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

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?

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

4 Reading Stock Listings

5 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

6 Present Value of Dividends P 0 = D 1 /(1+k)+ D 2 /(1+k) 2 + D 3 /(1+k) P 0 = D 1 /(1+k)+ D 2 /(1+k) 2 + D 3 /(1+k) With constant growth rateWith constant growth rate D 2 = D 1 (1+g), D 3 = D 2 (1+g), etc.D 2 = D 1 (1+g), D 3 = D 2 (1+g), etc. Hence, P 0 = D 1 /(k-g)Hence, P 0 = D 1 /(k-g)

7 Present Value of Dividends P 0 = D 1 /(1+k)+ D 2 /(1+k) 2 + D 3 /(1+k) P 0 = D 1 /(1+k)+ D 2 /(1+k) 2 + D 3 /(1+k) P 1 = D 2 /(1+k)+ D 3 /(1+k) 2 + D 4 /(1+k) P 1 = D 2 /(1+k)+ D 3 /(1+k) 2 + D 4 /(1+k) Using the above equations - P 0 = (P 1 + D 1 )/(1+k)Using the above equations - P 0 = (P 1 + D 1 )/(1+k)

8 Capital gain yield = g = dividend growth rate P 0 = D 1 /(k-g)P 0 = D 1 /(k-g) P 1 = D 2 /(k-g)P 1 = D 2 /(k-g) D 2 = D 1 (1+g)D 2 = D 1 (1+g) Using the above equations - (P 1 - P 0 )/P 0 = gUsing the above equations - (P 1 - P 0 )/P 0 = g

9 Discount rate k = rate of return on the stock = market capitalization rate on the stock Recall that P 0 = (P 1 + D 1 )/(1+k)Recall that P 0 = (P 1 + D 1 )/(1+k) Subtracting P 0 /(1+k) from both sides of the above equation and simplifying we get: k = (P 1 + D 1 - P 0 )/ P 0 = rate of return on the stock = market capitalization rate on the stockSubtracting P 0 /(1+k) from both sides of the above equation and simplifying we get: k = (P 1 + D 1 - P 0 )/ P 0 = rate of return on the stock = market capitalization rate on the stock

10 Discount rate k = Dividend yield plus capital gain yield k = (P 1 + D 1 - P 0 )/ P 0 = annual rate of return on the stock, ork = (P 1 + D 1 - P 0 )/ P 0 = annual rate of return on the stock, or k = D 1 / P 0 + (P 1 - P 0 )/ P 0k = D 1 / P 0 + (P 1 - P 0 )/ P 0 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

11 Solving for k k = D 1 / P 0 + (P 1 - P 0 )/ P 0k = D 1 / P 0 + (P 1 - P 0 )/ P 0 g = (P 1 - P 0 )/ P 0g = (P 1 - P 0 )/ P 0 Hence, k = D 1 / P 0 + gHence, k = D 1 / P 0 + g

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

13 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

14 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 The value of a company is equal to the present value of its expected earnings net of new investmentsThe value of a company is equal to the present value of its expected earnings net of new investments

15 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

16 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

17 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

18 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 shareholders.The management of Growthstock may be thought of as taking 60% of the shareholder’s value, and reinvesting it on behalf of the shareholders. The earnings retention rate is 60% and the dividend payout ratio is 40%The earnings retention rate is 60% and the dividend payout ratio is 40%

19 Growth Stock –The first year dividend is $15*0.4 = $6 –At the end of first period $9 is invested at 20% rate, which gives a perpetuity of $1.8 beginning second period. –The total earnings at the end of the second year are equal to $15 + $1.8 = $16.8 –Second year dividend is $16.8*0.4=$6.72 – 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

20 Growth Stock –At the end of second year $16.8*0.6 = $10.08 is invested at 20% rate, which gives a perpetuity of $2.016 beginning third period. –The total earnings at the end of the third year are equal to $15 + $1.8 + $2.016 = $ –Third year dividend is $18.816*0.4=$7.5264

21 Growth Stock –First year dividend = $6 –Second year dividend = $6.72 = $6(1.12) –Third year dividend = $ = $6.72(1.12) –The dividend growth rate of 12% is not a coincidence - it is equal to the earnings retention rate of 60% times the 20% rate of return of new investments. –g = 20% * 60% = 0.20 * 0.60 = 0.12=12%

22 Generalize Let theLet the –g = dividend growth rate –b = earnings retention rate –R = ROE on new investments –Then g = b * R

23 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

24 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

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

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

27 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

28 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

29 Illustration: Dividends

30 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

31 Illustration: Dividend Payment Was 2Was 10 Were 12

32 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

33 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

34 Illustration: Share Repurchase

35 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

36 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

37 Illustration: Share Repurchase Was 2Was 10 Were 12

38 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

39 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

40 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

41 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

42 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”