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**Unformatted text preview: **Finance 2007  2  Chapter 4,5 Discounted Cash Flow Valuation 4-2 Chapter Outline • Valuation: The One-Period Case • The Multiperiod Case • Compounding Periods • Simplifications (Annuities & Perpetuities) • What Is a Firm Worth? 4-3 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 … 4-4 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 4-5 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 4-6 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 4-7 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% 4-8 Future Values: compound effect 4-9 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 4-10 Future Values 4-11 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% 4-12 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. 4-13 Present Values • Example1: need $10,000 for a new car, 1 yr, 7% • Example2: prepare daughter’s college tuition $150,000 , 17 yr, 8% 1 PV=?...

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