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Time value-of-money
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- 2. contents What isTime Value ? The Terminology of Time Value Abbreviations Timelines Calculating the Future Value Calculating the Present Value Annuities Present Value of an Annuity The Future Value of an Annuity
- 3. Importance of TimeFactor Why is TIMETIME such an important element in our decision? TIME allows one the opportunity to postpone consumption and earn INTEREST.
- 4. What is TimeValue? We say that money has a time value because that money can be invested with the expectation of earning a positive rate of return In other words, “a rupee received today is worth more than a rupee to be received tomorrow” That is because today’s rupee can be invested so that we have more than one rupee tomorrow
- 5. The Terminology ofTime Value Present Value - An amount of money today, or the current value of a future cash flow Future Value - An amount of money at some future time period Period - A length of time (often a year, but can be a month, week, day, hour, etc.) Interest Rate - The compensation paid to a lender (or saver) for the use of funds expressed as a percentage for a period (normally expressed as an annual rate)
- 6. Abbreviations PV - Presentvalue FV - Future value Pmt - Per period payment amount N - the number of a specific period i - The interest rate per period
- 7. Timelines A timeline isa graphical device used to clarify the timing of the cash flows for an investment Each tick represents one time period 0 1 2 3 4 5 PV Today FV
- 8. Calculating the Future Value(Example) Suppose that you have an extra Rs100 today that you wish to invest for one year. If you can earn 10% per year on your investment, how much will you have in one year ? 0 1 2 3 4 5 -100 ?
- 9. “The greatestmathematical discovery of all time is compound interest.” - Albert Einstein
- 10. 0 1000 2000 3000 4000 5000 6000 70000 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Number of Years FVof$100 0% 5% 10% 15% FutureValues of $100 with Compounding Interest Rates
- 11. 0 5000 10000 15000 20000 1st Year 10th Year 20th Year 30th Year FutureValue of a Single $1,000 Deposit 10%Simple Interest 7%Compound Interest 10%Compound Interest Why Compound Interest?
- 12. Generalizing the Future Value Recognizingthe pattern that is developing, we can generalize the future value calculations as follows: If you extended the investment for a third year, you would have:
- 13. Calculating the Present Value So far, we have seen how to calculate the future value of an investment But we can turn this around to find the amount that needs to be invested to achieve some desired future value:
- 14. Present Value: An Example Suppose that your five-year old daughter has just announced her desire to attend college. After some research, you determine that you will need about Rs100,000 on her 18th birthday to pay for four years of college. If you can earn 8% per year on your investments, how much do you need to invest today to achieve your goal ?
- 15. Rule of 72 Rule of 72 is an approximate formula to determine the number of years it will take to double the value of your investment. Rule of 72: N = 72/interest rate in percentage Example 5.7 Using Rule of 72, determine how long it will take to double your investment of $10,000 if you are able to generate an annual return of 9%. Exact N=ln(2)/ln(1.09)=0.693/0.086=8.04 Approximate N=72/9=8.
- 16. Annuities An annuityis a series of nominally equal payments equally spaced in time Annuities are very common: Rent Mortgage payments Car payment Pension income The timeline shows an example of a 5- year, Rs100 per annum. 0 1 2 3 4 5 100 100 100 100 100
- 17. The Principle ofValue Additivity How do we find the value (PV or FV) of an annuity? First, you must understand the principle of value additivity: The value of any stream of cash flows is equal to the sum of the values of the components In other words, if we can move the cash flows to the same time period we can simply add them all together to get the total value
- 18. Present Value ofan Annuity We can use the principle of value additivity to find the present value of an annuity, by simply summing the present values of each of the components:
- 19. Present Value ofan Annuity (Example) Using the example, and assuming a discount rate of 10% per year, we find that the present value is:
- 20. Present Value ofan Annuity (shortcut) Actually, there is no need to take the present value of each cash flow separately We can use a closed-form of the PVA equation instead:
- 21. Present Value ofan Annuity (Example) Using the example, and assuming a discount rate of 10% per year, we find that the present value is:
- 22. The Future Valueof an Annuity We can also use the principle of value additivity to find the future value of an annuity, by simply summing the future values of each of the components:
- 23. The Future Valueof an Annuity (Example) Assuming a discount rate of 10% per year, we find that the future value is:
- 24. Benefits of theknowledge of the Time Value of Money For investment analysis – To decide the financial benefits of projects To compare investment alternatives To analyze how time impacts business activities such as loans, mortgages, leases, savings, and annuities.
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