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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)
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.
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.
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.
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.
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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