1. CHAPTER 5 How to Value Bonds and Stocks

12. Level-Coupon Bonds: Example PMT I/Y FV PV N PV 31.875 = 5 1,000 – 1,070.52 12 Find the present value (as of January 1, 2004), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent. 1,000 ×0.06375 2

14. YTM and 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. 800 1000 1100 1200 1300 $1400 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 6 3/8

15. Maturity and Bond Price Volatility Consider two otherwise identical bonds. The long-maturity bond will have much more volatility with respect to changes in the discount rate C Discount Rate Bond Value Par Short Maturity Bond Long Maturity Bond

16. Coupon Rate and Bond Price Volatility Consider two otherwise identical bonds. The low-coupon bond will have much more volatility with respect to changes in the discount rate Discount Rate Bond Value High Coupon Bond Low Coupon Bond

19. 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. ) 1 ( Div Div 0 1 g   g r P   1 0 Div 2 0 1 2 ) 1 ( Div ) 1 ( Div Div g g     . . 3 0 2 3 ) 1 ( Div ) 1 ( Div Div g g     .

21. Case 3: Differential Growth Assume that dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter . . . . . . ) (1 Div Div 1 0 1 g   2 1 0 1 1 2 ) (1 Div ) (1 Div Div g g     N N N g g ) (1 Div ) (1 Div Div 1 0 1 1      ) (1 ) (1 Div ) (1 Div Div 2 1 0 2 1 g g g N N N      

22. Case 3: Differential Growth Dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter ) (1 Div 1 0 g  2 1 0 ) (1 Div g  … 0 1 2 N g ) (1 Div 1 0  ) (1 ) (1 Div ) (1 Div 2 1 0 2 g g g N N     … N N +1 …

23. Case 3: Differential Growth We can value this as the sum of: an N -year annuity growing at rate g 1 plus the discounted value of a perpetuity growing at rate g 2 that starts in year N +1            T T A r g g r C P ) 1 ( ) 1 ( 1 1 1 N B r g r P ) 1 ( Div 2 1 N            

24. Case 3: Differential Growth To value a Differential Growth Stock, we can use Or we can cash flow it out. N T T r g r r g g r C P ) 1 ( Div ) 1 ( ) 1 ( 1 2 1 N 1 1                       

26. With the Formula N T T r g r r g g r C P ) 1 ( Div ) 1 ( ) 1 ( 1 2 1 N 1 1                        3 3 3 3 ) 12 . 1 ( 04 . 12 . ) 04 . 1 ( ) 08 . 1 ( 2 $ ) 12 . 1 ( ) 08 . 1 ( 1 08 . 12 . ) 08 . 1 ( 2 $                     P     3 ) 12 . 1 ( 75 . 32 $ 8966 . 1 54 $     P 31 . 23 $ 58 . 5 $   P 89 . 28 $  P

27. A Differential Growth Example (continued) … 0 1 2 3 4 0 1 2 3 The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3 . 08) . 2(1 $ 2 08) . 2(1 $ 3 08) . 2(1 $ ) 04 . 1 ( 08) . 2(1 $ 3 16 . 2 $ 33 . 2 $ 08 . 62 . 2 $ 52 . 2 $  89 . 28 $ ) 12 . 1 ( 75 . 32 $ 52 . 2 $ ) 12 . 1 ( 33 . 2 $ 12 . 1 16 . 2 $ 3 2 0      P

38. 5.9 Stock Market Reporting Gap ended trading at $19.25, down $1.75 from yesterday’s close Gap has been as high as $52.75 in the last year. Gap has been as low as $19.06 in the last year. Gap pays a dividend of 9 cents/share Given the current price, the dividend yield is ½ % Given the current price, the PE ratio is 15 times earnings 6,517,200 shares traded hands in the last day’s trading

39. 5.9 Stock Market Reporting Gap Incorporated is having a tough year, trading near their 52-week low. Imagine how you would feel if within the past year you had paid $52.75 for a share of Gap and now had a share worth $19.25! That 9-cent dividend wouldn’t go very far in making amends. Yesterday, Gap had another rough day in a rough year. Gap “opened the day down” beginning trading at $20.50, which was down from the previous close of $21.00 = $19.25 + $1.75 Looks like cargo pants aren’t the only things on sale at Gap.