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T8.1 Chapter Outline

CLICK MOUSE OR HIT SPACEBAR TO ADVANCE. T8.1 Chapter Outline. Chapter 8 Stock Valuation Chapter Organization 8.1 Common Stock Valuation 8.2 Common Stock Features 8.3 Preferred Stock Features 8.3 Stock Market Reporting 8.4 Summary and Conclusions. Irwin/McGraw-Hill 2005.

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T8.1 Chapter Outline

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  1. CLICK MOUSE OR HIT SPACEBAR TO ADVANCE T8.1 Chapter Outline Chapter 8Stock Valuation Chapter Organization • 8.1 Common Stock Valuation • 8.2 Common Stock Features • 8.3 Preferred Stock Features • 8.3 Stock Market Reporting • 8.4 Summary and Conclusions Irwin/McGraw-Hill 2005

  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. 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: D1 P1 D2 P2 P0 = + and P1 = + (1 + R)1 (1 + R)1 (1 + R)1 (1 + R)1 substituting for P1 gives D1 D2 P2 P0 = + + . Continuing to substitute, we obtain (1 + R)1 (1 + R)2 (1 + R)2 D1 D2 D3 D4 P0 = + + + + … (1 + R)1 (1 + R)2 (1 + R)3 (1 + R)4

  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. 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. 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, D1/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? P0 = $1/.10 = $10. Given no change in the variables, what will the stock be worth in one year?

  7. Common Stock Valuation: The Zero Growth Case (concluded) One year from now, the value of the stock, P1, must be equal to the present value of all remaining future dividends. Since the dividend is constant, D2 = D1 , and P1 = D2/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. 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: D1 D2 D3 D0(1+g)1 D0(1+g)2 D0(1+g)3 P0 = + + + … = + + + ... (1 + R)1 (1 + R)2 (1 + R)3 (1 + R)1 (1 + R)2 (1 + R)3 D0(1 + g) D1 P0 = = . R - g R- g • Now assume that D1 = $1.00, r = 10%, but dividends are expected to increase by 5% annually. What should the stock sell for today?

  9. Common Stock Valuation: The Constant Growth Case (concluded) The equilibrium value of this constant-growth stock is D1 $1.00 = = $20 R - g .10 - .05 What would the value of the stock be if the growth rate were only 3%? D1 $1.00 = = $14.29. R - g .10 - .03 Why does a lower growth rate result in a lower value?

  10. Stock Price Sensitivity to Dividend Growth, - ‘g’ Stock price ($) 50 45 D1 = $1 Required return, R, = 12% 40 35 30 25 20 15 10 5 Dividend growth rate, g 0 8% 10% 2% 6% 4%

  11. Stock Price Sensitivity to Required Return, - ’r’ Stock price ($) 100 90 80 D1 = $1 Dividend growth rate, g, = 5% 70 60 50 40 30 20 10 Required return, R 8% 14% 6% 10% 12%

  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 P0 = present value of dividends in the non-constant growth period(s) + present value of dividends in the “steady state” period.

  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. ABC Company - • 1st calculate the value of the stock at p3 using the constant growth formula • P3 = D4/r-g = $5.20/(.08-.04) = $130 • Next discount this value back to p0 • P3/(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. 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. 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 _____ ? P0 = D1/(R - g) = $5  ( 1.05 )/( .09 - .05 ) = $5.25/.04 = $131.25 per share • What will the price be in a year? Pt = Dt+1/(R - g) P1 = D 2 /(R - g) = ($5.25 1.05)/(.09 - .05) = $137.8125 • By what percentage does P1 exceed P0? Why? P1 exceeds P0 by 5% -- the capital gains yield.

  17. Components of the Required Rate of Return We know that P0 = D1/(r-g) Then r = D1/P0 + g • D1/P0 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. 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? P0 = D1/(R - g) (R - g) = D1/P0 R = D1/P0 + g = $5.25/$65.625 + .05 = dividend yield ( .08 ) + capital gains yield ( .05 ) = .13 = 13%

  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 12.4 page 349 in text Canadian equities – 10. 29% average return over past 50 years Long term Bonds - 9.01% ,,,many financial planners today are suggesting 8-10% as a realistic average rate of return to expect on a diversified portfolio

  20. Valuation Example • 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? Time Dividend 0 $ 5.00 1 $ 5.50 (10% growth) 2 $ 6.05 (10% growth) 3 $6.534 ( 8% growth) 4 $6.926 ( 6% growth)

  21. Valuation Example cont’d • At time 3, the value of the stock will be: P3 = D4/(R - g) = $6.926/(.12 - .06) = $115.434 • The value today of the stock is thus: P0 = D1/(1 + R) + D2/(1 + R)2 + D3/(1 + R)3 + P3/(1 + R)3 = $5.5/1.12 + $6.05/1.122 + $6.534/1.123 + $115.434/1.123 = $96.55

  22. Examples • 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, P0 = D1/(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 P3 = P0 (1 + g)3 = $30.00  (1.05)3 = $34.73, and P15 = P0 (1 + g)15 = $30.00  (1.05)15 = $62.37.

  23. Examples • 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: D1 = D2 = D3 = D4 = D5 = 0 D6 = $6.00 D7 = $6.00(1.05) = $6.30 . . .

  24. Examples • 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 deferredcash flow stream. • Therefore, the answer requires two steps: 1. By the constant-growth model, D6/(r - g) = P5; i.e., P5 = $6.00/(.21 - .05) = $37.50. 2. And, P0 = P51/(1 + .21)5 = $37.50  .3855 = $14.46.

  25. Summary of Stock Valuation (Table 8.1) I. The General Case In general, the price today of a share of stock, P0, is the present value of all of its future dividends, D1, D2, D3, . . . D1 D2 D3 P0 = + + + … (1 + R)1 (1 + R)2 (1 + R)3 where ris the required return. II. Constant Growth Case If the dividend grows at a steady rate,g, then the price can be written as: P0 = D1/(R - g) This result is the dividend growth model.

  26. T8.10 Summary of Stock Valuation (Table 8.1) (concluded) III.Non Constant or Supernormal Growth If the dividend grows steadily after t periods, then the price can be written as: D1 D2 Dt Pt P0 = + + . . . + + (1 + R)1 (1 + R)2 (1 + R)t (1 + R)t where Dt+1 (1 + g) Pt = (R - g) IV. The Required Return The required return, r, can be written as the sum of two things: R = D1/P0 + g where D1/P0 is the dividend yield and gis the capital gains yield (which is the same thing as the growth rate in dividends for the steady growth case).

  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. 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. 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. 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. 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. 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?

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