#001a prinsip dasar analisis [2007.05.lastest]

7/24/2019 #001a Prinsip Dasar Analisis [2007.05.Lastest]

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Prinsip dasar analisis investasi

Mine Planning & Investment Analysis

Time Value of Money

Discount Rate

Interest


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Mine Planning Process (1)

Technical Component- Mine layout, euipment pro!uctivity,pro!uction sche!ules etc"

#arro$ %conomic Component- Applies operating & capital cost- che!ules & alternative euipment ineconomic terms ' e"g" price per ton

(roa!ly %conomic Component- Inclu!e financial & )usiness strategy- %*amine ris+ of the proect


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nce a potential mining !evelopment has )eeni!entifie!,

.o$ !oes technical evaluation procee!

accounting for the %conomic of information &the economic of mining

Mining %conomic

Mine Planning is an iterative one The mining cost for any one type of mine

!esign is !erive! from a previous



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5/55


%conomic!ecisionsinmine

planning


6/55


&trategicissuesinmine!ev

elopment


7/55

Time value of money (1)

#ilai uang /purchasing po$er0 )eru)ah)ersamaan !engan peru)ahan $a+tu

1onsep umlah uang

Merupa+an +onsep )esaran matematis )iasa!imana hasilnya ti!a+ tergantung $a+tu"Rp"23"333 /24550 6 Rp"23"333 /24450

1onsep nilai uang

7umlah uang yang )er)e!a $a+tunya!iumlah+an a+an menghasil+an umlah yang)er)e!a"Rp"23"333 /24550 8 Rp"23"333 /24450


8/55


(esarnya nilai uang )ergantung pa!a 9

Discount rate /i0

Rp 233"333 /t6306 233"333 /t620 : /i * Rp 233"3330

7umlah tahun


9/55

;or a !iscount rate of 3, achieving 43< of thetotal present values reuires => years

;or a !iscount rate of =?


10/55


Pengertian time value of moneypenting !alamanalisis e+onomi tam)ang +arena )erha!apan!engan sum)er !aya yang ti!a+ ter)arui"


11/55

1arena +etergantungan a+an $a+tu ma+a cashflo$ C ti!a+ !apat !ioptimasi i+a terisolasi !ari

+eseluruhan !eposit

7i+a lau e+stra+si pa!a minimum cost, cashflo$ C ti!a+ a+an optimal tetapi i+a laue+stra+si pa!a saat MC 6 price, cash flo$ C!apat !ima+simal+an !an $a+tu e+stra+si a+an)er+urang"



12/55

V 6 V /T,R,0

V 6 Present Value

R 6 Availa)le reserve at time T

6 trategy /rate of mining0 that !rfines thesetting of the varia)le affecting V



13/55

.otellingBs rule /24@20

;or the fun!amental principle of the economic

of e*hausti)le resource use"

Resources shall )e !eplete! in such a $ay thatthe rate of the gro$th of value of the e*tracte!

resource shoul! eual the !iscount rate r



14/55

iscount !ate (1)

Analisis Discounte! Cash ;lo$ mengha!apimasalah penentuan nilai !iscount rate yangsesuai

Penentuan actual !iscount rate terlalu +omple+s

A!a )eragam !iscount rate


15/55

iscount !ate (2)

Type of Rate Description

Opportunity cost of capital Foregone benefits that would have been received fromthe next best investment opportunity

Risk-free alternative Return from a risk-free instrument, such as !"!

#reasury bill! $ote that even these instruments are notentirely risk-free because of risks related to the exchangerate and rate of inflation!

%ost of debt & rate based on the cost of borrowed funds

'eighted average cost ofcapital ('&%%)

& risk-ad*usted rate that weighs a firm+s cost of eualityand the cost of debt by the debt-to-euality ratio

istorical rate of return & rate of return based on constant or current performanceof past investments

Risk-ad*usted rate of return &ny rate based on a constant or current return ad*ustedfor pro*ect risk! #he capital asset pricing method(%&./) is often used to determine such a rate!


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iscount !ate (3)

Type of Rate Description

urdle rate &ny specified minimum rate of return, regardless of howderived

"ocial rate of return & rate used to determine the value of social pro*ects! #hisrate accounts for issues of euity and morality as well asfinancial aspects of an investment

0arying discount rate overtime

& rate that reflects changes in risk overtime! Forexample! #he risks can change once all capital has beenrecovered and minimum rate of return achieved

0arying discount rate bycash flow line item

& rate that reflects the difference in risk among variouscash flow components! For example, working capital andinventory charges have lower risks than capital chargesfor new tecnologies


17/55

"nterest (1)

Defnisi interest dalam terminologi ilmu ekonomi

Biaya tambahan yang dikenakan atas sejumlahuang yang dipinjamkan

Biaya sewa untuk peminjaman uang dalamperiode waktu tertentu

interest dinyatakan dalam persentase denganbasis perhitungan umumnya dalam tahun


18/55

;a+tor ' fa+tor mempengaruhi interest

Resi+o

Inflasi

(iaya transa+si

(iaya peluang

Penangguhan +esenangan

"nterest (2)


19/55

terdapat dua jenis interest

Simple InterestBs = P x i

Compound Interest

Bc = P !"#i$r% & PPn = P !"#i$r

keterangan ' i = interest rate !($P = uang di awal tahun !principal$Pn = uang di tahun ke)n

r = tahun

"nterest (3)


20/55

Per#itungan "nterest

Investor meminam uang se)esar Rp 2"333"333+epa!a )an+, uang terse)ut harus !i+em)ali+an

+epa!a )an+ !alam ang+a = tahun !enganinterest ratetahun se)esar E


21/55

Per#itungan $imple "nterest

P % 1&&&

T2% 1&6& ' 6&% 112&

2% 1&&& 6* % 6&

P % 1&&&

T1% 1&&& ' 6& % 1&6&

1% 1&&& 6* % 6&

P % 1&&&

+eterangan ,

P % Pin-aman a.al

% unga pin-aman

T % Total Pin-aman

i % interest rate = 6%$atuan dalam ri/uan

Ta#un & Ta#un 1 Ta#un 2


22/55

Per#itungan 0ompound "nterest (1)

P % 1&&&

T2% 1&6& ' 636% 11236

2% 1&6& 6* % 636

P % 1&&&

T1% 1&&& ' 6& % 1&6&

1% 1&&& 6* % 6&

P % 1&&&

$atuan dalam ri/uan


+eterangan ,

P % Pin-aman a.al

% unga pin-aman

T % Total Pin-aman

i % interest rate = 6%


23/55

P % 1&&&

T2% 1&&& (1'6*)2% 11236

P % 1&&&

T1% 1&&& (1'6*)1% 1&6&

P % 1&&&

$atuan dalam ri/uan


+eterangan ,

P % Pin-aman a.al

% unga pin-aman

T % Total Pin-aman

i % interest rate = 6%

Per#itungan 0ompound "nterest (2)


24/55

"nterest rate nominal dan efetif (1)

%ffective interest rate !inyata+an !alam )asis pertahun

#ominal interest rate !inyata+an !engan r

r

m

rm =

=

11

+=

m

m

r


25/55

#asa)ah men!apat +re!it usaha se)esar Rp =?7uta !engan nominal interest rate !itetap+an

25


26/55

"nterest rate nominal dan efetif (3)

r 6 25 < per tahun

m 6 2= +ali per tahun

Ting+at )unga efe+tif

per tahun234,15

116

2171

11

=

+=

+=

eff

m

eff

m

eff

i

i

m

ri


27/55

aria/el asar "nvestasi

; 6 nilai uang pa!a masa depan"

P 6 nilai uang saat ini"

A 6 pem)ayaran !alam satu seri n pembayaran

yang sama,i 6 ting+at )unga efe+tif per perio!e $a+tu

n 6 perio!e penelaahannya /perio!e $a+tu0


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!umusrumus interest

!*+P i(,n$Capital recoveryP*

!*+- i(,n$Sinking fund-*

!P+* i(,n$Uniform seriespresent worth

*P

!-+* i(,n$Uniform series com-

pound amount*-

.ni/orm series !annuities$ '

!P+- i(,n$Single paymentpresent worth-P

!-+P i(,n$Single payment

com-pound amound!"#i$nP-

Cash 0ows tunggal '

Simbol/aktor

/ungsional

1ama /aktorPersamaanDiberika

n

2encari

ni )1( 1+

i

i n

1)1( +

n

n

ii

i

)1(

1)1(

++

1)1( + nii

1)1(

)1(

++

n

n

i

ii


29/55

Ta/el interest

1&* 11* 12* 13* 14* 15*

1 11&& 111& 112& 113& 114& 115&

2 121& 1232 1254 1277 13&& 1323

3 1331 136 14&5 1443 142 1521

4 1464 151 1574 163& 16 174

5 1611 165 1762 142 125 2&11

6 1772 17& 174 2&2 215 2313

7 14 2&76 2211 2353 25&2 266&

2144 23&5 2476 265 253 3&5

235 255 2773 3&&4 3252 351

1& 254 23 31&6 335 37&7 4&46

ingle Payment Compoun! Amount

InterestFear


30/55

+onvensi iagram lir +as (1)

Garis horisontal !ise)ut s+ala $a+tu, !engan +emauan$a+tu )ergera+ !ari +iri +e +anan"

Tan!a ana+ panah menan!a+an aliran +as !an !itempat+anpa!a a+hir suatu perio!e" Ana+ panah +e atas / 0menggam)ar+an aliran +as positifpenerimaan,ana+ panah+e )a$ah / 0 menggam)ar+an aliran +asnegatifpengeluaran"

Diagram aliran +as tergantung !ari su!ut pan!ang piha+yang menilai" Diagram aliran +as !ari su!ut pan!ang piha+pem)eri pinaman a+an )er)ali+an !engan !ari su!ut

pan!ang peminam"

Aliran +as merupa+an penumlahan aliran +as masu+ /:0!an aliran +as +eluar /-0 pa!a perio!a yang sama /pertahun0"


31/55

+onvensi iagram lir +as (2)

Gam)ar !iagram alir +as untu+ ? tahun" i+a pa!a tahun3 !i+eluar+an uang Rp"2333" setiap tahun men!apat+anuang Rp"233 !an !ia+hir masa proye+ !i!apat uangRp"?33

2333

233 233 233 233 233?33

3 2 = @ H ?


32/55

Perhitungan untuk mendapatkan - berdasarkanP, n periode di masa depan dengan interestrate i per perioda

0 1 2 3 . . . . . .. n

P P (1+i) P(1+i)2

P(1+i)n=F

$ingle Payment 0ompound mount 8actor (1)


33/55

.itung nilai ; @ tahun +e!epan !engan P 6Rp"2"333"333 !an i 6 2=< tahun

; 6 P !-+P "3(,4$

6 2"333"333 /2:2=


34/55

Company has to pay a reclamation )on! to thegovernment for each hectare of lan! !istur)e!" Thefun!s are in trust, earning interest at E< compoun!e!annually, until reclamation is complete, $hereuponthey are returne!" If you !istur) H3 hectares of lan!

this year an! the )on! is ?3,333 per hectare, ho$much !o you e*pect to get )ac+ $hen reclamation iscomplete! in @ yearsB timeJ

Ans$er9 Present value /of money pai! out no$0 ?3,333 * H3

6 =,333,333 Compoun! factor

/2 : 3"3E0@ 6 2"242 ;uture value =,@5=,333

$ingle Payment 0ompound mount 8actor (3)


35/55

Perhitungan untu+ men!apat+an P )er!asar+an ;,n perio!e !i masa !epan !engan interest rate iper perio!a

0 1 2 3 . . . . . ..

n

P = ? F

$ingle Payment Present 9ort# 8actor (1)


36/55


.itung nilai P !ari nilai ; !alam ang+a $a+tu @tahun se)esar Rp"2"333"333 !an i 6 2=< tahun

P 6 ; !P+- "3(,4$

6 2"333"333 K2/2:2=2=0

6 >2="333

Tahun 3 Tahun 2 Tahun = Tahun @

P 6 >2="333 ; 6 2"333"333


37/55

Fou have receive! )i!s from t$o manufacturers forpurchase of a ne$ !ragline" The first )i! is verycompetitive )ut is from a company that reuirespayment in full on placement of an or!er" Thesecon! )i! is for a higher price, )ut no payment is

reuire! until the machine starts !igging @ yearshence" hich is the preferre! optionJ If the first!ragline is purchase!, $hat is the effective return oninvestment for the @ yearsJ

Dragline A )i! price /to!ay0 @3,333,333

Dragline ( )i! price /in @ yearsB time0 H3,333,333 Reuire! return on capital /!iscount rate i0 2?< Ta*ation Ignore Time /n0 @ years



38/55

Ans$er9 Present value of purchasing !ragline ( @ years

H3,333,333 N 3"E?>? 6 =E,@33,333

Thus, !ragline ( has a lo$er cost than !ragline A inpresent value terms"

Compoun! factor for investment in !ragline A vs!ragline (H3,333,333@3,333,333 6 2"@@@@

%ffective return on investment over @ years /2:i0@ 62"@@@@i 6 2"@@@@3"@@@@-26 23"3EH"H33

8(1 16 2) 1

16 2

+


; 6 @"@>H"H33

A 6 2"333"333 A 6 2"333"333 A 6 2"333"333


41/55

Perhitungan untuk mendapatkan P berdasarkanpenjumlahan * selama n perioda dengan interestrate i per perioda

P = ?

0 1 2 3 . . . . . .. .

n

A A A A

:niform $eries Present 9ort# 8actor (1)


42/55

:niform $eries Present 9ort# 8actor (2)

.itung nilai P !engan A se)esar Rp"2"333"333selama @ tahun !engan i 6 2=< tahun

P 6 A !P+* "3(,4$

6 2"333"333

6 2"333"333 /="H3=0

6 ="H3="333

( )

8

8

(1 16 2) 1

16 2 1 16 2

+

+


P 6 ="H3="333 A 6 2"333"333 A 6 2"333"333 A 6 2"333"333


43/55

Perhitungan untuk mendapatkan * selama nperioda berdasarkan - dengan interest rate i perperioda

A = ?

0 1 2 3 . . . . . . .

.

n

A= ?

A = ? A = ?

F

$ining 8und 8actor (1)


44/55


.itung ta)ungan pertahun A selama @ tahununtu+men!apat+an nilai ; 6 Rp"2"333"333 !engan

i 6 2=< tahun

A 6 ; !*+- "3(,4$

6 2"333"333

6 2"333"333 /3"=4E@0

6 =4E"@33

816 2(1 16 2) 1+


; 6 2"333"333

A 6 =4E"@33 A 6 =4E"@33 A 6 =4E"@33


45/55

A contractor has purchase! a ne$ hy!raulice*cavator for a ?-year-life o)" .e e*pects thee*cavator to last 5 years )ut +no$s that he $ill alsohave to perform a maor overhaul on it costing2,333,333 at the en! of the ?-year perio!" The

overhaul cost $ill )e )uilt into the )i! price for theo), $ith annual payments )eing place! in a sin+ingfun! investe! at 5< compoun!e! per year" If thee*cavator $or+s @,333 hours per year, ho$ muchshoul! )e )u!gete! /an! set asi!e0 per hour toprovi!e for the maor overhaulJ

in+ing fun! return on fun!s 5< Ta*ation Ignore for this e*ample Cost of maor overhaul 2,333,333 Time (n0 ? years



46/55

Ans$er9 in+ing fun! factor

6 3"35/2"35?' 206 3"353"HE4@

63"2>3?

%uivalent annual amount to set asi!e6 2,333,333 * 3"2>3?62>3,H?Eyear

.ourly cost6 2>3,H?E@,3336 ?E"5=hour



47/55

Perhitungan untuk mendapatkan * selama nperioda berdasarkan P dengan interest rate iper perioda

A = ?

0 1 2 3 . . . . . . ..

n

A= ?

A = ? A = ?P

0apital !ecovery 8actor (1)


48/55


.itung pen!apatan secara seri tiap tahun /A0 selama @tahun i+a P 6 Rp"2"333"333 !engan i 6 2=< tahun

A 6 P !*+P "3(,4$

6 2"333"333

6 2"333"333 /3"H2E@06 H2E"@33

( )

( )

8

8

16 2 1 16 2

1 16 2 1

+

+


P 6 2"333"333 A 6 H2E"@33 A 6 H2E"@33 A 6 H2E"@33


49/55

The e*pecte! life of a rope shovel is 2E years, after$hich time the mine $ill close an! the salvage value$ill )e effectively Oero" hat is the annual o$ningcost, inclu!ing allo$ance for return on your capitalinveste! in the rope shovelJ If the shovel $or+s

E,333 hours per year, $hat is the hourly costJ

Reuire! return on capital /!iscount rate i0 2?< Ta*ation Ignore for this e*ample Cost of rope shovel >,333,333 Time /n0 2E years



50/55

Ans$er9

Capital recovery factor

6 3"2?

6 3"2?

6 3"2E>4

%uivalent annual cost of shovel over 2E years

6 >,333,333 * 3"2E>4

6 2,2>?,@33year

.ourly cost2,2>?,@33E,333

6 24?"55hour


[ ]14)13!191(1

[ ]1:45!:1


51/55

Salah satu situasi yang sering muncul dalam analisis in5estasi adalah

peningkatan+penurunan pendapatan+ biaya secara gradien selama periodaanalisis6 Dalam analisis ekonomi, permasalahan ini disebut denganarithmatic gradient series

Qntu+ memu!ah+an pemecahan persoalan, arithmatic gradient series!iu)ah mena!i uniform series compound

* = B # g!*+7i,n$ dimana g !*+7i,n$ =

B + (n-

1)g

0 1 2 3 . . . . . . ..

n

B B + g B +

2g

-

rit#matic ;radien $eries (1)

( )

( )

+

+

iii

in

n

n

1

1i1g


52/55

e)uah perusahaan pa!a tahun-2 untung =3 uta"1euntungan terse)ut tiap tahunnya )ertam)ah ? uta rupiahsampai tahun +e-?" .itung +euntungan rata-rata perusahaanterse)ut tiap tahun i+a i62=


53/55

1euntungan rata-rata perusahaan 6 nilai annual

( 6 =3 !an g 6 ?

A 6 ( : g /AGi,n0

6 =3 : ? /AG 2=@

rit#matic ;radien $eries (3)

( )( )

++16!:16!:116!:

1316!:16!:13

3

=5"5>@

3 2 = @ H ?

=5"5>@ =5"5>@ =5"5>@=5"5>@


54/55

0om/ining Time alue 8unctions (1)

.itunglah nilai Present Value pa!a i 6 i

#001a prinsip dasar analisis [2007.05.lastest]

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