the growing perpetuity model: D 1 D 2 D 3 D 0 (1+g) 1 D 0 (1+g) 2 D 0 (1+g) 3 P 0 = + + + … = + + +... (1 + R) 1 (1 + R) 2 (1 + R) 3 (1 + R) 1 (1 + R) 2 (1 + R) 3 D 0 (1 + g) D 1 P 0 = =. R - g R- g Now assume that D 1 = $1.00, r = 10%, but dividends are expected to increase by 5% annually. What should the stock sell for today?

9. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 9 Common Stock Valuation: The Constant Growth Case (concluded) The equilibrium value of this constant-growth stock is D 1 $1.00 = = $20 R - g.10 -.05 What would the value of the stock be if the growth rate were only 3%? D 1 $1.00 = = $14.29. R - g.10 -.03 Why does a lower growth rate result in a lower value?

10. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 10 Stock Price Sensitivity to Dividend Growth, - ‘g’ 0 2% 4% 6% 8% 10% 50 45 40 35 30 25 20 Stock price ($) Dividend growth rate, g D 1 = $1 Required return, R, = 12% 15 10 5

11. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 11 Stock Price Sensitivity to Required Return, - ’r’ 6% 8% 10% 12% 14% 100 90 80 70 60 50 40 Stock price ($) Required return, R D 1 = $1 Dividend growth rate, g, = 5% 30 20 10

12. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 12 Common Stock Valuation - The Non-constant Growth Case For many firms (especially those in new or high-tech industries), dividends are low or non existent but are expected to be paid at some point in the future. As product markets mature, the dividend growth rate is then expected to evolve to a “steady state” rate. How should stocks such as these be valued? : We return to the fundamental theory of value - the value today equals the present value of all future cash flows. Put another way, the non-constant growth model suggests that P 0 =present value of dividends in the non-constant growth period(s) + present value of dividends in the “steady state” period.

13. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 13 Common Stock Valuation - Non Constant Growth Case Example Assume: company ABC pays a C/S dividend of $5.00 per share today no growth is assumed for 3 years followed by constant growth of 4% using a discount rate of 8% what is the value of the stock?

14. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 14 ABC Company - 1st calculate the value of the stock at p 3 using the constant growth formula  P 3 = D 4 /r-g = $5.20/(.08-.04) = $130 Next discount this value back to p 0  P 3 /(1+r) 3 = $130/1.25971 = $103.20 Add PV of dividends for first 3 years  $4.63 + 4.29 + 3.97 + 103.20 = $116.09 ……suggest drawing a dividend time line to visualize the cash flows

15. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 15 Common Stock Valuation - other theories Burton Malkiel in his book ‘ A Random Walk Down Wall Street’ gives his four ‘fundamental’ rules of stock prices:  investors pay a higher price the larger the dividend growth rate  investors pay a higher price the larger the proportion of earnings paid out in dividends  investors pay a higher price per share the less risky the company’s stock is  investors pay a higher price per share the lower the level of interest rates.....there are other theories!!

16. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 16 Examples Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 5% per year indefinitely. If the required return is 9%, then the price today is _____ ? P 0 = D 1 /(R - g) = $5  ( 1.05 )/(.09 -.05 ) = $5.25/.04 = $131.25 per share What will the price be in a year? P t = D t+1 /(R - g) P 1 = D 2 /(R - g) = ($5.25  1.05)/(.09 -.05) = $137.8125 By what percentage does P 1 exceed P 0 ? Why? P 1 exceeds P 0 by 5% -- the capital gains yield.

17. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 17 Components of the Required Rate of Return We know that P 0 = D 1 /(r-g) Then r = D 1 /P 0 + g D 1 /P 0 is the dividend yield The dividend growth rate – g is also the rate the stock price is expected to grow (consistent with the theory that future cash flows drive the value of the security)  This growth rate is interpreted as the capital gains yield

18. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 18 The Required Rate of Return Find the required return: Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 5% per year indefinitely. If the stock sells today for $65 5/8, what is the required return? P 0 = D 1 /(R - g) (R - g) = D 1 /P 0 R = D 1 /P 0 + g = $5.25/$65.625 +.05 = dividend yield (.08 ) + capital gains yield (.05 ) =.13 = 13%

19. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 19 What Discount Rate or Rate of Return to Use? Concept of risk vs return  The higher the risk the higher the return is needed to compensate for this risk Time horizon  Short term rates for long term Long Government of Canada Bonds - 5 % range Historical rates of return – table 12.3 page 389 in text Canadian equities – 13.20% average return over past 50 years Long term Bonds - 7.64%,,,many financial planners today are suggesting 8-10% as a realistic average rate of return to expect on a diversified portfolio

20. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 20 Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 10% for the next two years, the 8% for one year, and then 6% indefinitely. The required return is 12%. What is the stock’s value? TimeDividend 0$ 5.00 1$ 5.50(10% growth) 2$ 6.05(10% growth) 3$6.534( 8% growth) 4$6.926( 6% growth) Valuation Example

21. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 21 Valuation Example cont’d At time 3, the value of the stock will be: P 3 = D 4 /(R - g) = $6.926/(.12 -.06) = $115.434 The value today of the stock is thus: P 0 = D 1 /(1 + R) + D 2 /(1 + R) 2 + D 3 /(1 + R) 3 + P 3 /(1 + R )3 = $5.5/1.12 + $6.05/1.12 2 + $6.534/1.12 3 + $115.434/1.12 3 = $96.55

22. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 22 Solution to Problem 8.1 Green Mountain, Inc. just paid a dividend of $2.00 per share on its stock. The dividends are expected to grow at a constant 5 percent per year indefinitely. If investors require a 12 percent return on Favre stock, what is the current price? What will the price be in 3 years? In 15 years? According to the constant growth model, P 0 = D 1 /(R - g) = $2.00(1.05)/(.12 -.05) = $30.00 If the constant growth model holds, the price of the stock will grow at g percent per year, so P 3 = P 0  (1 + g) 3 = $30.00  (1.05) 3 = $34.73, and P 15 = P 0  (1 + g) 15 = $30.00  (1.05) 15 = $62.37.

23. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 23 Solution to Problem 8.10 Metallica Bearings, Inc. is a young start-up company. No dividends will be paid on the stock over the next 5 years. The company will pay a $6 per share dividend in six years and will increase the dividend by 5% per year thereafter. If the required return on this stock is 21%, what is the current share price? The current market price of any financial asset is the present value of its future cash flows, discounted at the appropriate required return. In this case, we know that: D 1 = D 2 = D 3 = D 4 = D 5 = 0 D 6 = $6.00 D 7 = $6.00(1.05) = $6.30.

24. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 24 Solution to Problem 8.10 (concluded) This share of stock represents a stream of cash flows with two important features: First, because they are expected to grow at a constant rate (once they begin), they are a growing perpetuity; Second, since the first cash flow is at time 6, the perpetuity is a deferred cash flow stream. Therefore, the answer requires two steps: 1.By the constant-growth model, D 6 /(r - g) = P 5 ; i.e., P 5 = $6.00/(.21 -.05) = $37.50. 2.And, P 0 = P 5  1/(1 +.21) 5 = $37.50 .3855 = $14.46.

25. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 25 Summary of Stock Valuation (Table 8.1) I. The General Case In general, the price today of a share of stock, P 0, is the present value of all of its future dividends, D 1, D 2, D 3,... D 1 D 2 D 3 P 0 = + + + … (1 + R) 1 (1 + R) 2 (1 + R) 3 where r is the required return. II. Constant Growth Case If the dividend grows at a steady rate, g, then the price can be written as: P 0 = D 1 /(R - g) This result is the dividend growth model.

26. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 26 T8.10 Summary of Stock Valuation (Table 8.1) (concluded) III. Supernormal Growth If the dividend grows steadily after t periods, then the price can be written as: D 1 D 2 D t P t P 0 = + +... + + (1 + R) 1 (1 + R) 2 (1 + R) t (1 + R) t where D t+1  (1 + g) P t = (R - g) IV. The Required Return The required return, r, can be written as the sum of two things: R = D 1 /P 0 + g where D 1 /P 0 is the dividend yield and g is the capital gains yield (which is the same thing as the growth rate in dividends for the steady growth case).

27. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 27 T8.11 Features of Common Stock Features of Common Stock The right to vote - including major events like takeovers The right to share proportionally in dividends paid The right to share proportionally in assets remaining after liabilities have been paid, in event of a liquidation The preemptive right Dividends…are paid from earnings Not a liability until declared by the Board of Directors Unlike interest on debt, dividends are not tax deductible to the firm However, shareholder receipt of dividends does have preferential tax treatment (See Chapter 2)

28. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 28 T8.11 Features of Common Stock Classes of Stock Dual Class shares are becoming more commonplace Usually classes divide into voting and non-voting shares “Coattail” provisionally invoked at the time of a takeover

29. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 29 T8.12 Features of Preferred Stock Features of Preferred Stock Preferences over common stock - dividends, liquidation Dividend arrearages Cumulative and non-cumulative Stated/liquidating value Typically non - voting Is preferred stock really debt? Preferred stock and taxes Tax treatment differs from debt Differential tax treatment suggests a preferred stock clientele

30. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 30 Preferred Stock - why it looks like debt Pref. Shareholders receive a stated dividend much like the stated coupon on a bond Pref. Shares often carry credit ratings much like a bond issues Pref. Stock is often callable by the issuer Some pref. Share issues even have sinking funds Floating rate pref. Shares are similar in concept to floating rate bond issues

31. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 31 Other Valuation Theories and Growth If a firm pays virtually all of its earnings out in the form of dividends – the value of the share = EPS/r or Dividends/r Where some cash is reinvested into growing the business then the share value = EPS/r + NPV of growth opportunities (GO) Application of the P/E ratio  Price per share/EPS = 1/r + NPVGO/EPS …..firm with higher growth opportunities should sell for higher valuations (prices)

32. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 32 Other Valuation Theories With Price Earnings and PEG Ratios The P/E ratio is partially impacted by the net present value of growth opportunities  for a given level of earnings, two stocks can trade at much different P/E ratios - one reason being investors are willing to pay more (a higher multiple of earnings) for the firm that has the greater growth opportunities. PEG ratio is the P/E ratio / earnings growth rate  useful when comparing stocks which have high P/E ratios - to help differentiate e.g -two stocks may both be trading at high P/E’s of say 50 -one may be growing earnings at 25 times per year and the other at 10 times....the two firms have PEG’s of 2.5 and 5. -all other things being equal - which one would be the better investment?