2. FIN 301-F09 Lab 2 TVM - Time Value of Money Part II...

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Time Value of Money Part II Seminar 2 Present Value, Future Value Annuities, Perpetuities
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TVM Continued… Last time, we looked at some simple  examples of annuities   More complicated examples this time… 2
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Example: Lottery Suppose you win $1,000,000 on a lottery However, the winner cannot collect one million  immediately Instead, you receive  $200,000 right now  and  25   payments of  $40,000  at the  beginning   of each year If the annual discount rate is  5% , what is the lottery  really worth? 3
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Example: Lottery CF decomposition: A lump sum + Annuity ( 29 ( 29 7 $791,945.6 79 . 13 000 , 40 $ 000 , 240 $ 1.05 1 1 0.05 $40,000 $240,000 r 1 1 1 r C $240,000 ) PV(annuity $40,000 $200,000 PV 24 T = = × + = = - × + = = + - × + = = + + = 0 24 2 1 25 $40,000 $40,000 $40,000 $40,000 $200,000  T is equal to No.  of payments   4
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Another Financing Example In 2006 you bought a motorcycle. Currently (Jan 1,  2009), you have 5 payments of $200 remaining on  your financing agreement. Since the time you purchased the motorcycle,  interest rates have dropped and you have the option  of re-financing your motorcycle which would reduce  the payments from $200 to $180.  There is a penalty  of $75 for refinancing payable at the time you  refinance. Assume payments are made annually at the end of  the year and the EAR is 5%. Is it cheaper to refinance or to stick to the original  financing arrangement? 5
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Long version Financing Problem Solution C     $0 $200      $200      $200      $200     $200   R     $75 $180      $180      $180      $180     $180           Jan 1, 2009        Dec 31, 2009       Dec 31, 2010     Dec 31, 2011     Dec 31, 2012   Dec 31, 2013 PV current  = PV refinance  = As the PV of the refinancing option is lower, it is better to refinance. 90 . 865 $ ) 05 . 0 1 ( 200 ) 05 . 0 1 ( 200 ) 05 . 0 1 ( 200 ) 05 . 0 1 ( 200 ) 05 . 0 1 ( 200 5 4 3 2 = + + + + + + + + + 31 . 854 $ ) 05 . 0 1 ( 180 ) 05 . 0 1 ( 180 ) 05 . 0 1 ( 180 ) 05 . 0 1 ( 180 ) 05 . 0 1 ( 180 75 5 4 3 2 = + + + + + + + + + + 6
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Short Version Solution to Financing Problem
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2. FIN 301-F09 Lab 2 TVM - Time Value of Money Part II...

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