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1 Chapter 9: Valuation of Common Stocks Copyright © Prentice Hall Inc Author: Nick Bagley Objective Explain equity evaluation using discounting Dividend policy and wealth

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2 Chapter 9 Contents 9.1 Reading stock listings 9.2 The discounted dividend model 9.3 Earning and investment opportunity 9.4 A reconsideration of the price multiple approach 9.5 Does dividend policy affect shareholder wealth?

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3 9.1 Reading Stock Listings The following newspaper stock listing is usually printed as a horizontal string of informationThe following newspaper stock listing is usually printed as a horizontal string of information The listing is for IBM, which is traded on the New York Stock ExchangeThe listing is for IBM, which is traded on the New York Stock Exchange

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4 Reading Stock Listings

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5 –Hi = 123 1/8: The highest price the stock has traded at over the last 52 weeks –Lo = 93 1/8: The lowest price the stock has traded at over the last 52 weeks –Stock = IBM: The stock’s name –Sym = IBM: The stock’s symbol

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6 Reading Stock Listings –Div = 4.84: The last quarterly dividend multiplied by 4 –Yld % = 4.2: Dividend yield; (Annualized dividend ÷ stock price) –PE = 16: Price-to-earnings; (Latest price ÷ last 4 actual dividends) –Vol 100s = 14591*100; Volume of exchange traded shares

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7 Reading Stock Listings –Hi = 115: Highest share price of the day –Lo = 113: Lowest share price of the day –Close = 114 3/4: Days closing share price –Chg = 1 3/8: Change in closing price from previous trading day

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8 Observation It is usual to trade shares in round lots of 100 sharesIt is usual to trade shares in round lots of 100 shares If you decide to trade shares as odd lots you will pay higher commissionsIf you decide to trade shares as odd lots you will pay higher commissions Stock splits and stock dividends can cause you to hold odd lotsStock splits and stock dividends can cause you to hold odd lots

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9 9.2 The Discounted Dividend Model A discounted dividend model is any model that computes the value of a share of a stock as the present value of the expected future cash dividendsA discounted dividend model is any model that computes the value of a share of a stock as the present value of the expected future cash dividends

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10 Equivalence of HPR and NPV The book starts from the holding period return, and uses an inductive argument to derive the NPV method for evaluating stocksThe book starts from the holding period return, and uses an inductive argument to derive the NPV method for evaluating stocks Equivalently, we start with the discounted cash flow model, and obtain the holding period returnEquivalently, we start with the discounted cash flow model, and obtain the holding period return

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11 Notation P j is the stock value in year jP j is the stock value in year j D j is the cash dividend in year jD j is the cash dividend in year j K is the required rate of return on the stockK is the required rate of return on the stock

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12 Present Value of Dividends

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13 Expected Rate of Return The price and dividend next year are expected prices, soThe price and dividend next year are expected prices, so –The expected rate of return in any period equals the market capitalization rate, k

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14 Rate Relationship This relationship tells you that next year’s expected dividend yield + the expected capital gain yield is equal to the required rate of returnThis relationship tells you that next year’s expected dividend yield + the expected capital gain yield is equal to the required rate of return

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15 Price 0 Is Discounted Expected (Dividend 1 + Price 1 ) Price is the present value of the expected dividend plus the end-of-year price discounted at the required rate of returnPrice is the present value of the expected dividend plus the end-of-year price discounted at the required rate of return

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16 Ease of Use Estimating next year’s dividend is straightforward, but estimating next year’s price appears to be much more difficultEstimating next year’s dividend is straightforward, but estimating next year’s price appears to be much more difficult The problem is that next year’s price is obtained (eventually) by estimating, and discounting, every future dividendThe problem is that next year’s price is obtained (eventually) by estimating, and discounting, every future dividend

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17 Ease of Use We have to introduce a simplifying assumption that captures our understanding of dividend behaviorWe have to introduce a simplifying assumption that captures our understanding of dividend behavior The second simplest assumption is that a dividend in any future year is the dividend in the prior year times a constant growth factor (1+g)The second simplest assumption is that a dividend in any future year is the dividend in the prior year times a constant growth factor (1+g)

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18 Ease of Use Think of this as some kind of dividend inflationThink of this as some kind of dividend inflation From chapter 5 we know that if k is the nominal discount rate, then the real discount rate, R, is given by R = (1+k)/(1+g) - 1From chapter 5 we know that if k is the nominal discount rate, then the real discount rate, R, is given by R = (1+k)/(1+g) - 1

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19 Ease of Use Recall from chapter 4 that, for a perpetuity, the present value is the real value of the first cash flow divided by the real rateRecall from chapter 4 that, for a perpetuity, the present value is the real value of the first cash flow divided by the real rate

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20 Putting This Together

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21 Solving for K

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22 G = Capital Gains Yield G = Capital Gains Yield Comparing prior results:Comparing prior results:

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23 Conclusion The capital gains yield is equal to the dividend growth rateThe capital gains yield is equal to the dividend growth rate

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24 Generalization This model captures many of the characteristics of dividend cash flowsThis model captures many of the characteristics of dividend cash flows You could next assume that the rate of growth, g 1, is valid from a 1 to b 1, followed by g 2 from a 2 (= b 1 +1) to b 2,...You could next assume that the rate of growth, g 1, is valid from a 1 to b 1, followed by g 2 from a 2 (= b 1 +1) to b 2,... –Just like the folk in chapter 5, businesses grow, mature, and decay

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25 More General Models Chapter 5 contains an alternative derivation of growing perpetuity formulaChapter 5 contains an alternative derivation of growing perpetuity formula It also contains the equations, Excel workbooks, and worked examples for growing annuity models of common stockIt also contains the equations, Excel workbooks, and worked examples for growing annuity models of common stock

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Earning and Investment Opportunity A second approach to DCF valuation focuses on future earnings and investment opportunitiesA second approach to DCF valuation focuses on future earnings and investment opportunities This focus, rather than the earlier dividend focus, concentrates the analyst’s attention on the core business determinants of valueThis focus, rather than the earlier dividend focus, concentrates the analyst’s attention on the core business determinants of value

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27 Cash Flow Statements In chapter 3 we reviewed cash flow statements. Algebraically,In chapter 3 we reviewed cash flow statements. Algebraically, Net income + depreciation - increased working capital - increase P&E - dividends + increase in debt - increase in investment in marketable securities = 0 Net income + depreciation - increased working capital - increase P&E - dividends + increase in debt - increase in investment in marketable securities = 0

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28 Cash Flow Statements We simplify thisWe simplify this –By rolling changes in working capital, and P&E, into change in investments –By assuming pure equity funding (no debt) –By assuming no marketable securities Net income + depreciation - dividends - change in investments = 0Net income + depreciation - dividends - change in investments = 0

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29 Cash Flow Statements –We want to retain net income as an accounting entity in order to make the analysis useful –Depreciation is “accounting depreciation” and not market value attrition. (Assume these happen to be equal) –Define net new investments as new investments - depreciation

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30 Earning and Investment Opportunity To simplify the analysis, suppose that no new shares are issued, and no taxesTo simplify the analysis, suppose that no new shares are issued, and no taxes Dividends = earnings - net new investment “D = E - I”. The formula for valuing stock is

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31 Interpretation The value of a company is not equal to the present value of its expected earningsThe value of a company is not equal to the present value of its expected earnings

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32 Interpretation –Net new investment may be positive or negative The loss of existing asset value may not always be compensated by new investmentThe loss of existing asset value may not always be compensated by new investment –Earnings are what accountants understand by the term, namely net income after interest and tax We are finance folk, but the accountants provide the informationWe are finance folk, but the accountants provide the information

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33 Nogrowth –Nogrowth Co has a policy of no net new investments This does not mean the firm does not invest in new plant and equipment--only that purchases match the loss of value of the existing assets (as measured by depreciation)This does not mean the firm does not invest in new plant and equipment--only that purchases match the loss of value of the existing assets (as measured by depreciation) If we assume everything is in real terms, it is reasonable to assume that Nogrowth will pay a constant (say) $15/share each yearIf we assume everything is in real terms, it is reasonable to assume that Nogrowth will pay a constant (say) $15/share each year

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34 Nogrowth If the real capitalization rate is 15%, then the value of Nogrowth is 15/0.15 = $100If the real capitalization rate is 15%, then the value of Nogrowth is 15/0.15 = $100

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35 Growth Stock Growthstock Co initially has the same earnings as Nogrowth, but reinvests 60% of its earnings each year into new investments that yield a real rate of return of 20% per yearGrowthstock Co initially has the same earnings as Nogrowth, but reinvests 60% of its earnings each year into new investments that yield a real rate of return of 20% per year

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36 Growth Stock The management of Growthstock may be thought of as taking 60% of the shareholder’s value, and reinvesting it on behalf of the shareholdersThe management of Growthstock may be thought of as taking 60% of the shareholder’s value, and reinvesting it on behalf of the shareholders –That is the share holders have $100*0.4 = $40 of the value of the old stream, and management invests the remaining $100*0.6 = $60

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37 Growth Stock –The first cash flow is the result of investing $15*0.6 = $9 in year 1 to obtain $15*0.6*0.20 = $1.8 forever –In year 1 this has a value of $1.8/0.15 = $12 –There is a second, third, fourth, … flow starting in year 3, 4, 5, … also $12 –The present value of these streams is 12/0.15 = $80

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38 Growth Stock Magic –Management has taken shareholder value of $60 and turned it into $80 –The magic does not stop here. Management will take 60% of the new cash flows and reinvest them to return a 80/60 reward to the shareholders, and reinvest 60% of those –The wealth of the shareholders will become progressively multiplied

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39 Growth Stock Original wealth Kept Reinvested Wealth Multiplier

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40 Growth Stock

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41 Generalize Let theLet the –V = value of the shares without reinvestment –G = the growth from new investment –R = retention ratio –M = wealth multiplier = g/i –Wealth g = wealth 0 *(1-r)/(1-w*r)

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42 Observation If management had selected a slightly higher retention ratio r = i/g = 0.20/0.15 =0.75, then the value of the company goes to infinityIf management had selected a slightly higher retention ratio r = i/g = 0.20/0.15 =0.75, then the value of the company goes to infinity When this kind of thing happens in finance, it is a sign that something has been missed out of the analysisWhen this kind of thing happens in finance, it is a sign that something has been missed out of the analysis –The required rate of return demanded by investors may need to be increased

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43 Alternative Solution Method Recognizing thatRecognizing that G = change in earnings ÷ earnings = (net investment ÷ earnings) * G = change in earnings ÷ earnings = (net investment ÷ earnings) * (Change in earnings ÷ net investment) (Change in earnings ÷ net investment) Growth is then the product of the earnings- retention rate and the rate of return on new investment Growth is then the product of the earnings- retention rate and the rate of return on new investment Price growth = 6 ÷( (0.6*0.2)) = $200 Price growth = 6 ÷( (0.6*0.2)) = $200

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44 Alternative Solution Method The increase in the value of the stock is the consequence of reinvestment at a higher rate of return than the investor required rate of returnThe increase in the value of the stock is the consequence of reinvestment at a higher rate of return than the investor required rate of return Normalgrowth has investment opportunities of 15%, but still reinvests 60% of the earningsNormalgrowth has investment opportunities of 15%, but still reinvests 60% of the earnings

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45 Reinvestment Under Normal Growth Retention Ratio Growth Rate Cost of Capital

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46 Reinvestment Under Normal Growth In this case there is no increased value to the shareholdersIn this case there is no increased value to the shareholders

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47 A Reconsideration of the Price Multiple Approach Recall theRecall the P 0 = e 1 /k + NPV of future investments P 0 = e 1 /k + NPV of future investments In terms of P/E In terms of P/E P 0 / E 1 = 1/k + NPV/ E 1 of future investments P 0 / E 1 = 1/k + NPV/ E 1 of future investments –Firms with high PE ratios are then interpreted as having low capitalization rates or excellent future investment opportunities

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48 Does Dividend Policy Affect Shareholder Wealth? Dividend policy of a corporationDividend policy of a corporation –The policy regarding paying out cash to its shareholders, holding constant its investment and borrowing decisions

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Reconsideration of the P/E Multiple Approach The formula for a growing perpetuity is:The formula for a growing perpetuity is:

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Does Dividend Policy Affect Shareholder Wealth? In a frictionless world where there are no taxes nor transaction costs, the dividend policy (as defined in the last slide) will have no affect on the wealth of stock holdersIn a frictionless world where there are no taxes nor transaction costs, the dividend policy (as defined in the last slide) will have no affect on the wealth of stock holders We shall examine: tax, regulations, cost of external financing, and information content of dividendsWe shall examine: tax, regulations, cost of external financing, and information content of dividends

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51 Cash Dividends and Share Repurchases A corporation may distribute cashA corporation may distribute cash –By paying dividends All shareholders are paid the same per shareAll shareholders are paid the same per share –By repurchasing its own stock Shareholders choosing to liquidate some or all of their holdings sell the shares at market price (as they normally do), and the company makes market purchasesShareholders choosing to liquidate some or all of their holdings sell the shares at market price (as they normally do), and the company makes market purchases

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52 Illustration: Dividend Payment The following table shows a simplified balance sheet of Cashrich CoThe following table shows a simplified balance sheet of Cashrich Co AssumeAssume –Number of shares outstanding = 500,000 –Share price = $20

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53 Illustration: Dividends

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54 Illustration: Dividend Payment If Cashrich declares a dividend of $2 / share it will pay 500,000 * $2 = $1,000,000If Cashrich declares a dividend of $2 / share it will pay 500,000 * $2 = $1,000,000 –Given its level of risk, the payment will reduce the market value of the shares by $1,000,000 to $20 * 500,000 - $1,000,000 = $9,000,000, so each share will be worth $9,000,000 / 500,000 = $18 / share

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55 Illustration: Dividend Payment Was 2Was 10 Were 12

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56 Illustration: Dividend Payment Before the dividend, every share was worth $20Before the dividend, every share was worth $20 After the $2 / share dividend, every share was worth $18After the $2 / share dividend, every share was worth $18 ConclusionConclusion –Shareholders wealth is unchanged

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57 Illustration: Share Repurchase The original balance is shown belowThe original balance is shown below –Share price is still $20 –Number of shares outstanding is 500,000

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58 Illustration: Share Repurchase

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59 Illustration: Share Repurchase The company repurchases 50,000 shares at $20 per share = $1,000,000The company repurchases 50,000 shares at $20 per share = $1,000,000 –The market value of the firm is now $10,000,000 less the loss of $1,000,000 cash, or $9,000,000 –The number of shares outstanding is now 500, ,000 = 450,000

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60 Illustration: Share Repurchase –The share price is then $9,000,000/450,000 = $20 The wealth of the shareholders who sold out is unchangedThe wealth of the shareholders who sold out is unchanged The wealth of the shareholders who held the stock is unchangedThe wealth of the shareholders who held the stock is unchanged

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61 Illustration: Share Repurchase Was 2Was 10 Were 12

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62 Stock Dividends Corporations sometimes declare a stock split and distribute stock dividendsCorporations sometimes declare a stock split and distribute stock dividends –These activities do not distribute cash to the shareholders –They increase the number of issued shares, but do not change the % of the company each shareholder owns They do not affect shareholder wealthThey do not affect shareholder wealth

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63 Modigliani and Miller In a frictionless environment, where there are no costs of issuing new shares of stock, nor costs of repurchasing existing shares, a firm’s dividend policy can have no effect on the wealth of current shareholdersIn a frictionless environment, where there are no costs of issuing new shares of stock, nor costs of repurchasing existing shares, a firm’s dividend policy can have no effect on the wealth of current shareholders

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64 The Real World: Share Repurchase Smart Co has had a good year, and is considering repurchasing some outstanding stock in order to prevent some of its shareholders paying personal income tax on the dividendSmart Co has had a good year, and is considering repurchasing some outstanding stock in order to prevent some of its shareholders paying personal income tax on the dividend There are restrictions on this kind of practice in many countries, including the USAThere are restrictions on this kind of practice in many countries, including the USA

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65 The Real World: Retaining Surplus Cash to Shelter It Smart Co has had a good year, but is considering not declaring a dividendSmart Co has had a good year, but is considering not declaring a dividend Smart doesn’t need the cash, but holding cash tax shelters the shareholdersSmart doesn’t need the cash, but holding cash tax shelters the shareholders –IRS rules provide huge penalties for this kind of activity

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66 The Real World: Asymmetric Information The management of Cryptic Co is concerned that the investment community does not understand its businessThe management of Cryptic Co is concerned that the investment community does not understand its business –It has decided to finance projects using cheaper retained earnings rather than issuing more stock at a discount from its “true” market value

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67 The Real World: Signaling The management of Trip Co has had a single bad year, but has decided not to reduce its dividendThe management of Trip Co has had a single bad year, but has decided not to reduce its dividend –Reducing the dividend may send a signal to the investment community saying “The fundamentals of Trip have changed: consider decreasing future dividend estimates and/or consider increasing the cost of capital to compensate for additional risk”

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68 A Final Thought: Are Frictionless Worlds Enough? Large firms usually have limited liabilityLarge firms usually have limited liability Earnings follow a stochastic trajectoryEarnings follow a stochastic trajectory –Could repurchasing shares (or paying dividends) change shareholder wealth (despite our arguments)?

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