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Chapter 4 Stock & Bond Valuation Professor XXXXX Course Name / Number © 2007 Chapter 4 Stock & Bond Valuation Professor XXXXX Course Name / Number © 2007 Thomson South-Western

Valuation Fundamentals q The greater the uncertainty about an asset’s future benefits, the higher Valuation Fundamentals q 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. q The valuation process links an asset’s risk and return to determine its price. 22

Valuation Fundamentals Future Cash Flows 33 Risk Valuation Valuation Fundamentals Future Cash Flows 33 Risk Valuation

Bond Valuation Fundamentals q Bonds are debt instruments used by business and government to Bond Valuation Fundamentals q Bonds are debt instruments used by business and government to raise large sums of money q Most bonds share certain basic characteristics q First, a bond promises to pay investors a fixed amount of interest, called the bond’s coupon. q Second, bonds typically have a limited life, or maturity. q Third, a bond’s coupon rate equals the bond’s annual coupon payment divided by its par value. q Fourth, a bond’s coupon yield equals the coupon payment divided by the bond’s current market price 44

Valuation Fundamentals Present Value of Future Cash Flows Link Risk & Return Expected Return Valuation Fundamentals Present Value of Future Cash Flows Link Risk & Return Expected Return on Assets Valuation 55

The Basic Valuation Model P 0 = Price of asset at time 0 (today) The Basic Valuation Model P 0 = Price of asset at time 0 (today) q CFt = cash flow expected at time t q r = discount rate (reflecting asset’s risk) q n = number of discounting periods (usually years) q 66 This model can express the price of any asset at t = 0 mathematically.

Valuation Fundamentals Bond Example q Company issues a 5% coupon interest rate, 10‑year bond Valuation Fundamentals Bond Example q Company issues a 5% coupon interest rate, 10‑year bond with a $1, 000 par value on 01/30/04 q Assume annual interest payments q Investors who buy company bonds receive the contractual rights q $50 coupon interest paid at the end of each year q $1, 000 par value at the end of the 10 th year 77 Using the P 0 equation, the bond would sell at a par value of $1, 000.

Bonds: Premiums & Discounts What Happens to Bond Values if the Required Return Is Bonds: Premiums & Discounts What Happens to Bond Values if the Required Return Is Not Equal to the Coupon Rate? The bond's value will differ from its par value R > Coupon Interest Rate = DISCOUNT R < Coupon Interest Rate 88 P 0 < par value P 0 > par value = PREMIUM

The Basic Equation (Assuming Annual Interest) q Cash flows include two components: the annual The Basic Equation (Assuming Annual Interest) q Cash flows include two components: 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 q (2) the par value, M, received at maturity in n years q (1) 99

Time Line for Bond: Valuation 91⁄8% Coupon, $1, 000 Par Bond, Maturing at End Time Line for Bond: Valuation 91⁄8% Coupon, $1, 000 Par Bond, Maturing at End of 2017, Required Return Assumed to be 8% 10 10

Bonds Semi-Annual Interest Payments An example. . Value a T-Bond Par value = $1, Bonds Semi-Annual Interest Payments An example. . Value a T-Bond Par value = $1, 000 Maturity = 2 years Coupon pay = 4% 11 11 r = 4. 4% per year = $992. 43

Yield to Maturity (YTM) Rate of return investors earn if they buy the bond Yield to Maturity (YTM) Rate of return investors earn if they buy the bond at P 0 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. 12 12

Risk-Free Bonds q. A risk-free bond is a bond that has no chance of Risk-Free Bonds q. A risk-free bond is a bond that has no chance of default by its issuer q Zero-coupon treasuries q Coupon-paying treasuries 13 13

Risky Bonds q Treasury bonds provide a known contractual stream of cash flows q Risky Bonds q Treasury bonds provide a known contractual stream of cash flows q q 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 q determine an appropriate discount rate q calculate the present value. q q Discount rate on corporate bond should be higher than on Treasury bond with the same maturity because corporate bonds carry default risk q q Yield spread between Treasury bonds and corporate bonds q 14 14 the risk that the corporation may not make all scheduled payments. The difference in yield to maturity between two bonds or two classes of bonds with similar maturities

Bond Issuers q Bond issuers q. Corporate bonds q. Municipal bonds q. Treasury bills Bond Issuers q Bond issuers q. Corporate bonds q. Municipal bonds q. Treasury bills q. Treasury notes q. Agency bonds 15 15

Bond Ratings q Bond ratings q. Moody’s q. Standard q. Fitch 16 16 & Bond Ratings q Bond ratings q. Moody’s q. Standard q. Fitch 16 16 & Poor’s

Bond Ratings 17 17 Bond Ratings 17 17

Bond Ratings and Spreads at Different Maturities at a Given Point in Time 18 Bond Ratings and Spreads at Different Maturities at a Given Point in Time 18 18

Bond Price Behavior q Bond price quotations q Bond spreads reflect a direct relationship Bond Price Behavior q Bond price quotations q Bond spreads reflect a direct relationship with default risk q Bond price behavior q Prices change constantly q. Passage of time q. Forces in the economy 19 19

Bond Prices and Yields for Bonds with Differing Times to Maturity, Same 6% Coupon Bond Prices and Yields for Bonds with Differing Times to Maturity, Same 6% Coupon Rate 20 20

Bonds: Time to Maturity 21 21 What does this tell you about the relationship Bonds: Time to Maturity 21 21 What does this tell you about the relationship between bond prices & yields for bonds with the equal coupon rates, but different maturities?

Bonds: Yield to Maturity (YTM) Rate of return investors earn if they buy the Bonds: Yield to Maturity (YTM) Rate of return investors earn if they buy the bond at P 0 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. 22 22

Evaluating the Yield Curve q Yields vary with maturity. q Yields offered by bonds Evaluating the Yield Curve q Yields vary with maturity. q Yields offered by bonds must be sufficient to offer investors a positive real return. q The real return on an investment approximately equals the difference between its stated or nominal return and the inflation rate. q The shape of the yield curve can change over time. q Research shows the yield curve works well as a predictor of economic activity, in the United States and other large industrialized economies. 23 23

Yield Curves for U. S. Government Bonds 24 24 Yield Curves for U. S. Government Bonds 24 24

Term Structure Theories q Expectations theory q Liquidity preference theory q Preferred habitat theory Term Structure Theories q Expectations theory q Liquidity preference theory q Preferred habitat theory 25 25

Expectations Theory 26 26 Expectations Theory 26 26

Term Structure of Interest Rates q Relationship between yield and maturity is called the Term Structure of Interest Rates q Relationship between yield and maturity is called the Term Structure of Interest Rates a Yield Curve securities are higher than on short-term securities q Generally look at risk-free Treasury debt securities q Graphical depiction is called q Usually, yields on long-term q Yield curves normally upwards-sloping q Long yields > short yields q Can be flat or even inverted during times of financial stress 27 27

Stock Valuation: Preferred Stock Preferred stock is an equity security that is expected to Stock Valuation: Preferred Stock Preferred stock is an equity security that is expected to pay a fixed annual dividend for its life PS 0 = 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% PS 0= 28 28 DP rp = $2. 30 0. 11 = $20. 90 / share

Valuation Fundamentals Common Stock Value of a Share of Common Stock P 0 = Valuation Fundamentals Common Stock Value of a Share of Common Stock P 0 = P 1 + D 1 (1+r) P 0 = Present value of the expected stock price at the end of period 1 D 1 = Dividends received r = discount rate 29 29

Valuation Fundamentals: Common Stock q But how is P 1 determined? q This is Valuation Fundamentals: Common Stock q But how is P 1 determined? q This is the PV of expected stock price P 2, plus dividend at time 2 q P 2 is the PV of P 3 plus dividend at time 3, etc. . . q 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 30 30

Zero Growth Model q To value common stock, you must make assumptions about the Zero Growth Model q To value common stock, you must make assumptions about the growth of future dividends q Zero growth model assumes a constant, non-growing dividend stream: D 1 = D 2 =. . . = D q Plugging constant value D into the common stock valuation formula reduces to simple equation for a perpetuity: 31 31 P 0 = D r

Constant Growth Model Assumes dividends will grow at a constant rate (g) that is Constant Growth Model Assumes dividends will grow at a constant rate (g) that is less than the required return (r) q If dividends grow at a constant rate forever, you can value stock as a growing perpetuity, denoting next year’s dividend as D 1: q D 1 P 0 = r-g Commonly called the Gordon Growth Model. 32 32

Variable Growth 33 33 Variable Growth 33 33

Variable Growth Model Example q Estimate the current value of Morris Industries' common stock, Variable Growth Model Example q Estimate the current value of Morris Industries' common stock, P 0 = P 2003 q Assume q q The firm's financial manager expects that these dividends will increase at an 8% annual rate over the next 3 years q 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 q 34 34 The most recent annual dividend payment of Morris Industries was $4 per share The firm's required return, r , is 12%

Variable Growth Model Valuation Steps #1 & #2 q Compute the value of dividends Variable Growth Model Valuation Steps #1 & #2 q Compute the value of dividends in 2004, 2005, and 2006 as (1+g 1)=1. 08 times the previous year’s dividend Div 2004= Div 2003 x (1+g 1) = $4 x 1. 08 = $4. 32 Div 2005= Div 2004 x (1+g 1) = $4. 32 x 1. 08 = $4. 67 Div 2006= Div 2005 x (1+g 1) = $4. 67 x 1. 08 = $5. 04 q Find the PV of these three dividend payments: PV of Div 2004= Div 2004 (1+r) = $ 4. 32 (1. 12) = $3. 86 PV of Div 2005= Div 2005 (1+r)2 = $ 4. 67 (1. 12)2 = $3. 72 PV of Div 2006= Div 2006 (1+r)3 = $ 5. 04 (1. 12)3 = $3. 59 Sum of discounted dividends = $3. 86 + $3. 72 + $3. 59 = $11. 17 35 35

Variable Growth Model Valuation Step #3 q Find the value of the stock at Variable Growth Model Valuation Step #3 q Find the value of the stock at the end of the initial growth period using the constant growth model q Calculate next period dividend by multiplying D 2006 by 1+g 2, the lower constant growth rate: D 2007 = D 2006 x (1+ g 2) = $ 5. 04 x (1. 05) = $5. 292 q Then use D 2007=$5. 292, g =0. 05, r =0. 12 in Gordon model: 36 36

Variable Growth Model Valuation Step #3 q Find the present value of this stock Variable Growth Model Valuation Step #3 q Find the present value of this stock price by discounting P(2006) by (1+r)3 37 37

Variable Growth Model Valuation Step #4 q Add the PV of the initial dividend Variable Growth Model Valuation Step #4 q Add the PV of the initial dividend stream (Step #2) to the PV of stock price at the end of the initial growth period (P 2006): P 2003 = $11. 17 + $53. 81 = $64. 98 Current (end of year 2003) stock price 38 38 Remember: Because future growth rates might change, the variable growth model allows for a changes in the dividend growth rate.

Time Line for Variable Growth Valuation 39 39 Time Line for Variable Growth Valuation 39 39

Free Cash Flow Approach by asking, what is the total operating cash flow (OCF) Free Cash Flow Approach by asking, what is the total operating cash flow (OCF) generated by a firm? q Next subtract from the firm’s operating cash flow the amount needed to fund new investments in both fixed assets and current assets. q The difference is total free cash flow (FCF). q Begin q Represents the cash amount a firm could distribute to investors after meeting all its other obligations 40 40

Common Stock Valuation: Other Options q Book value q Net assets per share available Common Stock Valuation: Other Options q Book value q Net assets per share available to common stockholders after liabilities are paid in full q Liquidation q Actual value net amount per share likely to be realized upon liquidation & payment of liabilities q More realistic than book value, but doesn’t consider firm’s value as a going concern 41 41

Common Stock Valuation: Other Options q Price / Earnings (P / E) multiples q Common Stock Valuation: Other Options q Price / Earnings (P / E) multiples q Reflects the amount investors will pay for each dollar of earnings per share q P / E multiples differ between & within industries q Especially helpful for privately-held firms 42 42