Features of Common Stock Valuation of Securities: Stocks • Voting rights (Cumulative vs. Straight) • Proxy voting Econ 422: Investment, Capital & Finance • Classes of stock University of Washington • Other rights Eric Zivot – Share proportionally in declared dividends Fall 2007 – Share proportionally in remaining assets during January 31, 2007 liquidation – Preemptive right – first shot at new stock issue E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 to maintain proportionalR.W. Parks/L.F. Davis 2004 ownership if desired Features of Preferred Stock The Stock Markets • Dealers vs. Brokers • Dividends • New York Stock Exchange (NYSE) – Stated dividend must be paid before dividends can be paid to common stockholders. – Largest stock market in the world – Dividends are not a liability of the firm, and –Members preferred dividends can be deferred • Own seats on the exchange indefinitely. • Commission brokers – Most preferred dividends are cumulative – any • Specialists missed preferred dividends have to be paid • Floor brokers before common dividends can be paid. • Floor traders • Preferred stock generally does not carry – Operations E. Zivot 2006 – Floor activity E. Zivot 2006 voting rights. R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 1 NASDAQ Stock Market Reporting 52 WEEKS YLD VOL NET • Not a physical exchange – computer-based HI LO STOCK SYMDIV % PE 100s CLOSECHG quotation system 25.72 18.12 Gap Inc GPS 0.18 0.8 18 39961 21.35 … Gap pays a • Multiple market makers dividend of 18 Gap has cents/share. Gap ended trading at • Electronic Communications Networks been as high $21.35, which is as $25.72 in unchanged from yesterday. • Three levels of information the last year. Given the current price, the dividend – Level 1 – median quotes, registered yield is .8%. representatives 3,996,100 shares traded – Level 2 – view quotes, brokers & dealers Gap has been as Given the current hands in the last day’s low as $18.12 in trading. – Level 3 – view and update quotes, dealers only price, the PE ratio is the last year. 18 times earnings. E. Zivot 2006 E. Zivot 2006 • Large portion of technologyR.W. Parks/L.F. Davis 2004 stocks R.W. Parks/L.F. Davis 2004 Valuing Stock Cash Flow • Valuing a firm’s equity involves the same ideas introduced for valuing a firm’s debt instruments A stock’s cash flow consists of: • Stream of dividend payments received during ownership of stock • To value a firm’s stock • The sale price for the stock upon deciding to sell 1. Determine the expected cash flows 2. Calculate the present value of the cash Note: flows • The dividend stream may continue indefinitely • The dividend stream may be finite • Valuing stock, however, is more complicated • The dividend stream may change over time than valuing bonds because the cash flows are • There may be no dividend stream not contractually specified or fixed. E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 2 Valuation of Stocks Valuation of Stocks Let’s calculate the rate of return for holding a stock r = [P1- P0]/P0 + D1/P0 for one Rewrite in terms of P : period (holding period return). Define: 0 P = D /(1+r) + P /(1+r) P0 = today’s price of the stock 0 1 1 P1 = next year’s price Today’s price equals the present value of next D1 = next year’s dividend year’s dividend plus the present value of next year’s price. HPR = r = [P1 + D1 - P0]/P0 = [P1- P0]/P0 + E. Zivot 2006 E. Zivot 2006 D1/P0 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 Example Valuation of Stocks continued P0 = D1/(1+r) + P1/(1+r) • P0 = 100, P1 = 110, D1 = 5. Solve for r: Similarly, we can write next year’s price as a 110− 100 5 r =+ function of the dividend in year 2 and the year 2 100 100 price of the stock: =+=0.10 0.05 0.15 P1 = D2/(1+r) + P2/(1+r) Given r, P , and D = 5 now solve for P 1 1 0 Substituting for P1: 5 110 P =+=100 P0 = D1/(1+r) + [D2/(1+r) + P2/(1+r)]/(1+r) 0 2 2 1.15 1.15 P0 = D1/(1+r) + D2/(1+r) + P2/(1+r) E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 3 Valuation of Stocks, continued 2 2 Example P0 = D1/(1+r) + D2/(1+r) + P2/(1+r) • r = 0.15, P = 100, P = 121, D = 5, This equation is recursive, upon further substitution 0 2 1 we can eventually arrive at the following expression: D2 = 5.5 55.5121 P = D /(1+r) + D /(1+r)2 + … + D /(1+r)T + … P0 =+22 + =100 0 1 2 T 1.15 ()1.15() 1.15 t P0 = Σ Dt/(1+r) for t = 1 to ∞ E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 Dividend Growth Models Dividend Growth Models • No growth in dividends: D1 = D2 = …=D t P0 = Σ D/(1+r) for t = 1 to ∞ • For a given discount rate r, stock prices will Note the right hand side is a perpetuity, such that: differ based on the firm dividends. P0 = D/r • The stock price is determined by how the firm dividends evolve. • Constant dividend growth: D1 = D; D2 = D(1+g); • Typical assumptions are 2 D3 = D(1+g) ; … – No growth in dividends t-1 t P0 = Σ D(1+g) /(1+r) for t = 1 to ∞ – Constant dividend growth Note the right hand side is a growing perpetuity, such that: P0 = D/(r-g) (for r > g) E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 4 Comparative Statics Numerical Examples • What happens to the stock price when the dividend growth rate changes? • D = 5, g = 0.10, r = 0.15 1 D P = 1 rg− D 5 No growth: P ==1 =33.33 dP 0 r 0.15 = −−()rg−2 D ⋅− (1) dg 1 D 5 Constant growth: P ===1 100 =−()rg−1 P 0 (rg− ) 0.05 dP ⇒≈−()rg−1 dg P E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 Determining the Dividend Growth Rate Numerical Example Q: What determines whether a firm will grow or issue increased dividends? • D1 = 5, r = 0.15, g0 = 0.10, g1 = 0.11 • A firm can either retain or payout earnings. dP −1 ≈−()rg dg • Dividends represent earnings that are paid out. P • Retained earnings are those earnings not paid out 0.01 0.01 ===0.2 as dividends that the firm plows back into the (0.15− 0.10) 0.05 business. • Investing retained earnings may provide growth = 20% opportunities for the firm. E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 5 Determining the Dividend Growth Rate Determining the Dividend Growth Rate • Investing retained earnings will improve If a firm elects to pay a lower dividend, and firm value (stock price) only if they are reinvest the funds, the stock price may increase invested in projects with positive Net because future dividends may be higher. Present Value; i.e., the return to the retained earnings (return on equity) must Payout Ratio - Fraction of earnings paid out as exceed the market discount rate. dividends • Investing retained earnings in positive NPV projects, all else constant, will allow Plowback Ratio - Fraction of earnings retained dividends to grow and the stock price to by the firm. Also called the retention ratio (RR) increase. Note: Payout Ratio + Plowback Ratio = 1 => Payout Ratio = 1 - RR E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 Determining the Dividend Growth Rate Example Growth in dividends can be derived from applying A company forecasts to pay a $8.33 the return on equity to the percentage of earnings dividend next year, which represents 100% of its plowed back into operations: earnings. This will provide investors with a 15% expected return. Suppose, instead, the Dividend growth = g company decides to plow back 40% of the earnings at the firm’s current return on equity of = return on equity * plowback ratio 25%. What is the value of the stock before and after the plowback decision? = ROE * RR E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 6 Stock price with no reinvestment of Stock price with no reinvestment of earnings: earnings: DEPS==$8.33 •With a fixed dividend forever, the stock price stays DEPS$8.33 fixed at 55.56 (no capital gains) P0 == = =$55.56 rr0.15 •The market rate of return on the stock is the dividend yield Where EPS = earnings per share D $8.33 r == =0.15 P0 = $55.56 = no dividend growth stock price P0 $55.56 E. Zivot 2006 E. Zivot 2006 R.W. Parks/L.F. Davis 2004 R.W. Parks/L.F. Davis 2004 Stock price after investment of retained If the company did not plowback some earnings, the stock price would remain at $55.56. With the earnings: plowback, the price rose to $100.00. gROERR=×=×=0.25 0.40 0.10 The difference between these two numbers is called D=−(1 RR ) × EPS = 0.60 × $8.33 = $5.00 the Present Value of Growth Opportunities (PVGO) D $5.00 $5.00 PVGO = $100−= $55.56 $44.44 P0 == = =$100 rg−−0.15 0.10 0.05 EPS =−P r P = $100 = stock price with growing dividends EPS 0 ⇒=P + PVGO r E.