Bond Prices and Gordon Growth (1-26-2010)

# Bond Prices and Gordon Growth (1-26-2010) - Gordon Growth...

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Gordon Growth 1 k P D V + + = 1 1 1 0 = = = k P D 1 1 Dividend to be received at the end of the first year. Price at the end of the first year. Required rate of return on the stock. (How do we estimate?)

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Gordon Growth Continued 2 k P D V + + = 1 2 2 1 2 2 2 1 0 ) 1 ( 1 k P D k D V + + + + = If we assume that V1 = P1, we can substitute V1 into the V0 equation to get the following…. . If we follow this logic we can get…. . H H H k P D k D k D V ) 1 ( ..... ) 1 ( 1 2 2 1 0 + + + + + + + =
Gordon Growth Conclusion 3 H H k g D k g D k g D V ) 1 ( ) 1 ( ..... ) 1 ( ) 1 ( 1 ) 1 ( 0 2 2 0 0 0 + + + + + + + + + = Using dividend forecasts, we can solve for intrinsic value as…… Which can be simplified to…… ) ( ) 1 ( 1 0 0 g k D g k g D V - = - + =

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Practice Problem BusMmt 401 Corp. recently paid an annual dividend of \$3/share. Its stock is currently priced at \$45. The expected rate of return on firms in the same industry is 15%. According to the Gordon Growth model, what annual growth rate do investors expect in Allston’s dividends? 4
5 Bond Price P : Price of a T-year coupon bond with a \$100 of principal and coupon C. r : yield-to-maturity Assume that the yield curve is flat. How sensitive is P to changes in r ? T T t t r r C P ) 1 ( 100 ) 1 ( 1 + + + = =

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6 Question: Suppose the current interest rate is 10% and the yield curve is flat. Compute the price of a 3-year, 8% annual coupon bond with a face value of \$100. Compute the change in the price if interest rates rise to 11%. Do the same for a 5-year, 8% coupon bond. Now see what happens if you increase rate further, from 11% to 12%?
7 Answer: Face value =\$100 Coupon (C) = (8%)*100=\$8 per year. Using the following identity, For r =10% Current Price: + - = + + - = + = = T T t t T T t t r r C r C r r r ) 1 ( 1 1 ) 1 ( ) 1 ( 1 1 1 ) 1 ( 1 1 1 03 . 95 \$ ) 10 . 1 ( 100 ) 10 . 1 ( 1 1 10 . 0 8 ) 1 ( 100 ) 1 ( 3 3 3 3 1 3 = + - = + + + = = r r C P t

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8 Answer (Continued): Current Price: Price if r increases to 11%: (a fall of 2.5% in price) 03 . 95 \$ ) 10 . 1 ( 100 ) 10 . 1 ( 1 1 10 . 0 8 ) 1 ( 100 ) 1 ( 3 3 3 3 1 3 = + - = + + + = = r r C P t 67 . 92 \$ ) 11 . 1 ( 100 ) 11 . 1 ( 1 1 11 . 0 8 ) 1 ( 100 ) 1 ( 3 3 3 3 1 3 = + - = + + + = = r r C P t
9 What about a 5-year bond? Current Price: Price if r increases to 11%: (a fall of 3.8% in price) 42 . 92 \$ ) 10 . 1 ( 100 ) 10 . 1 ( 1 1 10 . 0 8 ) 1 ( 100 ) 1 ( 5 5 5 5 1 5 = + - = + + + = = r r C P t 91 . 88 \$ ) 11 . 1 ( 100 ) 11 . 1 ( 1 1 11 . 0 8 ) 1 ( 100 ) 1 ( 5 5 5 5 1 5 = + - = + + + = = r r C P t

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10 Price if r increases further to 12%? Price if
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## This note was uploaded on 02/22/2012 for the course BUS M 401 taught by Professor Toddmitton during the Winter '10 term at BYU.

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Bond Prices and Gordon Growth (1-26-2010) - Gordon Growth...

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