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Unformatted text preview: Finance 2007  2  Chapter 4,5 Discounted Cash Flow Valuation 42 Chapter Outline Valuation: The OnePeriod Case The Multiperiod Case Compounding Periods Simplifications (Annuities & Perpetuities) What Is a Firm Worth? 43 Basic Definitions Time Line PV (Present Value, h&&& ): earlier money on a time line FV (Future Value, h&&& ): later money on a time line r (Interest rate, h& ): exchange rate between earlier money and later money Discount rate( h&& ), Cost of capital( h&&& ) Opportunity cost of capital, Required return( N G x ) 1 2 t PV FV 44 Future Values 1 $1,000 FV=? r = 5% Interest = 1000 x .05 = 50 Value in one year = principal + interest = 1,000 + 50 = 1,050 Future Value (FV) = 1,000 x (1 + .05) = 1,050 Example: 1 year Example: 2 year 2 $1,000 FV=? r = 5% 1 FV = 1,000 x 1.05 x 1.05 = 1,102.50 45 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 46 Effects of Compounding Simple interest( h& ) FV with simple interest = 1000 + 50 + 50 = 1100 Compound interest( h& ) FV with compound interest = 1000 + 50 + 52.50 = 1102.50 The extra 2.50 comes from the interest = .05 x 50 = 2.50 2 $1,000 FV=? r = 5% 1 47 Future Values Example: 5 year FV = 1,000 x (1.05) 5 = 1,276.28 The effect of compounding is small for a small number of periods increases as the number of periods increases FV with simple interest = $1,250 1 2 5 $1,000 FV=? r = 5% 48 Future Values: compound effect 49 Future Values Example: 200 year FV = 10 x (1.055) 200 = 447,189.84 1 2 200 $10 FV=? r = 5.5% The effect of compounding Simple interest = 10 + 200(10)(.055) = 120.00 Compounding added $447,069.84 to the value of the investment 410 Future Values 411 FV as a General Growth Suppose your company expects to increase unit sales of widgets by 15% per year for the next 5 years. If you currently sell 3 million widgets in one year, how many widgets do you expect to sell in 5 years? FV = 3,000,000(1.15) 5 = 6,034,072 1 2 5 3,000,000 FV=? r = 15% 412 Present Values How much do I have to invest today to have some amount in the future? FV = PV(1 + r) t PV = FV / (1 + r) t Discounting mean finding the present value of some future amount. Value the present value unless we specifically indicate that we want the future value. 413 Present Values Example1: need $10,000 for a new car, 1 yr, 7% Example2: prepare daughters college tuition $150,000 , 17 yr, 8% 1 PV=?...
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This note was uploaded on 04/18/2010 for the course BUSINESS 231 taught by Professor Steven during the Spring '10 term at 카이스트, 한국과학기술원.
 Spring '10
 steven
 Management, Compounding, Valuation

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