Stock Bond Valuation Professor XXXXX Course Name Number
Stock & Bond Valuation Professor XXXXX Course Name / Number
Valuation Fundamentals Present Value of Future Cash Flows Link Risk & Return Expected Return on Assets Valuation 2
The Basic Valuation Model • • P 0 = 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. 3
Valuation Fundamentals Bond Example • Company issues a 5% coupon interest rate, 10 -year bond with a $1, 000 par value on 01/30/05 – Assume annual interest payments • Investors in company’s bond receive the contractual rights – $50 coupon interest paid at the end of each year – $1, 000 par value at the end of the 10 th year 4 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 required return is not equal to the coupon rate? The bond's value will differ from its par value 5 R > Coupon Interest Rate P 0 < par value = DISCOUNT R < Coupon Interest Rate P 0 > par value = PREMIUM
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? 6
Bonds Semi-Annual Interest Payments An example. . Value a T-Bond Par value = $1, 000 Maturity = 2 years Coupon pay = 4% 7 r = 4. 4% per year = $992. 43
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. 8
The Fisher Effect And Expected Inflation • The relationship between nominal and real (inflationadjusted) interest rates and expected inflation called the Fisher Effect (or Fisher Equation). • Nominal rate (r) is approximately equal to real rate of interest (a) plus a premium for expected inflation (i). – If real rate equals 3% (a = 0. 03) and expected inflation equals 2% (i = 0. 02): r a + i 0. 03 + 0. 02 0. 05 5% • True Fisher Effect multiplicative, rather than additive: (1+r) = (1+a)(1+i) = (1. 03)(1. 02) = 1. 0506; so r = 5. 06% 9
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 What to you think a Yield Curve would look like graphically? 10
Yield Curves U. S. Treasury Securities 16 May 1981 14 Interest Rate % 12 10 January 1995 8 August 1996 6 October 1993 4 2 1 3 5 10 15 Years to Maturity 11 20 30
Valuation Fundamentals Preferred Stock Preferred stock is an equity security that is expected to pay a fixed annual dividend for its life • P 0 = Preferred stock’s market price • Dt+1 = next period’s dividend payment • r = discount rate An example: A share of preferred stock pays $2. 3 per share annual dividend and with a required return of 11% 12
Valuation Fundamentals Common Stock Value of a Share of Common Stock • P 0 = Present value of the expected stock price at the end of period 1 • D 1 = Dividends received • r = discount rate 13
Valuation Fundamentals Common Stock • But how is P 1 determined? – This is the PV of expected stock price P 2, plus dividends – P 2 is the PV of P 3 plus dividends, 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 14
Zero Growth Valuation Model • To value common stock, you must make assumptions about the growth of future dividends • Zero growth model assumes a constant, -growing dividend stream: non D 1 = D 2 =. . . = D • Plugging constant value D into the common stock valuation formula reduces to simple equation for a perpetuity: 15
Constant Growth Valuation 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 D 1: This is commonly called the Gordon Growth Model. 16
Variable Growth Model Example • Estimate the current value of Morris Industries' common stock, P 0 = P 2005 • 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% 17
Variable Growth Model Valuation Steps #1 & #2 • Compute the value of dividends in 2006, 2007, and 2008 as (1+g 1)=1. 08 times the previous year’s dividend Div 2006= Div 2005 x (1+g 1) = $4 x 1. 08 = $4. 32 Div 2007= Div 2006 x (1+g 1) = $4. 32 x 1. 08 = $4. 67 Div 2008= Div 2007 x (1+g 1) = $4. 67 x 1. 08 = $5. 04 • Find the PV of these three dividend payments: PV of Div 2006= Div 2006 (1+r) = $ 4. 32 (1. 12) = $3. 86 PV of Div 2007= Div 2007 (1+r)2 = $ 4. 67 (1. 12)2 = $3. 72 PV of Div 2008= Div 2008 (1+r)3 = $ 5. 04 (1. 12)3 = $3. 59 Sum of discounted dividends = $3. 86 + $3. 72 + $3. 59 = $11. 17 18
Variable Growth Model Valuation Step #3 • 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 D 2008 by 1+g 2, the lower constant growth rate: D 2009 = D 2008 x (1+ g 2) = $ 5. 04 x (1. 05) = $5. 292 • Then use D 2009=$5. 292, g =0. 05, r =0. 12 in Gordon model: 19
Variable Growth Model Valuation Step #3 • Find the present value of this stock price by discounting P 2008 by (1+r)3 20
Variable Growth Model Valuation Step #4 • 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 2008): P 2005 = $11. 17 + $53. 81 = $64. 98 Current (year 2005) stock price 21 Remember: because future growth rates might change, the variable growth model allows for changes in the dividend growth rate.
Common Stock Valuation Other Options • Book value – Net assets per share available to common stockholders after liabilities are paid in full • Liquidation value – Actual 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 • Price / Earnings (P / E) multiples – Reflects the amount investors will pay for each dollar of earnings per share – P / E multiples differ between & within industries – Especially helpful for privately-held firms 22
Questions?
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