# Time Value of Money

I. DEFINITIONS

* A peso received today is worth more than a peso received in the future * In economics, it is the opportunity cost of passing up the earning potential of a peso today. * The idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. * Holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

II. KEY CONCEPTS

* A single sum of money or a series of equal, evenly spaced payments or receipts promised in the future, can be converted to an equivalent value today. (Present Value of Cash Flows) * Conversely, you can determine the value to which a single sum or a series of future payments will grow to at some future date. (Future Value of Cash Flows)

III. What are the financial applications of time value of money?

* Equipment purchase or new product decision

* Present value of a contract providing future payments

* Future worth of an investment

* Regular payment necessary to provide a future sum

* Regular payment necessary to amortize a loan

* Determination of return on an investment

* Determination of the value of a bond.

IV. TIME LINE

* An important tool used in time value analysis; it is a graphical representation used to show the timing of cash flows.

* The first step in time value analysis is to set up a time line, which will help you visualize what’s happening in a particular problem.

The intervals from 0 to 1, 1 to 2, and 2 to 3 are time periods such as years or months. Time 0 is today, and it is the beginning of Period 1; Time 1 is one period from today, and it is both the end of Period 1 and the beginning of Period 2; and so forth.

V. PRESENT VALUE

* is an amount today that is equivalent to a future payment, or series of payments, that has been discounted by an appropriate interest rate. Since money has time value, the present value of a promised future amount is worth less the longer you have to wait to receive it. The difference between the two depends on the number of compounding periods involved and the interest (discount) rate.

The relationship between the present value and future value can be expressed as: PV = FV [ 1 / (1 + i)n ]|

Where:

PV = Present Value

FV = Future Value

i = Interest Rate Per Period

n = Number of Compounding Periods

Example: 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?

FV = 150,000

i =.06

n = 5

PV = 150,000 [ 1 / (1 + .06)5 ] = 150,000 (1 / 1.3382255776) = 112,088.73 End of Year| 1| 2| 3| 4| 5|

Principal| 112,088.73| 118,814.05| 125,942.89| 133,499.46| 141,509.43| Interest| 6,725.32| 7,128.84| 7556.57| 8,009.97| 8,490.57| Total| 118,814.05| 125,942.89| 133,499.46| 141,509.43| 150,000.00|

VI. FUTURE VALUE

* is the amount of money that an investment with a fixed, compounded interest rate will grow to by some future date. The investment can be a single sum deposited at the beginning of the first period, a series of equally-spaced payments (an annuity), or both. Since money has time value, we naturally expect the future value to be greater than the present value. The difference between the two depends on the number of compounding periods involved and the going interest rate.

The relationship between the future value and present value can be expressed as: FV = PV (1 + i)n|

Where:

FV = Future Value

PV = Present Value

i = Interest Rate Per Period

n = Number of Compounding Periods

Example: 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? PV = 10,000

i = .06

n = 5

FV = 10,000 (1 + .06)5 = 10,000...

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