Stock Valuation. Lakehead University. Fall 2004

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1 Stock Valuation Lakehead University Fall 2004

2 Outline of the Lecture Common Stock Valuation Common Stock Features Preferred Stock Features 2

3 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

4 Common Stock Valuation PV of the stock cash flows = = $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

5 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 k. 5

6 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 k. P 2 = D 3 + P k. 6

7 Common Stock Valuation Therefore, P 0 = D 1 + P k = D 1 + D 2+P 2 1+k 1 + k = D k + D 2 (1 + k) 2 + P 2 (1 + k) 2 = D k + D D3+P3 2 (1 + k) k (1 + k) 2 = D 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

8 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

9 Special Cases Zero Growth Suppose D t = D for all t. Then P 0 = t=1 D (1 + k) t = D k. 9

10 Special Cases Constant Growth Suppose D t = (1 + g)d t 1 for all t. P 0 = D k + D 2 (1 + k) 2 + D 3 (1 + k) = D k + (1 + g)d 1 (1 + k) 2 + (1 + g)2 D 1 (1 + k) = D 1 k g if g < k. 10

11 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 k + (1 + g)d 1 (1 + k) 2 + (1 + g)2 D 1 (1 + k) (1 + g)t 1 D 1 (1 + k) T + ( ( ) ) D T g1 1 + D T +1/(k g 2 ) k g k (1 + k) T D 1 k g 1 ( ( ) ) 1 + T g k + (1 + g 2)(1 + g 1 ) T 1 D 1 (k g 2 )(1 + k) T. P T (1 + k) T 11

12 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

13 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

14 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

15 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

16 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

17 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

18 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

19 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

20 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

21 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

22 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

23 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

Stock Valuation. Lakehead University. Outline of the Lecture. Fall Common Stock Valuation. Common Stock Features. Preferred Stock Features

Stock Valuation. Lakehead University. Outline of the Lecture. Fall Common Stock Valuation. Common Stock Features. Preferred Stock Features 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