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Unformatted text preview: Chapter 4 Discounted Cash Flow Valuation 42 Chapter Outline 4.1 The OnePeriod Case 4.2 The Multiperiod Case 4.3 Compounding Periods 4.4 Cash Flow Simplifications 4.5 Loan Types 4.6 What is a Firm Worth? 43 4.1 OnePeriod Case: Future Value In the oneperiod case, the formula for Future value (FV) is: FV = C ( 1 + r) C is cash flow today (time period zero) r is the appropriate interest rate. 44 OnePeriod Case: Present Value In the oneperiod case, the formula for present value (PV) is: r C PV + = 1 1 C 1 is the cash flow expected at date 1 r is the appropriate interest rate 45 OnePeriod Case: Net Present Value The Net Present Value (NPV) of an investment is the PV of the expected cash flows, minus the cost of the investment. In the oneperiod case: NPV = Cost + PV 46 4.2 Multiperiod Case: Future Value The general formula for the future value of an investment over many periods is: FV = C (1 + r) T Where C is cash flow at date 0, or the present value r is the appropriate interest rate, and T is the number of periods of investment . 47 4.2 Multiperiod Case: Future Value Assume Jay Ritter invested in the IPO of the M&M company. M&M pays a current dividend of $1.10 that is expected to grow at 40% per year for the next 5 years. What will the dividend be in 5 years? FV = C (1 + r) T $5.92 = $1.10(1.40) 5 48 Future Value and Compounding 1 2 3 4 5 10 . 1 $ 3 ) 40 . 1 ( 10 . 1 $ 02 . 3 $ ) 40 . 1 ( 10 . 1 $ 54 . 1 $ 2 ) 40 . 1 ( 10 . 1 $ 16 . 2 $ 5 ) 40 . 1 ( 10 . 1 $ 92 . 5 $ 4 ) 40 . 1 ( 10 . 1 $ 23 . 4 $ 49 Present Value and Discounting How much would an investor have to set aside today in order to have $20,000 five years from now if the current rate is 15%? 1 2 3 4 5 $20,000 PV 5 ) 15 . 1 ( 000 , 20 $ 53 . 943 , 9 $ = 410 How Long is the Wait? If you deposit $5,000 today in an account paying 10%, how long does it take to grow to $10,000? T r C FV ) 1 ( + = T ) 10 . 1 ( 000 , 5 $ 000 , 10 $ = FV = $ 10,000 PV = $5000 I/Y = 10 Solve for N = 7.27 years 411 Assume the total cost of a college education will be $50,000 when your child enters college in 12 years. You have $5,000 to invest today. What rate of interest must you earn on your investment to cover the cost of your childs education? What Rate Is Enough? T r C FV ) 1 ( + = 12 ) 1 ( 000 , 5 $ 000 , 50 $ r + = FV = $50,000 PV = $5000 N = 12 Solve for I/Y = 21.15% 412 Multiple Cash Flows Consider an investment that pays $200 one year from now, with cash flows increasing by $200 per year through year 4. If the interest rate is 12%, what is the present value of this stream of cash flows?...
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 Spring '06
 Hadaway
 Compounding, Corporate Finance, Valuation

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