Stock & Bond Valuation Professor XXXXX Course Name / Number

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

3 The Basic Valuation Model P 0 = Price of asset at time 0 (today) CF t = 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.

4 Valuation Fundamentals Bond Example Using the P 0 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 01/30/05 –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

5 P 0 < par valueP 0 > par value 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 R > Coupon Interest Rate R < Coupon Interest Rate DISCOUNT = PREMIUM =

6 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?

7 Bonds Semi-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

8 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.

9 The Fisher Effect And Expected Inflation The relationship between nominal and real (inflation- adjusted) 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   0.05  5% True Fisher Effect multiplicative, rather than additive: (1+r) = (1+a)(1+i) = (1.03)(1.02) = ; so r = 5.06%

10 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?

11 Yield Curves U.S. Treasury Securities Years to Maturity Interest Rate % August 1996 October 1993 May 1981 January

12 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 D t+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%

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

14 But how is P1 determined? –This is the PV of expected stock price P2, plus dividends –P2 is the PV of P3 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 Valuation Fundamentals Common Stock

15 Zero Growth Valuation 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: D 1 = D 2 =... = D  Plugging constant value D into the common stock valuation formula reduces to simple equation for a perpetuity:

16 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.

17 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%

18 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 = $ $ $3.59 = $11.17

19 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: Variable Growth Model Valuation Step #3

20 Find the present value of this stock price by discounting P 2008 by (1+r) 3 Variable Growth Model Valuation Step #3

21 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 = $ $53.81 = $64.98 Variable Growth Model Valuation Step #4 Current (year 2005) stock price Remember: because future growth rates might change, the variable growth model allows for changes in the dividend growth rate.

22 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

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