Time Value of Money Chapter 3 Magister Program.pptx

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 ? Opportunity Cost 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 FVA due = FVA ordinary (1+I) FVA due : FV Annuity Due FVA ordinary : 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: 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. 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 the renter continues to rent). PV = present value PMT = amount of continuous cash payment I = interest rate

16. CF t = 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 Annuity plus additional final payment uneven streams payment / cash flow disimbolkan deng an CF t 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 Konversikan interest rate ( annual rate ) menjadi periodic rate 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. I NOM / APR vs EAR Nominal Interest Rates (I NOM ) /Annual Percentage Rate (APR) … known as contracted/stated interest rates ( quoted rate ) … doesn’t take compounding into account … it is stated as S imple I nterest 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. I NOM or APR Nominal Interest Rates (I NOM ) /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.