# The Time Value of Money One of the most important concepts in corporate finance is the time value of money. This concept is crucial in areas like capital budgeting, lease-or-buy decisions, accounts receivable analysis and many others. The time value of money is the relationship between \$1 now and \$1 at some time in the future.

We can illustrate the time value of money with an example. Imagine someone offered you \$1000 as a gift. They said you could either have the \$1000 right now, or you could have the money in 10 years from now. Which would you choose? Most rational people would choose to get the money now. This is because if you get \$1000 now, you can make use of the money right away (to buy things, invest it, etc.) rather than wait. Additionally, who knows what the state of the world will be in 10 years, the dollar may have depreciated or even worse, the world may have ended. Clearly, receiving \$1000 now is more valuable to most people than receiving \$1000 in the future. In summary, benefits are foregone by waiting for money.

The time value of money is why “rational” people who lend money, require something more than just the principal to be repaid. The longer the lender has to wait for repayment and the riskier the loan, the more they require in return.

This means that dollar amounts received at different points in time must be converted to their values at a common date so that the amounts can be compared. To compare amounts at different time periods we introduce the two fundamental time value of money concepts: future value and present value.

## Future Value

Because of the time value of money, it’s better to have money now rather than some time in the future. Think about the difference between having \$100.00 now and \$100.00 in one year from now. If you have \$100 now, you can invest it in a savings account that earns, let’s say, 5% interest per year. This means that at after one year, you will have \$105.00. The \$105.00 is what is called the future value of \$100.00 in one year when the rate of return is 5%.

### Multiple Periods

For multiple years (or time periods), interest is compounded which means that interest is calculated on interest. Therefore, after two years at an interest rate of 5%, the future value of \$100 is:
\$100.00 x 1.05 x 1.05 = \$110.25

To summarize, future value is the amount a present some of money will be, given a specified time period and interest rate.

For those who are mathematically inclined, here is the general formula to calculate future value:

FutureValue = PresentValue x (1 + InterestRate)NumberOfPeriods

## Present Value

In order for investors to compare future cash inflows, it’s convenient to determine the value of money received in the future to its value today.

For example, suppose you need to accumulate \$100,000 over 10 years for your child’s education. You happen to have cash available to make an investment that returns 7% per year. How much would you need to invest now in order to have \$100,000 in 10 years? This amount represents the present value of \$100,000 in 10 years at a 7% interest rate. To find present values, we can rearrange the future value formula above to show that:

PresentValue = FutureValue / (1 + InterestRate)NumberOfPeriods

For our exampe:

Present Value = \$100,000 / (1 + 1.07)10 = \$50,834.93

This means that at a rate of return of 7%, you would have to invest \$50,834.93 for 10 years to accumulate \$100,000.

## Net Present Value (NPV)

Net Present Value or NPV for short, is another key concept for making financial decisions. Should you go ahead with that project? Should you buy that machine? NPV builds builds upon the idea of present value by including the current cost of an activity or investment, rather than just calculating the returns of the activity or investment. Simply put, the present value of all costs are calculated and compared with the present value of all future returns. The investment deciscion is then based on comparing these numbers.

NPV = Present value of investment returns – Present value of investment costs

As a rule, an investment is worth making if it has a positive NPV. The investment should be rejected if it has a negative NPV.

## Annuities

In many cases, cash from investments is received at over time at regular intervals. Retirement pensions, leases, mortgages and pension plans are all annuities.

Calculating present and future values of annuities is also possible but a bit more complicated.

## Financial Calculators Make Life Easier

Many calculators for calculating present values, future values and annuities are available. An easy to use financial calculator is available on our Free Financial Calculator page.