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Chap004 - OCT 12TH LECTURE

Chap004 - OCT 12TH LECTURE - Key Concepts and Skills Be...

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Key Concepts and Skills box3 Be able to compute the future value and/or present value of a single cash flow or series of cash flows 4-0 box3 Be able to compute the return on an investment box3 Be able to use a spreadsheet to solve time value problems (not now, after the midterm!) box3 Understand perpetuities and annuities
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Chapter Outline 4.1 Valuation: The One-Period Case 4.2 The Multiperiod Case 4.3 Compounding Periods 4-1 4.4 Simplifications 4.5 Loan Amortization (after midterm) 4.6 What Is a Firm Worth? (after midterm)
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4.1 The One-Period Case box3 If you were to invest $10,000 at 5-percent interest for one year, your investment would grow to $10,500. $500 would be interest ($10,000 × .05) 4-2 $10,000 is the principal repayment ($10,000 × 1) $10,500 is the total due. It can be calculated as: $10,500 = $10,000 × (1.05) boxshadowdwn The total amount due at the end of the investment is call the Future Value ( FV ).
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Future Value box3 In the one-period case, the formula for FV can be written as: FV = C 0 × (1 + r ) 4-3 Where C 0 is cash flow today (time zero), and r is the appropriate interest rate.
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Present Value box3 If you were to be promised $10,000 due in one year when interest rates are 5-percent, your investment would be worth $9,523.81 in today s dollars. 000 , 10 $ = 4-4 05 . 1 81 . 523 , 9 $ The amount that a borrower would need to set aside today to be able to meet the promised payment of $10,000 in one year is called the Present Value ( PV ). Note that $10,000 = $9,523.81 × (1.05).
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Present Value box3 In the one-period case, the formula for PV can be written as: C 4-5 r PV + = 1 1 Where C 1 is cash flow at date 1, and r is the appropriate interest rate.
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Net Present Value box3 The Net Present Value ( NPV ) of an investment is the present value of the expected cash flows, less the cost of the investment. 4-6 box3 Suppose an investment that promises to pay $10,000 in one year is offered for sale for $9,500. Your interest rate is 5%. Should you buy?
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Net Present Value 81 . 523 , 9 $ 500 , 9 $ 05 . 1 000 , 10 $ 500 , 9 $ + - = + - = NPV NPV 4-7 81 . 23 $ = NPV The present value of the cash inflow is greater than the cost. In other words, the Net Present Value is positive, so the investment should be purchased.
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Net Present Value In the one-period case, the formula for NPV can be written as: NPV = – Cost + PV 4-8 If we had not undertaken the positive NPV project considered on the last slide, and instead invested our $9,500 elsewhere at 5 percent, our FV would be less than the $10,000 the investment promised, and we would be worse off in FV terms : $9,500 × (1.05) = $9,975 < $10,000
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4.2 The Multiperiod Case box3 The general formula for the future value of an investment over many periods can be written as: FV = C × (1 + r ) T 4-9 0 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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Future Value box3 Suppose a stock currently pays a dividend of $1.10, which is expected to grow at 40% per year for the next five years.
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