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Stock Valuation

Chapter 9. Stock Valuation. Chapter Outline. Common Stock Valuation Some Features of Common and Preferred Stocks The Stock Markets. Reading Stock Quotes. Sample Quote 52 weeks. Remember : Discounted Series of Cash flows Perpetual and annuities (with and without growth)

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Stock Valuation

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  1. Chapter 9 Stock Valuation

  2. Chapter Outline • Common Stock Valuation • Some Features of Common and Preferred Stocks • The Stock Markets

  3. Reading Stock Quotes Sample Quote 52 weeks • Remember: • Discounted Series of Cash flows Perpetual and annuities (with and without growth) • Historical data : day

  4. The discounted Dividend Model (DDM) • The build up of the DDM: • Expected Return • If you buy a share, you receive cash in 2 ways: • The company pays dividends • You sell your shares, either to another investor or back to the company • So (as bond), the price of the stock is the PV of these expected cash flows • The risk -adjusted rate of return • Market Capitalization(k) is the expected rate of return that investor require. Given here & determined in chapter 13.

  5. Deriving The DDM • Derivation of P0 from the expected rate of return: • (1) • Multiply both sides by P0and solve for P0 • (2) • Example: Assume: k = E ( R)1 =15%, P1=110, D1 = 5. what is P0?

  6. Deriving The DDM • Problem: We don’t know P1 now. Forecast it: • (3) • Substitute(3) into(2), we express P0 in term of D1, D2, and P2: • we don’t know P2 (4) • (5) • Substitute (5) into (4)…so on………we can push the future price into the future forever. • Repeating subs., we get the general form of DDM • (6)**

  7. The DDM • kis market capitalization and should reflect risk. It is given here treated later and in chapter 13. • You would find that the price of the stock is really just the present value of all expected future dividends • Eq.(6) require forecast of an infinite future div. • It is not very practical. • We need some assumptions:

  8. Estimating Dividends: Special Cases • Special Cases • I- Constant dividend • The firm will pay a constant dividend forever • This is like preferred stock • The price is computed using the perpetuity formula • II- Constant dividend growth • The firm will increase the dividend by a constant percent every period • III- Non-constant Growth model • Dividend growth is not consistent initially, but settles down to constant growth eventually

  9. I- Zero Growth (Preferred stocks ) • Case I: Constant dividends (D1=D2=D3= D) • (7) • If dividends are expected at regular intervals forever, then this is like preferred stock and is valued as a perpetuity • P0 = D / k (8) • Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price? • P0 = .50 / (.1 / 4) = $20 • Suppose D = 8kr. Market capitalization ( required rate ofreturn)) =10%. • Then: P0 = 8/0.10 = 80kr.

  10. II-Dividend Growth Model • Case II: Growth Dividends • Dividends are expected to grow at a constant rate: • P0 = D1 /(1+k) + D2 /(1+k)2 + D3 /(1+k)3 + … • P0 = D0(1+g)/(1+k) + D0(1+g)2/(1+k)2 + D0(1+g)3/(1+k)3 + • With a little algebra, this reduces to: • (9) • (10) • EX: D0 = 2.30 g = 5% and k = 13%. • Then : • What is the stock price in 5 years (P5)? • D5=2.30 (1.05)5 = 2.935

  11. Examples -Dividend Growth Model • Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? • P0 = .50(1+.02) / (.15 - .02) = $3.92 • Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? • P0 = 2 / (.2 - .05) = $13.33

  12. Example -Dividend Growth Model • Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. • What is the current price? • P0 = 4 / (.16 - .06) = $40 • What is the price expected to be in year 4? • P4 = D4(1 + g) / (k – g) = D5 / (k – g) • P4 = 4(1+.06)4 / (.16 - .06) = 50.50 • What is the implied return given the change in price during the four year period?

  13. Using the DGM to Find k • Start with the DGM: from eq.(9) • Suppose a firm’s stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return? • k = [1(1.05)/10.50] + .05 = 15% • What is the dividend yield? • 1(1.05) / 10.50 = 10% • What is the capital gains yield? • g =5%

  14. Nonconstantgrowth • Macro Systems just paid an annual dividend of $0.32 per share. Its dividend is expected to double for the next four years (D1 through D4), after which it will grow at a more modest pace of 1% per year. If the required return is 13%, what is the current price? • A • B • A+B: P0= 6,485+ 26,437 =$32.91

  15. III- NonconstantGrowthModel, • ABB will pay dividends in the first time in 5 years. D5=0.5 per share. Dividends will then grow at 10% per year indefinitely. k = 20% . What is the price of the stock today? • Some implication the Constant Growth Model • If g = 0 , then the valuation formula is just PV for perpetuity : ( P0=D1/k) • Holding D1 and k, the higher the g the higher is the price of the stock • As (g) approaches (k), the model explodes  limitation of the model.

  16. Earning & investment opportunities • Alternativly, we can calculate the value of stock as: • PV of all future earning for ever (perpetuity) + • NPV of future investment Opportunities. • (12) • Two cases: • Case (1): NPV =0, where E is EPS -stable (13) • Case (2) : + NPV: (14) • Where Does (g) Come From? • g = ROE x Retention Ratio or • x Plowback ratio or • x (1-dividend payout ratio)

  17. Example- Earning & investment opportunities • A Cash Cow Firm (A) with : • All earning is paid dividends. • EPS = 15. k = 15% . Net investment =g=0. • Using DDM: (perpetuity) • Another firm (B) • EPS = 15, reinvest 60% (payout is 40%). k = 15% Investment gives 20% return per year (ROE) • g (earning) = 0.6 * .2 = .12 or 12% • Apply the DDM: • NPV = $200(P0B) -$100 (P0A) = $100 • IF instead rate of return = 15% • g (earning)=0.6 * .15 = 0,09 • Apply DDM: • What add value is investment that earn rate of returns > required (k). • When rate of return = k  stock value can estimated by: P0 = E1/k (as cash Cow firm).

  18. A Reconsiderationof P/E Approach • One way : • Ex: P/E industry = $15 • EPSAstra = $2 • • If selling at $100, that reflect expectation of investment

  19. Summary Special Cases P0 = D / k

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