# Finance

## What is Present Value?

Assume that parents promise their child, Bill, \$20,000 in three years, when he graduates from college. The theory of finance requires us to calculate how much money must be deposited today in order for it to grow to \$20,000 in three years. The answer depends on the rate of interest that the bank provides. Assume that the bank pays 8% annually.

Until you learn to calculate the amount, we will do it for you. The answer is \$15,877, meaning that \$15,877 deposited in the bank today at 8% annual interest will grow to \$20,000 in three years. The amount of money that we gave in the answer is called “the amount of the present value”, or, in short, “present value”. That means \$15,877 is the present value of the total \$20,000 to be received three years from now.

Indifference

The word indifference in economics describes a situation in which there is no economic reason to prefer one alternative (possibility) over another alternative, because each of the alternatives offers comparable benefits. In this situation, you are indifferent to the alternatives.

Example:

Assume that his parents improve their offer, and suggest two alternatives for receiving the money:

• Alternative 1 – \$15,877 today.

•  Alternative 2 – \$20,000 three years from now.

Bill calls the Bank of America and asks the clerk how much he will accumulate in three years if he deposits \$15,877 now (alternative 1), and the answer he receives is \$20,000.

In this situation, Bill is indifferent to the choice between receiving \$15,877 from his parents now or receiving \$20,000 three years from now (alternative 2). Each of these two alternatives will give him \$20,000 three years from now.

(It is assumed in this example that he does not have living expenses during these three years).

You are offered \$20,000, which you will receive three years from now.

The present value of this \$20,000 (that is to be received three years from now) is the sum you will demand today in order to make you indifferent to the choice between the two alternatives. In this example, the present value of \$20,000, which is to be received three years from now, is \$15,877.

Preference Versus Indifference

If Bill can receive more than \$15,877 today, even \$15,878 (\$1 more), he will prefer this to receiving \$20,000 three years from now.

Explanation: If Bill deposits \$15,878 today, he will have more than \$20,000 three years from now.

The same principle holds in the opposite direction: If Bill can receive more than \$20,000 three years from now (even \$20,001), he will prefer this to receiving \$15,877 now.

Explanation: If he deposits \$15,877 now, he will have only \$20,000 three years from now.

What is Present Value?532