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Chapter 11Cash Flow Estimation &
Risk Analysis
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Topics
Estimating cash flows: Relevant cash flows Working capital treatment
Risk analysis: Sensitivity analysis Scenario analysis Simulation analysis
Project’s Cash Flows (CFt)
Project’s Cash Flows (CFt)
Marketinterest rates
Project’s business risk
Project’s business risk
Marketrisk aversion
Project’sdebt/equity capacity
Project’s risk-adjustedcost of capital
(r)
Project’s risk-adjustedcost of capital
(r)
The Big Picture:Project Risk Analysis
NPV = + + ··· + − Initial cost
CF1
CF2
CFN
(1 + r )1 (1 + r)N(1 + r)2
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Relevant Cash Flows:Incremental Cash Flow for a Project
Project’s incremental cash flow is:
Corporate cash flow with the project
Minus
Corporate cash flow without the project.
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Free Cash Flow
Capital Operatingin Investment- OCF FCF
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Issues in Project Analysis
Purchase of Fixed Assets …………… Y Non-cash charges …………………….. Y Changes in Net Working Capital……Y Interest/Dividends …………..……….. N “Sunk” Costs …………………………….. N Opportunity Costs …………………….. Y Externalities/Cannibalism …………… Y Tax Effects ………………………..…….. Y
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Treatment of Financing Costs
Should you subtract interest expense or dividends when calculating CF?
NO. We discount project cash flows with a cost of capital
that is the rate of return required by all investors (not just debtholders or stockholders), and so we should discount the total amount of cash flow available to all investors.
They are part of the costs of capital. If we subtracted them from cash flows, we would be double counting capital costs.
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Sunk Costs
Suppose $100,000 had been spent last year to improve the production line site. Should this cost be included in the analysis?
NO. This is a sunk cost. Focus on incremental investment and operating cash flows.
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Externalities
If the new product line would decrease sales of the firm’s other products by $50,000 per year, would this affect the analysis?
Yes. The effects on the other projects’ CFs are “externalities.”
Net CF loss per year on other lines would be a cost to this project.
Externalities will be positive if new projects are complements to existing assets, negative if substitutes.
Depreciation Methods Straight Line Decline (SLD)
Asset depreciated in equal installments over its useful life.
Sum of the Year’s Digits (SYD)
Based upon an inverted scale which is the ratio of the number of digits in given year divided by total of all years digits.
Declining Balance (DB)
Asset Depreciation is straight-line depreciation calculated for the remaining balance of the asset for each year.
Double Declining Balance (DDB)
Doubling straight-line depreciation for the remaining balance of the asset for each year.
Straight Line Decline Method
Example
Investment : US$ 100
Useful Life : 4 years
Depreciation Rate: ¼ = 25%
Annual Depreciation : US$ 25
Sum of the Year’s Digits Method
Example
Investment : US$ 100
Useful Life : 4 years
4 Years Digits : (4+3+2+1) = 10
1st Year Depreciation : 4/10 x US$ 100 = US$ 40
2nd Year Depreciation : 3/10 x US$ 100 = US$ 30
3rd Year Depreciation : 2/10 x US$ 100 = US$ 20
4nd Year Depreciation : 1/10 x US$ 100 = US$ 10
Declining Balance Method
Example
Investment : US$ 100
Useful Life : 4 years
$100.00 InvestmentYear Cum % Depreciation
1 25% = 25.00% 25.00% $25.002 25% x (1 - 25%) = 18.75% 43.75% $18.753 25% x (1 - 43.75%) = 14.06% 57.81% $14.064 25% x (1 - 57.81%) = 10.55% 68.36% $10.55
31.64% 100.00% $31.64100.00% $100.00
Percentage
Double Declining Balance Method
Example
Investment : US$ 100
Useful Life : 4 years
$100.00 InvestmentYear Cum % Depreciation
1 50% = 50.00% 50.00% $50.002 50% x (1 - 50%) = 25.00% 75.00% $25.003 50% x (1 - 75%) = 12.50% 87.50% $12.504 50% x (1 - 87.5%) = 6.25% 93.75% $6.25
6.25% 100.00% $6.25100.00% $100.00
Percentage
Depreciation Methods Compared
Investment ($) 100.00 Useful Life (Year) 4
Year Annual Cum. Annual Cum. Annual Cum. Annual Cum.1 25.00 25.00 25.00 25.00 50.00 50.00 40.00 40.00 2 25.00 50.00 18.75 43.75 25.00 75.00 30.00 70.00 3 25.00 75.00 14.06 57.81 12.50 87.50 20.00 90.00 4 25.00 100.00 10.55 68.36 6.25 93.75 10.00 100.00 5 31.64 100.00 6.25 100.00
SLB Straight Line Decline
DB Declining Balance
DDB Double Declining Balance
SYD Sum of the Year Digits
SLD DB DDB SYD
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“Risk” in Capital Budgeting
Uncertainty about a project’s future profitability
Will taking on the project increase the firm’s and stockholders’ risk?
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0 E(NPV)
Flatter distribution,larger , largerrisk.
NPV
Probability Density
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Sensitivity Analysis
Shows how changes in an input variable affect NPV or IRR
Each variable is fixed except one Change one variable to measure the effect on
NPV or IRR Answers “what if” questions
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Results of Sensitivity Analysis
Steeper sensitivity lines = greater risk Small changes → large declines in NPV
Sales price & variable cost are the most sensitive
Sensitivity Ratio
%NPV = (New NPV - Base NPV)/Base NPV %VAR = (New VAR - Base VAR)/Base VAR
VAR
NPVSR
%
%
14-20
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Sensitivity Analysis:Weaknesses
Does not reflect diversification Says nothing about the likelihood of change
in a variable Ignores relationships among variables
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Sensitivity Analysis:Strengths
Provides indication of risk Identifies dangerous variables
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Scenario Analysis
Examines several possible situations, usually: Worst case Base case or most likely case, and Best case
Provides a range of possible outcomes
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Problems with Scenario Analysis
Only considers a few possible out-comes Assumes that inputs are perfectly correlated Focuses on stand-alone risk
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Monte Carlo Simulation Analysis
A computerized version of scenario analysis which uses continuous probability distributions
Computer selects values for each variable based on given probability distributions
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Monte Carlo Simulation Analysis
NPV and IRR are calculated Process is repeated many times (1,000 or
more) End result: Probability distribution of NPV
and IRR based on sample of simulated values
Generally shown graphically
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Histogram of Results
0%
2%
4%
6%
8%
10%
12%
($60
,000
)
($30
,000
) $0
$30,
000
$60,
000
$90,
000
$120
,000
$150
,000
$180
,000
$210
,000
$240
,000
$270
,000
$300
,000
$330
,000
$360
,000
NPV
Pro
ba
bil
ity
of
NP
V
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Advantages of Simulation Analysis
Reflects the probability distributions of each input
Shows range of NPVs, the expected NPV, σNPV, and CVNPV
Gives an intuitive graph of the risk situation
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Disadvantages of Simulation Analysis
Difficult to specify probability distributions and correlations
If inputs are bad, output will be bad:“Garbage in, garbage out”
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Decision Trees
A technique for reducing risk Analyze multi-stage projects “Decision Nodes”
Points where managers can take action based on new information
Assign probabilities to each leg
Working Area: Option to Explore
Developed Reserves: Options of Expanding, Temporary Stopping, and Abandonment.
Delineated but Undeveloped Reserves: Option to Develop ( to Produce )
Undelineated Field: Option to Appraise
Development Development InvestmentInvestment
Appraisal Appraisal InvestmentInvestment
Wildcat Wildcat InvestmentInvestment
Success Probability & Expected Volume of Reserve
RevisedVolume = B’
Example of Decision Tree Analysis:Upstream Oil & Gas
Apply/bidlicense
AcceptWorkProgr
3 DSeismic
Drill aWild-cat
Appraisal
Develop
DROP
DROP
DROP
DROP
DROP
Investment Decision Process
Example of Decision Tree Analysis:Upstream Oil & Gas
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United Robotics
Stage 1: (t=0) Invest $500,000 in market potential study
Stage 2: (t=1) If study results positive, invest $1 million in prototype
Stage 3: (t=2) Build plant at cost of $10 million
Stage 4: (t=3) Product acceptance?
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432433
A B C D E F G H ICost of capital = 11.5%
Joint=0 t=1 t=2 t=3 t=4 t=5 Probability NPV Prob.xNPV
$18,000 $18,000 $18,000 0.144 $25,635 $3,691
($10,000) $8,000 $8,000 $8,000 0.192 $6,149 $1,181
($1,000) ($2,000) Stop 0.144 ($10,883) ($1,567)
($500) Stop 0.320 ($1,397) ($447)
Stop 0.200 ($500) ($100)
1.000 Expected NPV= $2,758
= $10,584
0.8
0.2
0.6
0.4
0.40.3
0.3
United Robotics Decision Tree