1 Chapter 9: Valuation of Common Stocks Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley...

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Chapter 9: Valuation of Chapter 9: Valuation of Common StocksCommon Stocks

Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley

ObjectiveExplain equity evaluation

using discounting

Dividend policy and wealth

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Chapter 9 ContentsChapter 9 Contents

9.1 Reading stock listings9.1 Reading stock listings

9.2 The discounted dividend model9.2 The discounted dividend model

9.3 Earning and investment opportunity9.3 Earning and investment opportunity

9.4 A reconsideration of the price 9.4 A reconsideration of the price multiple approachmultiple approach

9.5 Does dividend policy affect 9.5 Does dividend policy affect shareholder wealth?shareholder wealth?

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9.1 Reading Stock Listings9.1 Reading Stock Listings

• The following newspaper stock The following newspaper stock listing is usually printed as a listing is usually printed as a horizontal string of informationhorizontal string of information

• The listing is for IBM, which is The listing is for IBM, which is traded on the New York Stock traded on the New York Stock ExchangeExchange

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Reading Stock ListingsReading Stock Listings

Yr Hi Yr Lo Stock Sym

123 1/8 93 1/8 IBM IBM

Div Yld % PE Vol 100

4.84 4.2 16 14591

Day Hi Day Lo Close Net Chg

115 113 114 3/4 +1 3/8

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9.2 The Discounted 9.2 The Discounted Dividend ModelDividend Model

• A A discounted dividend modeldiscounted dividend model is any is any model that computes the value of a model that computes the value of a share of a stock as the present share of a stock as the present value of the expected future cash value of the expected future cash dividendsdividends

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Present Value of Present Value of DividendsDividends

• PP00 = D = D11/(1+k)+ D/(1+k)+ D22/(1+k)/(1+k)22+ D+ D33/(1+k)/(1+k)3 3

+...++...+

• With constant growth rateWith constant growth rate

• DD22 = D = D11(1+g), D(1+g), D33 = D = D22(1+g), etc. (1+g), etc.

• Hence, PHence, P00 = D = D11/(k-g)/(k-g)

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Present Value of Present Value of DividendsDividends

• PP00 = D = D11/(1+k)+ D/(1+k)+ D22/(1+k)/(1+k)22+ D+ D33/(1+k)/(1+k)3 3

+...++...+

• PP11 = D = D22/(1+k)+ D/(1+k)+ D33/(1+k)/(1+k)22+ D+ D44/(1+k)/(1+k)3 3

+...++...+

• Using the above equations - Using the above equations - P P0 0 = (P= (P1 1 + + DD11)/(1+k))/(1+k)

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Capital gain yield = g = Capital gain yield = g = dividend growth ratedividend growth rate

• PP00 = D = D11/(k-g)/(k-g)

• PP11 = D = D22/(k-g)/(k-g)

• DD22 = D = D11(1+g)(1+g)

• Using the above equations - Using the above equations - (P (P11 - P - P00)/P)/P0 0 = g= g

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Discount rate k = rate of Discount rate k = rate of return on the stock = return on the stock = market capitalization rate market capitalization rate on the stockon the stock• Recall that PRecall that P0 0 = (P= (P1 1 + + DD11)/(1+k))/(1+k)

• Subtracting PSubtracting P00/(1+k) from both sides /(1+k) from both sides of the above equation and of the above equation and simplifying we get: simplifying we get: k = (P k = (P1 1 + + DD1 1 - P- P00)/ P)/ P0 0 = = rate of return on the stock = market rate of return on the stock = market capitalization rate on the stockcapitalization rate on the stock

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Discount rate k = Discount rate k = Dividend yield plus capital Dividend yield plus capital gain yieldgain yield

• k = (Pk = (P1 1 + + DD1 1 - P- P00)/ P)/ P0 0 = annual rate of = annual rate of return on the stock, or return on the stock, or

• k = Dk = D11/ P/ P0 0 + (P+ (P1 1 - P- P00)/ P)/ P00

• This relationship tells you that next This relationship tells you that next year’s expected dividend yield + the year’s expected dividend yield + the expected capital gain yield is equal to expected capital gain yield is equal to the required rate of returnthe required rate of return

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Solving for kSolving for k

• k = Dk = D11/ P/ P0 0 + (P+ (P1 1 - P- P00)/ P)/ P00

• g = (Pg = (P1 1 - P- P00)/ P)/ P00

• Hence, k = DHence, k = D11/ P/ P0 0 + g+ g

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9.3 Earning and 9.3 Earning and Investment OpportunityInvestment Opportunity

• A second approach to DCF valuation A second approach to DCF valuation focuses on focuses on future earningsfuture earnings and and investment opportunitiesinvestment opportunities

• This focus, rather than the earlier This focus, rather than the earlier dividend focus, concentrates the dividend focus, concentrates the analyst’s attention on the core analyst’s attention on the core business determinants of valuebusiness determinants of value

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Earning and Investment Earning and Investment OpportunityOpportunity

• To simplify the analysis, suppose that To simplify the analysis, suppose that no new shares are issued, and no taxesno new shares are issued, and no taxes

Dividends = earnings - net new investmentDividends = earnings - net new investment

““D = E - I”. The formula for valuing stock is D = E - I”. The formula for valuing stock is

1110

111 tt

t

tt

t

tt

t

k

I

k

E

k

Dp

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InterpretationInterpretation

• The value of a company is The value of a company is notnot equal equal to the present value of its expected to the present value of its expected earningsearnings

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

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NogrowthNogrowth

– Nogrowth Co has a policy of no net new Nogrowth Co has a policy of no net new investmentsinvestments• This does not mean the firm does not invest This does not mean the firm does not invest

in new plant and equipment--only that in new plant and equipment--only that purchases match the loss of value of the purchases match the loss of value of the existing assets (as measured by existing assets (as measured by depreciation)depreciation)

• If we assume everything is in real terms, it If we assume everything is in real terms, it is reasonable to assume that Nogrowth will is reasonable to assume that Nogrowth will pay a constant (say) $15/share each yearpay a constant (say) $15/share each year

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NogrowthNogrowth

• If the real capitalization rate is 15%, If the real capitalization rate is 15%, then the value of Nogrowth is then the value of Nogrowth is 15/0.15 = $10015/0.15 = $100

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Growth StockGrowth Stock

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

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• The management of Growthstock may The management of Growthstock may be thought of as taking 60% of the be thought of as taking 60% of the shareholder’s value, and reinvesting it shareholder’s value, and reinvesting it on behalf of the shareholders. on behalf of the shareholders.

• The earnings retention rate is 60% The earnings retention rate is 60% and the dividend payout ratio is 40% and the dividend payout ratio is 40%

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– The first year dividend is $15*0.4 = $6The first year dividend is $15*0.4 = $6

– At the end of first period $9 is invested at 20% rate, which gives a At the end of first period $9 is invested at 20% rate, which gives a perpetuity of $1.8 beginning second period. perpetuity of $1.8 beginning second period.

– The total earnings at the end of the second year are equal to $15 + $1.8 The total earnings at the end of the second year are equal to $15 + $1.8 = $16.8= $16.8

– Second year dividend is $16.8*0.4=$6.72Second year dividend is $16.8*0.4=$6.72

– in year 1 to obtain $15*0.6*0.20 = $1.8 foreverin year 1 to obtain $15*0.6*0.20 = $1.8 forever

– In year 1 this has a value of $1.8/0.15 = $12In 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 $12There is a second, third, fourth, … flow starting in year 3, 4, 5, … also $12

– The present value of these streams is 12/0.15 = $80The present value of these streams is 12/0.15 = $80

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– At the end of second year $16.8*0.6 = At the end of second year $16.8*0.6 = $10.08 is invested at 20% rate, which $10.08 is invested at 20% rate, which gives a perpetuity of $2.016 beginning gives a perpetuity of $2.016 beginning third period.third period.

– The total earnings at the end of the third The total earnings at the end of the third year are equal to $15 + $1.8 + $2.016 = year are equal to $15 + $1.8 + $2.016 = $18.816$18.816

– Third year dividend is Third year dividend is $18.816*0.4=$7.5264$18.816*0.4=$7.5264

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– First year dividend = $6First year dividend = $6

– Second year dividend = $6.72 = $6(1.12)Second year dividend = $6.72 = $6(1.12)

– Third year dividend = $7.5264 = $6.72(1.12)Third year dividend = $7.5264 = $6.72(1.12)

– The dividend growth rate of 12% is not a The dividend growth rate of 12% is not a coincidence - it is equal to the earnings coincidence - it is equal to the earnings retention rate of 60% times the 20% rate of retention rate of 60% times the 20% rate of return of new investments.return of new investments.

– g = 20% * 60% = 0.20 * 0.60 = 0.12=12%g = 20% * 60% = 0.20 * 0.60 = 0.12=12%

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GeneralizeGeneralize

• Let the Let the – g = dividend growth rate g = dividend growth rate

– b = earnings retention rateb = earnings retention rate

– R = ROE on new investments R = ROE on new investments

– Then g = b * RThen g = b * R

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A Reconsideration of the A Reconsideration of the Price Multiple ApproachPrice Multiple Approach

• Recall the Recall the

PP00 = e = e11/k + NPV of future investments/k + NPV of future investments

In terms of P/EIn terms of P/E

PP00// EE11 = 1/k + NPV/ E = 1/k + NPV/ E11 of future investments of future investments

– Firms with high PE ratios are then Firms with high PE ratios are then interpreted as having low capitalization rates interpreted as having low capitalization rates or excellent future investment opportunitiesor excellent future investment opportunities

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Does Dividend Policy Does Dividend Policy Affect Shareholder Affect Shareholder Wealth?Wealth?

• Dividend policy of a corporationDividend policy of a corporation– The policy regarding paying out cash to The policy regarding paying out cash to

its shareholders, its shareholders, holding constant its holding constant its investment and borrowing decisionsinvestment and borrowing decisions

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9.4 Reconsideration of the 9.4 Reconsideration of the P/E Multiple ApproachP/E Multiple Approach

• The formula for a growing perpetuity is: The formula for a growing perpetuity is:

investmentfurure111 NPVk

E

k

Pg

k

EP

gk

EP o

oo

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9.5 Does Dividend Policy 9.5 Does Dividend Policy Affect Shareholder Affect Shareholder Wealth?Wealth?

• In a frictionless world where there are In a frictionless world where there are no taxes nor transaction costs, the no taxes nor transaction costs, the dividend policy (as defined in the last dividend policy (as defined in the last slide) will have no affect on the wealth slide) will have no affect on the wealth of stock holdersof stock holders

• We shall examine: tax, regulations, We shall examine: tax, regulations, cost of external financing, and cost of external financing, and information content of dividendsinformation content of dividends

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Cash Dividends and Share Cash Dividends and Share RepurchasesRepurchases

• A corporation may distribute cashA corporation may distribute cash– By paying dividendsBy paying dividends

• All shareholders are paid the same per All shareholders are paid the same per shareshare

– By repurchasing its own stockBy repurchasing its own stock• Shareholders choosing to liquidate some or Shareholders choosing to liquidate some or

all of their holdings sell the shares at all of their holdings sell the shares at market price (as they normally do), and the market price (as they normally do), and the company makes market purchasescompany makes market purchases

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Illustration: Dividend Illustration: Dividend PaymentPayment

• The following table shows a The following table shows a simplified balance sheet of Cashrich simplified balance sheet of Cashrich CoCo

• AssumeAssume– Number of shares outstanding = Number of shares outstanding =

500,000500,000

– Share price = $20Share price = $20

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Illustration: DividendsIllustration: Dividends

Assets Liab\ Equ

Cash 2 Debt 2

Other 10 Equity 10

Total 12 Total 12

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• If Cashrich declares a dividend of $2 / If Cashrich declares a dividend of $2 / share it will pay 500,000 * $2 = share it will pay 500,000 * $2 = $1,000,000$1,000,000– Given its level of risk, the payment will Given its level of risk, the payment will

reduce the market value of the shares by reduce the market value of the shares by $1,000,000 to $20 * 500,000 - $1,000,000 $1,000,000 to $20 * 500,000 - $1,000,000 = $9,000,000, so each share will be worth = $9,000,000, so each share will be worth $9,000,000 / 500,000 = $18 / share$9,000,000 / 500,000 = $18 / share

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Assets Liab\ Equ

Cash 1 Debt 2

Other 10 Equity 9

Total 11 Total 11

Was 2Was 10

Were 12Were 12

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• Before the dividend, every share Before the dividend, every share was worth $20was worth $20

• After the $2 / share dividend, every After the $2 / share dividend, every share was worth $18share was worth $18

• ConclusionConclusion– Shareholders wealth is unchangedShareholders wealth is unchanged

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Illustration: Share Illustration: Share RepurchaseRepurchase

• The original balance is shown belowThe original balance is shown below– Share price is still $20Share price is still $20

– Number of shares outstanding is Number of shares outstanding is 500,000500,000

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Assets Liab\ Equ

Cash 2 Debt 2

Other 10 Equity 10

Total 12 Total 12

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• The company repurchases 50,000 The company repurchases 50,000 shares at $20 per share = shares at $20 per share = $1,000,000$1,000,000– The market value of the firm is now The market value of the firm is now

$10,000,000 less the loss of $10,000,000 less the loss of $1,000,000 cash, or $9,000,000$1,000,000 cash, or $9,000,000

– The number of shares outstanding is The number of shares outstanding is now 500,000 - 50,000 = 450,000now 500,000 - 50,000 = 450,000

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– The share price is then The share price is then $9,000,000/450,000 = $20$9,000,000/450,000 = $20

• The wealth of the shareholders who The wealth of the shareholders who sold out is unchangedsold out is unchanged

• The wealth of the shareholders who The wealth of the shareholders who held the stock is unchangedheld the stock is unchanged

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Assets Liab\ Equ

Cash 1 Debt 2

Other 10 Equity 9

Total 11 Total 11

Was 2Was 10

Were 12Were 12

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Stock DividendsStock Dividends

• Corporations sometimes declare a stock Corporations sometimes declare a stock split and distribute stock dividendssplit and distribute stock dividends

– These activities do not distribute cash to the These activities do not distribute cash to the shareholdersshareholders

– They increase the number of issued shares, They increase the number of issued shares, but do not change the % of the company but do not change the % of the company each shareholder ownseach shareholder owns

• They do not affect shareholder wealthThey do not affect shareholder wealth

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Modigliani and MillerModigliani and Miller

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

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The Real World: Share The Real World: Share RepurchaseRepurchase• Smart Co has had a good year, and Smart Co has had a good year, and

is considering repurchasing some is considering repurchasing some outstanding stock in order to prevent outstanding stock in order to prevent some of its shareholders paying some of its shareholders paying personal income tax on the dividendpersonal income tax on the dividend

• There are restrictions on this kind of There are restrictions on this kind of practice in many countries, including practice in many countries, including the USAthe USA

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The Real World: The Real World: Asymmetric InformationAsymmetric Information

• The management of Cryptic Co is The management of Cryptic Co is concerned that the investment concerned that the investment community does not understand its community does not understand its businessbusiness– It has decided to finance projects using It has decided to finance projects using

cheaper cheaper retained earningsretained earnings rather than rather than issuing more stock at a discount from issuing more stock at a discount from its “true” market valueits “true” market value

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The Real World: SignalingThe Real World: Signaling• The management of Trip Co has had The management of Trip Co has had

a single bad year, but has decided a single bad year, but has decided not to reduce its dividendnot to reduce its dividend– Reducing the dividend may send a signal Reducing the dividend may send a signal

to the investment community saying to the investment community saying

““The fundamentals of Trip have changed: The fundamentals of Trip have changed: consider decreasing future dividend consider decreasing future dividend estimates and/or consider increasing the estimates and/or consider increasing the cost of capital to compensate for cost of capital to compensate for additional risk”additional risk”

1 Chapter 9: Valuation of Common Stocks Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley...

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Transcript of 1 Chapter 9: Valuation of Common Stocks Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley...