4.PV,FV, NPV

1/19/2010 Pranoto.SA 1


Adik – adik, diam sebentar ya…….,Kita kuliah dulu yuck…..

Kita bahas:Future ValuePresent ValueSingle DepositAnnual Deposit Continue

Future Value• FV : Nilai yang akan datang

Contoh:

1Menabung saat ini, dengan rate interest tertentu, berapa nilai tabungan kita 3 tahun yad?

2.Menginvestasikan dana sekarang, menjadi berapa besar dana kita 5 tahun yang akan datang?



1 2 3 n

I I’

FUTURE VALUE ( FV )

1. Single Deposit

I’ = I ( 1+i) n


If : You are age 20, You invest $ 10,000 If : You are age 20, You invest $ 10,000 now, You obtain a compounded return of now, You obtain a compounded return of 6% annually, And withdraw at age 60. 6% annually, And withdraw at age 60. (after N = 40 years), (after N = 40 years), How much you will How much you will receive?receive?

Then you will have $ 102,857. (single Then you will have $ 102,857. (single Dep)Dep)FV = PV (present value) * ( F / P, 6%, 40 )FV = PV (present value) * ( F / P, 6%, 40 )

FV = $ 10,000 * (1,06)FV = $ 10,000 * (1,06)40 =40 = $ 10,000 * 10.2857 = $ 10,000 * 10.2857 = $102,857$102,857

n=40

P P’

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2. Annual Constant Deposit

1 2 3 n

C C C C CC’

C’= C ((1+i)n-1)/i


Invest $ 10,000 Invest $ 10,000 every end yearevery end year for 40 for 40 years,Obtain a compounded return of 6% years,Obtain a compounded return of 6% annually, Withdraw at age 60, annually, Withdraw at age 60, How much you will How much you will receive that?receive that?FV FV = = AV * (F/A, 6%, 40)AV * (F/A, 6%, 40)

FV = $ 10,000 * ( [ (1,06)FV = $ 10,000 * ( [ (1,06)40 40 – 1] / 0.06) – 1] / 0.06)

= $ 10,000 * 154.762 = $ 10,000 * 154.762 = $ 1 547 620= $ 1 547 620

(ann dep continue)(ann dep continue)

(formula for F/A)(formula for F/A) (look at the table)(look at the table)

GUARANTEED TO WORK EVERY TIME ! ACT TODAY !GUARANTEED TO WORK EVERY TIME ! ACT TODAY !n=40


3. Annual Constant Deposit (incomplete series)

1 2 3 j …. n

B B B B

B’

B’=B ((1+i)n-(1+i)n-j)/i


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Invest $ 10,000 Invest $ 10,000 every end yearevery end year for 40 for 40 years,Obtain a compounded return of 6% years,Obtain a compounded return of 6% annually, Withdraw at age 60. annually, Withdraw at age 60. ButBut cause cause of any problem then so you stop deposit of any problem then so you stop deposit after end of year 30. How much $ you will after end of year 30. How much $ you will receive? receive? (ann deposit incontinue)(ann deposit incontinue)FV FV = = A*((1,06)^40-(1.06)^10)/0.06A*((1,06)^40-(1.06)^10)/0.06

FV = $ 10,000 * ( [ (1,06)FV = $ 10,000 * ( [ (1,06)40 40 – (1.06)^10] / 0.06) – (1.06)^10] / 0.06) =$ 1.415.812=$ 1.415.812

GUARANTEED TO WORK EVERY TIME ! GUARANTEED TO WORK EVERY TIME ! ACT TODAY !ACT TODAY !

ContohContoh Lapangan Futzal akan dibangun di daerah Tembalang pada awal Lapangan Futzal akan dibangun di daerah Tembalang pada awal

tahun 2011, dengan biaya investasi cost and benefit sebagai tahun 2011, dengan biaya investasi cost and benefit sebagai berikut :berikut :

Investasi IInvestasi I11 sebesar Rp. 10 Milyar , untuk pembangunan dan sebesar Rp. 10 Milyar , untuk pembangunan dan selesai dalam kurun waktu 2 tahun.selesai dalam kurun waktu 2 tahun.

Operasional (C) diperkirakan Rp. 1 Milyar / tahun, dan Operasional (C) diperkirakan Rp. 1 Milyar / tahun, dan meningkat menjadi 2M sejak Rehabilitasi.meningkat menjadi 2M sejak Rehabilitasi.

Rehabilitasi pada awal th ke 5 dari saat mulai investasi sebesar Rehabilitasi pada awal th ke 5 dari saat mulai investasi sebesar 2M (waktu rehabilitasi abaikan=0)2M (waktu rehabilitasi abaikan=0)

Benefit untuk tahap I(pertama), sebesar Rp. 3 Milyar / tahun, Benefit untuk tahap I(pertama), sebesar Rp. 3 Milyar / tahun, dan meningkat setelah adanya rehabilitasi menjadi 6 M. dan meningkat setelah adanya rehabilitasi menjadi 6 M.

Bila Saudara sebagai investor diberi hak mengelola sampai Bila Saudara sebagai investor diberi hak mengelola sampai tahun 2017, bagaimana pendapat Saudara ?tahun 2017, bagaimana pendapat Saudara ?

Tunjukkan analisa finansial Saudara (FV), diawali dengan Tunjukkan analisa finansial Saudara (FV), diawali dengan gambar cashflow. (Gunakan asumsi bunga pengeluaran : gambar cashflow. (Gunakan asumsi bunga pengeluaran : I,R,C=15%, bunga pemasukan B;10%).I,R,C=15%, bunga pemasukan B;10%).

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04/19/23

14-

18

JAWABAN UTS EKOREK NOV 2010SOAL : 1

Pakai formula Single Deposit: Atau pakai formula (3) dan (2):B1' =3((1.10)^4+(1.10)^3)= 8.39 B1' = 3*((1.1)^5-(1.1)^3))/0.10 8.39B2' =6*((1.1)^2+(1.1)^1+(1.1)^0)= 19.86 B2'= 6*((1.1)^3-1)/0.1 19.86FVb 28.25 28.25

I' =10*(1.15)^7 26.60 I' = 10*(1.15)^7 26.60R' =2*(1.15)^3 3.04 R' = 2*(1.15)^3 3.04C1' =1*((1.15)^5+(1.15)^4) 3.76 C1'= 1*((1.15)^6-(1.15)^4/0.15 3.76C2' =2*((1.15)^3+(1.15)^2+(1.15)^1) 7.99 C2'= 2*((1.15)^4-(1.15)^1)/0.15 7.99

41.39 41.39FV= FVb-FVc = -13.14 FV= FVb-FVc = -13.14Fv negatif, berrti Not Go Fv negatif, berrti Not Go

I RC2

C1C1 C2C2

B2 B2 B2B1 B1

2011 20162014 20152012 2013 2017

1 2 3 4 5 6 7

I1 I2 CC C CC

B B B B B

1 3 4 5 6 72

Two things are equivalent when they produce the same effect.

Example:1.If the money $ 1000 was deposited at 5%

interest compounded annually, value whould be $’=1000(1+0.05)^5=$.1276.28

Its mean that $.1000 today is equivalent to $.1276.28 in 5 years from now.

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P F

n

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Example.2

100

A A

B

A

B B

1 2 4 5 63

177.15

A=40.21

B=53.52

i=10%

$100 today is equivalent of :

- $177.16 received 6 years from now

- 40.21 received at the end of each year for the next 3 years

- 53.52 received at the end of years 4,5,6

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PVFV

FV = PV ( 1+i) ^ n

PV = F V / ( 1+i) ^ n

( 1+i)^ n : compounding Factor

1/(1+i)^n: discounting Factor

PV=?

A A AA

PV=Σ(Ai/(1+i)^n)

Given FV , Find PV ?

Annual Deposit Incomplete

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PPT Selanjutnya

1/19/20101/19/2010 Pranoto.SAPranoto.SA 2020

NPV:Net Present ValueNPV:Net Present Value

NPV = NPV = ΣΣ PVB’- PVB’- ΣΣ PVC’ PVC’

Σ PVB’- Σ PVC’ (>0)

NBC =

Σ PVB’- Σ PVC’ (<0)

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Example:

The Hotel Project will be build withInvesment:10 M , for 1 year construction is finish. Second yearstart to opening with continue cost2 m, and benefit predicted 6MInterst rate 10%, How the project

Prospected? (Check with NPV,NBC)

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IRR; Internal Rate of Return

Value of interest , where’s the value of

NPV = Σ PVB’- Σ PVC’= 0

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4.PV,FV, NPV

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