Lecturer: Shaling LiAcc&Fin Dept, PBS

University of Portsmouth22 October, 2009

Re-cap from last week

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Theoretical world:

RationalityFrictionless

marketLiquidity

Government role+

Models, results

Real world:UK London exchange

Structure of this lectureNutshell of the Discounted Cash Flow

(DCF)modelKey definitionsModellingApplications

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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 assumptionsCannot explain everything, has limitations

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Nutshell of this model

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n

tt

t

i

FVPV

0 )1(

Input

Output

Key definitionsTime 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.

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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Key definitionsPresent 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

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)1( i

FVPV

FVPV

)1( iPVFV

Discounted Cash Flow ModelMore complexity added

1. Single-period case to the multiple-period

case

2. 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 + 3*100*5% = £115 Compounding interest method:

£100*(1+5%))3=£115.76

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PV with compounding interest

0 1 2 3 4 5

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tt

i

FVPV

)1(

FVPV

tt iPVFV )1(

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

0 1 2 3

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100

150

300

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

0 1 2 3

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100

150

300

The full DCF model

0 1 2 3 4 5

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n

tt

t

i

FVPV

0 )1(

FVPV

PV with multiple cash flowsIf 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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i

CPV

Important issues1. 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 investmentBond – 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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End of Year 2 Year 3 Year 4 Year 5 Year 6 Cash flow 100 100 100 100 1,100

665432 )1(

1000

)1(

100

)1(

100

)1(

100

)1(

100

)1(

100

)1(

100

iiiiiiiPV

Applications-Bond investmentThe 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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Application-Stock investmentInvest 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 250pConclusion: Buy

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How to calculate it with Excel

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Important issuesBond 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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SummaryWhy use model to describe the real world?Key definitions to understand DCF modelBasic modelComplexity added to the modelApplication: Bond and Stock investment

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