1 Finance School of Management Chapter 9. Valuation of Common Stocks Objective Explain equity...

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FinanceFinance School of Management School of Management

Chapter 9. Valuation of Chapter 9. Valuation of Common StocksCommon Stocks

ObjectiveExplain equity evaluation

Using discountingDividend policy

and wealth

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Chapter 9 ContentsChapter 9 Contents

Common Stock Reading Stock Listings The Discounted Dividend Model Earnings and Investment Opportunities A Reconsideration of the Price/Earnings Multiple

Approach Does Dividend Policy Affect Shareholder Wealth?

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Common StockCommon Stock

Common stock is the best known security, but many people know comparatively little about it.

People who own stock have an equity interest in the organization.

If a business has shares of stock, it is organized as a corporation rather than a proprietorship or a partnership.

Shareholder Rights:– the right to receive declared dividends on a pro rata basis,

– the right to vote,

– the right to maintain ownership percentage.

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Reading Stock ListingsReading Stock Listings

52 Weeks

Hi Lo Stock Sym Div Yld % PE Vol100s Hi Lo Close Net Chg

25.38 20.38 IBM IBM 1.54 7.2 12 371 21.25 20.88 21.25 +.13

Dividend Yield

Div

Close

Price/Earnings Ratio

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The Discounted Dividend ModelThe Discounted Dividend Model

Chapter 8 shows how the Law of One Price can be used to deduce the value of known cash flows from the observed market prices of bonds.

In this chapter we consider the valuation of uncertain cash flows using a discounted cash flow (DCF) approach.

The DCF approach to determining the value of a stock discounts the expected cash flows-either dividends paid to shareholders or net cash flows from trading.

Assume: buy and hold for ever

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Discount-dividend model (DDM) is defined as any model that computes the value of a share of stock as the present value of its expected future cash dividends.

The risk-adjusted discount rate or market capitalization rate is the expected rate of return that investors require to be willing to invest in the stock.

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The rate of return that investors expect, E(r1), equals the

market capitalization rate, k.

1 1 01

0

( )D P P

E r kP

k

PDP

1

110

The price is the present value of the expected end-of-year dividend plus the expected ex-dividend price discounted at the required rate return.

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Using the same logic employed to derive P0, the expected

price of stock at the beginning of the second year is:

2 21 1

D PP

k

By substitution, we can express P0 in terms of D1, D2, and

P2:

1 2 20 21 (1 )

D D PP

k k

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By repeating this chain of substitutions, we get the general formula of the DDM:

1 20 2

1(1 ) (1 ) (1 )t

tt

DD DP

k k k

The price of a share of stock is the present value of all expected future dividends per share, discounted at the market capitalization rate.

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Does the trading behavior affect the stock price？

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Suppose that an investor buys one stock from the beginning and sells it at time T T with the selling price with the selling price PPT T .

From the DDM, we have：

01 (1 ) (1 )

Tt T

t Tt

D PP

k k

and

1 (1 )T s

T ss

DP

k

Therefore

01 1 1(1 ) (1 ) (1 )

Tt t t

t t tt t T t

D D DP

k k k

The trading behavior has no effect on stock price.

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The Constant-Growth-Rate and the The Constant-Growth-Rate and the Discounted Dividend ModelDiscounted Dividend Model

The most basic assumption is that dividends will grow at a constant rate g.

Substituting the dividend growth forecast, Dt=D1(1+g)t-1,

into DDM formula, we find that the present value of a perpetual of dividends growing at a constant rate, g, is

10

DP

k g

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330 0.18

0.08k

k

IBM stock is expected to pay a dividend of $3 per share a year from now.

Its dividends are expected to grow by 8% per year thereafter.

If its price is now $30 per share, what must be the market capitalization rate?

An IllustrationAn Illustration

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If g equals to zero (D1=D2=…), the formula reduces to the formula for the present value of a level perpetuity:

1 10

1 (1 )tt

D DP

k k


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Another implication of the constant growth rate DDM is that the stock price is expected to grow at the same rate as dividends.

10

1

0

DP

k g

Dk g

P

0

01

0

01

0

1

0

1 &

P

PPg

P

PP

P

Dkg

p

Dk

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Earning and Investment OpportunityEarning and Investment Opportunity A second approach to DCF valuation focuses on future

earnings and investment opportunities. Focusing on earnings and investment opportunities

rather than dividend helps to concentrate the analyst's attention on the core business determinants of value.– Consider an investor planning to take over a firm.

To simplify the analysis, suppose that no new shares are issues, and no taxes.

Dividends = Earnings − Net New Investment

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Earnings and Investment OpportunitiesEarnings and Investment Opportunities

01 1 11 1 1

t t tt t t

t t t

D E IP

k k k

The formula for valuing stock is

The firm’s value equals the present value of its expected future earning less the present value of the earnings reinvested in the firm.– In a declining industry, net investment is negative and

capacity would decline over time. – In a stable or stagnant industry, net investment is zero and

capacity remains about constant over time.– In an expanding industry, net investment is positive and

capacity increases over time.

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A useful way to estimate a firm’s value based on earnings and investment opportunities is to partition the firm’s value into two parts:– The present value of the current level of earnings

projected into the future as a perpetuity, and– The net present value of any future investment

opportunities.

10

EP

k

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An ExampleAn Example

consider a firm called Nogrowth Corporation, whose earnings per share are $15.

It pays all of its earnings out as dividends, and there is no growth.

Assuming that the capitalization rate is 15% per year, Nogrowth's stock price would be:

P0 =$15/0.15=$100

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

Growthstock will pay out only 40% of $15 as dividends, or $6 per share.

Although Growth stock’s dividend per share is initially lower than Nogrowth’s, Growth stock’s dividends will grow over time.

g = Earnings Retention Rate × Rate of Return on New Investments

0

6 6$200

0.15 0.12 0.03P

g = 0.6 ×0.2 = 0.12

E I Eg

E E I

Another ExampleAnother Example

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The net present value of Growthstock’s future investments is the difference in price between its shares and Nogrowth’s shares:

NPV of Future Investments = $200 − $100 = $100

Continued

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Continued

It is important to realize that the reason that Growthstock has a higher share price than Nogrowth is not growth per se, but rather the fact that its reinvested earnings yield a rate of return in excess of the market capitalization rate.

Normalprofit's rate of return on future investments is 15% per year and it reinvests 60% of its earnings each year

g = 0.6 × 0.15=0.09

0

6 6$100

0.15 0.09 0.06P

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$166.67-$66.67 = $100

Further IllustrationFurther Illustration

An analyst uses the constant growth DDM to evaluate IBM stock.

She assumes expected earnings of $10 per share, an earnings retention rate of 75%, an expected rate of return on future investments of 18% per year, and a market capitalization rate of 15% per year.

What is the implied net present value of future investments?

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Growth per se does not add value. What adds value is the opportunity to invest in projects that can earn rates of return in excess of the required rate, k.

When a firm’s future investment opportunities yield a rate of return equals to k, the stock’s value can be estimated using the formula:P0=E1/k


0

(1 ) (1 )

(1 )

E rt E rt EP

k rt k k rt k

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A Reconsideration of the Price/Earnings A Reconsideration of the Price/Earnings Multiple ApproachMultiple Approach

A widely used approach for quickly estimating the value of a share of a firm's stock is to take its projected earnings per share and to multiply it by an appropriate price/earnings (P/E) multiple derived from other comparable firms.

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The expected earnings of Digital Biomed Corporation per share are $2 per year.

If you apply the industry average P/E, which is 15, the resultant value for Digital Biomed stock is $30.

However, the actual price at which Digital Biomed stock is trading in the stock market is $100 per share.

How can you account for the difference?

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10

EP

k

It is not growth per se that produces a high P/E ratio, but rather the presence of future investment opportunities that are expected to yield a rate of return greater than the market’s required risk-adjusted rate

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Effects of Dividend PolicyEffects of Dividend Policy

Dividend policy means a corporation’s regarding means a corporation’s regarding paying out cash to its shareholders to its shareholders holding constant its investment and borrowing decisions..

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

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Cash Dividends & Share RepurchasesCash Dividends & Share Repurchases

Cash dividends– All shareholders receive cash in amounts

proportional to the number of shares they own.

– All else the same, the share price declines immediately after payment by the amount of the dividend.

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Cash Dividends & Share RepurchasesCash Dividends & Share Repurchases

Share repurchases – The company pays cash to buy shares of its stock in

the stock market, reducing the number of shares outstanding.

– All else the same, the share price remains unchanged.

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Cash Dividends & Share RepurchasesCash Dividends & Share Repurchases Stock dividends

– Corporations sometimes declare stock splits and distribute stock dividend. These activities do not distribute cash to shareholders; they increase the number of shares of stock outstanding.

– Payment of a stock dividend can be seen as distributing a cash dividend to existing shareholders, and then requiring them to immediately use the cash to buy additional shares of the company's stock.

– All else the same, the share price declines immediately after payment of the dividend.

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Illustration: Cashrich CorporationIllustration: Cashrich Corporation

Total assets with a market value of $12 million: $2 million in cash, and $10 million in other assets.

The market value of its debts is $2 million, and the market value of its equity is $10 million.

500,000 shares of common stock outstanding, each with a market price of $20.

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Original Balance SheetOriginal Balance Sheet

Assets Liab\Equ

Cash 2 Debt 2

Other 10 Equity 10

Total 12 Total 12

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Dividend PaymentDividend Payment (A cash dividend of $2 per share, Price=$18)(A cash dividend of $2 per share, Price=$18)

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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Dividend PaymentDividend Payment (Repurchases shares worth $1 million, Price=$20)(Repurchases shares worth $1 million, Price=$20)

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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Dividend PaymentDividend Payment (10% stock dividend, 550,000 shares outstanding, Price=$18.18)(10% stock dividend, 550,000 shares outstanding, Price=$18.18)

Assets Liab\Equ

Cash 2 Debt 2

Other 10 Equity 10

Total 12 Total 12

Was 2Was 10

Were 12Were 12

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Dividend Policy in Frictionless Financial Dividend Policy in Frictionless Financial Environment—M&M TheoryEnvironment—M&M Theory

Does dividend policy affect stockholders’ wealth? Modigliani and Miller (1961) proves that

In a frictionless financial environment, corporations cannot increase stockholders’ wealth through dividend policy.

no taxes and no no taxes and no transaction coststransaction costs

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M&M Theory: Cashrich CorporationM&M Theory: Cashrich Corporation

Instead of paying $1 million cash dividends, the management of Cashrich decides to invest it in a project.

A stockholder, who holds 100 shares and wants to receive a cash dividend of $2 per share, can– sell 10 shares for $200 cash.

– His total wealth is 90 shares of stocks with a market value of $1,800+$200 cash.

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M&M Theory: Cashrich CorporationM&M Theory: Cashrich Corporation

Cashrich does distributes a cash dividend of $2 per share.

A stockholder, who holds 100 shares and does not wand to hold cash, can– use the cash dividends to buy shares with a value of $200.

– His total wealth is original 100 shares with a market value of $1,800+news shares with a market value of $200.

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Illustration: Cashpoor CorporationIllustration: Cashpoor Corporation

Total assets: $0.5 million in cash, and $1 million in plant and equipment.

The market value of its debts is $1 million. A project with NPV of $1.5 million needs an initial

investment of $0.5 million for plant and equipment. 1,000,000 shares of common stock outstanding, each

with a market price of $2.

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Balance Sheet of CashpoorBalance Sheet of Cashpoor

Assets Liab\Equ

Cash 0.5 Debt 1.0

Plant & Equipment 1.0

NPV of New Investment 1.5 Equity 2.0

Total 3.0 Total 3.0

The stock price fully reflects all the available information, including NPV of the new investment.

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M&M Theory: Cashpoor CorporationM&M Theory: Cashpoor Corporation

If Cashpoor uses its $0.5 million to finance the investment, – a $0.5 million reduction in the firm’s cash account,

– an increase of $0.5 million in plant and equipment,

– the stock price is still $2 per share.

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M&M Theory: Cashpoor CorporationM&M Theory: Cashpoor Corporation

If Cashpoor pays a cash dividend of $0.5 per share (total $0.5 million) to its shareholders, and issues new stocks to finance the purchase of plant and equipment,– the stock price will decline from $2 to $1.5,

– the wealth of old shareholders is still $2 million,

– 333,333 new shares should be issued to raise the $0.5 million needed for the new plant and equipment.

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Dividend Policy in the Real WorldDividend Policy in the Real World

In the real world, there are a number of frictions: taxes, regulations, the costs of external finance, and the information content of dividends.

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Personal taxes: paying cash dividends or repurchasing shares.

Regulations: laws that prevent corporations – from using shares repurchases as an alternative to

dividends as a regular mechanism for paying cash to shareholders,

– from retaining cash in the business that is not needed to run the business.

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Cost of raising funds externally– the fees the investment bankers charge

– a bargain price to induce outsiders to buy new shares Informational content of dividends

– a dividend increase: good sign and price increase

– a dividend decrease: bad sign and price decline

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ReviewReview

The discounted dividend model (DDM) shows that the current price of a share is the present value of all expected future dividends.

In the constant growth rate DDM, the growth rate of dividends is also the expected rate of price appreciation.

Growth per se does not add value to a share's current price.

What adds value is the opportunity to invest in projects that yield a rate of return in excess of the market capitalization rate.

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ReviewReview

In a frictionless financial environment, the wealth of shareholders is the same no matter what dividend policy the firm adopts.

In the real world there are a number of frictions that can cause dividend policy to have an effect on the wealth of shareholders.

These frictions include taxes, regulations, the costs of external finance, and the informational content of dividends.

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1 Finance School of Management Chapter 9. Valuation of Common Stocks Objective Explain equity...

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