NILAI WAKTU UANG �(TIME VALUE OF MONEY)

• Nilai waktu uang

- Uang diterima sekarang dengan jumlah yang sama lebih berharga nilainya dimasa depan.

• Alasan nilai uang sekarang lebih tinggi
• Faktor inflasi
• Faktor bunga
• Faktor ketidakpastian (the uncertainty)
• Kesempatan menggunakan uang tersebut

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Receiving $1 today is worth more than $1 in the future due to The opportunity cost of receiving $1 in the future is the we could have earned if we had received the $1 sooner.

• Translate $1 today into its equivalent in the future (COMPOUNDING).

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• Translate $1 in the future into its equivalent today (DISCOUNTING).

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Compound Value

1. a. Future Value of a Lump Sum (one time payment):

FV_n = PV(1+ i)ⁿ

1.b. Present Value of a Lump Sum (one time payment):

NILAI WAKTU UANG �(TIME VALUE OF MONEY)

NILAI WAKTU UANG �(TIME VALUE OF MONEY)

NILAI WAKTU UANG �(TIME VALUE OF MONEY)

NILAI WAKTU UANG �(TIME VALUE OF MONEY)

Hubungan antara nilai majemuk Future Value (FV),

tingkat suku bunga (i), jumlah tahun (n)

GRAFIK FUTURE VALUE

Present Value ($)

Periode

1,00 -

0,80 -

0,40 -

0,60 -

0,20 -

0

10

20

50

30

40

i = 0%

i = 10%

i = 20%

i = 5%

Hubungan antara nilai Present Value (PV),

tingkat suku bunga (i), jumlah tahun (n).

GRAFIK PRESENT VALUE

Four important variables

FV, PV, i, and n

• When doing problems, you will be given 3 of these variables and asked to solve for the 4^th variable.
• Keeping this in mind makes “time value” problems much easier!

0 n = ?

PV = FV =

i = ?

?

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Example 1: Calculating Future Value �If you invest Rp 100 million now, what is the Future Value of that Rp 100 million one year from now if the bank’s interest rate is 10% / year ?

0 ?

PV = ? FV = ?

i = ?

Example 1: Calculating Future Value �If you invest Rp 100 million now, what is the Future Value of that Rp 100 million one year from now if the bank’s interest rate is 10% / year ?

0 1

PV = 100 FV = ?

i = 10% / year

Example 1: Calculating Future Value �If you invest Rp 100 million now, what is the Future Value of that Rp 100 million one year from now if the bank’s interest rate is 10%/year ?

Solution:

FV₁ = PV x (1 + i)¹

FV₁ = 100 x (1+10%)¹ = Rp 110 million

0 1

PV = 100 FV = 110

i = 10% / year

Example 2: Calculating Present Value �If you will receive Rp 100 million one year from now, what is the Present Value of that Rp 100 million the bank’s interest rate is 10 % per year ?

0 ?

PV = ? FV = ?

i = ?

Example 2: Calculating Present Value �If you will receive Rp 100 million one year from now, what is the Present Value of that Rp 100 million the bank’s interest rate is 10 % per year ?

0 1

PV = FV = 100

i = 10% / year

Example 2: Calculating Present Value�If you will receive Rp 100 million ONE year from now, what is the Present Value of that Rp 100 million the bank’s interest rate is 10 % per year ?

Solution:

PV = FV / (1 + i)ⁿ

PV = 100 / (1+10%)¹ = Rp90.909 million

0 1

PV = -90.909 FV = 100

i = 10% / year

Example 3: Calculating Present Value, multi years�If you will receive Rp 100 million 10 year from now, what is the Present Value of that Rp 100 million the bank’s interest rate is 10 % per year ?

0 ?

PV = ? FV = ?

i = ?

Example 3: Calculating Present Value, multi years �If you will receive Rp 100 million 10 year from now, what is the Present Value of that Rp 100 million the bank’s interest rate is 10 % per year ?

0 10

PV = FV = 100

i = 10% / year

Example 3: Calculating Present Value, multi years �If you will receive Rp 100 million 10 year from now, what is the Present Value of that Rp 100 million the bank’s interest rate is 10 % per year ?

-38.55

0 10

PV = FV = 100

Solution:

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PV = FV / (1 + i)ⁿ

PV = 100 / (1+10%)¹⁰ = Rp 38.55 million

i = 10% / year

Example 4: Calculating interest rate�If you sold land for Rp 120 million that you bought 5 years ago for Rp 50 million, what is your annual rate of return?

Solution:

FV = PV * (1 + i)ⁿ

120 = 50 * (1+ i)⁵

2.4 = (1+i)⁵

(2.4)^1/5 = (1+i) i = 19.14 %

120

50

i = ?

Example 5: Calculating n (number of time periods)�Suppose you placed Rp 100 million in an account that pays10% interest per year. How long will it take for your account to grow to Rp 500 million ?

0 n = ?

PV = FV =

i = 10%/year

500

100

Solution:

FV = PV * (1 + i)ⁿ

500 = 100 * (1+ 0.1)ⁿ

500/100 = (1.1)ⁿ = 5

Ln (1.1)ⁿ = Ln 5

n Ln (1.1) = Ln 5 = 1.60944

n 0.09531 = 1.60944 🡺 n = 16.886 years

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100 x (1.1)^16.886 = 500

NILAI WAKTU UANG �(TIME VALUE OF MONEY)

• Anuitas (annuity)

Pembayaran/ penerimaan uang dalam jumlah yang sama setiap akhir periode (tahun)

Misal menabung untuk pendidikan, pembayaran coupon rate dari obligasi.

Types of Annuity

• Ada dua jenis anuitas yaitu:
• Anuitas biasa atau anuitas akhir periode (ordinary annuity/ deferred annuity) yaitu pembayaran dalam jumlah yang sama atau tetap pada setiap akhir periode (tahun).
• Anuitas jatuh tempo atau anuitas awal periode (annuity due) yaitu pembayaran terjadi pada setiap awal periode (tahun).
• Di dalam manajemen keuangan yang sering digunakaan adalah anuitas biasa 

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NILAI WAKTU UANG �(TIME VALUE OF MONEY)

Anuitas majemuk (future value of annuities/compound annuities)

Rumus:

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• Dimana : FVAn = Future Value Annuities ( nilai masa depan anuitas)

i = Interest rate (tingkat suku bunga tahunan)

n = Jumlah tahun selama anuitas

PMT = The annuity payment

NILAI WAKTU UANG �(TIME VALUE OF MONEY)

Nilai sekarang anuitas (present value of annuity)

Rumus:

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• Dimana : PVA,n = Present Value Annuities (nilai sekarang anuitas masa depan)

i = Interest rate (tingkat suku bunga tahunan)

n = Jumlah tahun selama anuitas

PMT = The annuity payment

NILAI WAKTU UANG �(TIME VALUE OF MONEY)

• Penerimaan tetap yang kekal (perpetuity)

Penerimaan tetap yang kekal (perpetuity) artinya adalah pembayaran tetap/pembayaran dalam jumlah yang sama untuk selamanya.

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• Dimana: PV = Nilai sekarang (Present value) dari perpetuity

PP = Jumlah uang yang tetap yang diberikan perpetuiy

i = Tingkat suku bunga (discount rate) pertahun

SOAL

. Penerimaan perpetuitas sebesar Rp 1.000.000,- yang didiskontokan kembali kemasa sekarang dengan tingkat 4%, berapa nilai sekarang (Present Value)

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APPLICATIONS OF TIME VALUE OF MONEY

• Mortgage (KPR) and car loan payments
• Life insurance
• Personal Financial Planning
• Time deposit
• Contract values
• Damages in court cases
• Investment values
• Company values

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