4400_Chapter_5 - The Time Value of Money 1 Outline 1 The...

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1 The Time Value of Money
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2 Outline 1 The One-Period Case 2 The Multiperiod Case 3 Compounding Periods 4 Simplifications 5 What Is a Firm Worth? 6 Summary and Conclusions
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3 1 The One-Period Case: Future Value The total amount due at the end of the investment is called the Future Value (FV). In the one-period case, FV = C 0 × (1 + r ) Where C 0 is cash flow at date 0 and r is the appropriate interest rate. FV = $10,500 Year 0 1 C 0 = $10,000 $10,000 · 1.05 C 0 ×(1 + r )
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4 1 The One-Period Case: Present Value 05 . 1 000 , 10 $ 81 . 523 , 9 $ = The amount that a borrower would need to set aside today to be able to meet the promised payment of a certain target C 1 (say $10,000) in one year is called the Present Value ( PV ). r C PV + = 1 1 ; Thus, with interest rate r = 5 percent, PV of $10,000 is:
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5 1 The One-Period Case: Net Present Value The Net Present Value ( NPV ) of an investment is the present value of the expected cash flows, less the cost of the investment. In the one-period case, the formula for NPV can be written as: PV Cost NPV + - =
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6 2 The Multiperiod Case: Future Value The general formula for the future value of an investment over many periods can be written as: FV = C 0 × (1 + r ) T Where C 0 is cash flow at date 0, r is the appropriate interest rate, and T is the number of periods over which the cash is invested.
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7 2 Example: The Multiperiod Case (Future Value) Jay Ritter invested in the initial public offering of the Modigliani company. Modigliani pays a current dividend of $1.10, which is expected to grow at 40- percent per year for the next five years. What will the dividend be in five years? FV = C 0 × (1 + r ) T $5.92 = $1.10 × (1.40) 5
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