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## Stock & Bond Valuation

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**Stock & Bond Valuation**Professor XXXXX Course Name / Number**Present Value of Future Cash Flows**Link Risk & Return Expected Return on Assets Valuation Valuation Fundamentals**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.**Valuation FundamentalsBond 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 10th year Using the P0 equation, the bond would sell at a par value of $1,000.**P0 < par value**DISCOUNT = P0> par value PREMIUM = BondsPremiums & 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**BondsTime to Maturity**What does this tell you about the relationship between bond prices & yields for bonds with the equal coupon rates, but different maturities?**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**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.**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 0.03 + 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%**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?**May 1981**January 1995 August 1996 October 1993 Yield CurvesU.S. Treasury Securities 16 14 12 10 Interest Rate % 8 6 4 2 1 3 5 10 15 20 30 Years to Maturity**P0 = 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% Valuation FundamentalsPreferred Stock Preferred stock is an equity security that is expected to pay a fixed annual dividend for its life**Value**of a Share of Common Stock Valuation FundamentalsCommon Stock • P0 = Present value of the expected stock price at the end of period 1 • D1 = Dividends received • r = discount rate**Valuation FundamentalsCommon Stock**• 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**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: D1 = D2= ... = D • Plugging constant value D into the common stock valuation formula reduces to simple equation for a perpetuity:**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 D1: This is commonly called the Gordon Growth Model.**Variable Growth ModelExample**• Estimate the current value of Morris Industries' common stock, P0 = P2005 • 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%**Variable Growth ModelValuation Steps #1 & #2**• Compute the value of dividends in 2006, 2007, and 2008 as (1+g1)=1.08 times the previous year’s dividend Div2006= Div2005 x (1+g1) = $4 x 1.08 = $4.32 Div2007= Div2006 x (1+g1) = $4.32 x 1.08 = $4.67 Div2008= Div2007 x (1+g1) = $4.67 x 1.08 = $5.04 • Find the PV of these three dividend payments: PV of Div2006= Div2006 (1+r) = $ 4.32 (1.12) = $3.86 PV of Div2007= Div2007 (1+r)2 = $ 4.67 (1.12)2 = $3.72 PV of Div2008= Div2008 (1+r)3 = $ 5.04 (1.12)3 = $3.59 Sum of discounted dividends = $3.86 + $3.72 + $3.59 = $11.17**Variable Growth ModelValuation 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 D2008 by 1+g2, the lower constant growth rate: D2009 = D2008 x (1+ g2) = $ 5.04 x (1.05) = $5.292 • Then use D2009=$5.292, g =0.05, r =0.12 in Gordon model:**Variable Growth ModelValuation Step #3**• Find the present value of this stock price by discounting P2008 by (1+r)3**Variable Growth ModelValuation 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 (P2008): P2005 = $11.17 + $53.81 = $64.98 Current (year 2005) stock price Remember: because future growth rates might change, the variable growth model allows for changes in the dividend growth rate.**Common Stock ValuationOther 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