ch2 - Chapter 2 The Time Value of Money ECO389 Spring 2010...

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Chapter 2: The Time Value of Money ECO389, Spring 2010 This chapter is Chapter 5 in the textbook. 1 Introduction This chapter is entitled “ Value ,” the time dimension of value is presented. The scope of business decisions covers a considerable length of time. The values of cash ﬂows related to those decisions occurring over this wide time period are affected by the time value of money. Most decisions focus on doing something today, investments, with returns ﬂowing over future time periods. It is important to understand that cash ﬂows in different time periods are not comparable and must be adjusted to a common time period, usually to the present, before comparison and analysis can be performed. This adjustment reﬂects the opportunity cost of alternative investment and the adjustment focus in most decisions is the current period, the present. The chapter starts relatively simple with compound interest and slowly builds. The cash ﬂows discussed in the first part of the chapter are assumed to hold their purchasing power across time periods. Inﬂation, or the steady decline in purchasing power, is introduced in the last section of the chapter. If the purchasing power of money is declining in the future, then one should “discount” this cheaper value via a higher “I” and a lower present value. This is the first “valuation” chapter and the authors have carefully included prob- lems and examples in the chapter with valuation concepts, ideas, examples, etc., that will be presented formally in the next few chapters. Review the concepts to come in the next couple of chapters and treat this chapter as a building block to accomplish understanding of the valuation process. 1

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2 Simple Interest 2.1 Definition Only the principal not the accrued interest from previous periods is used to calculate the interest payment in a period. 2.2 Example You decide to invest \$1,000 in a bank account which pays you 10% simple interest per year . How much do you receive at the end of five years? 3 Compound Interest 3.1 Definition Both the principal and the accrued interest from previous periods are used to calculate the interest amount in next period. (i.e. interest is earned on the interest) 3.2 Example Your saving account is calculated by compound interest. The bank calculate the interest you have earned every half year. You decide to invest \$1,000 in a bank account which pays you 10% interest per year compounded annually. How much do you receive at the end of five years? 2
Difference between compound interest and simple interest 3.3 Compound Interest Equation 1. value after 1 year = initial amount + interest = initial amount * (1+ int.rate/yr ) 2. value after 2 years = ( value after 1 year ) * (1 + int.rate/yr ) 3. value after 3 years = ( val. after 2 years ) * (1 + int.rate/yr ) = ( initial amt ) * (1 + int.rate ) * (1 + int.rate ) * (1 + int.rate ) 4. value after t years = ( initial amt ) * (1 + r ) t –Attention: the above equation assumes that interest is compounded ”annually”.

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