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1 Time Value Analysis Corporate Finance Dr. A. DeMaskey

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2 Learning Objectives Questions to be answered: What is time value of money? What is compounding? Discounting? How are the principles of time value analysis applied to the various types of cash flows? What different types of interest rates are used in finance?

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3 Basic Concepts Why time value of money? Evaluating financial transactions Expected cash flows Risk

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4 Time Lines CF 0 CF 1 CF 3 CF i% Tick marks at ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2.

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5 Single Cash Flow Year i% Time line for a $100 lump sum due at the end of Year 2.

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6 Even Cash Flows: Annuity i% Time line for an ordinary annuity of $100 for 3 years.

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i% -50 Uneven Cash Flows

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8 Compounding FV = ? % Finding FVs (moving to the right on a time line) is called compounding. 100

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9 10% Finding PVs is discounting, and it’s the reverse of compounding PV = ? Discounting

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10 Three Ways to Solve TVM Problems Solve the equation with a regular calculator. Use a financial calculator. Use a spreadsheet.

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11 Time Value of A Lump Sum Future Value Present Value

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12 Time Value of a Series of Even Cash Flows Types of Annuities Ordinary annuity Annuity due Perpetual annuity Future Value Present Value

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% FV= 331 Future Value of an Ordinary Annuity

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14 Present Value of an Ordinary Annuity % = PV

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15 Ordinary Annuity PMT 0123 i% PMT 0123 i% PMT Annuity Due Difference Between an Ordinary Annuity and an Annuity Due PVFV

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16 Time Value of Uneven Cash Flows Present Value Sum of PVs of individual cash flow components Future Value Sum of FVs of individual cash flow components

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17 Compounding Periods Periodic Rate i Per = i Nom /m Annual Percentage Rate (APR) i Nom = i Per x m Effective Annual Rate (EAR) EFF% = (1 + i Nom /m) m – 1.0

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