Time Value of Money

1. The Time
Value of
Money

2. Time Value of Money
01

3. Understanding of Time Value of Money
Faktor
Pendukung TVM
Konsep Time Value of
Money (TVM)
Mengapa TVM itu
penting ?
1. Opportunity Cost
2. Inflation
Sejumlah uang yang dimiliki
saat ini memiliki nilai lebih
tinggi dibandingkan uang
dalam jumlah serupa di masa
depan.
● Menjadi dasar perhitungan Net Present
Value (NPV)
● Membantu membuat keputusan
investasi
● Menghitung dan membuat anggaran
produksi, product development, hingga
inovasi bagi pemilik usaha
● Membantu perencanaan tabungan bagi
nasabah bank

4. Timelines
02
~time 0 is today ~

5. Timelines

6. Future Value
& Compounding
03

7. Formula Approach
Future Value
FV : Future
Value
PV : Present
Value
I : Interest
Rate
N : Number of
Period
Jumlah arus kas atau
serangkaian arus kas yang
akan tumbuh selama
periode waktu tertentu
ketika dimajemukkan pada
tingkat bunga tertentu
FV & Compounding
Compounding
Proses aritmatika dengan
menentukan nilai akhir dari
arus kas atau serangkaian
arus kas ketika bunga
majemuk diterapkan.
File Excel Latihan
https://bit.ly/ExcelTVM

8. Present Value
& Discounting
04

9. Formula Approach
Present Value
FV : Future
Value
PV : Present
Value
I : Interest
Rate
N : Number of
Period
Nilai saat ini dari arus kas
masa depan atau
serangkaian arus kas.
PV & Discounting
Discounting
Proses menemukan nilai
saat ini (PV) dari arus kas
atau serangkaian arus kas;
discounting kebalikan dari
compounding

10. Annuity
05
~ equal/constant payment, fixed
intervals, specified periods ~

11. Annuities
Annuity
A series of equal payments at fixed
intervals for a specified number of
periods
Ordinary Annuity
An annuity whose payments occur at the
end of each period
Annuity Due
An annuity whose payments occur at the
beginning of each period

12. Ordinary Annuity
Future Value (FVA)
PMT : Payment
I : Interest Rate
N : Number of Period
Present Value (PVA)
PMT : Payment
I : Interest Rate
N : Number of Period

13. Annuity Due
Future Value of An Annuity Due
FVAdue = FVAordinary(1+I)
FVAdue : FV Annuity Due
FVAordinary : FV Ordinary Annuity
I : Interest Rate

14. Perpetuity
06
~ annuity with an unlimited time ~

15. Perpetuity - Equal Payment
What is Perpetuity ?
an annuity in which the periodic payments
begin on a fixed date and continue
indefinitely
Formula mencari PV pada perpetuity
Contoh:
1. UK Government Bond known as a Consol.
Pemegang Consol gets annual fixed coupons
(interest payments) as long as they hold the
amount and the government does not
discontinue the Consol.
2. In the real-estate sector: The owner is entitled to
an infinite stream of cash flow from the renter as
long as the property continues to exist (assuming
PV = present value
PMT = amount of continuous cash payment
I = interest rate

16. CFt = cash flow pada periode t
I = interest rest
Perpetuity - Uneven Cash Flow
- a stream that consist of a series of annuity payments PLUS an additional final lump sum
- payment disimbolkan dengan PMT
Uneven (Non-constant Cash Flow)
A series of cash flows where the amount varies from one periode to the next
1. Annuity plus additional final payment
- uneven streams
- payment / cash flow disimbolkan dengan CFt
2. Irregular cash flow

17. Semi Annual and Other
Compounding Periods
07
~ interest added more than once
in a year ~

18. Annual Compounding Periods
Annual Compounding
interest is added once a year
Formula FV pada Annual Compounding
PV = present value
PMT = amount of continuous cash payment
I = interest rate
Semiannual Compounding
interest is added twice a year or every 6 months

19. Rumus konversi:
Untuk selain periode Tahunan (annual), maka:
Semiannual Compounding Periods
1. Konversikan interest rate (annual rate) menjadi periodic rate
2. Konversikan jumlah tahun (number of years) menjadi “numbers of periods”
M = number of payment periods per year

20. Fractional Time Period
08

21. disimbolkan r
daily, monthly, quarterly, semi annually
Formula
Assumed payment beginning or the end of periods but not within periods
M = number of compounding periods
disimbolkan n

22. Interest rate (‘r’) berbagai time periods

23. Comparing
Interest Rates
09

24. INOM / APR vs EAR
Nominal Interest Rates (INOM) /Annual Percentage Rate (APR)
… known as contracted/stated interest rates (quoted rate)
… doesn’t take compounding into account
… it is stated as Simple Interest
Effective Annual Rate (EAR/EFF%)
… rates that takes compounding into account
… it is the actual annual rate considering the compounding
If the interest rate is compounded annually, the nominal interest rates and the
effective interest rates would be the same. If there is compounding more than
annually, the effective interest rate is higher than the nominal interest rate.
Rule of Thumb

25. INOM or APR
Nominal Interest Rates (INOM) /Annual Percentage Rate (APR)
… the contracted interest rates (quoted rate)
… the interest rate charged per period multiplied by the number of periods per year
Formula APR:
M = number of compounding periods

26. EFF or EAR
Effective Annual Rate (EFF% or EAR)
… the annual rate of interest actually being earned, as opposed to the quotes rate.
Formula EFF% or EAR:
M = number of compounding periods

27. Amortized Loan
10

28. Amortized Loans
Amortized Loans
… a loan that is repaid in equal amounts on a monthly, quarterly, or annual basis
Amortization
… the distribution of the cost of an intangible asset, such as an intellectual property right, over
the project useful life of the asset
Amortization Schedule
… a table showing precisely how a loan will be repaid.
… showing how much is interest and how much is repayment of principal.