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
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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
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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 .
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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
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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
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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.
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Notas del editor
This type of problem separates the “A” students from the rest of the class.
To find the PVGO note that the firm retains $3.50 out of the first year’s earnings to invest at 20%. This results in a positive NPV of $0.875. A growing perpetuity of these positive NPVs is worth $43.75
No, it’s not exactly in the book, but it’s a great big world out there and you don’t want your students to learn this voodoo on the streets do you? Just delete the slide if you want to ignore it (I will).