1. Lecture 3: Discounted Cash Flow Model
Lecturer: Shaling Li
Acc&Fin Dept, PBS
University of Portsmouth
22 October, 2009

2. Liquidity Government role
Re-cap from last week
Real world:
UK London exchange
Theoretical world:
Rationality
Frictionless market
Liquidity Government role +
Models, results
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3. Structure of this lecture
Nutshell of the Discounted Cash Flow (DCF)model
Key definitions
Modelling
Applications
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4. 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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5. Nutshell of this model
Input
Output
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6. Key definitions Time value of money Interest rate (i)
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.
Today’s £100 is more valuable than tomorrow’s £100
Interest rate (i)
A measure of time value of money
Example: 5%
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7. Key definitions Present value (PV) Future value (FV)
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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8. A very basic example PV FV
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9. 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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10. 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*5% = £115
Compounding interest method: £100*(1+5%)3=£115.76
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11. PV with compounding interest FV PV
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12. 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*(1+5%)3 +150*(1+5%)2+300*(1+5%) = £596.14
100
150
300
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13. 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/(1+5%)+150/(1+5%)2+300/(1+5) 3= £490.44
300
150
100
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14. The full DCF model FV PV
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15. 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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16. Important issues Draw the timeline and cash flows
Be careful with money flow point (in the beginning or end of year t)
Be familiar with the simple model and the complex one
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17. 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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18. 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%, PV=£1092, buy
If actual interest rate is 10%, PV=£1000, buy
If actual interest rate is 12%, PV=£917, not buy
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19. 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 15/0.05=300p
Current price is 250p
Conclusion: Buy
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20. How to calculate it with Excel
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21. Important issues Bond investment Stock 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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22. 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
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