Lecture 3: Discounted Cash Flow Model

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Lecture 3 Discounted Cash Flow Model

• Lecturer Shaling Li
• AccFin Dept, PBS
• University of Portsmouth
• 22 October, 2009

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Re-cap from last week
Real world UK London exchange
Theoretical world Rationality Frictionless
market Liquidity Government role Models, results
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Structure of this lecture

• Nutshell of the Discounted Cash Flow (DCF)model
• Key definitions
• Modelling
• Applications

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Why use models?

• They are easy to understand representations of
  something we cannot normally see.
• Advantages
• Simplification of complex problems
• Scientific understanding of performance and
  fundamental Limits
• Simulations of systems
• Disadvantages
• Depends on the reliability of assumptions
• Cannot explain everything, has limitations

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Nutshell of this model
Input
Output
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Key definitions

• Time value of money
• The value of money earns a given amount of
  interest over a given amount of time
• Example 100 of today's money invested for one
  year and earning 5 interest will be worth 105
  after one year.
• Todays 100 is more valuable than tomorrows
  100
• Interest rate (i)
• A measure of time value of money
• Example 5

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Key definitions

• Present value (PV)
• Present value is the value on a given date of a
  future payment or series of future payments,
  discounted to reflect the time value of money and
  other factors.
• Example what is the present value of 100 one
  year later with interest rate 5? (Answer
  95.24)
• Future value (FV)
• Future value measures the nominal future sum of
  money that a given sum of money is "worth" at a
  specified time in the future assuming a certain
  interest rate.
• Example what is the future value of 100 in one
  year time with interest rate 5? (Answer 105)

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A very basic example
FV
PV
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Discounted Cash Flow Model

• More complexity added
• Single-period case to the multiple-period case
• Single cash flow to multiple of cash flows

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Complexity added-1

• The single-period case to the multiple-period
  case
• Example 100 of today's money invested for one
  year and earning 5 interest will be worth 105
  after one year.
• Example 100 of today's money invested for three
  years and earning 5 interest will be worth ???
  after three years.
• Simple interest method 100 31005 115
• Compounding interest method 100(15)3115.76

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PV with compounding interest

• 0 1
  2 3 4
  5

FV
PV
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Complexity added-2

• Future values (FV) of multiple of cash flows
• Example Invest 100 of today's money invested
  for first year, 150 in the beginning of the
  second year and 300 in the beginning of the
  third year, earning 5 interest. What would be
  the future value in the beginning of third year.
• Future value 100(15)3 150(15)2300(15
  ) 596.14
• 0 1 2
  3

100
150
300
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Complexity added-2

• Present values (PV)of multiple of cash flows
• Example Receive 100 in the end of the first
  year, 150 in the end of the second year and 300
  in the end of the third year, earning 5
  interest. What would be the present value of
  today.
• Present value 100/(15)150/(15)2300/(15)
  3 490.44
• 0 1 2
  3

300
150
100
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The full DCF model

• 0 1
  2 3 4
  5

FV
PV
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PV with multiple cash flows

• If there is a perpetual cash flow (in theory),
  how to calculate the present value?
• C constant cash flow in an unlimited years in
  the future
• i discount rate

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Important issues

1. Draw the timeline and cash flows
2. Be careful with money flow point (in the
   beginning or end of year t)
3. Be familiar with the simple model and the complex
   one

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Applications-Bond investment

• Bond should you buy the bond or not
• Here is the deal pay 977 to purchase the bond
  with face value 1000 with 10 fixed interest
  rate on the paper, matured in six years.
• Calculate present value of all the future cash
  flows

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Applications-Bond investment

• The present value of the bond will depend on the
  actual interest rate / discount rate (not the
  fixed interest rate on the bond)
• If actual interest rate is 8, PV1092, buy
• If actual interest rate is 10, PV1000, buy
• If actual interest rate is 12, PV917, not buy

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Application-Stock investment

• Invest in a stock and receive dividend annually
  (suppose perpetual cash flow)
• Example, the price for one share of company ABC
  is 250p per share and the dividend payout is 15p
  per share. The discount rate is 5
• Present value of the perpetual annual dividend
  income is 15/0.05300p
• Current price is 250p
• Conclusion Buy

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How to calculate it with Excel
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Important issues

• Bond investment
• How to know the interest rate/discount rate?
• Stock investment
• How to know the future cash flow?
• How to know the discount factor?
• There are the gaps between theory and real world.

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Summary

• Why use model to describe the real world?
• Key definitions to understand DCF model
• Basic model
• Complexity added to the model
• Application Bond and Stock investment