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Investment AppraisalPart II
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© Copyright Coleago 2010
Learning Objectives
DCF Learning how to carry out a Discounted Cash Flow Analysis
NPV Appreciate the relevance of Net Present Value to
decision making including a worked example
IRR Understand the concept of the Internal Rate of
Return
AdditionalMaterial
Expected Net Present Value: a tool to incorporateprobable outcomes
1
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© Copyright Coleago 2010
Learning Objectives
DCF Learning how to carry out a Discounted Cash Flow Analysis
NPV Appreciate the relevance of Net Present Value to
decision making including a worked example
IRR Understand the concept of the Internal Rate of
Return
AdditionalMaterial
Expected Net Present Value: a tool to incorporateprobable outcomes
2
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A simple way to examine a project
Invest $560 now to get a $200 per year for the next three years
Decision Rule: Invest in all projectswith a positive Net Value
Result: Invest
Year Cash Flow $
2011 (560)
2012 200
2013 200
2014 200
Net Value 40
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Another investment opportunity
Invest $500 now
Receive immediately
– 10,000 Japanese Yen
– 200 Euros
– 350 Swiss Francs
Invest?
– Value = 10,000 + 200 + 350 – 500 = 10,050
To assess the opportunity the different currencies must be converted to acommon currency, for example $, to allow a “like-for-like” comparison
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If you had a choice of a today or a dollar in a years time – which would you
choose?
– A dollar today!
A dollar in a years time is worth less than a dollar today as a dollar today can beinvested in a bank, risk free, and will be worth more than the dollar received in ayears time
To compare a cash flow now with a cash flow in the future you have to take intoaccount the time value of money
A dollar today is worth more than a dollar tomorrow
Now Year Later
$1 $1*(1+5%) = $1.05
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Making a like-for-like comparison
We cannot compare directly $560 investedin 2011 with, for example, $200 receivedin 2012
– $200 received in a year’s time is worthless than $200 now
We need to convert the future cash flowsto an equivalent amount receivable now –the task of Discounted Cash Flow
Year Cash Flow $
2011 (560)
2012 200
2013 200
2014 200
Net Value 40
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Compound interest
Compound interest answers the question
– What will a $ invested now be worth at some point in the future
Year Value of $ Calculation Alternatively
0 $ 1.00 $ 1.00 $ 1.00
1 $ 1.05 $ 1.00 * ( 1 + 5%) $ 1.00 * ( 1 + 5%)
2 $ 1.1025 $ 1.05 * ( 1 + 5%) $ 1.00 * ( 1 + 5%)
2
3 $ 1.157625 $ 1.1025 * ( 1 + 5%) $ 1.00 * ( 1 + 5%)3
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Discounting
Discounting answers the question
– What would a $ receivable in the future be equivalent to if it were receivednow?
Year $s received in
the future
CalculationEquivalent
Receivable Now $
0 $ 1.00 $ 1.00 $ 1.00
1 $ 1.05 $ 1.05 / ( 1 + 5%) $ 1.00
2 $ 1.1025 $ 1.1025 / ( 1 + 5%)2 $ 1.00
3 $ 1.157625 $ 1.157625 / ( 1 + 5%)3 $ 1.00
© Copyright Coleago 2010 9
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Discounting – further examples
Year AmountReceived $
Equivalent AmountReceived Now $
Calculation
0 $ 1.00 $ 1.00 $ 1.00
1 $ 125 $ 119.05 $ 125 / ( 1 + 5%)
2 $ 210 $ 190.48 $ 210 / ( 1 + 5%)2
3 $ 200 $ 172.77 $ 200 / ( 1 + 5%)3
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Simple investment problemsyou can earn 5% at the Bank of England or
Year Bank 1 Bank 2 Bank 3
0 £(1.00) £ (1.00) £ (1.00)
1 £ 1.10 £ 1.05 £ 1.02
Invest?
Year Bank 1 Bank 2 Bank 3
0 £(1.00) £ (1.00) £ (1.00)
1 £ 1.10 £ 1.05 £ 1.02
Year 1 equivalent atYear 0 at 5%
£1.10 / (1+5%) =£1.047
£1.05 / (1+5%)= £1.00
£1.02 / (1+5%) =£0.97
Invest?
© Copyright Coleago 2010 13
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© Copyright Coleago 2010
Learning Objectives
DCF
Learning how to carry out a Discounted Cash Flow Analysis
NPV Appreciate the relevance of Net Present Value to
decision making including a worked example
IRR Understand the concept of the Internal Rate of
Return
AdditionalMaterial
Expected Net Present Value: a tool to incorporateprobable outcomes
14
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Comparing like-for-like
Decision Rule: Invest in all projects with a positive NPV
Result: Do not invest because the NPV is negative
Year Cash Flow $ Calculation at 5% Equivalent $ Now
2011 (560) (560) (560.00)
2012 200 = 200 / ( 1 + 5% ) 190.48
2013 200 = 200 / ( 1 + 5% )2 181.41
2014 200 = 200 / ( 1 + 5% )3 172.76
Net Value 40 Net Present Value (15.35)
© Copyright Coleago 2010 15
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Worked Example
Decision Rule: Invest in all projects with a positive NPV
Result:
Year Cash Flow $ Calculation at 5% Equivalent $ Now
2011 (600)
2012 220
2013 230
2014 240
Net Value 90 Net Present Value
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Worked Example - Solution
Decision Rule: Invest in all projects with a positive NPV
Result: Invest
Year Cash Flow $ Calculation at 5% Equivalent $ Now
2011 (600) (600) (600.00)
2012 220 = 220 / ( 1 + 5% ) 209.52
2013 230 = 230 / ( 1 + 5% )2 208.62
2014 240 = 240 / ( 1 + 5% )3 207.32
Net Value 90 Net Present Value 25.46
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Introducing Risk
So far we have compared the returns from one bank with another bank
– If both banks were generating a return of 5% you would be indifferentbetween the two
If you had the choice between investing in a bank at 5% and investing in a 3G
Mobile Business at 5% which would you prefer?
– The bank, as its safer
What might persuade you to invest in the 3G Mobile Business?
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Risk
An investment decision requires the investor to take on risk
The risk is that there may be variability in the level of the future cash flowsactually received
The Future
$
Now ?? ? ? ?
?
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A safe dollar is worth more than a risky dollar
You are faced with two investment decisions
– Invest in the Bank with an anticipated return of 5%
– Invest in 3G Mobile with an anticipated return of 5%
A rational investor would prefer the Bank where the expected variability is very
low
– A rational investor can earn 5% return risk free and so would not be attractedto a riskier investment with the same level of anticipated return
In order to persuade an investor to invest in 3G and assume additional risk theywill demand an additional return in excess of the return achievable risk free at
the Bank
– This is called the risk premium
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Selecting a suitable discount rate
In using a discount rate of 5% we have implicitly assumed that the riskassociated with this investment is the same as investing in a bank
– The investor only needs to be compensated for the Time Value of Money
Year Cash Flow $ Calculation at 5% Equivalent $ Now
2011 (600) (600) (600.00)
2012 220 = 220 / ( 1 + 5% ) 209.52
2013 230 = 230 / ( 1 + 5% )2 208.62
2014 240 = 240 / ( 1 + 5% )3 207.32
Net Value 90 Net Present Value 25.46
© Copyright Coleago 2010 23
Suppose the previous example represented an investment in a 3G
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Suppose the previous example represented an investment in a 3GMobile business
The investor now needs to be compensated for the Time Value of Money or the
Risk Free Rate and a Risk Premium (say 5%)
Discount Rate = Risk Free Rate + Risk Premium
Discount Rate = 5% + 5% = 10%
Year Cash Flow $ Calculation at 10% Equivalent $ Now
2011 (600) (600) (600.00)
2012 220 = 220 / ( 1 + 10% ) 200.00
2013 230 = 230 / ( 1 + 10% )2 190.08
2014 240 = 240 / ( 1 + 10% )3 180.31
Net Value 90 Net Present Value (29.61)
© Copyright Coleago 2010 24
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W k d E l Di R f 10%
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Worked Example – at a Discount Rate of 10%
It is normal to assume that all cash flows in a period take place either at the midpoint of the period or at the end of the year
Here we have assumed that they occur at the end of the year and we discount back to1st January 2011
2011 2012 2013 2014 2015 2016 2017
Revenue 12,000 24,000 30,000 40,000 55,000 75,000
Gross Profit 8,400 17,280 22,200 30,400 42,900 60,000Operating Costs (14,000) (14,280) (14,566) (14,857) (15,154) (15,457) (15,766)
EBITDA (14,000) (5,880) 2,714 7,343 15,246 27,443 44,234
Capital Expenditure (5,000) (2,000) (500) (250) (250) (250) (250)
Free Cash Flow (19,000) (7,880) 2,214 7,093 14,996 27,193 43,984
Discount Factor 1.10 1.21 1.33 1.46 1.61 1.77 1.95
Discounted FCF (17,273) (6,512) 1,664 4,845 9,311 15,350 22,571
Net Present Value $29,995© Copyright Coleago 2010 26
E i C l l t NPV f th N D t P j t
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Exercise – Calculate a NPV for the New Data Project
Assume cash flows take place at the end of the year
Calculate the NPV as at the 1st January, 2011
Use a Discount Rate of 10%
– Step 1 – Calculate the Discount Factors
– Step 2 – Divide FCF by the Discount Factor
– The result should be smaller!
– Step 3 – Add up the discounted cash flows
© Copyright Coleago 2010 27
W k d E l t Di t R t f 10%
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Worked Example – at a Discount Rate of 10%
2011 2012 2013 2014 Total
Free Cash Flow n/a
Discount Factor 1.1
Discounted FCF
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The rough guide to financial hurdles NPV
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The rough guide to financial hurdles - NPV
Net Present Value
– Financial theory states that provided cash flows are discounted at theappropriate discount rate any positive NPV will enhance shareholder value
– In reality business cases should be significantly positive at the appropriatediscount rate but the absolute value of the NPV will depend on the scale of
the project
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Discounted Cash Flow & NPV Strengths
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Discounted Cash Flow & NPV - Strengths
Deals with the timing of cash flows
Deals with the risk of cash flows
Uses all appropriate cash flows
Deals with scale
Focuses on increasing shareholder value
Can be used at any stage of maturity of a project or company
© Copyright Coleago 2010 31
Discounted Cash Flow & NPV - Weaknesses
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Discounted Cash Flow & NPV - Weaknesses
Not easily understood by managers
Difficult to perform
Requires an appropriate Discount Rate
Requires comprehensive financial forecasts
© Copyright Coleago 2010 32
Learning Objectives
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© Copyright Coleago 2010
Learning Objectives
DCF Learning how to carry out a Discounted Cash Flow
Analysis
NPV Appreciate the relevance of Net Present Value to
decision making including a worked example
IRR Understand the concept of the Internal Rate of Return
AdditionalMaterial
Expected Net Present Value: a tool to incorporateprobable outcomes
33
The Internal Rate of Return: IRR
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The Internal Rate of Return: IRR
Let’s look at the two previous examples we used, applying a discount rate of 5%and then 10% to a series of future cash flows.
There must be a discount rate which produces an NPV of zero.
This is the internal rate of return.
Year Cash Flow
$
Discount Rate
of 5%
Discount Rate of
10%2011 (600.00) (600.00) (600.00)
2012 220.00 209.52 200.00
2013 230.00 208.62 190.08
2014 240.00 207.32 180.32
NPV 25.46 (29.60)
Discount Rate of
7.22%
(600.00)
205.19
200.08
194.73
Nil
© Copyright Coleago 2010 34
Internal Rate of Return
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Internal Rate of Return
The Discount Rate used in NPV calculations is set by management based on a
review of the returns achievable on similar projects
The Internal Rate of Return (IRR) is closely related to Discounted Cash Flowtheory
The IRR is the “Discount Rate” which, when applied to a cash flow series,
generates a Net Present Value of zero
The IRR is the return generated by the investment
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Calculating the IRR using Excel
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g g
Calculating the IRR is an iterative process, laborious and time consuming
Do not attempt to calculate an IRR, use Excel!
Excel contains an Internal Rate of Return function
– = IRR ( values, guess )
The Values are the series of cash flows to be evaluated
The guess is an initial estimate of the IRR to assist Excel in the iterativecalculation that it performs
– This does not always need to be included
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Internal Rate of Return - Strengths
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g
Takes into account all cash flows
Timing is explicitly dealt with
Calculating a discount rate is not required
Gives a percentage result which is usually better understood
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Internal Rate of Return - Weaknesses
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IRR calculations say nothing about the size of a project
If the cash flows contains a sequence of negative, then positive then negativevalues etc., then there can be more than one value of the IRR
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The rough guide to financial hurdles - IRR
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Internal Rate of Return
IRRs will vary significantly depending on the nature of the project
The minimum acceptable range is probably 15% to 20%
20% to 50% is probably a reasonable expectation for major investment
projects
Excessively high IRRs 60-70% plus may also attract extra scrutiny
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Session Summary
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Investment AppraisalPart IIAdditional Material
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Expected Net Present Value
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In order to calculate an Expected NPV a number of different scenarios need to
be identified and cash flow projections made for the same project
The free cash flow projections for each scenario are discounted to give a NPVfor each scenario
– If four scenarios were identified there would be 4 separate NPVs
Each scenario is given a probability of occurring
– The sum of all the probabilities must sum to 1 or 100%
Each NPV is multiplied by the probability of the scenario occurring
The sum of each of these calculations is then computed to give the ExpectedNet Present Value
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Expected Net Present Value for Multi Media Messaging (MMS)
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Scenario NPV$000s
Probability Expected NPV$000s
Scenario 1 – MMS’s OK 30 30% 9
Scenario 2 – MMS Goes MM 40 10% 4
Scenario 3 – Teens love MMS 25 30% 7.5
Scenario 4 – MMS disappoints 15 30% 4.5
Total 100% 25
© Copyright Coleago 2010 44