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Unformatted text preview: Time Value of Money Lecture 6 Myung Joo Song ECON 393 Fall 2011 Myung Joo Song (ECON 393) Time Value of Money Fall 2011 1 / 31 Chapter Outline Future Value and Compounding Present Value and Discounting More about Present and Future Values (Examples) Myung Joo Song (ECON 393) Time Value of Money Fall 2011 2 / 31 Present and Future Value Present Value: earlier money on a time line. Future Value: later money on a time line Single Future Cash Flow in this lecture. (Next lecture, multiple Future Cash Flows) Interest and Interest Rate: Exchange rate between earlier money and later money. Discount rate Cost of capital Opportunity cost of capital Required return Myung Joo Song (ECON 393) Time Value of Money Fall 2011 3 / 31 Future Value: One period Suppose you deposit present value of $1,000 in your saving account for one year at 5% interest rate per year. What is the future value in one year? You collect after 1 year: Interest = 1,000(.05) = $50 Principal or Present Value = $1000 Future Value (FV) = 1,000 +1000 (.05) = $1,050 Note that: Future Value = Principal + Interest Payments Myung Joo Song (ECON 393) Time Value of Money Fall 2011 4 / 31 Future Value: Two and More Periods Suppose you leave the money in for another year. How much will you have two years from now? After first year you receive $1050: Principal of $1000 Interest of $50 After second year you receive 1000+1050(.05): Principal of $1000 Interest of 1050*(.05) = 1000 (.05)+50(.05) 50(.05) is interest on interest FV = 1000*(1+.05)(1+.05) = PV(1 + interest rate) 2 Myung Joo Song (ECON 393) Time Value of Money Fall 2011 5 / 31 Future Value: General Formula Single cash flow formula: FV = PV (1 + r ) T = PV (1 + r )(1 + r ) ... (1 + r )  {z } T times where FV: Future Value or Future Cash Flow PV: Amount you invest r: Interest rate per one period  discount rate T: Number of periods Myung Joo Song (ECON 393) Time Value of Money Fall 2011 6 / 31 Effects of Compounding Simple interest: Calculated on the original principal (e.g. $1000) only. Compound interest: Calculated on the original principal and all interest accumulated (Interest on Interest) In previous example: FV with simple interest = 1,000 + 50 + 50 = $1,100 FV with compound interest = $1,102.50 The extra 2.50 comes from the interest of .05(50) = $2.50 earned on the first interest payment Myung Joo Song (ECON 393) Time Value of Money Fall 2011 7 / 31 Example: Future Values Suppose you invest the $1,000 from the previous example for 5 years. How much would you have?...
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This note was uploaded on 10/25/2011 for the course ECON 393 taught by Professor D during the Spring '10 term at Rutgers.
 Spring '10
 D

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