## Time Value of Money: Explaining With Examples

written by: N Nayab•edited by: Donna Cosmato•updated: 7/27/2011

Time Value of Money (TVM) is the future value of an amount after factoring in interest for the period or the present value of a future amount after discounting interest. It finds use in financial management to estimate the true worth of investments, savings, annuities, and other instruments.

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### The Concept

Investments are an exchange of money at one point in time for the rights to future cash flows. The passage of time between the cash outflows and inflows distorts the actual values of the inflow and outflow, and merely adding up the total inflows and outflows does not provide a correct picture of the returns of the investment.

The time value of money concept entails bringing all the monetary values, spread over time to a common point, thereby allowing for a level ground or a uniform platform on which to calculate returns. It holds that other things remaining the same, the same amount is worth more today than at a future date, and involves estimating the future value of money on hand, or the present value of money obtainable at a late date, to make financial decisions.

An example best explains this concept:

A dollar today will be worth more at a future date when invested. For example, \$100 invested at 5 percent per annum would be worth \$105 at the end of the year. Using this methodology, it is also possible to calculate the present value of money. The present value of \$105 available after a year, assuming 5 percent interest is \$100, and the present value of \$100 available after a year, assuming 5 percent interest is \$95.24.

The potential earning capacity of money over time means that the same amount of money is worth more when obtained today than at a future date. For instance, \$100 obtainable today is worth more than \$100 obtainable a year later, as \$100 invested would become \$105 at the end of the year. Extending this principle, \$100 obtainable today is even worth more than \$104 obtainable after a year assuming bank interest is 5 percent.

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### Calculation

Finding out the time value of money involves calculating either the future value or the present value of the amount.

The future value of money is the compound interest the sum earns for the specified period, assuming the money remains untouched.

For example, if \$10,000 is deposited in the bank, and earns 5 percent interest in the first year, and 6 percent interest in the second year, the future value of \$10,000 after two years is:

\$10,000 x 5% +\$10,000 = \$ 10,500 at the end of year 1

\$10,500 x 6% +\$10,500 = \$ 11,130 at the end of year 2

When the interest rate is constant, the formulae to calculate future value of a sum of money is

Original amount (1+annual interest rate)^number of years.

The present value of money is the discounted value of the money, or the sum, which invested today, would grow with interest to the amount in question. The formulae to calculate present value of money is Future value / (1+interest rate) ^ number of years.

For instance, to determine the present value of \$10,000 obtainable after two years at 5 percent interest:

\$10,000 / (1+5)^2 = 10,000 / (1.05*1.05 ) = 10,000/1.1025 = \$ 9,070.3

Thus, the present value of \$1000, assuming 5 percent interest, is \$9,070.3.

Now assume an investment that requires 10 monthly payments of \$20,000 and promising a lump sum return of \$300,000 at the end of five years. A quick calculation reveals a total investment of \$200,000 and a return of \$300,000, or a return of 50 percent in five years. The actual rate, however, varies.

The actual rate of return is the rate at which the present value of the return equals the net outgo. In this case, the interest rate is approximately 8.5 percent, for the present value of \$300,000 at 8.5 percent per annum for five years is \$199513.6. Factoring in the present value of the future installments would distort this figure slightly.

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### Application

The time value of money concept finds common use when making investments and comparing between alternative investment choices. It reveals the opportunity cost of a certain investment. For instance, \$100,000 invested in a business would otherwise have yielded 5 percent or \$5,000 annually. The business would have to yield a net profit of more than \$5,000 to justify the investment.

Businesses may apply the concept to offer discounts for down payments. For instance, when negotiating contracts, businesses may offer a discount of 3 percent for the amount paid upfront since the same money invested would yield 5 percent. Individuals can apply this concept to find out the true returns they obtain on their investments and annuities.

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### Distorters

A proper explanation of the time value concept needs to factor in many assumptions and distortions.

The concept assumes that money on hand earns interest. However, if the money is stashed away and not deposited in a bank or put to any other secure return generating investment, inflation may erode the true value of the money and reduce its purchasing power.

For instance, if the annual inflation rate is 3 percent, \$100 stashed away would remain \$100, but the purchasing power may decline, and the same \$100 would only purchase items worth about \$97. Such erosion of the purchasing power of money does not affect the present value, but may distort actual returns.

Regardless of the type of investment made, all future values, including bank interest are only promises carrying a risk of default, and in the strict sense hypothetical.

The concept of time value of money substantiates the maxim “time is money." Intelligent investors and decision makers factor in time to understand the true worth of their investments.

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### Reference

1. Bruce J. Sherrick, Paul N. Ellinger & David A. Lin. “Time Value of Money and Investment Analysis." http://agmarketing.extension.psu.edu/Business/FinancialTools/TimeValueMoneyP1.PDF
2. "Understanding Time Value of Money." http://www.investopedia.com/articles/03/082703.asp#axzz1SrWnKE40

Image Credit: flickr.com/Emily Jones