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- 1. Valuing common stocks The plan of the lecture Review what we have accomplished in the last lecture Application of the DCF approach Some terms about stocks TIP Valuing stocks using If you do not understand something, Dividend growth model ask me! Corporate value model the multiples of comparable firms 2 Some terms about stocks What have we accomplished? PV concepts Common Stock - Ownership shares in a Discount rates publicly held corporation. NPV rules for taking a project Book Value – Total common equity on the The formula for calculating perpetuity balance sheet. and annuity Market Value – Stock price per share * # of Compounding interest rate shares outstanding. 3 4 Some terms about stocks Facts about common stock Dividend - Periodic cash distribution from Represents ownership the firm to the shareholders. Ownership implies control P/E Ratio – Stock Price per share divided Stockholders elect directors by earnings per share (EPS). Directors elect management Dividend yield – Dividends per share Management’s goal: Maximize the stock (DPS) over the stock price of per share price 5 6
- 2. Types of stock market Stock Market Reporting transactions 52 WEEKS YLD VOL NET HI LO STOCK SYM DIV % PE 100s HI LO CLOSE CHG 52.75 19.06 Gap Inc GPS 0.09 0.5 15 65172 20.50 19 19.25 -1.75 Initial public offering market (“going Gap pays a dividend of 9 Gap ended trading public”) (Company sells shares to the public Gap has cents/share at $19.25, down been as for the 1st times.) $1.75 from high as Given the yesterday’s close Primary market (Company sells shares to $52.75 in current price, the last the dividend the public for the 2nd, 3rd,…times.) year. yield is ½ % Secondary market (stockholders sell shares Given the Gap has to each other) current price, the 6,517,200 shares been as low traded hands in the as $19.06 in PE ratio is 15 times earnings last day’s trading the last year. 7 8 Expected return Expected Return Expected Return - The percentage return that an The formula for the expected return can be investor forecasts from a specific investment over a set period of time. broken into two parts: At this stage, you do not need to distinguish Expected return = Dividend Yield + Capital between expected return and the discount rate. Appreciation Yield Div1 + P1 − P0 Div1 P1 − P0 Expected Return = r = Expected Return = r = + P0 P0 P0 9 10 Example Example If Fledgling Electronics is selling for $100 per share Jennifer has bought one IBM share in the today and is expected to sell for $110 one year from now, what is the expected return if the dividend one beginning of this year and decides to hold year from now is forecasted to be $5.00? this share until next year. The expected dividend this year is $10 per share and the stock is expected to sell at $110 per share in the end of the year. If the discount rate 5 + 110 − 100 is 10%, what is the current stock price? Expected Return = = . 15 100 P=(110+10)/(1+0.1)=$109.1 11 12
- 3. Valuing Common Stocks using Valuing common stocks using dividends dividends Stock value equals the present value of all Example expected future dividends plus the selling Current forecasts for XYZ Company’s dividends are price of the stock. $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What Div1 Div2 Div H + PH is the price of the stock now given a 12% discount P0 = + +...+ rate? (1 + r ) (1 + r ) 1 2 (1 + r ) H H - Time horizon for your investment. 13 14 Valuing common stocks using Solution dividends If we forecast no dividend growth, and plan to 3.00 3.24 3.50 + 94.48 hold out stock indefinitely, we will then value P = + + the stock as the PV of a PERPETUITY. (1 + .12) (1 + .12) 1 2 (1 + .12)3 Div1 EPS1 P = $75.00 PV ( perpetuity ) = P = or r r Assumes all earnings are paid to shareholders. 15 16 Example Solution Suppose that a stock is going to pay a (a) P0=3/0.1=$30 dividend of $3 every year forever. If the (b)P0=PV (annuity) + PV( the stock price at year 2) discount rate is 10%, what is the current = 3/1.1 + 3/1.12+(3/0.1)/1.12 stock price for the following cases: = 3/0.1=$30 (a) you invest and hold it forever? (c) P0=PV (annuity of 20 years) + (b) you invest and hold it for two years? PV (the stock price at the year of 20) (c) you invest and hold it for 20 years? =$30 17 18
- 4. Conclusion Dividend growth model The stock price does not depend on how Since the stock value does not depend on the investment horizon, let’s assume the investor will hold onto it long you intend to hold it! forever. So, value of a stock is the present value of all future dividends expected to be generated by the stock. D1 D2 D3 D∞ P = + + + ... + (1 + r )1 (1 + r )2 (1 + r )3 (1 + r )∞ 19 20 Constant growth stock I: Dividend Growth Model A stock whose dividends are expected to Under the assumption that dividends grow at a grow forever at a constant rate, g. constant rate, stocks can be valued as a D1 = D0 (1+g)1 perpetuity with a growth rate, (still remember D2 …...D0 (1+g)2 = the PV of a growth perpetuity?) that is Dt = D0 (1+g)t Div1 P = r−g 21 22 What happens if g > r? Example If g > r, the constant growth formula leads Suppose that a stock is going to pay a to a negative stock price, which does not dividend of $3 next year. Dividends grow make sense. at a growth rate of 3%. If the discount rate is 10%, what is the stock price? 23 24
- 5. Using dividends models to estimate Solution the discount rate or the growth rate P=3/(0.1-0.03)=$42.86 Discount Rate can be estimated by: Will the stock value change if you plan to (a) buy and hold it forever? Div1 (b) buy and hold it for two years? P = (c) buy and hold it for 20 years? r−g No. Div1 r= +g P 25 26 Some terms about dividend Valuing Common Stocks growth rates Example- continued If a firm elects to pay a lower dividend, and A stock is selling for $100 in the stock market. Next reinvest the retained earnings, the stock price may increase because future dividends may be year’s dividend is $3. The discount rate for this stock higher. is 12%.what is the market estimate about the growth Payout Ratio : Fraction of earnings paid out as in dividends? dividends=dividend per share/EPS Plowback (Retention) Ratio : Fraction of earnings $3.00 retained by the firm. $100 = .12 − g Payout ratio=1-plowback ratio g = .09 27 28 Deriving the dividend growth rate g Example Growth can be derived from applying the Our company forecasts to pay a $5.00 return on equity to the percentage of dividend next year, which represents earnings plowed back into operations. 100% of its earnings. The discount rate is 12%. Instead of paying out all ROE = Return on Equity earnings, we decide to plow back 40% of EPS the earnings at the firm’s current return = on equity of 20%. What is the value of Book Equity Per Share the stock before and after the plowback g = return on equity X plowback ratio decision? 29 30
- 6. Solution Example (continued) Without growth 5 The difference between these two numbers (75.00- P = = $41.67 41.67=33.33) is called the Present Value of Growth 0.12 Opportunities (PVGO). With growth g = 0.4* 0.2 = 0.08 Present Value of Growth Opportunities (PVGO) : Net present value of a firm’s future investments. 5* 0.6 P = = $75 0.12 − 0.08 31 32 The importance of growth II: Corporate value model (Free Cash opportunity Flow model) We often use earnings to value stocks as Also called the free cash flow method. Suggests the value of the entire firm equals the present value of the firm’s free cash flows. EPS1 P = + PVGO r A firm generates free cash flows for its stock holders and debt holders, so: Why do some hi-tech stocks have high Market value of a firm=Market value of stocks + prices even though they have little or market value of debt negative earnings? 33 34 Issues regarding the corporate Applying the corporate value model value model Find the market value (MV) of the firm. Similar to dividend growth model, often Find PV of firm’s future FCFs assumes at some point free cash flow will Subtract MV of firm’s debt (and preferred stock, if grow at a constant rate. any) to get MV of common stock. MV of common stock = MV of firm– MV of debt Terminal value (TVn) represents value of firm at the point of time that growth Divide MV of common stock by the number of becomes constant. shares outstanding to get intrinsic stock price (value). P = MV of common stock / # of shares of common stock 35 36
- 7. Valuing common stocks using FCF (free cash flows) FCF and PV The value of a business is usually computed as the discounted value of FCF out to a FCF1 FCF2 FCFH PVH valuation horizon (H). PV = + + ... + + (1 + r )1 (1 + r ) 2 (1 + r ) H (1 + r ) H The value after H is sometimes called the terminal value or horizon value. PV (free cash flows) PV (terminal value) FCF1 FCF2 FCFH PVH PV = + + ... + + (1 + r )1 (1 + r ) 2 (1 + r ) H (1 + r ) H 37 38 Given the long-run gFCF = 6%, and firm discount rate of If the firm has $40 million in debt and has 10 10%, use the corporate value model to find the firm’s million shares of stock, what is the firm’s stock value. value per share? MV of equity = MV of firm – MV of debt = $416.94m - $40m 0 r = 10% 1 2 3 4 = $376.94 million ... g = 6% Value per share = MV of equity / # of shares -5 10 20 21.20 = $376.94m / 10m -4.545 8.264 = $37.69 15.026 21.20 398.197 530 = = TV3 0.10 - 0.06 416.942 39 40 Usually it is more difficult to predict How to get free cash flows dividend than free cash flows (FCF)? The corporate value model is often preferred to Remember, free cash flow is the firm’s after-tax operating income (NOPAT) less the net capital the dividend growth model, especially when investment considering firms that don’t pay dividends or FCF = NOPAT – Net capital investment when dividends are hard to forecast. NOPAT (net operating profit after tax)= EBIT* (1 – Projecting free cash flows might give us more Tax rate) accurate estimates of a firm’s value. FCF = NOPAT – Net capital investment A lot of accounting information to predict free cash flow (FCF). How to get net capital investment then? 41 42
- 8. How to get net capital investment then? (Not required) III: Firm multiples method net capital investment =change in operating capital between adjacent years. Analysts often use the following multiples to net capital investment in year t =operating capital at the end of year t - operating capital at the end of year t-1. value stocks. P/E Operating capital = NOWC + Net Fixed Assets NOWC = Current assets - Non-interest bearing current liability P/B Examples of Non-interest bearing current liability: account payable, P / Sales unearned revenue. Example of interest bearing current liability: note payable EXAMPLE: Based on comparable firms, estimate the appropriate P/E. Multiply this If we ignore change in working capital, then net capital investment =capital expenditure - depreciation by expected earnings per share to figure out an estimate of the stock price. 43 44 Example Firm ABC has EPS=$2, a similar firm in the same industry has a P/E ratio of 30. What’s you estimate of ABC’s stock price? $2*30=$60 Simple and useful. 45

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