Chapter 8 -Chapter 8 - Stock Stock ValuationValuation

Security ValuationSecurity Valuation

In general, the In general, the intrinsic valueintrinsic value of of an asset = the an asset = the present valuepresent value of the of the stream of expected cash flows stream of expected cash flows discounted at an appropriate discounted at an appropriate required rate of returnrequired rate of return..

Security ValuationSecurity Valuation

$10,000 in Harley-Davidson July $10,000 in Harley-Davidson July 8, 1986, and reinvested all 8, 1986, and reinvested all dividendsdividends

$1,663,000 at the end of 2001.$1,663,000 at the end of 2001.

Preferred StockPreferred Stock

A hybrid securityA hybrid security:: It’s like common stock - no fixed It’s like common stock - no fixed maturity.maturity.

Technically, it’s part of equity capital.Technically, it’s part of equity capital.

It’s like debt - preferred dividends are It’s like debt - preferred dividends are

fixed.fixed. Missing a preferred dividend does not Missing a preferred dividend does not

constitute default, but preferred dividends are constitute default, but preferred dividends are cumulativecumulative..

Usually sold for $25, $50, or $100 per Usually sold for $25, $50, or $100 per share.share.

Dividends are fixed either as a dollar Dividends are fixed either as a dollar amount or as a percentage of par value.amount or as a percentage of par value.

Example:Example: In 1988, Xerox issued $75 In 1988, Xerox issued $75 million of 8.25% preferred stock at $50 million of 8.25% preferred stock at $50 per share.per share. $4.125 is the fixed, annual dividend per $4.125 is the fixed, annual dividend per

share.share.

Preferred Stock

Firms may have Firms may have multiple classesmultiple classes of of preferreds, each with different features. preferreds, each with different features.

PriorityPriority: lower than debt, higher than : lower than debt, higher than common stock.common stock.

Cumulative featureCumulative feature: all past unpaid : all past unpaid preferred stock dividends must be paid preferred stock dividends must be paid before any common stock dividends are before any common stock dividends are declared.declared.

Preferred Stock Features

Protective provisions Protective provisions are commonare common.. ConvertibilityConvertibility: many preferreds are : many preferreds are

convertible into common shares.convertible into common shares. Adjustable rateAdjustable rate preferreds have preferreds have

dividends tied to interest rates.dividends tied to interest rates. ParticipationParticipation: some (very few) preferreds : some (very few) preferreds

have dividends tied to the firm’s earnings. have dividends tied to the firm’s earnings.

Preferred Stock Features

PIK PreferredPIK Preferred: Pay-in-kind preferred : Pay-in-kind preferred stocks pay additional preferred shares stocks pay additional preferred shares to investors rather than cash dividends.to investors rather than cash dividends.

RetirementRetirement: Most preferreds are : Most preferreds are callable, and many include a callable, and many include a sinking sinking fundfund provision to set cash aside for the provision to set cash aside for the purpose of retiring preferred shares.purpose of retiring preferred shares.

Preferred Stock Features

Preferred Stock ValuationPreferred Stock Valuation

A preferred stock can usually be A preferred stock can usually be valued like a perpetuity:valued like a perpetuity:

V =Dk

psps

Example: Example:

Xerox preferred pays an Xerox preferred pays an 8.25%8.25% dividend on a dividend on a $50$50 par value. par value.

Suppose our required rate of Suppose our required rate of return on Xerox preferred is return on Xerox preferred is 9.5%9.5%..

VVpsps ==4.1254.125

.095.095== $43.42$43.42

Expected Rate of Return Expected Rate of Return on Preferredon Preferred

Just adjust the valuation model:Just adjust the valuation model:

D

Po

kps =

ExampleExample

If we know the preferred stock price is If we know the preferred stock price is $40$40, and the preferred dividend is , and the preferred dividend is $4.125$4.125, the expected return is:, the expected return is:

D

Po

kps = = = .10314.125

40

The Financial Pages:The Financial Pages:Preferred StocksPreferred Stocks

52 weeks 52 weeks Yld Yld Vol Vol

Hi Lo Sym Hi Lo Sym Div % PE 100s Close Div % PE 100s Close

27278888 25 250606 GenMotor pfG 2.28 8.9 … 86 25 GenMotor pfG 2.28 8.9 … 86 25 5353

Dividend:Dividend: $2.28 on $25 par value $2.28 on $25 par value

= 9.12% dividend rate.= 9.12% dividend rate.

Expected return:Expected return: 2.28 / 25.53 = 2.28 / 25.53 = 8.9%.8.9%.

Common StockCommon Stock

Is a Is a variable-incomevariable-income security. security. Dividends may be increased or decreased, Dividends may be increased or decreased,

depending on earnings.depending on earnings.

Represents Represents equity equity or ownership.or ownership. Includes Includes voting rightsvoting rights.. Limited liabilityLimited liability: liability is limited to : liability is limited to

amount of owners’ investment.amount of owners’ investment. PriorityPriority: lower than debt and preferred. : lower than debt and preferred.

Common Stock CharacteristicsCommon Stock Characteristics

Claim on IncomeClaim on Income - a stockholder has a - a stockholder has a claim on the firm’s residual income.claim on the firm’s residual income.

Claim on AssetsClaim on Assets - a stockholder has a - a stockholder has a residual claim on the firm’s assets in case residual claim on the firm’s assets in case of liquidation.of liquidation.

Preemptive RightsPreemptive Rights - stockholders may - stockholders may share proportionally in any new stock share proportionally in any new stock issues. issues.

Voting RightsVoting Rights - right to vote for the firm’s - right to vote for the firm’s board of directors.board of directors.

You expect XYZ stock to pay a You expect XYZ stock to pay a $5.50$5.50 dividend at the end of the year. The stock dividend at the end of the year. The stock price is expected to be price is expected to be $120$120 at that time. at that time.

If you require a If you require a 15%15% rate of return, what rate of return, what would you pay for the stock now?would you pay for the stock now?

Common Stock ValuationCommon Stock Valuation(Single Holding Period)(Single Holding Period)

0 1

? 5.50 + 120

Common Stock ValuationCommon Stock Valuation(Single Holding Period)(Single Holding Period)

Solution:Solution:

Vcs Vcs = (5.50/1.15) + (120/1.15)= (5.50/1.15) + (120/1.15)

= 4.783 + 104.348= 4.783 + 104.348

== $109.13 $109.13

Common Stock ValuationCommon Stock Valuation(Single Holding Period)(Single Holding Period)

Financial Calculator solution:Financial Calculator solution:

I = 15, n=1, FV= 125.50I = 15, n=1, FV= 125.50

solve:solve: PV = -109.13 PV = -109.13

or:or:

I = 15, n=1, FV= 120, I = 15, n=1, FV= 120,

PMT = 5.50PMT = 5.50

solve:solve: PV = -109.13 PV = -109.13

The Financial Pages:The Financial Pages:Common StocksCommon Stocks

52 weeks 52 weeks Yld Yld Vol Vol NetNet

Hi Lo Sym Div % PE 100s Hi Lo Close ChgHi Lo Sym Div % PE 100s Hi Lo Close Chg

135 80 IBM .52 .5 21 142349 99 93 94135 80 IBM .52 .5 21 142349 99 93 949696 -3 -34343

82 18 CiscoSys … 47 1189057 21 19 2082 18 CiscoSys … 47 1189057 21 19 202525 -1 -11313

Common Stock ValuationCommon Stock Valuation(Multiple Holding Periods)(Multiple Holding Periods)

Constant Growth ModelConstant Growth Model Assumes common stock dividends Assumes common stock dividends

will grow at a constant rate into will grow at a constant rate into the future.the future.

Vcs =D1

kcs - g

Constant Growth ModelConstant Growth Model Assumes common stock dividends will grow at Assumes common stock dividends will grow at

a constant rate into the future.a constant rate into the future.

DD11 = the dividend at the end of period 1. = the dividend at the end of period 1. kkcscs = the required return on the common stock.= the required return on the common stock. gg = the constant, annual dividend growth rate. = the constant, annual dividend growth rate.

Vcs =D1

kcs - g

Growth RateGrowth Rate

g = ROE * rg = ROE * r g: the growth rate of the companyg: the growth rate of the company ROE: return on equityROE: return on equity r: the company’s percentage of profit r: the company’s percentage of profit

retainedretained

Growth RateGrowth Rate

Example: Example: If return on equity for A is 16%, and if If return on equity for A is 16%, and if

management keeps 50% of the profits for management keeps 50% of the profits for reinvestment, what is the company’s growth rate?reinvestment, what is the company’s growth rate?

g = 16% * 0.5 = 8%g = 16% * 0.5 = 8%

ExampleExample

XYZ stock XYZ stock recentlyrecently paid a paid a $5.00$5.00 dividend. The dividend is expected to dividend. The dividend is expected to grow at grow at 10%10% per year indefinitely. per year indefinitely. What would we be willing to pay if our What would we be willing to pay if our required return on XYZ stock is required return on XYZ stock is 15%15%??

D0 = $5, so D1 = 5 (1.10) = $5.50

ExampleExample

XYZ stock XYZ stock recentlyrecently paid a paid a $5.00$5.00 dividend. The dividend is expected to dividend. The dividend is expected to grow at grow at 10%10% per year indefinitely. per year indefinitely. What would we be willing to pay if our What would we be willing to pay if our required return on XYZ stock is required return on XYZ stock is 15%15%??

Vcs = = = $110 D1 5.50

kcs - g .15 - .10

Expected Return on Expected Return on Common StockCommon Stock

Just adjust the valuation modelJust adjust the valuation model

Vcs =D

kcs - g

k = ( ) + gD1

Vcs

Expected Return on Expected Return on Common StockCommon Stock

Just adjust the valuation modelJust adjust the valuation model

Vcs =D

kcs - g

k = ( ) + gD1

Po

ExampleExample We know a stock will pay a We know a stock will pay a $3.00$3.00

dividend at time 1, has a price of dividend at time 1, has a price of $27$27 and an expected growth rate of and an expected growth rate of 5%5%..

kcs = ( ) + gD1

Po

kcs = ( ) + .05 = 16.11%3.00

27