Introduction To Valuation: The Time Value Of Money

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Introduction To Valuation The Time Value Of Money

• Chapter 4

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Topics

• How To Determine The Future Value Of An
  Investment
• How To Determine The Present Value Of Cash To Be
  Received At A Future Date
• How To Find The Return On An Investment

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Fundamental Financial Concept

• A dollar received today is worth more than a
  dollar received later
• This is because of interest ?
• This is because of the discount rate ?

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Definitions

• Simple interest
• Interest earned only on the original principal
  amount invested
• Compound interest
• Interest earned on both the initial principal and
  the interest reinvested from prior periods
• Interest on interest
• Interest earned on the reinvestment of pervious
  interest payments
• Compounding
• The process of accumulating interest in an
  investment over time to earn more interest

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Future value

• The amount an investment is worth after one or
  more periods

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Future Values (Textbook formula)

• Textbook FV PV(1 r)t
• FV future value
• PV present value
• r period interest rate, expressed as a decimal
• T number of periods
• Future value interest factor (1 r)t

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How To Determine The Future Value Of An Investment

• Suppose you invest 1000 for one year at 5 per
  year, compounded yearly. What is the future
  value in one year?
• Interest 1000(.05) 50
• Value in one year principal interest 1000
  50 1050
• Future Value (FV) 1000(1 .05) 1050
• Suppose you leave the money in for another year.
  How much will you have two years from now?
• FV 1000(1.05)(1.05) 1000(1.05)2 1102.50

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Effects of Compounding

• Simple interest
• Compound interest
• Consider the previous example
• FV with simple interest 1000 50 50 1100
• FV with compound interest 1102.50
• The extra 2.50 comes from the interest of .05(50)
  2.50 earned on the first interest payment

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Future Values Example 2

• Suppose you invest the 1000 from the previous
  example for 5 years, compounded yearly. How much
  would you have?
• 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, for a difference of
  26.28.)

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Future Values Example 3

• Suppose you had a relative deposit 10 at 5.5
  interest 200 years ago , compounded yearly. How
  much would the investment be worth today?
• FV 10(1.055)200 447,189.84
• What is the effect of compounding?
• Simple interest 10 200(10)(.055) 210.55
• Compounding added 446,979.29 to the value of the
  investment

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Present Value

• How much should you put in the bank today in
  order to receive a future value amount after one
  or more periods
• The current value of future cash flows discounted
  at the appropriate rate

If you know the future amount you would like,
assume an interest rate, and take all the
interest that you will need to earn out of the
future value amount
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Present Values (Textbook formula)

• How much do I have to invest today to have some
  amount in the future?
• Textbook 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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Definitions

• Discount Rate
• The rate used to calculate the present value of
  future cash flows
• Discount
• Calculate the present value of some future
  amounts
• Discounted Cash Flow (DCF) valuation
• Calculating the present value of future cash
  flows to determine its value today

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How To Determine The Present Value Of Cash To Be
Received At A Future Date

• 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, compounded yearly,
  how much do you need to invest today?
• PV 150,000 / (1.08)17 40,540.34

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Present Values Example 2

• 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, compounded yearly, how much
  did your parents invest?
• PV 19,671.51 / (1.07)10 10,000

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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,
  compounded yearly.
• 5 years PV 500 / (1.1)5 310.46
• 10 years PV 500 / (1.1)10 192.77

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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? (both
  compounded yearly).
• 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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How To Find The Return On An Investment

• If you invest 100 today in an account that
  compounds interest yearly and in 8 years you have
  200, what is the interest rate?
• Rule of 72 A reasonable estimate for the
  required rate to have an investment double
  72/(i/n) Number of periods

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How To Find The Number Of Periods Required For An
Investment

• If you want to buy an asset that cost 100,000
  and you have 50,000 to invest now, at a rate of
  12, compounded annually, how many years must you
  wait?

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Example Spreadsheet Strategies

• Use the following formulas for TVM calculations
• FV(rate,nper,pmt,pv)
• PV(rate,nper,pmt,fv)
• RATE(nper,pmt,pv,fv)
• NPER(rate,pmt,pv,fv)

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Real assets/ Financial assets

• Present value and future value are fundamental to
  finance
• Most instruments
• Real assets
• Buildings, trucks
• Financial assets
• Debt, Equity, Preferred stock, derivatives
• Can be analyzed using DCF valuation techniques