《债券与股票估价》PPT课件

1、Chapter 6,Bond Valuation and Stock Valuation,Bond,Stock,Bond Definitions,Bond Par value (face value)（面值） Coupon rate（票面利率） Coupon payment （票面利息） Maturity date（到期期限） Yield or Yield to maturity（到期收益率）,Chapter Outline,Bonds and Bond Valuation More on Bond Features Common Stock Valuation Some Features o

2、f Common and Preferred Stocks,1. Bond Pricing,P193,80 80 80 80 80 80 80 80 80 80,Price=PV (annuity) + PV (Par) = 356.81+463.19 = 1000 Price=Par Only if Coupon rate=Yield to maturity,Present Value of Cash Flows as Rates Change,Bond Value = PV of coupons + PV of par Bond Value = PV annuity + PV of lum

3、p sum Remember, as interest rates increase present values decrease So, as interest rates increase, bond prices decrease and vice versa,When,Coupon rateYield to maturity,Bond Value = PV of coupons + PV of par,Discount bond PricePar,When,Coupon rateYield to maturity,Bond Value = PV of coupons + PV of

4、par,Premium bond PricePar,Valuing a Discount Bond with Annual Coupons,Consider a bond with a coupon rate of 10% and annual coupons. The par value is $1000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond? Using the formula: B = PV of annuity + PV of l

5、ump sum B = 1001 1/(1.11)5 / .11 + 1000 / (1.11)5 B = 369.59 + 593.45 = 963.04,Given up annuity PV = 10(1-1/1.115)/0.11=36.96 The gain from lower price than par compensates the loss from below-market coupon rate,Valuing a Premium Bond with Annual Coupons,Suppose you are looking at a bond that has a

6、10% annual coupon and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond? Using the formula: B = PV of annuity + PV of lump sum B = 1001 1/(1.08)20 / .08 + 1000 / (1.08)20 B = 981.81 + 214.55 = 1196.36,Additional gain from higher ann

7、uity PV = 20(1-1/1.0820)/0.08=196.36 The gain from higher price than par reveals the additional gain from higher annuity, thus the bond has more value.,Graphical Relationship Between Price and Yield-to-maturity,YTM,Coupon rate,Price,Bond Prices: Relationship Between Coupon and Yield,If YTM = coupon

8、rate, then par value = bond price If YTM coupon rate, then par value bond price Why? Selling at a discount, called a discount bond If YTM coupon rate, then par value bond price Why? Selling at a premium, called a premium bond,The Bond-Pricing Equation,2. Question from Bond Feature,If there is no pay

9、ment risk Is there any other risk?,Interest Rate Risk,Given other conditions: Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds,Figure 7.2 P197,Long-term bonds have more price risk than short-term bonds,面值（Par）主导,票面利息(Co

10、upon)主导,3. Computing Yield-to-maturity,Yield-to-maturity is the rate implied by the current bond price,YTM with Annual Coupons,Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09. Will the yield be more or less than 10%? N = 15;

11、PV = 928.09; FV = 1000; Coupon = 100 R= 11%,YTM with Semiannual Coupons,P196 Example 7.1,Current Yield vs. Yield to Maturity,现行收益率 Current Yield = annual coupon / price 票面利率 Coupon rate = annual coupon / Par value 到期利率 Yield to maturity = current yield + capital gains yield,来自年金,来自本金,折价债券：CY低，CGY补偿。

12、 折价债券：CY高，CGY损失。,Table 7.1,Bond Pricing Theorems,债券的价格由未来的收益和市场利率决定。由于收益不变，因此由市场利率决定。 对于不同的投资选择，投资者都要求相同的回报率，这是债券、股票定价的基础。,4. Cash Flows for Stockholders,If you buy a share of stock, you can receive cash in two ways The company pays dividends You sell your shares, either to another investor in the m

13、arket or back to the company As with bonds, the price of the stock is the present value of these expected cash flows,One Period Example,Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock f

14、or $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay? Compute the PV of the expected cash flows Price = (14 + 2) / (1.2) = $13.33 Or FV = 16; R = 20%; N = 1; PV = 13.33,Two Period Example,Now what if you decide to hold the s

15、tock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay? PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33,Three Period Example,Finally, what if you decide to ho

16、ld the stock for three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435. Now how much would you be willing to pay? PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 =

17、13.33,Developing The Model,D1,P1,D2,P2,D1,D3,P3,D1,D2,P0,P0,P0,Estimating Dividends: Special Cases,Constant dividend Constant dividend growth Supernormal growth Dividend growth is not consistent initially, but settles down to constant growth eventually,Zero growth model,Dividend growth model Example

18、 8.3 P238,Supernormal growth model Example 8.4 P240,Zero Growth,Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price? P0 = .50 / (.1 / 4) = $20,Dividend Growth Model (DGM),Dividends are expected to grow at a cons

19、tant percent per period. P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + With a little algebra and some series work, this reduces to:,Example 8.3 Gordon Growth Company - I,Gordon Growth Company is expected to pay a dividend of $4 next period and di

20、vidends are expected to grow at 6% per year. The required return is 16%. What is the current price? P0 = 4 / (.16 - .06) = $40,Example 8.3 Gordon Growth Company - II,What is the price expected to be in year 4? P4 = D4(1 + g) / (R g) = D5 / (R g) P4 = 4(1+.06)4 / (.16 - .06) = 50.50 What is the impli

21、ed return given the change in price during the four year period? 50.50 = 40(1+return)4; return = 6% PV = 40; FV = 50.50; N = 4; R= 6% The price grows at the same rate as the dividends,Example 1,Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year.

22、If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? P0 = .50(1+.02) / (.15 - .02) = $3.92,Example 2,Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return i

23、s 20%, what is the price? P0 = 2 / (.2 - .05) = $13.33 Why isnt the $2 in the numerator multiplied by (1.05) in this example?,Stock Price Sensitivity to Dividend Growth, g,Stock Price Sensitivity to Required Return, R,Nonconstant Growth Problem,Suppose a firm is expected to increase dividends by 20%

24、 in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?,0 1 2 3 4 ,+20% +15% +5% +5% ,1,Example Solution,Compute the dividends until growth levels off D

25、1 = 1(1.2) = $1.20 D2 = 1.20(1.15) = $1.38 D3 = 1.38(1.05) = $1.449 Find the expected future price P2 = D3 / (R g) = 1.449 / (.2 - .05) = 9.66 Find the present value of the expected future cash flows P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67,5. Using the DGM to Find R,Start with the DGM:,债券与

26、股票收益率的比较,current yield,capital gains yield,Dividend yield,Capital gains yield,Finding the Required Return - Example,Suppose a firms stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return? R = 1(1.05)/10.50 + .05 = 15%

27、What is the dividend yield? 1(1.05) / 10.50 = 10% What is the capital gains yield? g =5%,Table 8.1 - Summary of Stock Valuation,Features of Common Stock,Voting Rights（投票权） Proxy voting （委托投票权） Other Rights（分享股利/分享资产/决策投票）,Features of Preferred Stock,Dividends Stated dividend that must be paid before

28、 dividends can be paid to common stockholders（优先获得股利） Dividends are not a liability of the firm and preferred dividends can be deferred indefinitely（股利递延） Most preferred dividends are cumulative any missed preferred dividends have to be paid before common dividends can be paid（股利累计） Preferred stock

29、generally does not carry voting rights（无投票权）,Quick Quiz,How do you find the value of a bond and why do bond prices change? How to valuate the price of a stock? What are the zero growth model and Dividend growth model?,Key Concepts and Skills,Know the important bond features and bond types Understand

30、 bond values and why they fluctuate Understand how stock prices depend on future dividends and dividend growth Be able to compute stock prices using the dividend growth model,Summary,Bond pricing Bond interest rate Stock pricing Zero growth model and dividend growth model,练习,债券/面值/票面利息/票面利率/到期期限 到期收

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