lecture_chap05_06A

lecture_chap05_06A - Time Value of Money Introduction to...

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Time Value of Money Introduction to the time value of money Chapter 5 (All sections) Future Value, Present Value, Interest rates and number of periods Chapter 6 (Sections 6.1 and 6.2) Annuities and perpetuities Remainder of chapter will be covered next week
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Basic Definitions Time value of money – a dollar in hand now is worth more than a dollar later 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. Also called the discount rate, cost of capital, opportunity cost of capital or required return
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Introduction to interest Simple interest for a single year is calculated as: Interest amount = Present value * r For example, if you invest $100 for one year at 5%, then: Interest amount = 100 * 5% = 5 The future value of the investment is: Future value = Present value + interest amount = 100 + 5 = 105 Stated another way: Future value = Present value * (1+r) Future value = 100 * (1+5%) = 100 * 1.05 = 105 Next: Extend this to multiple periods
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Future Value: General Formula FV = PV(1 + r) t FV = future value PV = present value r = period interest rate, expressed as a decimal (for example r = 0.05) t = number of periods Future value interest factor is (1 + r) t
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Future Value – Example 1 – 5.1 1. Suppose you invest $1000 for one year at 5% per year. What is the future value in one year? The present value is $1000, the interest rate is 5% and the future value is the unknown. FV= 1000(1 + .05) = 1050 1. Suppose you invest $1000 for two years at 5% per year. What is the future value in two years? FV = 1000(1.05)(1.05) = 1000(1.05) 2 = 1102.50
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Effects of Compounding Simple interest – earn interest on principal only Compound interest – earn interest on principal and reinvested interest Consider the previous example FV with simple interest = 1000 + 50 + 50 = 1100 FV with compound interest = 1102.50 The extra 2.50 comes from the interest of . 05(50) = 2.50 earned on the first interest payment
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Calculator Your financial calculator performs these types of calculations efficiently. Financial calculators include these variables and label them as: Future value as “FV” Present value as “PV” Interest rate as “I” or “I/YR” or “%i” Number of periods as “N” There is variation across calculators. See the calculator manual for the entry pattern. For example, some calculators make you hit Enter and Compute and others don’t. Read the calculator tips on pages 123 to 125 if you’re having trouble operating your calculator. Excel works similarly – you just need to use the functions PV and FV.
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Future Value – Example 2 Suppose you invest $1000 for 5 years. How much would you have?
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