# L2-2 - Lecture 2 The Time Value of Money Key Concepts and...

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Lecture 2 The Time Value of Money

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2 Key Concepts and Skills -- Part 1 Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received at some future date Be able to compute the return on an investment
3 Lecture Outline -- Part 1 Future Value and Compounding Present Value and Discounting More on Present and Future Values

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4 Congratulations! You have just won the lottery! The lottery officials told you that there were three options for you to claim the prize. (A) Receiving \$3,000,000 now (B) Receiving \$1,000,000 now and \$2,002,500 three years later (C) Receiving \$3,008,000 one year from now 1\$ today = 1\$ tomorrow  ?
5 Factors Affecting Cost of Money Time preferences for consumption Higher savings lead to lower cost. Risk Higher risk lead to higher cost. Expected inflation Higher inflation rate lead to higher cost. Production opportunities More opportunities during economic expansion means more corporate demand for capital, causing higher cost of money.

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6 Basic Definitions Present Value – earlier money on a time line Future Value – later money on a time line Interest rate – “exchange rate” between earlier money and later money Discount rate Cost of capital Opportunity cost of capital Required return
7 Time lines Show the timing of cash flows. Eg. , time 1 is the end of the first period (year, month, etc.) or the beginning of the second period. CF 0 CF 1 CF 3 CF 2 0 1 2 3

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8 Future Values Suppose you invest \$1000 for one year at 5% per year. What is the future value in one year? Interest = 1,000(.05) = 50 Value in one year = principal + interest = 1,000 + 50 = 1,050 Future Value (FV) = 1,000(1 + .05) = 1,050 Suppose you leave the money in for another year. How much will you have two years from now? FV = 1,000(1.05)(1.05) = 1,000(1.05) 2 = 1,102.50
9 Future Values: General Formula FV = PV(1 + r) t FV = future value PV = present value r = period interest rate, expressed as a decimal T = number of periods Future value interest factor = (1 + r) t

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10 Effects of Compounding Simple interest (interest is earned only on the original principal) Compound interest (interest is earned on principal and on interest received) Consider the 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

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12 Effects of Compounding– Example Suppose you invest the \$1,000 from the previous example for 5 years. How much would you have? FV = 1,000(1.05)
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L2-2 - Lecture 2 The Time Value of Money Key Concepts and...

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