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Lecture: 3 - Stock and Bond Valuation How to Get a “k” to Discount Cash Flows - Two Methods I.Required Return on a Stock (k) - CAPM (Capital Asset Pricing.

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Presentation on theme: "Lecture: 3 - Stock and Bond Valuation How to Get a “k” to Discount Cash Flows - Two Methods I.Required Return on a Stock (k) - CAPM (Capital Asset Pricing."— Presentation transcript:

1 Lecture: 3 - Stock and Bond Valuation How to Get a “k” to Discount Cash Flows - Two Methods I.Required Return on a Stock (k) - CAPM (Capital Asset Pricing Model) or Other Securities k = r f + B(r m - r f ) where r f = Risk-Free Rate B = Beta (Risk Measure) r m = Expected Market Return Example: k =.05 + 2(.12 -.05) =.19 II. Risk Premium Approach k b = R b = r real + r risk + E(I) = Productivity Growth + Risk Premium + Expected Inflation = 2 - 4% + 0 - 10% + 2 - 6% (Estimates)

2 Lecture: 3 - Stock and Bond Valuation III.Bond Valuation Bond = Annuity Plus Single Par Payment (often Semi-Annual Payments) a. Par Value -face value, maturity value - usually $1000 b. Coupon Interest Rate - stated as a % of Par - 10%coupon on $1000 par => coupon = $100. c. Maturity - length of time until Par value is paid off

3 Lecture: 3 - Stock and Bond Valuation

4 Bond Valuation “A Bond is an Annuity Plus a Single Face Value Payment” Annual Coupon Lecture 3 - Stock and Bond Valuation I.Bond Valuation General Formula B 0 = I[PVA k,n ] + M[PV k,n ] B 0 = Bond Price I = Interest (coupon) Payment M = Par Value II.Example: Suppose a bond offers a 10% coupon, on $1000 par, for 3 years, and the expected inflation rate is 2%, the real rate is 3% and the bond’s risk is 1%. What is its price? B 0 = $100[PVA.06,3 ] + $1000[PV.06,3 ] = $100(2.673) + $1000(.84) = $1107

5 QUESTION: If the company only agrees to pay $1000 at maturity, won’t those who buy this bond lose $107 at maturity? QUESTION: Would you buy this bond? Why? - greater coupon than par bonds. A par bond would cost $1000 but only pays a $60 coupon. The present value of the difference in coupons (100 - 60)(2.673) = 107 which is the difference in price between this bond and a par bond. Alternatively, a bond that offered a 2% coupon when rates are 6% will have a price of B 0 = 20[PVA.06, 3 ] + 1000[PV.06, 3 ] = 893 or $107 less than the par bond.

6 Bond Valuation “A Bond is an Annuity Plus a Single Face Value Payment” Semi-Annual Coupon Lecture 3 - Stock and Bond Valuation I. Adjustments For Semi-Annual Coupon Bonds a. n = the number of semi-annual payments (maturity x 2) b. k = one-half the bond’s annual yield c. I = one-half the bond’s annual coupon II.Example: Suppose a bond pays 10% coupon, semi-annually, has 10 years until maturity and has a required return (or Yield to Maturity) of 8%. What is its price? B 0 = $50[PVA.04,20 ] + $1000[PV.04,20 ] = $50(13.59) + $1000(.456) = $1135.5 QUESTION: Consider two identical bonds except that one pays an annual coupon and the other a semi-annual coupon. Which should have the higher price? ANSWER: The semi-annual bond.

7 YIELD TO MATURITY - The return one can expect on an investment in a bond if the bond pays all its coupons and par and yields do not change after you purchase the bond. PROBLEM: Suppose you observe a bond in the market with a price of $803 that pays a coupon of 10% till maturity in 5 years. What is its implied yield to maturity? Try 16% 803= 100(PVA ?,5 ) + 1000(PV ?,5 ) = 100(3.274) + 1000(.476) = 803 REALIZED YIELD - The actual return one receives on the initial investment in a bond. QUESTION: If you buy a 20% coupon, par bond, with 3 years maturity and you hold it for three years are you sure to earn 20%? ANSWER: No because the calculation of YTM assumes that the coupons are reinvested at 20%, if rates change your realized yield will change because you'll earn more or less than 20% on their reinvested coupons. Yield to Maturity and Realized Yield Lecture 3 - Stock and Bond Valuation

8 Example: When you bought the bond, YTM was 20%. But suppose rates fell to 5% the day after you bought and stay there for three years. Your realized yield will be: use PV = FV[PV k,n ] 1000 = (200(1+.05) 2 + 200(1+.05) + 1200)[PV k,3 ] = 1630.5[PV k,3 ] => 1000/1630.5 = [PV k,3 ] =.6133 => k = 17% realized yield falls when reinvestment rate falls QUESTION: Then how can you truly lock-in a rate? ANSWER: Buy a bond with no coupons - called zero coupon bonds. QUESTION: How would you price a zero coupon bond? ANSWER: Use the second term in the bond pricing formula. QUESTION: Some find this attractive but is there a problem with being locked-in? ANSWER: Yes. How about if rates rise. You lose out on earning extra interest on reinvested coupons.

9 Stock Valuation “Valuation is Based Upon Expected Dividend Flow and the Future Expected Market Value of the Stock” Lecture 3 - Stock and Bond Valuation I.Common Stock Valuation General Formula P 0 = E(D 1 )/(1+k e ) + E(D 2 )/(1+k e ) 2 +... + E(D n )/(1+k e ) n + E(P n )/(1+k e ) n where E means expectation, D t means dividend at time t, P means stock price, and k e is the cost of equity. II.Example: Suppose a firm pays $4 in Dividends, which will increase by $1 in each of the next 3 years and we expect the price to be $30 at the end of the 3rd year. Assume stock beta = 1, the risk free rate is 10%, and the expected market return is 15%. What is the stock price? K e =.10 + 1(.15 -.10) P 0 = $4/(1.15) + $5/(1.15) 2 + $6/(1.15) 3 +$30/(1.15) 3 = $4(.87) + $5(.756) + $6(.658) + $30(.658) = $30.94

10 Stock Valuation - Constant Growth “Valuation is Based Upon Expected Dividends That Grow at a Constant Rate For Ever” Lecture 3 - Stock and Bond Valuation Constant Growth Discounted Cash Flow Model, or DCF. P 0 = = where D 0 = present dividend paid at time 0 D 1 = dividend expected at time 1 g = constant future growth in dividends k = required return (discount rate) Note: Works only for k>g and dividend paying firm PROBLEM: Suppose a company will pay a dividend of $5 in one year, has a required return of 10% and dividends grow 5% per year. What is the stock price? P = Mixture of Dividends PROBLEM: Suppose a firm will pay a dividend of $5 per year for 5 years and then increases the dividend by 10% per year thereafter. The firm has a required return of 15%. What is its price now? P = 5(PVA.15, 5 ) + [PV.15, 5 ] = 5(3.352) + 110(.497) = 71.43

11 PROBLEM: Suppose we know the price of the stock in the market is $80, and it pays a dividend of $3 that will grow by 10% per year. What is the return the market requires on the stock? k = = =.14 Stock Valuation - Implied Required Returns and Growth Rates “Just Manipulate the Constant Growth Formula” Lecture 3 - Stock and Bond Valuation PROBLEM: If the market price of a stock is $50, its required return is 15 percent and next year’s dividend is expected to be $5, by what percent must the market expect the company’s dividends to grow. g = k - so g =.15 - =.05

12 PRICE-EARNINGS RATIOS “PE’s Are Commonly Used to Compare Stocks” Lecture 3 - Stock and Bond Valuation PE Ratio - This is the number of dollars investors are willing to pay for each dollar of a company’s earnings. You can use the growth model to see why stocks have different price-earnings ratios P = = => = where E= earnings per share d = dividend payout ratio = Clearly, a larger growth rate and payout ratio and a smaller discount rate (k) makes for a larger price earnings ratio.


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