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  • Chap005

    1. 1. How to Value Bonds and Stocks
    2. 2. Chapter Outline <ul><li>5.1 Definitions and Example of a Bond </li></ul><ul><li>5.2 How to Value Bonds </li></ul><ul><li>5.3 Bond Concepts </li></ul><ul><li>5.4 The Present Value of Common Stocks </li></ul><ul><li>5.5 Estimates of Parameters in the Dividend- Discount Model </li></ul><ul><li>5.6 Growth Opportunities </li></ul><ul><li>5.7 The Dividend Growth Model and the NPVGO Model </li></ul><ul><li>5.8 Price-Earnings Ratio </li></ul>
    3. 3. 5.1 Definition of a Bond <ul><li>A bond is a legally binding agreement between a borrower and a lender that specifies the: </li></ul><ul><ul><li>Par (face) value </li></ul></ul><ul><ul><li>Coupon rate </li></ul></ul><ul><ul><li>Coupon payment </li></ul></ul><ul><ul><li>Maturity Date </li></ul></ul><ul><li>The y ield t o m aturity ( YTM ) is the required market interest rate on the bond. </li></ul>
    4. 4. 5.2 How to Value Bonds <ul><li>Primary Principle: </li></ul><ul><ul><li>Value of financial securities = PV of expected future cash flows </li></ul></ul><ul><li>Bond value is, therefore, determined by the present value of the coupon payments and par value . </li></ul><ul><li>Interest rates are inversely related to present (i.e., bond) values. </li></ul>
    5. 5. The Bond Pricing Equation
    6. 6. Pure Discount Bonds <ul><li>Make no periodic interest payments (coupon rate = 0%) </li></ul><ul><li>The entire yield to maturity comes from the difference between the purchase price and the par value . </li></ul><ul><li>Cannot sell for more than par value </li></ul><ul><li>Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) </li></ul>
    7. 7. Pure Discount Bonds <ul><li>Information needed for valuing pure discount bonds: </li></ul><ul><ul><li>Time to maturity ( T ) = Maturity date - today’s date </li></ul></ul><ul><ul><li>Face value ( F ) </li></ul></ul><ul><ul><li>Discount rate ( r ) </li></ul></ul>Present value of a pure discount bond at time 0:
    8. 8. Pure Discount Bond: Example <ul><li>Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%. </li></ul>
    9. 9. Level Coupon Bonds <ul><li>Make periodic coupon payments in addition to the maturity value </li></ul><ul><li>The payments are equal each period. Therefore, the bond is just a combination of an annuity and a terminal (maturity) value . </li></ul><ul><li>Coupon payments are typically semiannual . </li></ul><ul><li>Effective annual rate (EAR) = </li></ul><ul><li>(1 + R/m) m – 1 </li></ul>
    10. 10. Level Coupon Bond: Example
    11. 11. Consols <ul><li>Not all bonds have a final maturity. </li></ul><ul><li>British consols pay a set amount (i.e., coupon) every period forever. </li></ul><ul><li>These are examples of a perpetuity. </li></ul>
    12. 12. 5.3 Bond Concepts <ul><li>Bond prices and market interest rates move in opposite directions . </li></ul><ul><li>When coupon rate = YTM, price = par value </li></ul><ul><li>When coupon rate > YTM, price > par value (premium bond) </li></ul><ul><li>When coupon rate < YTM, price < par value (discount bond) </li></ul>
    13. 13. YTM and Bond Value 800 1000 1100 1200 1300 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Discount Rate Bond Value When the YTM < coupon, the bond trades at a premium. When the YTM = coupon, the bond trades at par . When the YTM > coupon, the bond trades at a discount. 6 3/8
    14. 14. Bond Example Revisited (p.133)
    15. 15. Computing Yield to Maturity (p.134) <ul><li>Yield to maturity is the rate implied by the current bond price. </li></ul>
    16. 16. 5.4 The Present Value of Common Stocks <ul><li>The value of any asset is the present value of its expected future cash flows . </li></ul><ul><li>Stock ownership produces cash flows from: </li></ul><ul><ul><li>Dividends </li></ul></ul><ul><ul><li>Capital Gains </li></ul></ul><ul><li>Valuation of Different Types of Stocks </li></ul><ul><ul><li>Zero Growth </li></ul></ul><ul><ul><li>Constant Growth </li></ul></ul><ul><ul><li>Differential Growth </li></ul></ul>
    17. 17. Case 1: Zero Growth <ul><li>Assume that dividends will remain at the same level forever </li></ul><ul><li>Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity: </li></ul>
    18. 18. Case 2: Constant Growth Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity: Assume that dividends will grow at a constant rate, g , forever, i.e., . . .
    19. 19. Case 3: Differential Growth <ul><li>Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter . </li></ul><ul><li>To value a Differential Growth Stock, we need to: </li></ul><ul><ul><li>Estimate future dividends in the foreseeable future . </li></ul></ul><ul><ul><li>Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2). </li></ul></ul><ul><ul><li>Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate. </li></ul></ul>
    20. 20. 5.5 Estimates of Parameters <ul><li>The value of a firm depends upon its growth rate, g , and its discount rate, R . </li></ul><ul><ul><li>Where does g come from? </li></ul></ul><ul><ul><li>g = Retention ratio × Return on retained earnings ( ROE ) </li></ul></ul>
    21. 21. Where does R come from? <ul><li>Start with the DGM: </li></ul>Rearrange and solve for R:
    22. 22. Where does R come from? <ul><ul><li>R = Div 1 /P 0 + g </li></ul></ul><ul><li>The discount rate can be broken into two parts. </li></ul><ul><ul><li>The dividend yield </li></ul></ul><ul><ul><li>The growth rate (in dividends) or capital gain yield </li></ul></ul><ul><ul><li>In practice, there is a great deal of estimation error involved in estimating R. </li></ul></ul>
    23. 23. <ul><li>A Healthy Sense of Skepticism </li></ul><ul><ul><li>Estimate of g is based on a number of assumptions: </li></ul></ul><ul><ul><ul><li>return on reinvestment </li></ul></ul></ul><ul><ul><ul><li>future retention ratio </li></ul></ul></ul><ul><ul><li>Some financial economists suggest calculating the average R for an entire industry . </li></ul></ul>
    24. 24. Two polar cases <ul><li>Case1: A firm paying no dividend , and going from no dividends to a positive number of dividends </li></ul><ul><li>Case2: An analyst whose estimate of g for a particular firm is equal to or above R must have made a mistake. </li></ul>
    25. 25. 5.6 Growth Opportunities <ul><li>Imagine a company with a level stream of earnings per share in perpetuity </li></ul><ul><li>The company pays off these earnings out to stockholders as dividends . Hence. </li></ul><ul><li>EPS = Div (Cash cow) </li></ul><ul><li>It’s value equals </li></ul><ul><li>EPS/r = Div/r </li></ul>
    26. 26. <ul><li>Growth opportunities are opportunities to invest in positive NPV projects . </li></ul><ul><li>Suppose the firm retains the entire dividend at date 1 in order to invest in a particular capital budgeting project </li></ul><ul><li>Stock Price after Firm Commits to the New Project: EPS/r + NPVGO </li></ul>
    27. 27. Example <ul><li>EPS/r + NPVGO </li></ul><ul><li>= 【〔 $1,000,000/1.1 〕 + 〔 $1,000,000/(1.1) 2 〕 +…+ 〔 $1,000,000/(1.1) n 〕】 + 【〔 -$1,000,000+( $210,000/0.1 ) 〕 /1.1 】 </li></ul><ul><li>= 〔 $1,000,000/0.1 〕 + 〔 -$1,000,000 + ($210,000/0.1 ) 〕 / 1.1 = $ 10,000,000 +$ 1,000,000 = $11,000,000 The price per share: </li></ul><ul><li>$11,000,000/100,000 = $110 </li></ul>
    28. 28. <ul><li>Two conditions must be met in order to increase value: </li></ul><ul><ul><li>Earnings must be retained so that projects can be funded. </li></ul></ul><ul><ul><li>The projects must have positive net present value . </li></ul></ul>
    29. 29. Growth in Earnings and Dividends versus Growth Opportunities <ul><li>A policy of investing in projects with negative NPVs rather than paying out earnings as dividends will lead to growth in dividends and earnings , but will reduce value . </li></ul>
    30. 30. Dividends or Earnings : Which to discount? <ul><li>Dividends , or would ignore the investment that a firm must make today in order to generate future returns. (only a portion of earnings goes to the stockholders as dividends) </li></ul>
    31. 31. The No-Dividend Firm <ul><li>A firm with many growth opportunities faces two choices: pays out dividends now, or forgoes dividends now and makes investments. </li></ul><ul><li>The actual application of the dividend discount model is difficult for firms of this type. </li></ul>
    32. 32. 5.7 The Dividend Growth Model and the NPVGO Model <ul><li>A steady growth in dividends results from a continual investment in growth opportunities, not just in a single opportunity. </li></ul>
    33. 33. 5.7 The Dividend Growth Model and the NPVGO Model <ul><li>We have two ways to value a stock: </li></ul><ul><ul><li>The dividend discount model </li></ul></ul><ul><ul><li>The sum of its price as a “cash cow” plus the per share value of its growth opportunities </li></ul></ul>
    34. 34. Example <ul><li>C has EPS of $10 at the end of the first year, a dividend-payout ratio of 40%, a discount rate of 16%, and a return on its retained earnings of 20%. </li></ul>
    35. 35. Solution <ul><li>The Dividend-Growth Model </li></ul><ul><li>P 0 = Div 1 /(R-g) </li></ul><ul><li>The NPVGO Model </li></ul><ul><li>P 0 = EPS/R + NPVGO (5.10) </li></ul>
    36. 36. The Dividend-Growth Model <ul><li>Div 1 /(R-g) = $4/(.16-.12) </li></ul><ul><li>=$100 </li></ul>
    37. 37. Solution <ul><li>The NPVGO Model </li></ul><ul><ul><li>Value Per Share of a Single Growth Opportunities -$6 + $1.20/0.16 = $1.5 </li></ul></ul><ul><ul><li>Value Per Share of All Opportunities NPVGO = $1.50/(0.16-0.12) =$37.50 </li></ul></ul><ul><ul><li>Value Per Share if Firm Is a Cash Cow Div/r = $10/0.16 = $62.50 </li></ul></ul><ul><ul><li>Summation P 0 = EPS/r + NPVGO = $62.5 + $37.5 = $100.0 </li></ul></ul>
    38. 38. 5.8 Price-Earnings Ratio <ul><li>Many analysts frequently relate earnings per share to price. </li></ul><ul><li>The price-earnings ratio is calculated as the current stock price divided by annual EPS . </li></ul>
    39. 39. 5.8 Price-Earnings Ratio (P/E ratio) <ul><li>P (Price per share) = EPS/r + NPVGO </li></ul><ul><li>P/E = 1/r + NPVGO / EPS </li></ul><ul><li>The market is merely pricing perceptions of the future, not the future itself. </li></ul><ul><li>It implies that P/E ratio is a function of growth opportunities , risk , and the choice of accounting methods . </li></ul>