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Unformatted text preview: in&nite amounts, to get in&nite pro&ts today. Perpetuity P = c 1+ r + c (1+ r ) 2 + c (1+ r ) 3 + ::: = & 1 t =1 c (1+ r ) t = c 1+ r 1 1 & 1 1+ r = c r = : 1 : 1 = 1 A perpetuity pays you a coupon forever. A price of a perpetuity is equal to the price of a bond that pays a coupon for T periods and then returns the principal (see next question). Tenyear Bond Assume the coupon is 10% of the principal, which implies a principal of 1000$. PV ( coupon ) = & T t =1 c (1+ r ) t = c 1+ r 1 & ( 1 1+ r ) T 1 & 1 1+ r PV ( principal ) = c=r (1+ r ) T PV ( bond ) = c 1+ r 1 & ( 1 1+ r ) T 1 & 1 1+ r + c=r (1+ r ) T = c r & 1 1 1+ r T + c=r (1+ r ) T = c r = 100 : 1 = 1000 Here, & 10 t =1 100 (1+0 : 1) t = 614 : 46 , 100 = : 1 (1+0 : 1) 10 = 385 : 54 ; Hence, PV ( bond ) = 614 : 46 + 385 : 54 = 1000 4...
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 Fall '08
 Serra
 Macroeconomics

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