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**Unformatted text preview: **Chapter 4 Discounted Cash Flow Valuation 4-2 Chapter Outline 4.1 The One-Period 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? 4-3 4.1 One-Period Case: Future Value • In the one-period 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. 4-4 One-Period Case: Present Value • In the one-period 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 4-5 One-Period 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 one-period case: NPV = – Cost + PV 4-6 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 . 4-7 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 4-8 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 $ 4-9 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 $ = 4-10 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 4-11 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 child’s 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% 4-12 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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