Discounted Cash Flow Valuation

Discounted Cash Flow Valuation - Discounted Cash Flow...

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Discounted Cash Flow Valuation
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Outline Do you remember? How to calculate present value, future value, interest rate, with and without calculator. Net Present Value Perpetuities and Annuities
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1 The One-Period Case: Future Value The total amount due at the end of an investment is called the Future Value ( FV ). In the one-period case, the formula for FV can be written as: FV = PV ×(1 + r ) Where PV (present value) is the cash flow today (time zero) and r is the appropriate interest rate.
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1 The One-Period Case: Future Value Example: If you invest $10,000 at 5% annual interest, how much will your investment grow in 1 year? $10,000 is the principal repayment ($10,000 × 1) $500 is the interest ($10,000 × .05) $10,500 is the total due. It can be calculated as: $10,000×(1.05) = $10,500 = FV
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1 The One-Period Case: Present Value In the one-period case, the formula for the present value PV can be written as: r FV PV + = 1 Where FV (future value) is the cash flow at date 1 and r is the appropriate interest rate.
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1 The One-Period Case: Present Value If you make $10,000 in one year when interest rates are at 5%, how much is your investment worth today? 81 . 523 , 9 $ 05 . 1 000 , 10 $ = The amount that a borrower would need to set aside today to to able to meet the promised payment of $10,000 in one year is call the Present Value (PV) of $10,000. Note that $9,523.81×(1.05) = $10,000 = + = r FV PV 1
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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: NPV = – Cost + PV Example : Suppose an investment that promises to pay $10,000 in one year is offered for sale for $9,500. Your interest rate is 5% (the interest you get by putting the money in the bank instead of buying the investment). Should you buy?
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1 The One-Period Case: Net Present Value If we did not undertake the positive NPV project, and instead invested our $9,500 in the bank at 5 %, our FV would be less than $10,000 and we would be worse off: $9,500×(1.05) = $9,975 < $10,000. 81 . 23 $ 81 . 523 , 9 $ 500 , 9 $ 05 . 1 000 , 10 $ 500 , 9 $ = + - = + - = NPV NPV NPV Yes!
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2 The Multiperiod Case: Future Value The general formula for the future value of an investment over many periods can be written as: FV = PV ×(1 + r ) T Where PV is the cash flow at date 0, r is the appropriate interest rate T is the number of periods over which the cash is invested.
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Future Value Example: Suppose that Jay Ritter invested in the Modigliani company. Modigliani pays a current dividend of $1.10 per year, which is expected to grow at 40 % per year for the next five years. What will the dividend be in five years?
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Discounted Cash Flow Valuation - Discounted Cash Flow...

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