Figure 4'2

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Figure 4.2
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4.1.5 Calculator Keys

• Texas Instruments BA-II Plus
• FV future value
• PV present value
• I/Y period interest rate
• Interest is entered as a percent, not a decimal
• P/Ypayment per year
• C/Ycompounding period per year
• N number of periods
• Remember to clear the registers (CE/C)(2ND) (CLR
  TVM) before solving each problem
• Other calculators are similar in format

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4.1.6 Settings

• Decimal (2)
• (2ND) (FORMAT) (2 OR 4) (ENTER)
• P/Y (Payments per year) 1
• C/Y (Compounding periods per year) 1
• (2ND) (P/Y) (1) (ENTER) (shift DOWN)
  (1)(ENTER)
• END-OF-PERIOD
• (2ND)(BGN)(2ND)(SET)(CE/C)
• How to avoid mistakes in using the calculator(P94)

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4.1.7 Example 1 (on P93)

• -100 (key in 100 and key in /-) PV
• 5 N
• 10 (decimal) I/Y
• CPT FV
• Got FV 161.05

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4.1.8 Future Values Example 2

• Suppose you invest the 1000 at 5 for 5 years.
  How much would you have at maturity?
• FV 1000(1.05)5 1276.28
• The effect of compounding is small for a small
  number of periods, but increases as the number of
  periods increases.
• Simple interest would have a future value of
  1250 (1000 (10.055) 1250), for a difference
  of 26.28

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4.1.9 Future Values Example 3

• Suppose you had a deposit 10 at 5.5 interest
  200 years ago. How much would the investment be
  worth today?
• FV 10(1.055)200 447,189.84
• What is the effect of compounding?
• Simple interest 10(1 2000.055) 120.00
• Compounding added 447,069.84 to the value of the
  investment

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4.1.10 Example 4-the value of Manhattan

• The deal of for Manhanttan (P92)
• In 1626, Peter Minuit bought Manhattan Island for
  USD24 in goods and trinkets(???? ). Is it a good
  deal to Peter?
• Suppose Peter invested USD24 at 8, what is the
  value at 2006 (total 380 years)?

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4.1.10 Example 4-the value of Manhattan
Work it with calculator, N380, I/Y8, PV-24,
CPT FV we get the same result.
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4.1.10 Example 4-the value of Manhattan

• 8 is too high, what about 5?
• N5
• FV27.05? ?!

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4.1.11 Example 5- WARRAN BUFFETS MIRACLE

• http//cn.finance.yahoo.com/q?sBRKA

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????? 83,350.00 ???? 2009?3?19? ?? 1,150.00
(1.40) ???? 82,200.00 ?? 83,500.00 ?? ?
?? ? ?????? 92,500.00 ?????? 81,700.00
- 84,850.00 52????? 78,800.00 - 92,000.00 ???
1,453 ?????(3??) 48,578.1 ?? 1,294.43?
???(12??) 25.85 ????(12??) 3,224.10 ?????
N/A ()
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4.1.11 Example 5- WARRAN BUFFETS MIRACLE

• BERKSHIRE HATHAWAY-No dividend payout all the
  years.
• Share price in 1965 19
• Share price in 2009? 83350
• What is the compounding interest rate through the
  years(44 years)?

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4.1.11 The growth rate of Birkshere Hathaway

• (CE/C)(2ND) (CLR TVM)
• -19 PV
• 44 N
• 83350 FV
• (2ND) P/Y 1 ENTER C/Y 1 ENTER
• CPT I/Y
• 20.9974

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4.1.11 Example 5- WARRAN BUFFETS MIRACLE

• Simple interest
• If BIRKSHIRE HATHAWAY had paid out all its profit
  every year to the shareholders, what is the total
  value which the shareholders received (suppose
  the shareholder had hold 1 share and sold in
  2006)
• 19(10.2144)194.56

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????????????

• ?????????????????????
• ???,1850 ???,????????????60 ??????,???6??????,?1
  50 ??????,???????????30 ??????? ???
  ????

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????????????

• ??????,????,?????????????????????????????????100?
  ??,??????18?,16???????(???)??? ??? ????
• ???????!

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????????????

• ???????,?????????????????,????????????????

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4.2 Present Values ??

• How much do I have to invest today to have some
  amount in the future?
• FV PV(1 r)t
• Rearrange to solve for PV FV / (1 r)t
• When we talk about discounting, we mean finding
  the present value of some future amount.
• When we talk about the value of something, we
  are talking about the present value unless we
  specifically indicate that we want the future
  value.

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4.2.1 Present value ??

• Discounting factor

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4.2.2 PV One Period Example

• Suppose you need 10,000 in one year for the down
  payment (??) on a new car. If you can earn 7
  annually, how much do you need to invest today?
• PV 10,000 / (1.07)1 9345.79
• Calculator
• 1 N
• 7 I/Y
• 10,000 FV
• CPT PV -9345.79

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4.2.3 Present Values Example 2

• You want to begin saving for you daughters
  college education and you estimate that she will
  need 150,000 in 17 years. If you feel confident
  that you can earn 8 per year, how much do you
  need to invest today?
• PV 150,000 / (1.08)17 40,540.34

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4.2.4 Present Values Example 3

• Your parents set up a trust fund for you 10 years
  ago that is now worth 19,671.51. If the fund
  earned 7 per year, how much did your parents
  invest?
• PV 19,671.51 / (1.07)10 10,000

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4.2.5 PV Important Relationship I

• For a given interest rate the longer the time
  period, the lower the present value
• What is the present value of 500 to be received
  in 5 years? 10 years? The discount rate is 10
• 5 years PV 500 / (1.1)5 310.46
• 10 years PV 500 / (1.1)10 192.77

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4.2.6 PV Important Relationship II

• For a given time period the higher the interest
  rate, the smaller the present value
• What is the present value of 500 received in 5
  years if the interest rate is 10? 15?
• Rate 10 PV 500 / (1.1)5 310.46
• Rate 15 PV 500 / (1.15)5 248.58

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Figure 4.3
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4.3.1 The Basic PV Equation - Refresher

• PV FV / (1 r)t
• There are four parts to this equation
• PV, FV, r and t
• If we know any three, we can solve for the fourth
• If you are using a financial calculator, be sure
  and remember the sign convention (????),e.g.
  (/-) or you will receive an error when solving
  for r or t

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4.3.2 Discount Rate

• Often we will want to know what the implied
  interest rate is in an investment
• Rearrange the basic PV equation and solve for r
• FV PV(1 r)t
• r (FV / PV)1/t 1
• If you are using formulas, you will want to make
  use of both the yx and the 1/x keys

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4.3.3 Discount Rate Example 1

• You are looking at an investment that will pay
  1200 in 5 years if you invest 1000 today. What
  is the implied rate of interest?
• r (1200 / 1000)1/5 1 .03714 3.714
• Calculator the sign convention matters!!!
• N 5
• PV -1000 (you pay 1000 today)
• FV 1200 (you receive 1200 in 5 years)
• CPT I/Y 3.714

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4.3.4 Discount Rate Example 2

• Suppose you are offered an investment that will
  allow you to double your money in 6 years. You
  have 10,000 to invest. What is the implied rate
  of interest?
• r (20,000 / 10,000)1/6 1 .122462 12.25