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## CHAPTER 7

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**CHAPTER 7**Stocks, Stock Valuation, and Stock Market Equilibrium**Topics in Chapter**Features of common stock Valuing common stock Preferred stock Stock market equilibrium Efficient markets hypothesis Implications of market efficiency for financial decisions**EQUITIES**Why? Business Application For Investor: Determine value of asset/business/company For Firm: Determine cost of attracting investors & raising equity capital Selling ownership stake to raise $ • Key to understanding valuations • What is investment worth today? • Value of: • Enterprise • Entity • Company/Firm**Equities**• Valuing companies that don’t pay dividends • Alternative valuation methods**D2**D1 D∞ ValueStock = + + + (1 + rs )1 (1 + rs)2 (1 + rs)∞ The Big Picture: The Intrinsic Value of Common Stock Free cash flow (FCF) Dividends (Dt) ... Firm’s debt/equity mix Market interest rates Cost of equity (rs) Firm’s business risk Market risk aversion**Common Stock: Owners, Directors, and Managers**Represents ownership. Ownership implies control. Stockholders elect directors. Directors hire management. Preemptive right. Since managers are “agents” of shareholders, their goal should be: Maximize stock price.**When is a stock sale an initial public offering (IPO)?**• A firm “goes public” through an IPO when the stock is first offered to the public. • Prior to an IPO, shares are typically owned by the firm’s managers, key employees, and, in many situations, venture capital providers**What is a seasoned equity offering (SEO)?**• A seasoned equity offering occurs when a company with public stock issues additional shares. • After an IPO or SEO, the stock trades in the secondary market, such as the NYSE or Nasdaq.**Classified Stock**Classified stock has special provisions. Could classify existing stock as founders’ shares, with voting rights but dividend restrictions. New shares might be called “Class A” shares, with voting restrictions but full dividend rights.**Tracking Stock**The dividends of tracking stock are tied to a particular division, rather than the company as a whole. Investors can separately value the divisions. Its easier to compensate division managers with the tracking stock. But tracking stock usually has no voting rights, and the financial disclosure for the division is not as regulated as for the company.**Bonds vs. Stocks**IssuerCost (company) int. paid out (i) Cost (dividends pd out Cap gains Stock value or price today Discount the CFs by (R) (reqr’d return) Cfs = Dividends • Bond value or price today • Discount the CFs by (i) (reqr’d return) • Cfs = Int pmts; principal • PV, PMT,FV,N,i**Bonds vs. Stocks**Bond’s Value or Price Today Stock’s Value or Price Today = sum of the PVs of the future CFs; Discount CFs (divids) by (R) (reqr’d return) to get Po (PV) • = sum of the PVs of the future CFs; • That is – discount CFs (int Pmts (PMT) & Principal (FV)) by i% over some period (N) to get PV • PMT,FV,N,I known; solve for PV**Different Approaches for Valuing Common Stock**Dividend growth model Constant growth stocks Nonconstant growth stocks Free cash flow method Using the multiples of comparable firms**Why Invest in Stock?**• For Growth in Value • From Dividends & Cap Gains • Generating Total Return = R • Stock Price = Growth = g • Dividend Return or Yield = Annual divid / Price of stock= D1 / Po • Return on Stock = Return on Divid + Growth (cap gains) • R = D1 /Po + g (but want price today) • R – g = D1 /Po • Finally: Po = D1 / R - g**Constant Growth Approach to Equity Valuations**• Po = D1 / R – g • Discounting the Divids (or CFs) by R-g (return adjusted for constant growth) • Constant growth model: works when g is constant rate (%) & R > g • If g > R, then have supernormal or non-constant growth • If so, then look at PVs of CFs generated the stock to determine its price today • If we need R (req’d return) to use as disct factor, we can use SML relationship from CAPM • SML: Ri = rRF + (RM - rRF)bi .**Stock Value = PV of Dividends**D1 D2 D3 D∞ ^ P0 = + + … + + (1 + rs)1 (1 + rs)2 (1 + rs)3 (1 + rs)∞ What is a constant growth stock? One whose dividends are expected to grow forever at a constant rate, g.**For a constant growth stock:**D1 = D0(1 + g)1 D2 = D0(1 + g)2 Dt = D0(1 + g)t If g is constant and less than rs, then: D0(1 + g) D1 ^ P0 = = rs – g rs – g**Dividend Growth and PV of Dividends: P0 = ∑(PV of Dt)**$ Dt = D0(1 + g)t Dt 0.25 PV of Dt = (1 + r)t If g > r, P0 = ∞ ! Years (t)**What happens if g > rs?**D0(1 + g)1 D0(1 + g)2 D0(1 + rs)∞ ^ P0 = + … + + (1 + rs)1 (1 + rs)2 (1 + rs)∞ (1 + g)t ^ > 1, and P0 = ∞ (1 + rs)t So g must be less than rs for the constant growth model to be applicable!! If g > rs, then**Required rate of return: beta = 1.2, rRF = 7%, and RPM = 5%.**Use the SML to calculate rs: rs = rRF + (RPM)bFirm = 7% + (5%)(1.2) = 13%.**Projected Dividends**D0 = $2 and constant g = 6% D1 = D0(1 + g) = $2(1.06) = $2.12 D2 = D1(1 + g) = $2.12(1.06) = $2.2472 D3 = D2(1 + g) = $2.2472(1.06) = $2.3820**Expected Dividends and PVs (rs = 13%, D0 = $2, g = 6%)**0 1 2 3 g = 6% 2.12 2.2472 2.3820 1.8761 13% 1.7599 1.6508**Intrinsic Stock Value: D0 = $2.00, rs = 13%, g = 6%**Constant growth model: ^ D0(1 + g) D1 P0 = = rs – g rs – g $2.12 $2.12 = = = $30.29. 0.13 – 0.06 0.07**Expected value one year from now:**D1 will have been paid, so expected dividends are D2, D3, D4 and so on. D2 ^ $2.2472 P1 = = = $32.10 rs – g 0.07**Return = Dividend Yield + Capital Gains Yield**D1 Dividend yield = P0 ^ P1 – P0 CG Yield = = P0 New - Old Old**Expected Dividend Yield and Capital Gains Yield (Year 1)**D1 $2.12 Dividend yield = = = 7.0%. P0 $30.29 ^ P1 – P0 $32.10 – $30.29 CG Yield = = P0 $30.29 = 6.0%.**Total Year 1 Return**Total return = Div yield + Cap gains yield. Total return = 7% + 6% = 13%. Total return = 13% = rs. For constant growth stock: Capital gains yield = 6% = g.**Rearrange model to rate of return form:**D1 D1 ^ ^ P0 = to rs + g. = rs – g P0 ^ Then, rs = $2.12/$30.29 + 0.06 = 0.07 + 0.06 = 13%.**If g = 0, the dividend stream is a perpetuity.**0 1 2 3 rs = 13% 2.00 2.00 2.00 PMT $2.00 ^ P0 = = = $15.38. r 0.13**Supernormal Growth Stock I**Supernormal growth of 30% for first three years, then 6% constant g thereafter. Just paid dividend of $2.00 /sh, & required return for investments of this risk is 13%. What’s the price today (Po)? Can no longer use constant growth model. However, growth becomes constant after 3 years.**Nonconstant growth followed by constant growth**0 1 2 3 4 rs = ? % g = ? % g = ? % g = ? % g = ? % Do=?(1+g) D1=? D2=? D3=? D4=? ? ? ? D4 ^ P3 = ? R - g ^ ?? = P0**Nonconstant growth followed by constant growth (D0 = $2):**0 1 2 3 4 rs = 13% g = 30% g = 30% g = 30% g = 6% Do=2.00(1+g) D1=2.60 D2=3.38 D3=4.39 D4=4.66 2.30 2.65 3.05 $4.66 ^ = $66.54 P3 = 46.11 0.13 – 0.06 ^ 54.11 = P0**Using Cfs**After Determining: Future Divs & gkterminal value (price) CFo = 0 CF1 = 2.60 CF2 = 3.38 CF3 = 4.39 + 66.54 =70.93 i = 13 % Po = NPV = ? = $54.11 • CFo = Do • CF1 = D1 • CF2 = D2 • CF3 = D3 + P3 • i = R % • Po = NPV = ?**Expected Dividend Yield and Capital Gains Yield (t = 0)**Today (@ t =0): D1 $2.60 Dividend yield = = = 4.81% P0 $54.11 CG Yield = 13.0% – 4.81% = 8.19%.**Expected Divd & Cap Gains Yield (after t = 3)**• During nonconstant growth, dividend yield and capital gains yield are not constant. • If current growth is greater than gk, current capital gains yield is greater than g. • After year 3 (t = 3), gk = constant = 6%, so CGY = 6%. • Because rs = 13%, after yr 3 div yld = • 13% – 6% = 7%.**The current stock price is $54.11.**The PV of dividends beyond Year 3 is: $46.11 = 85.2%. $54.11 Is stock price based onshort-term growth? =terminal or horizon value in year 3 (P3)discounted to present by req’d Return (R=13%) = $46.11 ^ % of stock price due to “long-term” dividends is:**Intrinsic Stock Value vs. Quarterly Earnings**If most of a stock’s value is due to long-term cash flows, why do so many managers focus on quarterly earnings?**Intrinsic Stock Value vs. Quarterly Earnings**Sometimes changes in quarterly earnings are a signal of future changes in cash flows. This affects current stock price (Po). Sometimes managers have bonuses tied to quarterly earnings.**Supernormal Growth Stock II**Supernormal growth of 30% for Year 0 to Year 1, 25% for Year 1 to Year 2, 15% for Year 2 to Year 3, and then long-run constant g = 6%. Can no longer use constant growth model. However, growth becomes constant after 3 years.**Nonconstant growth followed by constant growth (D0 = $2):**0 1 2 3 4 rs = 13% g = 30% g = 25% g = 15% g = 6% 2.6000 3.2500 3.7375 3.9618 2.3009 2.5452 2.5903 $3.9618 ^ = $56.5971 P3 = 39.2246 0.13 – 0.06 ^ 46.6610 = P0**Expected Dividend Yield and Capital Gains Yield (t = 0)**At t = 0: D1 $2.60 Dividend yield = = = 5.6% P0 $46.66 CG Yield = 13.0% – 5.6% = 7.4%. (More…)**Expected Dividend Yield and Capital Gains Yield (after t =**3) • During nonconstant growth, dividend yield and capital gains yield are not constant. • If current growth is greater than g, current capital gains yield is greater than g. • After t = 3, g = constant = 6%, so the capital gains yield = 6%. • Because rs = 13%, after t = 3 dividend yield = 13% – 6% = 7%.**The current stock price is $46.66.**The PV of dividends beyond Year 3 is: $39.22 = 84.1%. $46.66 Is the stock price based onshort-term growth? ^ P3 / (1+rs)3 = $39.22 The percentage of stock price due to “long-term” dividends is:**Suppose g = 0 for t = 1 to 3, and then g is a constant 6%.**0 1 2 3 4 rs = 13% g = 0% g = 0% g = 0% g = 6% 2.00 2.00 2.00 2.12 1.7699 1.5663 1.3861 2.12 = = P 30.2857 20.9895 0.07 3 25.7118 ^**Dividend Yield and Capital Gains Yield (t = 0)**Dividend Yield = D1/P0 Dividend Yield = $2.00/$25.72 Dividend Yield = 7.8% CGY = 13.0% – 7.8% = 5.2%.**Dividend Yield and Capital Gains Yield (after t = 3)**Now have constant growth, so: Capital gains yield = g = 6% Dividend yield = rs – g Dividend yield = 13% – 6% = 7%**Suppose negative growth:If g = -6%, would anyone buy stock?**If so, at what price? Firm still has earnings and still pays dividends, so P0 > 0: ^ D0(1 + g) D1 ^ P0 = = rs – g rs – g $2.00(1-.06) $1.88 = = = $9.89. 0.13 – (-0.06) 0.19**Annual Dividend and Capital Gains Yields**Capital gains yield = g = -6.0%. Dividend yield = 13.0% – (-6.0%) = 19.0%. Both yields are constant over time, with the high dividend yield (19%) offsetting the negative capital gains yield.**What if company pays no dividends?**• Discount Free Cash Flows (CFs which can be returned to investors) instead of dividends • Where FCF = NOPAT – Net Capital Spending**Uses of Free Cash Flows**• Pay interest on debt • Repay principal on debt • Pay dividends to equityholders • Repurchase stock from equityholders • Buy mrktbl securities or other non-operating assets