Time Value of Money

Abstract

This article will explain the financial concept of time value of money. The overview provides an introduction to the principles at work when money grows in value over time. These principles include future value of money, present value of money, simple interest and compound interest. In addition, other concepts that relate to factors that can impede the growth in value of money over time are explained, including risk, inflation and accessibility of assets. Basic formulas and tables have been provided to assist in calculating various formulations of time value of money problems. Explanations of common financial dealings in which the time value of money is an important consideration, such as annuities, loan amortization and tax deferral options, are included to help illustrate the concept of the time value of money in everyday life.

The time value of money is a fundamental financial principle. Its basic premise is that money gains value over time. As a result, a dollar saved today will be worth more in the future, and a dollar paid today costs more than a dollar paid later in time. The reason for the increasing value in money over time is that money can be invested to earn interest, and the gain in interest can be significant over time. This is also why a dollar paid today costs more than a dollar paid in the future. Money expended today cannot be invested for the future and thus the loss is essentially two-fold -- the money is spent on the payment and any earning potential it could have had in an investment vehicle is forgone.

The concept of time value of money is an important consideration in any long-term, and even short-term, investment or financial obligation. Financial managers and advisers frequently use time value of money formulas to determine the true costs of various investment opportunities. In addition, people consider the time value of money concept-perhaps without even realizing it-in making common financial decisions, such as considering whether to take out a loan or mortgage, sign a lease, deposit money in a savings account or an annuity or perhaps even to spend the money or pay off bills.

Although calculating the changing value of money over time requires formulas and mathematical computations, the underlying principle that money in hand is more valuable than money down the road is almost self-evident. Most people, if given a choice as to whether they would rather have money today or in the future, would instinctively choose money today. Ready money, or money that is presently accessible, is available to be invested in a range of vehicles that can return the money-plus interest-down the road. The sooner the money is invested, the sooner it can begin earning interest, and the longer the money is invested, the more capacity it has to grow in value. However, money that is not readily available but is to be paid in the future will only then become available for investment upon receipt, and thus it lacks present interest-earning potential.

To understand the economics of the time value of money, it is important to first grasp its underlying concepts of future value of money and present value of money. The future value of money is the value that money will grow to when invested at a given rate for a specified period of time. The present value of money is the amount that an investment earned in the future is worth today. For instance, if a person invests one dollar for one year at a 6% annual interest rate, the dollar accumulates six cents in interest while invested and thus is worth $1.06 at the end of the year. Since the time value of money is measured according to the future value and the present value of an investment of money, the future value of the person's dollar is $1.06 at a 6% interest rate for a one-year period. The present value of the $1.06 that could be earned at the end of one year is $1.

The following sections provide a more in-depth explanation of these concepts.

Overview

Basic Financial Concepts

Future Value of Money. The future value of money is the value of a sum of money, invested at a given interest rate for a defined period of time, at a specified date in the future and that is equivalent in value to a specified sum today. The future value of money can be calculated if given the interest rate of the investment, the length of time of the investment and the amount of the initial deposit. The calculation can determine the future value of a single sum investment that is deposited at the beginning of the duration of the investment. Or, if an investment consists of a series of equally spaced payments, generally known as an annuity, the future value of this investment can also be calculated. When calculating the future value of money, we commonly assume that the future value of an investment will be greater than its present value, and we use mathematical formulas to solve for the exact increase of an investment over time. The rate that money gains in value over time depends on the number of compounding periods that an investment is allowed to grow and the interest rate that the investment is earning. In other words, assume you have $10, 000 to invest today. If you spend it, the money will be gone and thus no interest will be earned on it and the money has no future value. If instead you decide to invest the $10, 000, you can increase the future value of your money over time because you will have the $10, 000 plus any interest that investment has earned. If you invest the money at 5% interest for one year, you would multiply $10, 000 by 5% to determine annual interest earned of $500. Thus, the future value of your investment is $10, 500. This calculation is explained in more detail below.

Calculating Future Value. Investors frequently calculate the future value of their investment options to determine the most profitable way to grow their money. Suppose an investor sets aside $100 to deposit in her money market account at her local bank, which is paying an annual interest rate of 10% on money market savings accounts. If she keeps her money in her money market account for one year, at the end of that year she will be able to withdraw both her initial $100 deposit plus the $10 she earned in interest. The following formula illustrates this concept:

Original deposit + Interest on deposit = FV

$100 + (10%) ($100) = $110

Thus, the investor can calculate the future value of her money by plugging in her deposit of $100 plus the 10% interest rate that her bank is paying on savings accounts to solve for the future value of her original deposit. When she performs the calculations, she will find that the future value of her $100 after one year is equal to $110 ($100 plus 10). While this calculation is relatively straightforward, another investor may want to calculate how much money he would have if he invested his money in a retirement plan and left it there to earn interest for 20 years. Luckily, there is an easy formula that he could use to determine the future value of his investment:

FV = P(1 + R)N

FV = future value

P = principal (initial deposit)

R = annual rate of interest

N = number of years

This equation can be used for any number of years. The investor must simply have the amount of the principal, the annual interest rate of the investment vehicle he is considering and the number of years the money will be invested. Once an investor has these figures accessible, he can solve for the future value of his investment. For instance, here is how an investor could compare his earning potential of two different investment options by solving for the future value of a $100 deposit at a 10% interest rate for one year and again for two years:

1 Year on Deposit. FV = P(1 + R)1

FV = $100(1 + .10)

FV = $100(1.10)

FV = $110

2 Years on Deposit. FV = P(1 + R)2

FV = $100(1 + 0.10)2

FV = $100(1.10)(1.10)

FV = $121

While these calculations illustrate the growth in the value of money over a one and two-year time period, the same formula can be used to calculate the time value of money for any number of years. For instance, if an investor wanted to figure the amount of her account if she invested $100 at a 10% annual interest rate for 10 years, she would need to multiply $100 by 1.10 and then repeat that calculation using the sum of each calculation for a total of ten times. If she performed this calculation, she would determine that (1.10)10 equals 2.594, and multiplying $100 by 2.594, she would discover that the future value of her initial $100 investment at 10% annual interest rate for 10 years would be $259.40.

Solving future value of money calculations can become more complicated the longer the money is invested. This is because almost all investments earn interest every year, and this interest is added to the principal at the end of each year, so that the next year interest is earned on both the principal plus all of the interest that has been earned. This financial concept, known as compound interest, is described in more detail below. Because making these calculations grows increasingly complicated the longer the investment, most investors and money managers use future value tables as a shortcut to solve these calculations. These tables have been completed with the calculation of one dollar invested at various annual interest rates for certain given periods of time. Thus, if an investor knows the annual rate of interest of an investment option and the length of time he plans to invest, he can quickly find the factor he will need to use to multiply by his principal, or initial deposit, in order to determine the future value of his investment.

The following future value table contains factors that are used in determining various future values. To read the future value table, you simply identify the column that represents the annual interest rate of your investment and the row that represents the duration of your investment. The cell where the column and row meet contains the factor that you will use to multiply by your original investment. For example, suppose you wish to find the future value of an original investment of $1,000 over a 5-year period at 10% interest. Look up the factor (1.61), and multiply it by the original investment: $1,000(1.61) = $1, 610. Thus, the future value of $1,000 invested for five years at a 10% annual interest rate is $1,610. You can also calculate how fast your investment will grow over the five years you invest it. To do this, simply deduct 1.00 from the factor and you get the total percentage increase (1.61 – 1.00 = .61, or 61%). In other words, a $1, 000 investment that grows to $1,610 in five years represents an increase in value of 61%.

You can also use future value tables to determine annual rates of compound interest and the number of years you must invest your principal in order for it to grow by a certain percentage at a known interest rate. For instance, to calculate the annual rate of compound interest that applies to an investment of $1,000, which is expected to grow 61% in five years, you would calculate the factor by adding .61 + 1.00 to get 1.61. You would then go to the fifth year row since you plan to invest for five years, and move along the row until you find 1.61. You would then trace up the column to find the annual interest rate of 10%. Thus, you would know that the rate of interest for a $1,000 investment expected to grow 61% in five years is 10%. Finally, if you want to find out how many years it will take for an investment growing at 10% annually to increase 61%, you would find the column representing 10% and trace down to find the factor of 1.61. You would then follow the row across the table until you reach the Periods column, and you would then find that you must invest your $1,000 at a 10% interest rate for five years in over for your investment to increase 61%. Thus, the future value formulas and tables provide investors with a relatively quick and easy method to solve for the future value of a range of investment opportunities to decide which options are the most profitable.

Present Value of Money. While the future value of money calculates the value of an investment in the future, the present value of money represents the amount of money that would be required today to equal a desired future sum of money that has been discounted by an appropriate interest rate. The future amount of money could be the result of a long-term investment or the payment of a single sum that will be received or paid at a set date in the future or a series of payments of equal amounts paid or received at equal durations over a period of time. A series of equivalent, equally spaced payments is known as an annuity. Annuities will be discussed in more detail in the sections below. If the principle of time value of money holds that money today is more valuable than money tomorrow, the inverse of this principle is also true. Money to be received in the future is less valuable than money received today. Thus, the longer an investor must wait to receive her money, the less value she will obtain from the asset.

Like the future value of money, we can use mathematical calculations to determine the present value of money. The reason investors like to solve for the present value of money is so that they can figure out how much money they need to invest today in order to obtain the future value of money that they are seeking down the road. For instance, if a person is planning for his future and he determines how much money he will want to have in his retirement account at age 65, he will want to know how much he will need to invest and save today in order to have that amount available to him when he retires.

One brief example would be as follows: If you received a graduation gift of $5,000 today, the present value of this money would simply be $5,000 because the present value equals the money's spending power, or what your investment is worth today should you decide to spend it. If you are still in school and will not expect to receive your graduation gift for another two years, the present value of the $5,000 upon receipt will no longer be $5,000 because you do not have the money to spend today, in the present. You will not have the opportunity to invest the $5,000 to earn interest on that money until you receive it, and so the $5,000 must be discounted by the appropriate discount rate to determine its present value today.

To calculate the present value of the $5,000 you will receive in the two years, you must first assume that the $5,000 is the future value of the amount of a sum of money you invested today, plus the interest you will have earned on that investment. Depending on the annual rate of interest on your $5,000, we can calculate how much you would have to invest today in order to earn enough interest over the next two years for you to have the full $5,000 upon your graduation. Since money grows in value over time by earning interest, you would not have to invest $5,000 today to have $5,000 two years from now when you graduate. You would only have to invest the present value today of a sum of money that will grow into $5,000 in two years. The sum of this money will depend on the rate of annual interest that the investment will earn over the two years. Once the annual interest rate of an investment is known, the present value of the investment needed to reach $5,000 can be calculated. In other words, to find the present value of the future $5,000, we need to find out how much we would have to invest today at a specified annual interest rate in order to receive that $5,000 in the future. The following formulas will show you how to do this.

Calculating Present Value. The present value of a future sum of money is inversely related to the length of time being calculated. In other words, the present value of money decreases as the length of time increases. The reason for this is because the longer money is invested, the more time it has to earn interest. This interest is added to the principal to calculate the future value of money. The more interest a principal deposit can earn, the less the deposit required to grow to a certain amount of money in the future. In other words, the present value of a future return is merely the reverse of a future value calculation.

The equation to calculate present value is:

PV = FV/P(1+R)^N

To calculate present value, assume that you wish to find out the present value of $10,000 five years from now, and the annual interest rate of your investment will be 10%. To find the future value, use the future value table to determine the interest rate for the period of time in the calculation. In this example, the interest rate is 10% per year for a period of five years. Thus, the present value of $1,000 looking five years out can be calculated by multiplying 1.10, which represents a period of one year at 10%, by five for the 5-year period (1.10 × 1.10 × 1.10 × 1.10 × 1.10 = 1.61). This can also be calculated using the following equation:

$1,000/(1+.10)5= $620 or $1, 000/$620=1.61

Like calculating future value, present values can also be easily computed by using tables that have already calculated various present value factors of a sequence of time periods and discount rates. The cells of the table indicate the factor which, when multiplied by a future value, will yield a given present value. As illustrated by the table below, the present value of money decreases over time and as the discount rate increases.

Learning to calculate the present value of money can be helpful in evaluating the merits of various investment options or business opportunities. The idea behind calculating the present value of money is to discount future returns by a specified level of risk, or a discount rate, plus a specified period of time in order to evaluate the real-time cost of an investment in today's dollars. Essentially, computing the present value of money helps you to determine the present value, or the cost in today's dollars, of the amount of the net return or cash flow you expect to receive in the future from an investment or a business opportunity. Once you have made this calculation, you can compare your results with the actual real-time costs of an investment or opportunity to determine whether the investment or business opportunity is financially advantageous for you. For instance, if the present value of a project is greater than its actual cost, the project likely will be profitable. If you have multiple projects or investment opportunities, you can compute the present value of each of them and then choose the option with the greatest difference between its present value and cost. Thus, learning to calculate the future value and the present value of investment options is an important part of carefully weighing various investment options so that you make sound financial decisions.

Calculating Interest. The central component of the rising value of money over time is the accrual of interest. Interest is a sum of money that is paid for the use of another's money for a given period of time, usually one year. The lender, or the person whose money is being borrowed, is compensated for allowing her funds to be used for purposes other than her own personal consumption. The original amount lent is known as the principal and the percentage of the principal that is charged for its use over a period of time is the interest rate. The two most common types of interest are simple interest and compound interest.

Simple Interest. Simple interest is interest that is paid or earned solely on the original amount, or principal, that is borrowed or lent. Simple interest is calculated using the following formula:

X = P × R × T

X = Simple interest: the dollar amount of interest earned or paid only on the principal

P = Principal: the amount of money borrowed or lent

R = Rate: the annual interest rate

T = Time: the number of years the amount is deposited or borrowed

To see this formula at work, suppose that an investor deposited $100 in a simple interest bearing account that paid 10% annual interest. For the first year, the calculation to determine the simple interest earned would be: $100 × .10 ×. 1 = $10 in interest. The next year, the basic calculation would remain the same, with only the initial principal bearing interest. While the interest earned is not added to the initial principal to earn its own interest, it is added to the principal at the end of each period of time. Thus, the growth of the investment is linear, not exponential. Over time, simple interest grows in a stable, predictable pattern as follows:

Year 1: 10% of $100 = $10 + $100 = $110

Year 2: 10% of $100 = $10 + $110 = $120

Year 3: 10% of $100 = $10 + $120 = $130

Year 4: 10% of $100 = $10 + $130 = $140

Year 5: 10% of $100 = $10 + $140 = $150

Compound Interest. Compound interest is interest that is earned on both the principal and on any accrued interest. The use of compound interest is always assumed in time value of money calculations. Interest is compounded at the end of every time period during the life of the investment, which is generally every year. However, interest may be compounded more frequently, and the effect of more frequent compounding is different for lenders and borrowers. Lenders and investors prefer more frequent compounding because compounding produces higher interest earnings in that as interest is added to the principal at the end of each time period, the amount of accrued interest grows with each subsequent time period, and more frequent addition of accrued interest to the principal to gain further interest ultimately yields higher interest returns. Borrowers, on the other hand, prefer simple interest or compound interest with less frequent compounding because this minimizes the amount of accrued interest that they must repay in addition to principal owed.

To calculate compound interest, the interest is calculated not only on the principal, but also on any interest that accumulates during the specified period of time. The formula for calculating compound interest is as follows:

X = P(1 + R)N

X = Compound interest: the dollar amount of interest earned or paid

P = Principal: the amount of money borrowed or lent

R = Rate: the annual interest rate

N = the number of years the amount is deposited or borrowed

For instance, if an investor were to receive 10% compound interest on an initial investment of $100, the first year's returns would mirror the earnings of simple interest, or $10. However, the $10 would be added to the $100 principal and thus for the second year, interest would accrue on the sum of the principal plus the first year's interest, or $110. As the interest compounds over the five years of the investment, the growth in the initial principal would look like this:

Year 1: 10% of $100.00 = $10.00 + $100.00 = $110.00

Year 2: 10% of $110.00 = $11.00 + $110.00 = $122.00

Year 3: 10% of $122.00 = $12.20 + $122.00 = $134.20

Year 4: 10% of $134.20 = $13.42 + $134.20 = $147.62

Year 5: 10% of $147.62 = $14.76 + $147.62 = $162.38

Thus, as these illustrations indicate, compound interest grows an initial investment far more quickly than does simple interest. Investments with simple interest grow in a linear fashion while investments with compound interest grow exponentially. Most investment opportunities today, including savings accounts, retirement plans and securities grow by compound interest. This is part of the reason for the popularity of these investment options, especially for long-term investments. With these investments, the longer they are allowed to accrue compound interest, the more dramatic their growth becomes.

Factors Affecting the Time Value of Money. While the concept of time value of money holds that money grows in value over time, there are factors that can undermine, or erode, the value that money gains over time. These factors include inflation, risk and a generalized preference among investors for readily accessible assets. The following sections explain these factors in more detail.

Inflation. Inflation refers to a general price increase in the economy. Inflation is defined as a sustained increase in the general level of prices for goods and services. Economists assess the extent of inflation in the economy at specified time periods and then represent its growth as a percentage increase. Most commonly, inflation is measured at one-year intervals and reported as an annual inflation rate.

Inflation affects the time value of money because as inflation rises, the purchasing power of money decreases. This means that as inflation goes up, each dollar buys a smaller percentage of goods and service. Inflation affects the time value of money in that as prices are generally expected to rise in the future, the future value of one dollar will be less one year from now than it is today, and the dollar will buy even less two years from now than it will today. This contradicts the idea that money will become more valuable over time. To illustrate, if general prices for goods and services increase by 4% annually, each and every dollar losses 4% purchasing power every year. In other words, if inflation rises 4% in one year, $1.00 at the beginning of the year depreciates in value to $0.96 by the end of the year. Likewise, if consumers could buy 100 marbles with a dollar at the beginning of the year, they could buy only 96 marbles at the end of the year.

In sum, inflation erodes the value of money by diminishing its value over time. As the rate of inflation rises and the length of an investment increases, the less the investment will be worth in the future. Yet, according to the principle of time value of money, over time money becomes more valuable because it has an opportunity to earn interest. What happens, then, is that rising inflation undermines the time value of money. The degree to which inflation can diminish the growth in the time value of money depends on the difference between the two interest rates at work. If an investment is growing at a 10% annual interest rate and inflation is rising at 3%, the money will still gain value over time because the inflation rate is significantly lower than the degree at which the investment is growing. However, if an investment is only growing at a 5% annual interest rate and the inflation rate is 4%, you can see that inflation will erode most of the purchasing power that the investment will gain over time.

Risk. Another factor that can impede the growth in value of money over time is risk. Risk is the uncertainty about the future growth of an investment, a financial market or the local, national or international economy. Risk can potentially minimize the rise in the value of money over time because risk increases with time. Since investors cannot be certain about the future, they may be more hesitant or less likely to invest their money in an opportunity with a higher level of risk, instead preferring to have their money immediately available as cash. However, investors may be willing to forgo their immediate access to cash to invest in an opportunity with a higher degree of risk if the opportunity also has a chance of yielding a higher rate of return. In other words, the assumption of higher levels of risk may be counterbalanced, or compensated, by the potential to earn higher levels of interest. However, the longer investors must forfeit access to their funds, the greater the risk, and thus the lower the likelihood that investors will be open to keeping their money invested and inaccessible. Thus, though the value of money increases over time in the form of interest earned, so level of risk also increases over time.

Every investor, then, must weigh the level of risk against the potential for earning interest when making any investment decision. The higher the level of risk associated with an investment, the greater the financial reward must be in order to convince an investor to commit to the investment. No financial analyst can precisely predict the future of any investment, financial market or local, national or international economy. Thus, every investment involves a certain level of risk. Since uncertainty, and therefore risk, increases the further one looks into the future, the value of money decreases going forward into the future because the greater the risk, the greater the possibility that an investment may wind up a loss.

Accessibility of Assets. In addition to inflation and risk, another factor that can erode the growth in value of money over time is the principle that most investors prefer relatively liquid assets. An asset is liquid if it can be converted to cash with relative ease. Investors generally prefer to keep their assets readily accessible; that is, able to be converted into cash within a minimal amount of time and with a minimal amount of effort. Investors would generally decide to liquidate an asset or an investment in instances such as a personal financial need for cash, a decision that an investment is no longer reliable or because the level of risk associated with an investment has surpassed the investor's expectation of a profitable return.

While the value of money increases over time, some long-term investments may be less attractive to investors, even though they have the potential to yield higher returns, because the investor would have to give up ready access to a liquid asset for an extended period of time. Most investors would only be willing to make such an investment for the expectation of a very high return. However, there is no guarantee that any particular investment will yield its exact projected return, and so investors must weigh these factors carefully when making any investment decision. In sum, while the increase in the value of money over time is a central tenet of financial theory, inflation, risk and a preference for easily accessible assets can work to erode the expected returns on an investment and undermine the purchasing power of money in the future.

Applications

Time Value of Money at Work in Financial Calculations. Financial planners spend a great deal of time going through calculations to figure out the present value and the future value of money in order to determine how best to advise clients in managing their assets. Determining the time value of money is an important calculation in several different financial transactions such as purchasing an asset, investing in securities, paying debt and calculating tax obligations. Tax attorneys, in particular, are often paid to counsel clients on managing their tax payments. Tax attorneys must perform sophisticated tax calculations to determine whether and how much tax obligations can be deferred and how to best structure tax reporting and repayments so that a client complies with the relevant tax regulations while protecting and maximizing their personal and business assets. The following sections illustrate how the time value of money calculation is figured into various financial planning considerations.

Annuities. An annuity refers to a sequence of periodic and equal payments that are made at regular time intervals. Examples are the monthly mortgage payments on a house, pensions or Social Security and periodic loan payments.

In an ordinary annuity, the investor makes a payment at the end of the relevant time period. In contrast, in an annuity due, contributions are made at the beginning of the time period. Annuities can be calculated to determine not only payments from an investor into an investment, but also payments made from an investment to an investor. For instance, many people contribute to a 401(k) or 403(b) through their place of employment, and this is a form of payment from them into an annuity that will make payments to them upon their retirement. Annuities can be calculated to determine the amount of payment that an investment will pay to an investor over the remainder of his or her life, which is approximated by expectancy of life averages, or the amount of money that an investor will need to deposit in order to accrue a desired investment total. Thus, calculating annuities makes use of the formulas that are frequently used in calculating the future value of money.

Calculating Annuities. Calculating the future value of an annuity requires using the following formula:

FVa = P(1 + R)¹ + P(1 + R)² + P(1 + R)³ + ...... + P(1 + R)^N-1

This equation can also be expressed as:

(1 + R)^N – 1

FVa = P × R

= P × FVIFAR, N

Where FVa = Future value of an annuity

P = Payment

R = Annual rate of interest

N = Number of periods

FVIFAR, N = Annuity factor, or future value interest annuity factor

For instance, an investor may want to calculate the future value of a $1,000 annuity over a period of four years with a 10% compound interest rate. To do so, she would use the future value of an annuity formula as follows:

P = $1,000 per year

N = 4 years

R = 10%

[(1 + 0.10)⁴ – 1]/0.10

FVa = 1, 000 × 4.641

FVa = $4, 641.00

Loan Amortization. An amortized loan is a loan that requires an equal payment each month that is comprised of some interest and some principal. The initial payments made on an amortized loan are mostly interest and the last payments are mostly principal. This is because as the loan begins to be paid off and balance of the loan is gradually lowered, more of each payment goes toward reducing principal while less goes toward paying interest. Thus, at the beginning of an amortized loan, a high percentage of the payment goes toward paying the interest and only the remainder of the payment is applied to reducing the principal. As the interest is paid off, less of the payment needs to go toward the remaining interest, so a greater percentage of the loan payment is allocated to reducing the loan principal.

Loan amortizations are typically represented by an amortization schedule. A loan amortization schedule is a table that shows each payment that is required to pay off an amortized loan. Each row in the table shows the amount of the payment that is needed to pay the accrued interest, the amount that is used to reduce principal and the balance of the loan remaining at the end of the period. Most mortgages are amortized loans, and thus the homeowner can consult the amortization schedule to track the amount of each payment that is going toward paying the interest and the amount that is actually reducing the amount of the principal.

Tax Deferral. Deferring the payment of taxes is advantageous to a taxpayer because he can invest the deferred tax and earn income on it until it is paid to the government. However, tax regulations do not permit unlimited, or even extensive, deferrals of tax payments. Thus, while deferring a tax payment can allow the money that would be used to pay the taxes to instead accrue interest, tax payments generally may be postponed for relatively short periods of time and thus the money has a shorter period of time in which to earn interest and gain value. Full compliance with tax requirements is an important part of sound financial management, and because the tax regulations can be more extensive and complicated the more assets an investor has, many investors choose to consult with a tax attorney for advice on their tax deferral options.

Conclusion

An investment involves making a present commitment of money with the expectation of a financial gain in the future. The financial gain that most people expect to receive for their investments is known as interest. The time value of money is based on the concept that a dollar today is worth more than a dollar in the future because you can invest the dollar you have today so that it will begin earning interest. The inverse of this is also true—a dollar paid today costs more than a dollar paid in the future. The reason for this is that there are factors that can decrease the value of money over time, such as inflation, risk and a typical preference for cash or other liquid assets. While inflation can erode the purchasing power of money over time, in general, the longer the period of time between money paid or received today and money paid or received in the future, the greater the increase in the value of the money. This principle, known as the time value of money, is one of the most foundational principles of money management and can be readily seen in common financial transactions such as annuities, amortized loans and tax deferral considerations.

Terms & Concepts

Assets: Economic resources acquired and owned by an entity.

Balance Sheet: A financial report listing the assets, liabilities and owners' equity as of a specific date.

Bond: One of a series of notes that are sold to investors.

Capitalization of earnings: The computation of the investment amount that will yield, at a desired rate of return, an amount equal to the net income of a company.

Cash flow: The cash that can be generated by a business, or a particular project, over a period of time.

Cost: The amount of money or other asset paid for a purchase, expense or other asset, such as inventory.

Future value: The value that a payment today will have at a specified date in the future.

Internal rate of return: The interest rate on an investment in equipment or a project that would generate income equal to the cash flow from the equipment or project.

Lease: A written agreement relative to rent of facilities such as buildings and equipment. It obligates the owner (lessor) of the facilities to rent them to the user of the facilities (lessee) over a period of time for a specified rent.

Lessee: One who rents facilities from the owner of the facilities.

Lessor: One who owns facilities that he or she rents to a lessee.

Loan: A transfer of an asset from a person or entity to another person or entity with the expectation it will be repaid.

Loss: An outgo of expenses or costs without offsetting revenue.

Present value: The value today of a future sum of money, either paid or received.

Purchase: Acquisition of goods or services, either for business use or for resale to customers. A purchase occurs when title to goods is passed or services are rendered.

Time value of money: A financial concept describing the effect of interest on money over a set period of time.

Bibliography

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Brickner, D. R., & Mahoney, L. S. (2018). Factoring in the time value of money with Excel. Journal of Accountancy, 225(3), 42–54. Retrieved March 6, 2018, from EBSCO Online Database Business Source Ultimate. http://search.ebscohost.com/login.aspx?direct=true&db=bsu&AN=128282032&site=ehost-live&scope=site

Chen, J. (1998). An inventory model for deteriorating items with time-proportional demand and shortages under inflation and time discounting. International Journal of Production Economics, 55(1), 21–30. Retrieved April 5, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=12156098&site=ehost-live

Chiu, H. & Chen, H. (1997). The effect of time-value of money on discrete time-varying demand lot-sizing models with learning and forgetting considerations. Engineering Economist, 42(3), 203–222. Retrieved April 5, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=9712225167&site=ehost-live

Darwish, M. (2006). Imperfect production systems with imperfect preventive maintenance, inflation, and time value of money. Asia-Pacific Journal of Operational Research, 23(1), 89–105. Retrieved April 5, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=20577939&site=ehost-live

Ghosh, D. (2012). Classroom contents and pedagogy: Time value of money in one lesson. International Journal of Finance, 24(2), 7127–7168. Retrieved October 31, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=86957391&site=ehost-live

Hariga, M. (1995). Effects of inflation and time-value of money on an inventory model with time-dependent demand rate and shortages. European Journal of Operational Research, 81(3), 512–520. Retrieved April 5, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=7926068&site=ehost-live

Hutensky, B. (1999). Understanding rates of return. In Finance for Shopping Center Nonfinancial Professionals. (pp. 103–137). Retrieved April 5, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=23997433&site=ehost-live

O'Leary, J. (2002). Learn to speak the language of ROI. Harvard Management Update, 7(10), 3. Retrieved April 5, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=9003848&site=ehost-live

Shankar, S., Anderson, G. A., & Jha, A. (2012). A few precise and simple methods for understanding changes in cash flow patterns in financial education. International Journal of Finance, 24(2), 7169–7185. Retrieved October 31, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=86957392&site=ehost-live

Stuebs, M. (2011). Revealing money's time value. Journal of Accounting Education, 29(1), 14–36. Retrieved October 31, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=67624182&site=ehost-live

Suggested Reading

Eroglu, A. & Ozdemir, G. (2005). A note on the effect of time-value of money on discrete time-varying demand lot-sizing models with learning and forgetting considerations. Engineering Economist, 50(1), 87–90. Retrieved April 5, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=16471877&site=ehost-live

Forbes, S. (1991). A note on teaching the time value of money. Financial Practice & Education, 1(1), 91. Retrieved April 5, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=9607240016&site=ehost-live

Jordan, D. (2017). Time-value of money. Alaska Business Monthly, 33(2), 48–49. Retrieved March 6, 2018, from EBSCO Online Database Business Source Ultimate. http://search.ebscohost.com/login.aspx?direct=true&db=bsu&AN=121778989&site=ehost-live&scope=site

Stevens, Sue. (2007). It's not just money, it's an investment: Help your kids get a good financial start in life. Morningstar Practical Finance, 3(2), 1–2. Retrieved April 5, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=24519572&site=ehost-live