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Time Value of Money

Introduction

Time Value of Money (TVM) is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities.

TVM is based on the concept that a dollar that you have today is worth more than the promise or expectation that you will receive a dollar in the future. Money that you hold today is worth more because you can invest it and earn interest. After all, you should receive some compensation for foregoing spending. For instance, you can invest your dollar for one year at a 6% annual interest rate and accumulate $1.06 at the end of the year.  You can say that the future value of the dollar is $1.06 given a 6% interest rate and a one-year period. It follows that the present value of the $1.06 you expect to receive in one year is only $1.

A key concept of TVM is that 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.  Conversely, you can determine the value to which a single sum or a series of future payments will grow to at some future date.

You can calculate the fifth value if you are given any four of: Interest Rate, Number of Periods, Payments, Present Value, and Future Value.  Each of these factors is very briefly defined in the right-hand column below.  The left column has references to more detailed explanations, formulas, and examples.

 

Interest

Interest is a charge for borrowing money, usually stated as a percentage of the amount borrowed over a specific period of time.   Simple interest is computed only on the original amount borrowed. It is the return on that principal for one time period.  In contrast, compound interest is calculated each period on the original amount borrowed plus all unpaid interest accumulated to date.  Compound interest is always assumed in TVM problems.

 

Number of Periods

Periods are evenly-spaced intervals of time. They are intentionally not stated in years since each interval must correspond to a compounding period for a single amount or a payment period for an annuity.

 

Payments

 

Payments are a series of equal, evenly-spaced cash flows.  In TVM applications, payments must represent all outflows (negative amount) or all inflows (positive amount).

 

Present Value

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.  The future amount can be a single sum that will be received at the end of the last period, as a series of equally-spaced payments (an annuity), or both.  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.

 

Future Value

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.

 

Loan Amortization

A method for repaying a loan in equal installments. Part of each payment goes toward interest and any remainder is used to reduce the principal. As the balance of the loan is gradually reduced, a progressively larger portion of each payment goes toward reducing principal.

 

Cash Flow Diagram

A cash flow diagram is a picture of a financial problem that shows all cash inflows and outflows along a time line.  It can help you to visualize a problem and to determine if it can be solved by TVM methods.

References:

Gallager, T; Andrew Jr., J., Financial Management: Principals and Practices, Upper Saddle River, NJ: Prentice Hall, 1996

Kieso, D; Weygandt, Jerry, Intermediate Accounting, 9th Ed., New York, NY:John Wiley & Sons, Inc., 1993

BA II Plus Guidebook, Texas Instruments, Inc., 1996

HP-10B Business Calculator Owner's Manual, Hewlett Packard, 1994

Concepts

 
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