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Money has time value even in the absence of inflation, although inflation increases 1 your preference for an early receipt or delayed expenditure. 03: Page 1 of 29 MODULE 03 THE MATHEMATICS OF FINANCE AND TIME VALUE OF MONEY Making financial choices requires converting values from one period to another. For example, you may want to choose between putting cash in an account at a savings and loan or investing in a corporate bond. Or you may consider financing the purchase of a car with either a three-year bank loan or a four-year loan from a finance company like GMAC or Chrysler Credit. Each deals with cash flows occurring at different points in time. To compare them, you must express them as values on a common date. The time value of money sets up a common date for cash flows at different points in time. Probably the first reference to the time value of money is in Shakespeare's play Troilus and Cressida , written just after 1600. Ulysses comments that "Time hath. . . a wallet at his back." There are neither cash flows not equations in Shakespeare's work, but the bard probably had at least an intuitive grasp of the concepts you will study in this module. You will see in this module that equations and cash flows are the central features to understanding the time value of money. Cash flows often occur at times other than annually. For example, borrowers make payments on car loans monthly, and corporations pay interest on bond money semiannually. Thus, the module concentrates on how to use equations to deal with other than annual cash flows and compounding. When you finish this module you will be able to do the following: 1. Understand the concept of time value and the role of opportunity cost in determining the value of money received (or paid) at different times. 2. Calculate present and future values of individual cash flows and of annuities with periodic interest rates. 3. Solve financial problems involving mixed streams of cash flows and deferred annuities. 4. Understand the meaning of deferred annuity and of annuity due and to solve problems containing these types of annuities. 5. Use a business-financial calculator to make solving time value of money problems a quick and easy task. THE CONCEPT OF TIME VALUE To say that money has time value means that money's value depends upon when received. Receiving a dollar immediately permits people to use the dollar immediately. They can invest or buy consumer goods, each of which may be desirable. Waiting for a dollar means incurring an opportunity cost because you forgo the opportunity to invest in an alternative investment of equivalent risk. 1
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03: Page 2 of 29 Timing of Cash Flows A simple example illustrates the way the timing of cash flows affects financial decisions. Suppose that someone offers you a choice between receiving $10 six months from now or $10 one year from now. Cash-flow timelines illustrate each choice. Choice 1: Choice 2: Which would you prefer? Be careful, there’s a snake in the grass in the sense that your answer probably involves an implicit assumption. You would be
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This note was uploaded on 05/10/2010 for the course FINA 3770 taught by Professor Chandy during the Fall '08 term at North Texas.

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