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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 2 0123 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 100 012 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 100 0123 i% Time line for an ordinary annuity of $100 for 3 years.

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7 100 50 75 0123 i% -50 Uneven Cash Flows

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8 Compounding FV = ? 0123 10% 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. 100 0123 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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13 100 0123 10% 110 121 FV= 331 Future Value of an Ordinary Annuity

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14 Present Value of an Ordinary Annuity 100 0123 10% 90.91 82.64 75.13 248.69 = 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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