lecture04 - Introduction to Valuation: The Time Value of...

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Introduction to Valuation: The Time Value of Money 1
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2 Key Concepts and Skills We will compute the future value of an investment made today the present value of cash to be received at some future date the return on an investment the number of periods that equates a present value and a future value given an interest rate We will use a financial calculator and a spreadsheet to solve time value of money problems
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3 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
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4 Future Values Suppose you invest $1,000 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
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5 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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6 Effects of Compounding Simple interest Compound interest 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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7 Calculator Keys Texas Instruments BA-II Plus FV = future value PV = present value I/Y = period interest rate P/Y must equal 1 for the I/Y to be the period rate Interest is entered as number of percent, not a decimal N = number of periods Remember to clear the registers (CLR TVM) after each problem Other calculators are similar in format
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8 Future Values – Example 2 Suppose you invest the $1,000 from the previous example for 5 years. How much would you have? FV = 1,000(1.05) 5 = 1,276.28 5 N; 5 I/Y; -1,000 PV CPT FV = 1,276.28 Note the sign convention on the calculator: Cash outflows are negative and inflows are positive. The effect of compounding is small for a small number of
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This note was uploaded on 03/13/2009 for the course BUAD FINANCE taught by Professor Selvili during the Fall '08 term at USC.

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lecture04 - Introduction to Valuation: The Time Value of...

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