© 2007 Thomson South-Western

Chapter 4Stock & Bond Valuation

Professor XXXXXCourse Name / Number

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Valuation Fundamentals

The greater the uncertainty about an asset’s future benefits, the higher the discount rate investors will apply when discounting those benefits to the present.

The valuation process links an asset’s risk and return to determine its price.

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Valuation Fundamentals

Future Cash Flows Risk

Valuation

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Bond Valuation Fundamentals

Bonds are debt instruments used by business and government to raise large sums of money

Most bonds share certain basic characteristics First, a bond promises to pay investors a fixed

amount of interest, called the bond’s coupon. Second, bonds typically have a limited life, or

maturity. Third, a bond’s coupon rate equals the bond’s

annual coupon payment divided by its par value. Fourth, a bond’s coupon yield equals the coupon

payment divided by the bond’s current market price

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Valuation Fundamentals

Present Value of Future Cash Flows

Link Risk & Return

Expected Return on Assets

Valuation

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The Basic Valuation Model

P0 = Price of asset at time 0 (today)

CFt = cash flow expected at time t r = discount rate (reflecting asset’s risk) n = number of discounting periods (usually years)

This model can express the price of any asset at t = 0 mathematically.

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Valuation FundamentalsBond Example

Using the P0 equation, the bond would sell at a par value of $1,000.

Company issues a 5% coupon interest rate, 10‑year bond with a $1,000 par value on 01/30/04Assume annual interest payments

Investors who buy company bonds receive the contractual rights$50 coupon interest paid at the end of

each year $1,000 par value at the end of the 10th

year

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P0 < par value

P0 > par value

Bonds: Premiums & Discounts

The bond's value will differ from its par value

R > Coupon Interest Rate DISCOUNT =

PREMIUM =

What Happens to Bond Values if the Required Return Is Not Equal to the Coupon

Rate?

R < Coupon Interest Rate

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The Basic Equation (Assuming Annual Interest)

Cash flows include two components:(1) the annual coupon, C, which equals the stated

coupon rate, i, multiplied by M, the par value (that is, C i M), received for each of the n years

(2) the par value, M, received at maturity in n years

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Time Line for Bond: Valuation 91⁄8% Coupon,$1,000 Par Bond, Maturing at End of 2017, Required Return Assumed to be 8%

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BondsSemi-Annual Interest Payments

An example....

Value a T-Bond

Par value = $1,000

Maturity = 2 years

Coupon pay = 4%

r = 4.4% per year

= $992.43

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Yield to Maturity (YTM)

Rate of return investors earn if they buy

the bond at P0 and hold it until maturity.

The YTM on a bond selling at par will always equal the coupon interest rate.

YTM is the discount rate that equates the

PV of a bond’s cash flows with its price.

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Risk-Free Bonds

A risk-free bond is a bond that has no chance of default by its issuerZero-coupon treasuriesCoupon-paying treasuries

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Risky Bonds

Treasury bonds provide a known contractual stream of cash flows if you can observe the market price of a bond, you can infer

what the market’s required return must be. Valuing an ordinary corporate bond involves the same steps:

write down the cash flows determine an appropriate discount rate calculate the present value.

Discount rate on corporate bond should be higher than on Treasury bond with the same maturity because corporate bonds carry default risk the risk that the corporation may not make all scheduled

payments. Yield spread between Treasury bonds and corporate bonds

The difference in yield to maturity between two bonds or two classes of bonds with similar maturities

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Bond Issuers

Bond issuersCorporate bondsMunicipal bondsTreasury billsTreasury notesAgency bonds

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Bond Ratings

Bond ratingsMoody’sStandard & Poor’sFitch

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Bond Ratings

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Bond Ratings and Spreads at DifferentMaturities at a Given Point in Time

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Bond Price Behavior

Bond price quotationsBond spreads reflect a direct

relationship with default riskBond price behavior

Prices change constantlyPassage of timeForces in the economy

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Bond Prices and Yields for Bonds with Differing Times to Maturity, Same 6% Coupon Rate

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Bonds: Time to Maturity

What does this tell you about the relationship between bond prices & yields for bonds with the

equal coupon rates, but different maturities?

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Bonds: Yield to Maturity (YTM)Rate of return investors earn if they buy the bond at P0 and hold it until maturity.

The YTM on a bond selling at par will always equal the coupon interest rate.

YTM is the discount rate that equates the PV of a bond’s cash flows with its price.

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Evaluating the Yield Curve

Yields vary with maturity. Yields offered by bonds must be sufficient to

offer investors a positive real return. The real return on an investment

approximately equals the difference between its stated or nominal return and the inflation rate.

The shape of the yield curve can change over time.

Research shows the yield curve works well as a predictor of economic activity, in the United States and other large industrialized economies.

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Yield Curves for U.S. Government Bonds

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Term Structure Theories

Expectations theoryLiquidity preference theoryPreferred habitat theory

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Expectations Theory

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Term Structure of Interest Rates

Relationship between yield and maturity is called the Term Structure of Interest Rates Graphical depiction is called a Yield Curve Usually, yields on long-term securities are

higher than on short-term securities Generally look at risk-free Treasury debt

securities Yield curves normally upwards-sloping

Long yields > short yields Can be flat or even inverted during times of

financial stress

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Stock Valuation: Preferred Stock

Preferred stock is an equity security that is expected to pay a fixed annual dividend for its life

PS0 = Preferred stock’s value

DP = preferred dividend

rp = required rate of return

An example: A share of preferred stock pays $2.3 per share annual dividend and with a required return of 11%

PS0

=

DP

=

$2.30 = $20.90 /

sharerp

0.11

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Valuation FundamentalsCommon Stock

P0=P1 + D1

(1+r)

Value of a Share of

Common Stock

P0 = Present value of the expected stock price at the end of period 1D1 = Dividends received r = discount rate

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Valuation Fundamentals: Common Stock

But how is P1 determined? This is the PV of expected stock price P2,

plus dividend at time 2 P2 is the PV of P3 plus dividend at time 3,

etc... Repeating this logic over and over, you

find that today’s price equals PV of the entire dividend stream the stock will pay in the future

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Zero Growth Model

To value common stock, you must make assumptions about the growth of future dividends

Zero growth model assumes a constant, non-growing dividend stream:

D1 = D2 = ... = D

Plugging constant value D into the common stock valuation formula reduces to simple equation for a perpetuity:

P0 = D

r

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Constant Growth Model

Assumes dividends will grow at a constant rate (g) that is less than the required return (r)

If dividends grow at a constant rate forever, you can value stock as a growing perpetuity, denoting next year’s dividend as D1:

P0=D1

r-g

Commonly called the Gordon Growth Model.

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Variable Growth

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Variable Growth ModelExample Estimate the current value of Morris Industries'

common stock, P0 = P2003

Assume

The most recent annual dividend payment of Morris Industries was $4 per share

The firm's financial manager expects that these dividends will increase at an 8% annual rate over the next 3 years

At the end of the 3 years the firm's mature product line is expected to result in a slowing of the dividend growth rate to 5% per year forever

The firm's required return, r , is 12%

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Variable Growth ModelValuation Steps #1 & #2 Compute the value of dividends in 2004, 2005, and 2006

as (1+g1)=1.08 times the previous year’s dividend

Div2004= Div2003 x (1+g1) = $4 x 1.08 = $4.32

Div2005= Div2004 x (1+g1) = $4.32 x 1.08 = $4.67

Div2006= Div2005 x (1+g1) = $4.67 x 1.08 = $5.04

Find the PV of these three dividend payments:

PV of Div2004= Div2004 (1+r) = $ 4.32 (1.12) = $3.86

PV of Div2005= Div2005 (1+r)2 = $ 4.67 (1.12)2 = $3.72

PV of Div2006= Div2006 (1+r)3 = $ 5.04 (1.12)3 = $3.59

Sum of discounted dividends = $3.86 + $3.72 + $3.59 = $11.17

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Find the value of the stock at the end of the initial growth period using the constant growth model

Calculate next period dividend by multiplying D2006 by 1+g2, the lower constant growth rate:

D2007 = D2006 x (1+ g2) = $ 5.04 x (1.05) = $5.292

Then use D2007=$5.292, g =0.05, r =0.12 in

Gordon model:60.75

07

292.5

2

292.576 $ =

0.

$ =

0.05 -0.1

$ =

g -rD = P

2

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Variable Growth ModelValuation Step #3

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Variable Growth ModelValuation Step #3 Find the present

value of this stock price by discounting P(2006) by (1+r)3

81.53405.1

60.75$

)12.1(

60.75$

)1( 33

6 $ = = = r

P =PV 200

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Add the PV of the initial dividend stream (Step #2) to the PV of stock price at the end of the initial growth period (P2006):

P2003 = $11.17 + $53.81 = $64.98

Variable Growth ModelValuation Step #4

Current (end of year 2003)

stock price

Remember: Because future growth rates might change, the variable growth model

allows for a changes in the dividend growth rate.

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Time Line for Variable Growth Valuation

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Free Cash Flow Approach

Begin by asking, what is the total operating cash flow (OCF) generated by a firm?

Next subtract from the firm’s operating cash flow the amount needed to fund new investments in both fixed assets and current assets.

The difference is total free cash flow (FCF). Represents the cash amount a firm could

distribute to investors after meeting all its other obligations

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Common Stock Valuation:Other Options

Book valueNet assets per share available to

common stockholders after liabilities are paid in full

Liquidation valueActual net amount per share likely to

be realized upon liquidation & payment of liabilities

More realistic than book value, but doesn’t consider firm’s value as a going concern

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Common Stock Valuation:Other Options

Price / Earnings (P / E) multiplesReflects the amount investors will pay

for each dollar of earnings per shareP / E multiples differ between & within

industriesEspecially helpful for privately-held

firms