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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416417418419420421422423424425426427428429430431

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