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’ CwLCdeV 4530000 C C(1+g) C(Hg)2 (:{1+g)3 C(1+g)‘5 C(1+g)‘” initial investment at t=0 is $30,000 Let C represent the value of first withdrawal at t=1 (Le. after ﬁrst month)
Total monthly withdrawals T = 48 It is a growing annuity with r = 0.7% and g = 0.3% Present Value (PV) of this annuity should equal $30,000. Pv=—C~§ x [1 — (“iif] = 30000 r— (Li1")T . C __ (1.003)“3 _
"6‘ 00074003 x [1 (1.0030431 _ 30000 Therefore, first monthly withdrawal C = $690.05 Growing Annuity: Cash Flows on time line: 0 1 2 3 T c C(1+g) C(1+g)2 C(1+g}T1 Formula for present value of a growing annuity: [1 — (1:01 \fa.‘ Mann;  v 5L 1
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Problem. MixedCash Flow ; at“, _ b “:3; _ .. .._.. .1, ,.___ an additionai $ 000 (in addition to the $2000).  How much rnone does Trey have in the its? W account now if the ank pays an annual interest of 6% for the ﬁrst 5 years and 8% thereafter? ED $3 ODD m “ab .
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t, a; WKLFVFMﬁﬁiimsi‘g : $30,061.58 @‘Mw : When The was born, his arents estabiished a 43 ban account to he p with his ccliege 6 {I 8? p; expenses “.r “11 0 At the time of his birth, they deposited $5000 in s . a the account f' '83” ii garb @Q/ﬂ
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g  Yesterday {Tre 's 18th birthday) they deposited ® 2' g 3“ (a) I
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"Wt 2.4m ‘ Delayed Perpetuity Problem What is the present value of e perpetuity that
starts paying $1.000 annually after three years?
The time value of money is 10% (annual) until I =
3 years. decreases to 8% (annual) for the next 10 years and further decreases to 5% (annual)
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bummer. 3 Farms Weill 71mi ‘3 51 “VF{922% a) How much money will you have in your bank acoountdmLBW if you make ten
annual epos'rte of $100,000 st ' ?
The bank pays an annual (state interest of
10%, mmundedjemtamualw. Answer: $7,685,563 (,.e021cL1a—.10L$)“=$5M m age,
Q €195,059 b) How much should each of the ten de osits be
if you want to have $5 million after 2 years? Answer: $65,056 mhmao Wefk w'r’k Ll (team! Places, rm 2 Mutual PM : L3o'z‘7.il§( willie3X
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This note was uploaded on 01/15/2010 for the course FIN 357 taught by Professor Hadaway during the Fall '06 term at University of Texas at Austin.
 Fall '06
 Hadaway
 Corporate Finance

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