Chapter 4 Stock & Bond Valuation

1. Chapter 4Stock & Bond Valuation Professor XXXXX Course Name / Number

2. 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.

3. Valuation Fundamentals Future Cash Flows Risk Valuation

4. 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

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

6. 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.

7. Valuation FundamentalsBond Example • Company issues a 5% coupon interest rate, 10‑year bond with a $1,000 par value on 01/30/04 • Assume 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 Using the P0 equation, the bond would sell at a par value of $1,000.

8. DISCOUNT = PREMIUM = 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 P0 < par value R < Coupon Interest Rate P0> par value

9. 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

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

11. 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

12. 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.

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

14. 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

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

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

17. Bond Ratings

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

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

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

21. 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?

22. 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.

23. 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.

24. Yield Curves for U.S. Government Bonds

25. Term Structure Theories • Expectations theory • Liquidity preference theory • Preferred habitat theory

26. Expectations Theory

27. 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

28. 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%

29. Valuation FundamentalsCommon Stock Value of a Share of Common Stock P0 = Present value of the expected stock price at the end of period 1 D1 = Dividends received r = discount rate

30. 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

31. 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:

32. 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: Commonly called the Gordon Growth Model.

33. Variable Growth

34. 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%

35. 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

36. 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 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:

37. Variable Growth ModelValuation Step #3 • Find the present value of this stock price by discounting P(2006) by (1+r)3

38. 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 (P2006): P2003 = $11.17 + $53.81 = $64.98 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.

39. Time Line for Variable Growth Valuation

40. 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

41. 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

42. Common Stock Valuation:Other Options • 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