6thCh5P

# 6thCh5P - CHAPTER5...

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1 CHAPTER 5   (note: this is chapter 2 in the 5th edition of the text) Time Value of Money Future value Present value Annuities Rates of return Amortization

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2 A Dollar Today is Worth More  than a Dollar Tomorrow If you invest a dollar today, you will earn  interest during the year so that you will  have more than a dollar in the future.
3 Calculating Discounted  Cash Flows Where: PV = Present Value, FV = Future Value n = Number of periods i = Discount Rate, Hurdle Rate, or Opportunity Cost of Capital The ratio 1/(1+ i ) n Is often called the Discount Factor . ( 29 ) ( 1 1 or ) ( 1 , , n i n n n n i n n PVIF FV i FV PV FVIF PV i PV FV = + = = + =

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6 Investing for One Period Suppose you invest \$100 today at i =  0.1 per year. At the end of the year, you will receive:  FV = PV x (1 + i) = \$100 x (1.10) = \$110
7 How Much Do You Have to Invest  Today to Receive \$110 in a Year? PV = FV/(1+i) = \$110/1.1 = \$100 \$100 is the market value today of an  asset that generates \$110 in a year’s  time.

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8 Time lines show timing of cash  flows. CF 0 CF 1 CF 3 CF 2 0 1 2 3 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.
9 Four Ways to Find FVs and PVs Solve the equation with a regular  calculator. Use tables. Use a financial calculator. Use a spreadsheet.

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10 Solving for FV: The calculator method Solves the general FV equation. Requires 4 inputs into calculator, and will  solve for the fifth. (Set to P/YR = 1 and  END mode.) INPUTS OUTPUT N I/YR PMT PV FV 3 10 0 133.10 -100
11 PV = ? 100 What is the present value (PV) of \$100  due in 3 years, if I/YR = 10%? Finding the PV of a cash flow or series of  cash flows when compound interest is  applied is called discounting (the reverse of  compounding). The PV shows the value of cash flows in  terms of today’s purchasing power. 0 1 2 3 10%

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12 Solve FV n  = PV(1 + i ) n  for PV: ( 29 n n n n i + 1 1 FV = i + 1 FV = PV ( 29 ( 29 PV = \$100 1 1.10 = \$100 PVIF = \$100 0.7513 = \$75.13. i,n 3 .
13 Financial Calculator Solution Either PV or FV must be negative.  Here  PV = -75.13. Put in \$75.13 today, take out  \$100 three years from today. INPUTS OUTPUT N I/YR PMT PV FV 3 10 0 100 -75.13

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14 Time line for an ordinary  annuity of \$100 for 3 years   100 100 100 0 1 2 3 i%
15 What is the difference between an  ordinary annuity and an annuity due? Ordinary Annuity PMT PMT PMT 0 1 2 3 i% PMT PMT 0 2 3 PMT Annuity Due

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16 What is the PV of this uneven  cash flow stream? 0
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## This note was uploaded on 03/02/2011 for the course BMGT 340 taught by Professor White during the Spring '08 term at Maryland.

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6thCh5P - CHAPTER5...

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