02a-timevaluemoney 2013
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TIME VALUE OF MONEYsyamsul irham
TIME VALUE of MONEY
Economic basis to
evaluate engineeringprojects
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Learning Objective
After this class the studentsshould be able to:
•Understanding andCalculating Time Value ofMoney and Its Applications
•Define the interest rate forcalculating the time value of
money
•Contrast simple andcompound interest
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Warm-up ( !"
!# If $ou %a& t%e po''ibiit$ to receive ) !*+***#** no, oranot%er amount one $ear from no,+ %o, muc% ,ou& $ouie to receive one $ear from no,.
/# T%e engineering group of 0aer 1e'ign' mu't &eci&e,%et%er to 'pen& )2*M (M for t%ou'an&'" on a ne, project#T%i' project ,i co't )3M per $ear for operation'+ an& it ,iincrea'e revenue' b$ )/*M annua$# 0ot% t%e co't' an& t%erevenue' ,i continue for !* $ear'# 4%ou& t%e project be&one.
Eac% per'on %a' a &ifferent an',er for t%e'e 5ue'tion'+ butt%e interaction among peope in t%e financia maret+ un&ert%e 'ame con&ition+ offer u' on$ one an',er+ ,%ic% can be&etermine& t%roug% t%e intere't rate#
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Warm-up ( /"
6 A &oar to&a$+ a &oar a $ear from no,+
an& a &oar !* $ear' from no, &iffer in
vaue# T%e'e &oar' t%at occur at &ifferenttime' mu't be combine& to evauate
engineering project'# 7o, i' t%e &ifference
in vaue &ue to t%e time vaue of mone$accounte& for.
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8e$ Wor&' an& 9oncept'
6 Interest : T%e return on capita#6 Capital : Inve'te& mone$ an& re'ource'
6 Cash Flow diagram : T%e pictoria &e'cription of,%en &oar' are receive& an& 'pent#
6 Equivalence Occurs : ,%en &ifferent ca'% fo,' at&ifferent time' are e5ua in economic vaue at agiven intere't rate#
6 Present worth : A time * ca'% fo, t%at i'e5uivaent to one or more ater ca'% fo,'#
6 Nominal interest rate : T%e rate per $ear ,it%outa&ju'ting for t%e number of compoun&ing perio&'#
6 Effective interest rate : T%e rate per $ear aftera&ju'ting for t%e number of compoun&ing perio&'
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!#!# W%at i' Intere't.
6 Intere't i' a renta fee for mone$: t%at i'+ afee pai& or a fee earne& for t%e u'e ofmone$#
6 Engineering econom$ generai;e' t%i'&efinition# Intere't i' t%e return on 9apita#9apita+ in turn+ i' inve'te& mone$ an&re'ource'# #
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Intere't
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Intere't
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Intere't rate an&
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Intere't an& t%e time vaue of mone$
Intere't i' u'e& to cacuate t%e time
vaue of mone$+ an& it i' crucia to t%e
practice of engineering#
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!#/# 0UN>A 4E1E
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Contoh 1:Contoh 1:Contoh 1:Contoh 1:
$ 10.000 dipinjam dari sebuah bank dengan bunga
16%/thn. ika utang tersebut diba!ar pada
pertengahan tahun" berapa jumlah !ang harus
diba!ar #
aab : aab : aab : aab :
! " # $% & in' " %(((( $% & (%)*(+'" , %(-((
.imple Interest
1.2. BUNGA SEDERHANA (Simple interest)
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!#?# 0unga Majemu (compoun& intere't"
ilai bunga !ang dihasilkan pada akhir setiap periode
ditambahkan kembali pada pokok pinjaman semula.
&p. 1000"' disimpan dengan tingkat bunga (% per tahun"
pada akhir tahun ke tiga uang tersebut akan menjadi &p.
11()"6"'
Nilai uang pada masa datang dirumuskan :
F = P (1+i)n F = P = P (F/P, i%, n)
(1+i)n = = (!"#i$#n) % &uture 'alue &atr
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Perubahan nilai uang terhadap waktu untuk kasus tertentu dapat
dirumuskan pada Tabel-1 berikut :
Perubahan nilai uang terhadap waktu untuk kasus tertentu dapat
dirumuskan pada Tabel-1 berikut :
o.o. *aktor*aktor *ormula*ormula otasiotasi
1. Pembayaran Tunggal Bunga Berbunga (CompoundAmount Factor)
$ % & i ' n$!/#0 i 10 n'
2. Pembayaran Tunggal Nilai Sekarang (Preent !alueFactor)
$ % & i ' 2 n$#/!0 i 10 n'
". Pembayaran #ni$orm (Serie Compound AmountFactor). $% & i 'n
– %i
$!/A0 i 10 n'
%. Simpanan Teratur (Sinking Fund Factor). i$% & i 'n – %
$A/!0 i 10 n'
&. Penerimaan Teratur (Capital 'ecoery Factor).i $ % & i ' n
$% & i 'n-%
$A/#0 i 10 n'
. Nilai ekarang pembayaran uni$orm (erie P!) $% & i 'n – %i $% & i 'n
$#/A0 i 10 n'
*. +radient #ni$orm % n n i $% & i 'n – %
$A/30 i 10 n'
,. +radient Preent !alue. % – $% + ni' / $1+i'n
i 2$#/30 i 10 n'
# " a present lump sum of money
! " a future lump sum of money $received n periods from no4'
A " an end of period payment or received in a uniform series continuing for n periods
Tabe bunga @ ormua Niai Watu &ari UAN>
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ContohContoh 11 ::ContohContoh 11 ::
+ang sebesar &p. 1.000.000"' jika disimpan selama , tahun
dengan tingkat bunga 10% per tahun akan menjadi :
aab : aab : aab : aab :
F = P (F/P, i %, n) = P (F/P, 10%, ) = P (1!i) n = P (1!0,10)
= "p# 1#000#000 $ (1!0,10)
= "p# #1&'#00,-
Present alue *a+trInterest Rate & TIME VALUE OF MONEY Interest Rate & TIME VALUE OF MONEY
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Contoh - :Contoh - :Contoh - :Contoh - :
+ang sebesar &p. 1.000.000"' !ang diterima , tahun mendatang
dengan tingkat bunga 10 persen per tahun" nilai sekarangn!a
adalah :
aab : aab : aab : aab :
P = F (P/F, i %, n)
= F (P/F, 10%, )
= F (1!i) -n
= "p# 1#000#000 $ (1!0,10)-
= "p# 1#000#000,- $ (0,&)
= "p# �,-
5
6p%((((((
% 7 8 +9 ) -
Present .alue *a+trInterest Rate & TIME VALUE OF MONEY Interest Rate & TIME VALUE OF MONEY
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Contoh ( :Contoh ( :Contoh ( :Contoh ( :
ika anda ingin menjadi seorang milioner 0 tahun dari sekarang "
berapa !ang harus ditabung setiap bulan jika bunga bank 1
%/bulan #
aab : aab : aab : aab :
F = # 1#000#000
i = 0#01 per bulan
n = (0)(1) = &0
2 = 3
2 = F (2/F, i %, n) = 1#000#000 $ 0#01/4(1!0#01)&0 -15 = 1#000#000# (2/F, 0#01, &0)
2 = 1#011
inking *und *a+tr (simpanan teratur)
Interest Rate & TIME VALUE OF MONEY Interest Rate & TIME VALUE OF MONEY
Simpanan Teratur (Sinking Fund Factor). i$% & i 'n – %
$A/!0 i 10 n'
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Contoh 6 :Contoh 6 :Contoh 6 :Contoh 6 :
ika kita mengharapkan mempun!ai tabungan seban!ak &p.
10.000.000"' pada akhir tahun kedelapan dengan tingkat bunga 10
persen per tahun" maka tiap tahun kita harus menabung :
aab : aab : aab : aab :
2 = F (2/F, i %, n)
= F (2/F, 10%, )
= "p# 10#000#000 $
= "p# 10#000#000,- $ (0,06&)
= "p# 6ʼ,-
0,10
(1!0,10) - 1
Interest Rate & TIME VALUE OF MONEY Interest Rate & TIME VALUE OF MONEY
inking *und *a+tr (simpanan teratur)
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Contoh ) :Contoh ) :Contoh ) :Contoh ) :
ika kita meminjam &p. 10.000.000"' dengan bunga 1( persen per
tahun dan hendak melunasin!a selama 10 tahun" maka tiap tahun
harus memba!ar :
aab : aab : aab : aab :
2 = P (2/P, i %, n)
= P (2/P, 1%, 10)
= "p# 10#000#000 $
= "p# 10#000#000,- $ (0,177)
= "p# 1#770#000,-
0,1 (1 ! 0,1) 10
(1!0,1)10
- 1
Penerimaan teratur (+apital re+er8 *a+tr)Interest Rate & TIME VALUE OF MONEY Interest Rate & TIME VALUE OF MONEY
Penerimaan Teratur (Capital 'ecoery Factor). i $ % & i 'n
$% &i
'n-
%
$A/#0 i 10 n'
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Contoh , :Contoh , :Contoh , :Contoh , :
ika kita memba!ar cicilan &p. 1.000.000"' per tahun dengan
bunga 1(% per tahun selama 10 tahun" maka nilai sekarangn!a
adalah :
aab : aab : aab : aab :
P = 2 (P/2, i %, n)
= 2 (P/2, 1%, 10)
= "p# 1#000#000 ,
= "p# 1#000#000,- $ (,017)
= "p# #017#000,-
(1!0,1)10 - 1
0,1 (1 ! 0,1) 10
Interest Rate & TIME VALUE OF MONEY Interest Rate & TIME VALUE OF MONEY
Nilai ekarang pembayaran uni$orm (erie P!) $% & i 'n – %i $% & i 'n
$#/A0 i 10 n'
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abel *ormula ubungan erbagai *aktor ungaabel *ormula ubungan erbagai *aktor ungaabel *ormula ubungan erbagai *aktor ungaabel *ormula ubungan erbagai *aktor unga
oo..
*aktor*aktor ubunganubungan
1. (F-P) dan P-F) $!/#0 i 10 n' " % / $#/!0 i10 n'
2. (F-A) dan (A-F) $!/#0 i 10 n' " % / $A/!0 i10 n'
". (A-P) dan (P-A) $A/#0 i 10 n' " % / $#/A0 i10 n'
%. (A-P) dan (P-A)
n
$ P / A0 i 10 n' " & / $# / !0 i10 t' t"%
&. (P-A) dan (P-F) n;%$ F / A0 i 10 n' " % & $ F / P 0 i10 t' t"%
. (F-A) dan (F-P) $A/#0 i10 n' " $A/!0 i10 n' & i1
Interest Rate & TIME VALUE OF MONEY Interest Rate & TIME VALUE OF MONEY
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Fui;
6 0uat Tabe Cre'ent Vaue actor (!Gi"-n
6 Untu intere't rate i @ 3= &an /3 =
6 1engan n @ 3 + !*+ !3+ &an /3 ta%un6 Cot &aam 'et'a grafi @ Cre'ent Vaue
actor v' n+ untu ma'ing-ma'ing intere't
rate i
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En& Vie,
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