Stock Valuation Lakehead University Fall 2004
Outline of the Lecture Common Stock Valuation Common Stock Features Preferred Stock Features 2
Common Stock Valuation Consider a stock that promises to pay a $1 dividend one year from now. If the stock price in one year is expected to be $25, then the overall cash flow to a stockholder one year from now is expected to be $26. If the return an investor requires to invest in such a stock is 12%, how much will he accept to pay for the stock? 3
Common Stock Valuation PV of the stock cash flows = 26 1.12 = $23.21, An investor should then never pay more than $23.21 for this stock. Similarly, a stockholder with the same beliefs would never sell the stock for less than $23.21, and thus this value must be the equilibrium stock price (without transaction costs). 4
Common Stock Valuation More generally, let P 0 today s stock price; P 1 stock price one year from now; D 1 dividend payment one year from now; k required return on this type of investment. Then P 0 = D 1 + P 1 1 + k. 5
Common Stock Valuation Let P t,d t denote the stock price and dividend in year t. What is P 1? What is P 2? P 1 = D 2 + P 2 1 + k. P 2 = D 3 + P 3 1 + k. 6
Common Stock Valuation Therefore, P 0 = D 1 + P 1 1 + k = D 1 + D 2+P 2 1+k 1 + k = D 1 1 + k + D 2 (1 + k) 2 + P 2 (1 + k) 2 = D 1 1 + k + D D3+P3 2 (1 + k) 2 + 1+k (1 + k) 2 = D 1 1 + k + D 2 (1 + k) 2 + D 3 (1 + k) 3 + P 3 (1 + k) 3. = T t=1 D t (1 + k) t + P T (1 + k) T. 7
Common Stock Valuation If lim T P T (1 + k) T = 0, then P 0 = t=1 D t (1 + k) t. That is, the price of a stock is the present value of its future dividend payments into perpetuity. 8
Special Cases Zero Growth Suppose D t = D for all t. Then P 0 = t=1 D (1 + k) t = D k. 9
Special Cases Constant Growth Suppose D t = (1 + g)d t 1 for all t. P 0 = D 1 1 + k + D 2 (1 + k) 2 + D 3 (1 + k) 3 +... = D 1 1 + k + (1 + g)d 1 (1 + k) 2 + (1 + g)2 D 1 (1 + k) 3 +... = D 1 k g if g < k. 10
Special Cases Two-Stage Growth Suppose g = g 1 for the first T years, after which g = g 2 into perpetuity. Then P 0 = = = D 1 1 + k + (1 + g)d 1 (1 + k) 2 + (1 + g)2 D 1 (1 + k) 3 +... + (1 + g)t 1 D 1 (1 + k) T + ( ( ) ) D 1 1 + T g1 1 + D T +1/(k g 2 ) k g 1 1 + k (1 + k) T D 1 k g 1 ( ( ) ) 1 + T g1 1 1 + k + (1 + g 2)(1 + g 1 ) T 1 D 1 (k g 2 )(1 + k) T. P T (1 + k) T 11
Components of the Required Return Rearranging we obtain P 0 = D 1 k g, k = D 1 P 0 + g, where D 1 P 0 can be referred to as the dividend yield and g can be referred to as the capital gains yield. 12
Growth Opportunities How can we estimate the growth rate of a stock s dividends? Consider a firm that never invests its earnings in new projects, i.e. it pays all of its earnings as dividends. Suppose, moreover, that earnings are expected to be constant forever. For such a firm, P 0 = D k = EPS k. 13
Growth Opportunities Suppose now that the firm retains some of its earnings to invest in new projects. More specifically, suppose the firm always retains a fraction b of its earnings each year and suppose the new projects the firm invests in generate a constant return k i each year. That is, EPS t = EPS t 1 + k i beps t 1, and thus EPS t = (1 + k i b)eps t 1. 14
Growth Opportunities The growth rate in earnings being k i b, the growth rate in dividends is D t D t 1 D t 1 = (1 b)eps t (1 b)eps t 1 (1 b)eps t 1 = EPS t EPS t 1 EPS t 1 = k i b. The stock price is then P 0 = D 1 k k i b = (1 b)eps 1. k k i b 15
Growth Opportunities If k i > k, then P 0 = (1 b)eps 1 k k i b > (1 b)eps 1 k kb = (1 b)eps 1 (1 b)k = EPS 1 k, so we could say that P 0 = EPS 1 k + NPVGO, where NPVGO stands for net present value of growth opportunities. If k i > k, then NPVGO > 0. 16
Growth Opportunities If, on the other hand, k i < k, then Since P 0 < EPS 1 k P 0 = EPS 1 + NPVGO, k we would have NPVGO < 0 in this case.. 17
Estimating the Growth Rate We found earlier that the growth rate in dividends was k i b. What is k i?. The return on the firm s investments can be approximated by firm s return on equity, and thus the growth rate in dividends can be approximated by ROE b = ROE (1 Payout ratio). 18
Common Stock Features Common shareholders have the right to: Vote for the firm s directors at the annual meeting, vote on matters of significant importance such as merger. Share proportionally in the dividends paid. Share proportionally in the firm s assets after liquidation (once creditors have been paid). 19
Common Stock Features Notes on Dividends Unless declared by the board of directors, a dividend is not a liability. Shareholders cannot force the firm into bankruptcy for non-payment of dividends. The payment of dividends is not a business expense. Dividends received by individuals are partially sheltered by a dividend tax credit. 20
Common Stock Features Classes of Stock Voting shares Non-voting shares Coattail provision: Non-voting shares can be converted into voting shares in the case of a hostile takeover. 21
Preferred Stock Features Preferred shares are issued with a stated value and the dividend attached to the share is usually a pre-specified amount ($2.25 per share) or a pre-specified percentage of the stated value (9% of $25). Preferred are similar to perpetual bonds. If the pre-specified dividend is D and the required return is k, the value of a preferred share is given by P = D k. 22
Preferred Stock Features Preferred shareholders must receive their dividends before common shareholders. Dividends may or may not be cumulative, most are cumulative. Unpaid cumulative dividends are a liability. Some preferred shares can be converted into common stock. Depending on their specific characteristics, preferred shares can either be classified as debt or equity. 23