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THE TIME VALUE OF MONEY

Companies invest in lots of things. Some are tangible assets that is, assets you can kick, like factories, machinery, and offices. Others are intangible assets, such as patents or trademarks. In each case the company lays out some money now in the hope of receiving even more money later. Individuals also make investments. For example, your college education may cost you $20,000 per year. That is an investment you hope will pay off in the form of a higher salary later in life. You are sowing now and expecting to reap later.

Companies pay for their investments by raising money and in the process assuming liabilities. For example, they may borrow money from a bank and promise to repay it with interest later. You also may have financed your investment in a college education by borrowing money which you plan to pay back out of that fat salary.

All these financial decisions require comparisons of cash payments at different dates. Will your future salary be sufficient to justify the current expenditure on college tuition? How much will you have to repay the bank if you borrow to finance your education? In this material we take the first steps toward understanding the relationship between the value of dollars today and that of dollars in the future. We start by looking at how funds invested at a specific interest rate will grow over time. We next ask how much you would need to invest today to produce a specified future sum of money, and we describe some shortcuts for working out the value of a series of cash payments. Then we consider how inflation affects these financial calculations. After studying this material you should be able to

_ Calculate the future value to which money invested at a given interest rate will grow.

_ Calculate the present value of a future payment.

_ Calculate present and future values of streams of cash payments.

_ Find the interest rate implied by the present or future value.

_ Understand the difference between real and nominal cash flows and between real and nominal interest rates.

_ Compare interest rates quoted over different time intervals for example, monthly versus annual rates.

There is nothing complicated about these calculations, but if they are to become second nature, you should read the material thoroughly, work carefully through the examples (we have provided plenty), and make sure you tackle the self-test questions. We are asking you to make an investment now in return for a payoff later.