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Professor Del Hawley Finance 634

Chapter 4. Stock And Bond Valuation. Professor Del Hawley Finance 634. Fall 2003. Valuation Fundamentals. Value of any financial asset is the PV of future cash flows Bonds: PV of promised interest & principal payments Stocks: PV of all future dividends

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Professor Del Hawley Finance 634

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  1. Chapter 4 Stock And Bond Valuation Professor Del HawleyFinance 634 Fall 2003

  2. Valuation Fundamentals • Value of any financial asset is the PV of future cash flows • Bonds: PV of promised interest & principal payments • Stocks: PV of all future dividends • Patents, trademarks: PV of future royalties • Valuation is the process linking risk & return • Output of process is asset’s expected market price • A key input is the required [expected] return on an asset • Defined as the return an arms-length investor would require for an asset of equivalent risk • Debt securities: risk-free rate plus risk premium(s) • Required return for stocks found using CAPM or other asset pricing model • Beta determines risk premium: higher beta, higher reqd return

  3. The Basic Valuation Model Can express price of any asset at time 0, P0, mathematically as Equation 4.1: • Where: • 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)

  4. Illustration Of Simple Asset Valuation Assume you are offered a security that promises to make four $2,000 payments at the end of years 1-4. If the appropriate discount rate for securities of this risk is 2%, what price should you pay for this security? Security would be worth $7,615.53 each.

  5. Illustration Of Simple Asset Valuation With most debt securities, the cash flows are smooth (equal amounts at equal time intervals, except possibly the last cash flow) and so it can be treated like an annuity or an annuity with a balloon. PV = Price or value of the security FV = Maturity or par value (usually $1000) n = Number of remaining interest payments i = Market required return per payment period PMT = Periodic interest payment (Coupon Rate x 1000) FV = 0 n = 4 I = 2 PMT = 2000 PV = $7,615.53

  6. Illustration Of Bond ValuationUsing U.S. Treasury Securities The simplest debt instruments to value are U.S. Treasury securities since there is no default risk. Instead, the discount rate to use (rf) is the pure cost of borrowing. rf = Real Rate of Interest + Inflation Premium

  7. The Fisher Effect And Expected Inflation • The relationship between nominal (observed) and real (inflation-adjusted) interest rates and expected inflation is called the Fisher Effect (or Fisher Equation). • Fisher said the nominal rate (r) is approximately equal to the real rate of interest (a) plus a premium for expected inflation (i). • If the real rate equals 3% (a = 0.03) and expected annual inflation rate equals 2% (i = 0.02), then: r  a + i  0.03 + 0.02  0.05  5% • The true Fisher Effect is multiplicative, rather than additive: (1+r) = (1+a)(1+i) = (1.03)(1.02) = 1.0506; so r = 5.06%

  8. Illustration Of Bond ValuationUsing U.S. Treasury Securities Assume you are asked to value two Treasury securities, when rf is 1.75 percent: • A (pure discount) Treasury bill with a $1,000 face value that matures in three months, and • A 1.75% coupon rate Treasury note, also with a $1,000 face value, that matures in three years.

  9. Illustration Of Bond Valuation Using U.S. Treasury Securities (Continued) • The 3-month T-Bill pays no interest; return comes from the difference between purchase price and maturity value. • 3-year T-Note makes two end-of-year $17.5 coupon payments (CF1=CF2=$17.5), plus end-of-year 3 payment of interest plus principal (CF3 = $1,017.5) • Can value both with variation of Equation 4.1:

  10. Illustration Of Bond Valuation Using U.S. Treasury Securities (Continued) For the 3-month Treasury Bill:

  11. Illustration Of Bond Valuation Using U.S. Treasury Securities (Continued) For the 3-year Treasury Note:

  12. Illustration Of Bond Valuation Using U.S. Treasury Securities (Continued) For the 3-year Treasury Note: For Excel: =PV(rate,nper,PMT,FV,Type)

  13. Bond Valuation Fundamentals Most U.S. corporate bonds: • Pay interest at a fixed coupon interest rate • Have an initial maturity of 10 to 30 years, and • Have a par value (also called face or principal value) of $1,000 that must be repaid at maturity.

  14. Bond Valuation Fundamentals The Sun Company, on January 3, 2004, issues a 5 percent coupon interest rate, 10‑year bond with a $1,000 par value • Assume annual interest payments for simplicity • Will value later assuming semi-annual coupon payments Investors in Sun Company’s bond thus receive the contractual right to: • $50 coupon interest (C) paid at the end of each year and • The $1,000 par value (Par) at the end of the tenth year.

  15. Bond Valuation Fundamentals (Continued) • Assume required return, r, also equal to 5% • The price of Sun Company’s bond, P0, making ten (n=10) annual coupon interest payments (C = $50), plus returning $1,000 principal (Par) at end of year 10, is determined as:

  16. Bond Valuation Fundamentals (Continued) For Excel: =PV(rate,nper,PMT,FV,Type)

  17. Bond Valuation Fundamentals (Continued) A bond’s value has two separable parts: (1) PV of stream of annual interest payments, t=1 to t=10 (2) PV of principal repayment at end of year 10. Therefore, we can also value a bond as the PV of an annuity plus the PV of a single cash flow.

  18. Bond Values If Required Return Is Not Equal To The Coupon Rate • Whenever the required return on a bond (r) differs from its coupon interest rate, the bond's value will differ from its par, or face, value. • Will only sell at par ifr= coupon rate • When r is greater than the coupon interest rate, P0 will be less than par value, and the bond will sell at a discount. • For Sun, ifr>5%, P0 will be less than $1,000 • When r is below the coupon interest rate, P0 will be greater than par, and the bond will sell at a premium. • For Sun, ifr<5%, P0 will be greater than $1,000 • Value Sun Company, 10-year, 5% coupon rate bond if required return, r =6% and again if r = 4%.

  19. Bond Values If Required Return Is Not Equal To The Coupon Rate (Continued) At r = 6%, the bond sells at a discount of $1,000 - $926.405 = $73.595 At r = 4%, the bond sells at a premium of $1,081.45 - $1,000 = $81.45 Premiums & discounts change systematically as r changes

  20. Bond Value & Required Return, Sun Company’s 5 % Coupon Rate, 10-year, $1,000 Par, January 1, 2004 Issue Paying Annual Interest 1,200 1,100 1,081 Premium Market Value of Bond P0 ($) Par 1,000 Discount 926 900 800 0 1 2 3 4 5 6 7 8 Required Return, r (%)

  21. The Dynamics Of Bond Valuation Changes For Different Times To Maturity • Whenever r is different from the coupon interest rate, the time to maturity affects bond value even if the required return remains constant until maturity. • The shorter is n, the less responsive is P0 to changes in r. Assume r falls from 5% to 4% • For n=8 years,P0 rises from $1,000 to $1,067.33, or 6.73% • For n=3 years,P0 rises from $1,000 to $1,027.75, or 2.775%

  22. The Dynamics Of Bond Valuation Changes For Different Times To Maturity • The same relationship holds if r rises from 5% to 6%, (though the percentage decline in price is less than the percentage increase was in the previous example). For n=8 years, P0 falls from $1,000 to $937.89, or 6.21% For n=3 years,P0 falls from $1,000 to $973.25, or 2.675% • Even if r doesn’t change, premiums and discounts will decline towards the bond’s par value as the bond nears maturity.

  23. Relation Between Time to Maturity, Required Return & Bond Value, Sun Company’s 5%, 10-year, $1,000 Par Issue Paying Annual Interest 1,100 Premium Bond, Required Return, r = 4% 1,081 1,067.3 1,050 1,027.75 Par-Value Bond, Required Return, r = 5% 1,000 M Market Value of Bond P0 ($) 950 926 r Discount Bond, Required Return, r = 6% 900 10 9 8 7 6 5 4 3 2 1 0 Time to maturity (years)

  24. Relationship Between Bond Prices & Yields, Bonds Of Differing Original Maturities But Same Coupon Rates

  25. Semi-Annual Bond Interest Payments • Most bonds pay interest semi-annually rather than annually • Can easily modify the basic valuation formula; divide both coupon payment (C) and discount rate (r) by 2, as in Eq 4.3: • N is always the number of PAYMENT PERIODS • I is always the required return PER PERIOD

  26. Valuing A Bond With Semi-Annual Bond Interest Payments Value a T-Bond with a par value of $1,000 that matures in exactly 2 years and pays a 4% coupon if r = 4.4% per year.

  27. Valuing A Bond With Semi-Annual Bond Interest Payments Value a T-Bond with a par value of $1,000 that matures in exactly 2 years and pays a 4% coupon if r = 4.4% per year.

  28. The Importance And CalculationOf Yield To Maturity • Yield to Maturity (YTM) is the rate of return investors earn if they buy the bond at P0 and hold it until maturity. • YTM is the discount rate that equates the PV of a bond’s cash flows with its price. • The YTM on a bond selling at par (P0 = Par) will always equal the coupon interest rate. When P0Par, the YTM will differ from the coupon rate.

  29. The Importance And CalculationOf Yield To Maturity Suppose you purchase a T-Bond for $875.00 that has 2 years to maturity and pays its 5% coupon rate in semi-annual payments. What is the YTM for the bond? This is the semi-annual yield on the bond, whereas the YTM is always stated as an annual rate. To annualize the semi-annual yield, simply multiply it by 2. So, the YTM on the bond is 12.23%.

  30. The Importance and Calculation of Yield to Maturity For the 3-year Treasury Note: For Excel: =RATE(nper,PMT,PV,FV,<Type>,<guess>)

  31. The “Current Yield” is anApproximation of the YTM In bond quotes, the Current Yield (Cur Yld) is computed as: Cur Yld = Annual $ of Interest / Price It is an approximation of the YTM. The long the time to maturity and the larger the coupon rate, the better the approximation. See http://www.bondpickers.com/?source=gglBondPrice for detailed price quotes for corporate bonds.

  32. Holding-Period Returns If you purchase a bond with YTM = 10% and hold it until maturity, you will earn an average of 10% return on the bond over its life even though the value of the bond will fluctuate throughout its life. BUT, if you sell the bond prior to maturity your average return will depend on the selling price of the bond, which will depend on the prevailing level of interest rates and the relative risk of the bond at the time you sell it. This is called “Interest rate risk” or “price risk”. Even “riskless” treasury bonds have this risk.

  33. Holding-Period Returns The value of the bond will move inversely with the prevailing level of interest rates. Increase in required yield → decrease in value Decrease in required yield → increase in value So, if required return on your bond rises while you hold it your selling price will be lower that you expected and your holding period return (the average you earn over the time you hold the bond) will fall. And vice versa.

  34. Valuing A Bond With Semi-Annual Bond Interest Payments Suppose you purchase a bond today for $960 that has a 15-year maturity, $1000 face value, 8% coupon rate, and pays interest semi-annually. The next coupon payment is due in exactly six months. Also suppose that you sell the bond four years from now, immediately after the 8th coupon payment you receive. At the time that you sell the bond, its required return in the market is 12%. What is your average annual holding period return on this bond?

  35. Holding Period Returns First, find the selling price of the bond in four years.

  36. Holding Period Returns Next, use the price you just found as the FV, and determine the rate that you would earn over four years.

  37. The Term Structure Of Interest Rates • At any point in time, there will be a systematic relationship between YTM and maturity for securities of a given risk. • Usually, yields on long-term securities are higher than the yields on short-term securities. • The relationship between yield and maturity is called the Term Structure of Interest Rates. • The graphical depiction of the term structure is called a Yield Curve. • Yield curves are normally upwards-sloping (long yields > short), but can be flat or even inverted during times of financial stress • We won’t cover term structure in depth, but three principal “expectations” theories explain the term structure: • Pure expectations hypothesis: YC embodies prediction • Liquidity premium theory: Investors must be paid to invest L-T • Preferred habitat hypothesis: Investors prefer maturity zones

  38. Yield Curves for US Treasury Securities 16 May 1981 14 12 10 January 1995 Interest Rate % 8 August 1996 6 October 1993 4 2 1 3 5 10 15 20 30 Years to Maturity

  39. Yield Curve, February 12, 2003From www.cnnfn.com % % Years to maturity

  40. Yield Curve Today % For detailed current information on the yield curve, go to http://www.bondsonline.com/asp/news/yieldcurve.html

  41. Changes In The Shape And Level Of Treasury Yield Curve During Early October 1998 5.1 October 9 4.9 October 8 4.7 October 2 4.5 Yield % 4.3 4.1 3.9 3.7 1 5 10 30 Maturity in Years

  42. Bond Risk Premiums, February 97-November 98 97 98

  43. Equity Valuation • As you learned in MBA 611, the required return on common stock is based on its beta coefficient, which is derived from the CAPM • Valuing common stock is the most difficult, both practically and theoretically, since nothing (except the current price, is known with certainty. • Preferred stock valuation is much easier (the easiest of all) • Whenever investors feel the expected return, rˆ, is not equal to the required return, r, prices will react: • If exp return declines or req’d return rises, stock price will fall • If exp return rises or req’d return declines, stock price will rise • Asset prices can change for reasons besides their own risk • Changes in the asset’s liquidity or tax status can change price • Changes in market risk premium can change all asset values • Most dramatic change in market risk: Russian default Fall 98 • Caused required return on all risky assets to rise, price to fall

  44. Preferred Stock Valuation • PS is an equity security that is expected to pay a fixed annual dividend over its (assumed infinite) life. • Preferred stock’s market price, P0, equals next period’s dividend payment, Dt+1, divided by the discount rate, r, appropriate for securities of its risk class: • A share of PS paying a $2.3 per share annual dividend and with a required return of 11% would thus be worth $20.90: • Formula can be rearranged to compute required return, if price and dividend known:

  45. Common Stock Valuation The basic formula for valuing a share of stock easy to state; P0 is equal to the present value of the expected stock price at end of period 1, plus dividends received during the period, as in Eq 4.4: The problem is how to determine P1.

  46. Common Stock Valuation P1 is the PV of expected stock price P2, plus dividends received during period 1. P2 in turn, the PV of P3 plus dividends, and so on. Repeating this logic over and over, you will find that today’s price equals the PV of the entire dividend stream the stock will pay in the future, as in Eq 4.5:

  47. The Zero Growth Valuation Model • To value common stock, we must make an assumption about the growth rate of future dividends. • The simplest approach, the zero growth model, assumes a constant, non-growing dividend stream: D1 = D2= ... = D • Plugging the constant value D into Eq 4.5 reduced the valuation formula to the simple equation for a perpetuity:

  48. The Zero Growth Valuation Model Assume the dividend of Disco Company is expected to remain at $1.75/share indefinitely, and the required return on Disco’s stock is 15%. The next dividend will be one year from now. P0 is determined to be $11.67 as:

  49. The Constant Growth Valuation Model • The most widely used simple stock valuation formula, the constant growth model, assumes dividends will grow at a constant rate, g, that is less than the required return (g<r) • If dividends grow at a constant rate forever, we can value stock as a growing perpetuity. Denoting next year’s dividend as D1: • This is commonly called the Gordon Growth Model, after Myron Gordon, who popularized model in the 1960s.

  50. The Constant Growth Valuation Model The Gordon Company’s dividends have grown by 7% per year, reaching $1.40 per share this year. This growth is expected to continue, so D1=$1.40 x 1.07=$1.50. If the required return on this stock is 15%, then its market value should be:

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