TIME VALUE of MONEY
Present value and Future value
The present value is value of the amount today that is the equivalent to the value of future payments. The non-annuity is a lump sum of money that paid out at the end of the investment period. This would be the form of a trust; it scheduled to be pay out at a future date. The future value is the growth of an investment of money that promised in the future. The non-annuity type is a lump sum that invested at present value with the expected future value when it paid out or released. Present and Future values have an equivalent relationship. The difference depends on the number of compounding periods involved and the interest rate.
PV = FV [ 1 / ( 1 + i ) n ]
FV = PV ( 1 + i ) n
FV = Future Value
PV = Present Value
i = Interest Rate Per Period
n = Number of Compounding Periods
Examples:
Present Value:
You want to buy a house 5 years from now for $150,000. Assuming a 6%, interest rate compounded annually, how much should you invest today to yield $150,000 in 5 years?
PV = FV [ 1 / ( 1 + i ) n ]
FV = Future Value $150,000
PV = Present Value NEED?
i = Interest Rate Per Period 6% or 0.06
n = Number of Compounding Periods lets say 5… 1 payment per year
PV = $150,000 [ 1 / ( 1 + 0.06 ) 5 ]
PV = $150,000 [ 1 / ( 1.06 ) 5 ]
PV = $150,000 [ 1 / 1.338226 ]
PV = $150,000 [0.7472581]
PV = $112,088.73
Future Value:
You can afford to put $10,000 in a savings account today that pays 6% interest compounded annually. How much will you have 5 years from now if you make no withdrawals?
FV = PV ( 1 + i ) n
FV = Future Value NEED?
PV = Present Value $10,000
i = Interest Rate Per Period 6% or 0.06
n = Number of Compounding Periods annually… 5, once per year
FV = $10,000 ( 1 + 0.06 ) 5
FV = $10,000 ( 1.06 ) 5
FV = $10,000 x 1.338226
FV = $10,000 x 1.338226
FV = $13,382.26
Present value and Future value of an annuity
The annuity form of present and future value makes payment or takes payment on a period. The period could be anything from one day to every hundred years. A present value annuity is a set of payments paid out over the life of the annuity. A future annuity is a set of payment in to an investment over a period. They do not have an equivalent relationship like present and future non-annuity value.
PVa = PMT [ ( 1 – ( 1 / ( 1 + i ) n ) ) / i ]
FVa = PMT [ ( ( 1 + i ) n – 1 ) / i ]
PVa = Present Value of an Annuity
FVa = Future Value of an Annuity
PMT = Amount of each payment
i = Discount Rate Per Period
n = Number of Periods
Examples;
Present Value Annuity:
What amount must you invest today at 6% compounded annually, so that you can withdraw $5,000 at the end of each year for the next 5 years?
PVa = PMT [ ( 1 – ( 1 / ( 1 + i ) n ) ) / i ]
PVa = Present Value of an Annuity NEED
PMT = Amount of each payment $5,000
i = Discount Rate Per Period 6% or 0.06
n = Number of Periods annually… 5 withdraws
PVa = PMT [ ( 1 – ( 1 / ( 1 + i ) n ) ) / i ]
PVa = $5,000 [ ( 1 – ( 1 / ( 1 + 0.06 ) 5 ) ) / 0.06 ]
PVa = $5,000 [ ( 1 – ( 1 / ( 1.06 ) 5 ) ) / 0.06 ]
PVa = $5,000 [ ( 1 – ( 1 / 1.3382255776 ) ) / 0.06 ]
PVa = $5,000 [ ( 1 – ( 0.74725817286605716719189988974845 ) ) / 0.06 ]
PVa = $5,000 [ 0.252741827133942832808100110252 / 0.06 ]
PVa = $5,000 [ 4.2123637855657138801350018375333 ]
PVa = $21,061.82
Future Value Annuity:
What amount will accumulate if we deposit $5,000 at the end of each year for the next 5 years? Assume an interest of 6% compounded annually.
FVa = PMT [ ( ( 1 + i ) n – 1 ) / i ]
FVa = Future Value of an Annuity NEED?
PMT = Amount of each payment $5,000
i = Discount Rate Per Period 6% or 0.06
n = Number of Periods annually… 5 deposits
FVa = PMT [ ( ( 1 + i ) n – 1 ) / i ]
FVa = $5,000 [ ( ( 1 + 0.06 ) 5 – 1 ) / 0.06 ]
FVa = $5,000 [ ( 1.3382255776 – 1 ) / 0.06 ]
FVa = $5,000 [ 0.3382255776 / 0.06 ]
FVa = $5,000 [5.63709296 ]
FVa = $28,185.46
Summary;
Explain the time value of money and its importance in the business world, money grows over time when it earns interest. Money expected or promised in the future is worth less than the same amount of money in hand today. This is because we lose the opportunity to earn interest when we have to wait to receive money. Similarly, money we owe is less burdensome if it is to be paid in the future rather than now. These concepts are at the heart of investment and valuation decisions of a firm.
Calculate the future value and present value of a single amount, to calculate the future value and the present value of a single amount, we may use the algebraic, table, or calculator methods. Future value and present value are mirror images of each other, they are compounding and discounting, respectively. With future value, increases in k and n result in an exponential increase in future value. Increases in k and n result in an exponential decrease in present value.
Find the future and present values of an annuity, annuities are a series of equal cash flows. An annuity that has payments that occur at the end of each period is an ordinary annuity. An annuity that has payments that occur at the beginning of each period is an annuity due. A perpetuity is a perpetual annuity, to find the future and present values of an ordinary annuity, we may use the algebraic, table, or financial calculator method. To find the future and present values of an annuity due, multiply the applicable formula by (1 + k) to reflect the earlier payment.
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Nice Share Pak, give me more educated about time value 🙂
Great articles. Very impprtant to calculate time value before we invest.
good articles mas Hari, thanks for sharing. it is very helpful for me especially when i need to decide an investment.
Good article Pak Hari. Now I can explain it to my customer why they need to pay on time…
“Money expected or promised in the future is worth less than the same amount of money in hand today”