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Chapter 2 The Time Value of Money Time Discounting One of the basic concepts of business economics and managerial decision making is that the value of an amount of money to be received in the future depends on the time of receipt or disbursement of the cash. A dollar received today is more valuable than a dollar to be received in the future. The only requirement for this concept to be valid is that there be a positive rate of interest at which funds can be invested. The time value of money affects a wide range of business decisions, and a knowledge of how to incorporate time value considerations systematically into a decision is essential to an understanding of Fnance. This chapter is devoted to describing the mathematical models of compound interest. The objective is to develop skills in Fnding the present equivalent of a future amount and the future equivalent of a present amount. The Interest Rate A dollar available today is more valuable than a dollar available one period from now if desirable investment opportunities exist. There are two primary reasons why real investments can generate an interest return: 1. Some types of capital increase in value through time because of changes in physical characteristics, for example, cattle, wine, and trees. 2. There are many work processes where roundabout methods of production are desirable, leading to increased productivity. If you are going to cut down a large tree, it may be worth investing some time to sharpen your axe. A sharp axe may result in less time being spent cutting down trees (including sharpening time) than working with a dull axe. If you are going to dig a hole, you might want to 13
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14 An Introduction to Accounting and Managerial Finance build or buy a shovel, or even spend the time to manufacture a backhoe if it is a big hole. The investment increases productivity sufFciently compared to the alternative methods of production without capital so that the new asset can earn a return for the investor. These characteristics of capital lead to a situation in which business entities can pay interest for the use of money. If you invest $1 in an industrial Frm, the Frm may be able to pay you $1 plus interest if your investment enabled the Frm to use some roundabout method of production or to delay the sale of an item while it increased in value. Future Value Assume that you have $1.00 now and can invest it to earn r interest. After one period, you will have the $1.00 plus the interest earned on the $1. Let FV be the future value and r be the annual interest rate. Then, FV = 1 + r. Repeating the process, at time 2 you will have FV = ( 1 + r) + r( 1 + r) = ( 1 + r) 2 and the future value of $1.00 invested for n periods is FV = ( 1 + r) n . If r = 0 . 10 and n = 2, we have FV = ( 1 + r) n = ( $1 . 10 ) 2 = $1 . 21 . If instead of starting with $1 we start with a present value, PV , of $50, the value at time 2 is FV = PV( 1 + r) n (2.1) FV = 50 ( 1 . 10 ) 2 = $60 . 50 .
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This note was uploaded on 05/10/2010 for the course FMT 0438310384 taught by Professor Hung during the Spring '10 term at Aarhus Universitet, Aarhus.

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