Chapter 11 - Cash Flow Estimation and Risk Analysis.ppt

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1. ByBy::
ProfProf. . Saad Abdel-Hamid Abdel-Hamid MetawaSaad Abdel-Hamid Abdel-Hamid Metawa
((Full Professor of Investment & FinanceFull Professor of Investment & Finance))
((Faculty of Commerce Faculty of Commerce -- Mansoura University) Mansoura University)))
20212021
Chapter 11Chapter 11
Cash Flow Estimation and Risk AnalysisCash Flow Estimation and Risk Analysis

2. •Estimating cash flows:Estimating cash flows:
•Relevant cash flowsRelevant cash flows
•Working capital treatmentWorking capital treatment
•InflationInflation
•Risk Analysis: Sensitivity Analysis, Scenario Risk Analysis: Sensitivity Analysis, Scenario
Analysis, and Simulation AnalysisAnalysis, and Simulation Analysis

3. •Cost: $200,000 + $10,000 shipping + Cost: $200,000 + $10,000 shipping +
$30,000 installation.$30,000 installation.
•Depreciable cost $240,000.Depreciable cost $240,000.
•Economic life = 4 years.Economic life = 4 years.
•Salvage value = $25,000.Salvage value = $25,000.
•MACRS 3-year class.MACRS 3-year class.
Proposed Project

4. •Annual unit sales = 1,250.Annual unit sales = 1,250.
•Unit sales price = $200.Unit sales price = $200.
•Unit costs = $100.Unit costs = $100.
•Net operating working capital (NOWC) = Net operating working capital (NOWC) =
12% of sales.12% of sales.
•Tax rate = 40%.Tax rate = 40%.
•Project cost of capital = 10%.Project cost of capital = 10%.

5. Incremental Cash Flow for a Incremental Cash Flow for a
ProjectProject
•Project’s incremental cash flow is:Project’s incremental cash flow is:
•Corporate cash flow Corporate cash flow withwith the project the project
• Minus Minus
•Corporate cash flow Corporate cash flow withoutwithout the project. the project.

6. •NONO..We discount project cash flows with a We discount project cash flows with a
cost of capital that is the rate of return required by cost of capital that is the rate of return required by
all investors (not just debtholders or all investors (not just debtholders or
stockholders), and so we should discount the total stockholders), and so we should discount the total
amount of cash flow available to all investors. amount of cash flow available to all investors.
•They are part of the costs of capital. If we They are part of the costs of capital. If we
subtracted them from cash flows, we would be subtracted them from cash flows, we would be
double counting capital costs. double counting capital costs.
Should you subtract interest expense or
dividends when calculating CF?

7. •NONO. This is a . This is a sunk costsunk cost. Focus on . Focus on
incremental investment and operating cash incremental investment and operating cash
flows.flows.
Suppose $100,000 had been spent last year
to improve the production line site. Should
this cost be included in the analysis?

8. •YesYes. Accepting the project means we will not . Accepting the project means we will not
receive the $25,000. This is an receive the $25,000. This is an opportunity costopportunity cost
and it should be charged to the project.and it should be charged to the project.
•A.T. opportunity cost = $25,000 (1 - T) = $15,000 A.T. opportunity cost = $25,000 (1 - T) = $15,000
annual cost.annual cost.
Suppose the plant space could be leased out for
$25,000 a year. Would this affect the analysis?

9. •YesYes. The effects on the other projects’ CFs . The effects on the other projects’ CFs
are are “externalities“externalities”.”.
•Net CF loss per year on other lines would be Net CF loss per year on other lines would be
a cost to this project.a cost to this project.
•Externalities will be Externalities will be positivepositive if new projects if new projects
are complements to existing assets, are complements to existing assets, negativenegative
if substitutes.if substitutes.
If the new product line would decrease
sales of the firm’s other products by
$50,000 per year, would this affect the
analysis?

10. Basis = Cost
+ Shipping
+ Installation
$240,000
What is the depreciation basis?

11. Year
1
2
3
4
%
0.33
0.45
0.15
0.07
Depr.
$ 79.2
108.0
36.0
16.8
x Basis =
Annual Depreciation Expense (000s)
$240

12. Annual Sales and CostsAnnual Sales and Costs
Year 1Year 1 Year 2Year 2 Year 3Year 3 Year 4Year 4
UnitsUnits 12501250 12501250 12501250 12501250
Unit priceUnit price $200$200 $206$206 $212.18$212.18$218.55$218.55
Unit costUnit cost $100$100 $103$103 $106.09$106.09$109.27$109.27
SalesSales $250,000$250,000$257,500$257,500$265,225$265,225$273,188$273,188
CostsCosts $125,000$125,000$128,750$128,750$132,613$132,613$136,588$136,588

13. Why is it important to include Why is it important to include
inflation when estimating cash inflation when estimating cash
flowsflows??
•Nominal r > real r. The cost of capital, r, Nominal r > real r. The cost of capital, r,
includes a premium for inflation.includes a premium for inflation.
•Nominal CF > real CF. This is because Nominal CF > real CF. This is because
nominal cash flows incorporate inflation.nominal cash flows incorporate inflation.
•If you discount real CF with the higher If you discount real CF with the higher
nominal r, then your NPV estimate is too low. nominal r, then your NPV estimate is too low.

14. Inflation (Continued)Inflation (Continued)
•Nominal CF should be discounted with Nominal CF should be discounted with
nominal r, and real CF should be discounted nominal r, and real CF should be discounted
with real r.with real r.
•It is more realistic to find the nominal CF (i.e., It is more realistic to find the nominal CF (i.e.,
increase cash flow estimates with inflation) increase cash flow estimates with inflation)
than it is to reduce the nominal r to a real r.than it is to reduce the nominal r to a real r.

15. Operating Cash Flows (Years 1 and 2)Operating Cash Flows (Years 1 and 2)
Year 1Year 1 Year 2Year 2
SalesSales $250,000$250,000 $257,500$257,500
CostsCosts $125,000$125,000 $128,750$128,750
Depr.Depr. $79,200$79,200 $108,000$108,000
EBITEBIT $45,800$45,800 $20,750$20,750
Taxes (40%)Taxes (40%) $18,320$18,320 $8,300$8,300
NOPATNOPAT $27,480$27,480 $12,450$12,450
+ Depr.+ Depr. $79,200$79,200 $108,000$108,000
Net Op. CFNet Op. CF $106,680$106,680 $120,450$120,450

16. Operating Cash Flows (Years 3 and 4)Operating Cash Flows (Years 3 and 4)
Year 3Year 3 Year 4Year 4
SalesSales $265,225$265,225 $273,188$273,188
CostsCosts $132,613$132,613 $136,588$136,588
Depr.Depr. $36,000$36,000 $16,800$16,800
EBITEBIT $96,612$96,612 $119,800$119,800
Taxes (40%)Taxes (40%) $38,645$38,645 $47,920$47,920
NOPATNOPAT $57,967$57,967 $71,880$71,880
+ Depr.+ Depr. $36,000$36,000 $16,800$16,800
Net Op. CFNet Op. CF $93,967$93,967 $88,680$88,680

17. Cash Flows due to Investments in Cash Flows due to Investments in
Net Operating Working Capital Net Operating Working Capital
(NOWC)(NOWC)
NOWC NOWC
SalesSales (% of sales)(% of sales) CFCF
Year 0Year 0 $30,000$30,000-$30,000-$30,000
Year 1Year 1$250,000$250,000$30,900$30,900-$900-$900
Year 2Year 2$257,500$257,500$31,827$31,827-$927-$927
Year 3Year 3$265,225$265,225$32,783$32,783-$956-$956
Year 4Year 4$273,188$273,188$32,783$32,783

18. Salvage Cash Flow at t = 4 (000s)Salvage Cash Flow at t = 4 (000s)
Salvage value
Tax on SV
Net terminal CF
$25
(10)

$15

19. What if you terminate a What if you terminate a
project before the asset is fully project before the asset is fully
depreciateddepreciated??
Cash flow from sale = Sale proceeds
- taxes paid.
Taxes are based on difference between sales price and tax basis, where:
Basis = Original basis - Accum. deprec.

20. •Original basisOriginal basis= $240.= $240.
•After 3 yearsAfter 3 years= $16.8 remaining.= $16.8 remaining.
•Sales priceSales price = $25.= $25.
•Tax on saleTax on sale = 0.4($25-$16.8)= 0.4($25-$16.8)
= $3.28.= $3.28.
•Cash flow Cash flow = $25-$3.28=$21.72.= $25-$3.28=$21.72.
Example: If Sold After 3 Years (000s)

21. Net Cash Flows for Years 1-3Net Cash Flows for Years 1-3
Year 0Year 0 Year 1Year 1 Year 2Year 2
Init. CostInit. Cost -$240,000-$240,000 00 00
Op. CFOp. CF 00 $106,680$106,680 $120,450$120,450
NOWC CFNOWC CF -$30,000-$30,000 -$900-$900 -$927-$927
Salvage CFSalvage CF 00 00 00
Net CFNet CF -$270,000-$270,000 $105,780$105,780 $119,523$119,523

22. Net Cash Flows for Years 4Net Cash Flows for Years 4-5-5
Year 3Year 3 Year 4Year 4
Init. CostInit. Cost 00 00
Op CFOp CF $93,967$93,967 $88,680$88,680
NOWC CFNOWC CF -$956-$956 $32,783$32,783
Salvage CFSalvage CF 00 $15,000$15,000
Net CFNet CF $93,011$93,011 $136,463$136,463

23. Project Net CFs on a Time LineProject Net CFs on a Time Line
Enter CFs in CFLO register and I = 10.
NPV = $88,030.
IRR = 23.9%.
0 1 2 3 4
(270,000) 105,780 119,523 93,011 136,463

24. What is the project’s MIRR? (000s)What is the project’s MIRR? (000s)
(270,000)
MIRR = ?
0 1 2 3 4
(270,000) 105,780 119,523 93,011
136,463
102,312
144,623
140,793
524,191

25. 1.Enter positive CFs in CFLO:
I = 10; Solve for NPV = $358,029.581.
2.Use TVM keys: PV = -358,029.581, N =
4, I = 10; PMT = 0; Solve for FV = 524,191.
(TV of inflows)
3.Use TVM keys: N = 4; FV = 524,191;
PV = -270,000; PMT= 0; Solve for I =
18.0.
MIRR = 18.0%.
Calculator SolutionCalculator Solution

26. What is the project’s payback? (000s)What is the project’s payback? (000s)
Cumulative:
Payback = 2 + 44/93 = 2.5 years.
0 1 2 3 4
(270)*
(270)
106
(164)
120
(44)
93
49
136
185

27. What does “risk” mean in What does “risk” mean in
capital budgetingcapital budgeting??
•Uncertainty about a project’s Uncertainty about a project’s
future profitability.future profitability.
•
Measured by Measured by 
NPVNPV, , 
IRRIRR, beta., beta.
•Will taking on the project increase Will taking on the project increase
the firm’s and stockholders’ risk?the firm’s and stockholders’ risk?

28. Is risk analysis based on Is risk analysis based on
historical data or subjective historical data or subjective
judgmentjudgment??
•Can sometimes use historical data, but Can sometimes use historical data, but
generally cannot.generally cannot.
•So risk analysis in capital budgeting is So risk analysis in capital budgeting is
usually based on subjective judgments.usually based on subjective judgments.

29. What three types of risk are What three types of risk are
relevant in capital budgetingrelevant in capital budgeting??
•Stand-alone riskStand-alone risk
•Corporate riskCorporate risk
•Market (or beta) riskMarket (or beta) risk

30. How is each type of risk measured, and how How is each type of risk measured, and how
do they relate to one anotherdo they relate to one another??
1. 1. Stand-Alone RiskStand-Alone Risk::
•The project’s risk if it were the firm’s only asset The project’s risk if it were the firm’s only asset
and there were no shareholders.and there were no shareholders.
•Ignores both firm and shareholder diversification. Ignores both firm and shareholder diversification.
•Measured by the Measured by the  or CV of NPV, IRR, or or CV of NPV, IRR, or
MIRR.MIRR.

31. 0 E(NPV)
Probability Density
Flatter distribution,
larger , larger
stand-alone risk.
Such graphics are increasingly used
by corporations.
NPV

32. 2. 2. Corporate RiskCorporate Risk::
•Reflects the project’s effect on Reflects the project’s effect on
corporate earnings stability.corporate earnings stability.
•Considers firm’s other assets Considers firm’s other assets
(diversification within firm).(diversification within firm).
•Depends on:Depends on:
•project’s project’s , and, and
•its correlation, its correlation, , with returns , with returns
on on firm’s other assets.firm’s other assets.
•Measured by the project’s corporate Measured by the project’s corporate
beta.beta.

33. Profitability
0 Years
Project X
Total Firm
Rest of Firm
1.Project X is negatively correlated to
firm’s other assets.
2.If  < 1.0, some diversification benefits.
3.If  = 1.0, no diversification effects.

34. 3. 3. Market RiskMarket Risk::
•Reflects the project’s effect on a well-Reflects the project’s effect on a well-
diversified stock portfolio.diversified stock portfolio.
•Takes account of stockholders’ other Takes account of stockholders’ other
assets. assets.
•Depends on project’s Depends on project’s  and correlation and correlation
with the stock market.with the stock market.
•Measured by the project’s market beta.Measured by the project’s market beta.

35. How is each type of risk usedHow is each type of risk used??
•Market risk is theoretically best in most Market risk is theoretically best in most
situations.situations.
•However, creditors, customers, suppliers, However, creditors, customers, suppliers,
and employees are more affected by and employees are more affected by
corporate risk.corporate risk.
•Therefore, corporate risk is also relevant.Therefore, corporate risk is also relevant.

36. •Stand-alone risk is easiest to measure, Stand-alone risk is easiest to measure,
more intuitive.more intuitive.
•Core projects are highly correlated with Core projects are highly correlated with
other assets, so stand-alone risk other assets, so stand-alone risk
generally reflects corporate risk.generally reflects corporate risk.
•If the project is highly correlated with If the project is highly correlated with
the economy, stand-alone risk also the economy, stand-alone risk also
reflects market risk.reflects market risk.

37. What is sensitivity analysisWhat is sensitivity analysis??
•Shows how changes in a variable such Shows how changes in a variable such
as unit sales affect NPV or IRR.as unit sales affect NPV or IRR.
•Each variable is fixed except one. Each variable is fixed except one.
Change this one variable to see the Change this one variable to see the
effect on NPV or IRR.effect on NPV or IRR.
•Answers “what if” questions, e.g. “What Answers “what if” questions, e.g. “What
if sales decline by 30%?”if sales decline by 30%?”

38. Sensitivity AnalysisSensitivity Analysis
--30%30%$113$113$17$17 $85$85
--15%15%$100$100 $52$52 $86$86
0%0%$88$88 $88$88 $88$88
15%15%$76$76 $124$124 $90$90
30%30%$65$65 $159$159 $91$91
Change from Resulting NPV (000s)
Base Level r Unit Sales Salvage

39. -30 -20 -10 Base 10 20 30
Value (%)
88
NPV
(000s)
Unit Sales
Salvage
r

40. Results of Sensitivity AnalysisResults of Sensitivity Analysis
•Steeper sensitivity lines show greater risk. Steeper sensitivity lines show greater risk.
Small changes result in large declines in NPV.Small changes result in large declines in NPV.
•Unit sales line is steeper than salvage value or Unit sales line is steeper than salvage value or
r, so for this project, should worry most about r, so for this project, should worry most about
accuracy of sales forecast.accuracy of sales forecast.

41. What are the weaknesses ofWhat are the weaknesses of
sensitivity analysissensitivity analysis??
•Does not reflect diversification.Does not reflect diversification.
•Says nothing about the likelihood of Says nothing about the likelihood of
change in a variable, i.e. a steep sales change in a variable, i.e. a steep sales
line is not a problem if sales won’t fall.line is not a problem if sales won’t fall.
•Ignores relationships among variables.Ignores relationships among variables.

42. Why is sensitivity analysis Why is sensitivity analysis
usefuluseful??
•Gives some idea of stand-alone risk.Gives some idea of stand-alone risk.
•Identifies dangerous variables.Identifies dangerous variables.
•Gives some breakeven information.Gives some breakeven information.

43. What is scenario analysisWhat is scenario analysis??
•Examines several possible situations, Examines several possible situations,
usually worst case, most likely case, and usually worst case, most likely case, and
best case.best case.
•Provides a range of possible outcomes.Provides a range of possible outcomes.

44. Best scenario: 1,600 units @ $240Best scenario: 1,600 units @ $240
Worst scenario: 900 units @ $Worst scenario: 900 units @ $160160
ScenarioScenario ProbabilityProbabilityNPV(000)NPV(000)
Best 0.25 $ 279
Base 0.50 88
Worst 0.25 -49
E(NPV) = $101.5
(NPV) = 116.6
CV(NPV) = (NPV)/E(NPV) =1.15

45. Are there any problems with scenario
analysis?
•Only considers a few possible out-comes.
•Assumes that inputs are perfectly correlated--
all “bad” values occur together and all “good”
values occur together.
•Focuses on stand-alone risk, although
subjective adjustments can be made.

46. What is a simulation analysisWhat is a simulation analysis??
•A computerized version of scenario analysis A computerized version of scenario analysis
which uses continuous probability which uses continuous probability
distributions.distributions.
•Computer selects values for each variable Computer selects values for each variable
based on given probability distributions.based on given probability distributions.

47. •NPV and IRR are calculated.NPV and IRR are calculated.
•Process is repeated many times (1,000 Process is repeated many times (1,000
or more).or more).
•End result: Probability distribution of End result: Probability distribution of
NPV and IRR based on sample of NPV and IRR based on sample of
simulated values.simulated values.
•Generally shown graphically.Generally shown graphically.

48. Simulation ExampleSimulation Example
•Assume a:Assume a:
• Normal distribution for unit sales:Normal distribution for unit sales:
•Mean = 1,250Mean = 1,250
•Standard deviation = 200Standard deviation = 200
•Triangular distribution for unit price:Triangular distribution for unit price:
•Lower boundLower bound = $160= $160
•Most likelyMost likely= $200= $200
•Upper boundUpper bound = $250= $250

49. Simulation ProcessSimulation Process
•Pick a random variable for unit sales and sale Pick a random variable for unit sales and sale
price.price.
•Substitute these values in the spreadsheet and Substitute these values in the spreadsheet and
calculate NPV.calculate NPV.
•Repeat the process many times, saving the Repeat the process many times, saving the
input variables (units and price) and the output input variables (units and price) and the output
(NPV).(NPV).

50. Simulation Results (1000 trials)Simulation Results (1000 trials)
(See Ch 11 Mini Case Simulation.xls)(See Ch 11 Mini Case Simulation.xls)
Units PriceNPV
Mean 1260$202 $95,914
St. Dev. 201$18 $59,875
CV 0.62
Max 1883 $248 $353,238
Min 685$163 ($45,713)
Prob NPV>0 97%

51. Interpreting the ResultsInterpreting the Results
•Inputs are consistent with specificied Inputs are consistent with specificied
distributions.distributions.
•Units: Mean = 1260, St. Dev. = 201.Units: Mean = 1260, St. Dev. = 201.
•Price: Min = $163, Mean = $202, Max = $248.Price: Min = $163, Mean = $202, Max = $248.
•Mean NPV = $95,914. Low probability of Mean NPV = $95,914. Low probability of
negative NPV (100% - 97% = 3%).negative NPV (100% - 97% = 3%).

52. Histogram of ResultsHistogram of Results
-$60,000 $45,000 $150,000 $255,000 $360,000
NPV ($)
Probability

53. What are the advantages of What are the advantages of
simulation analysissimulation analysis??
•Reflects the probability Reflects the probability
distributions of each input.distributions of each input.
•Shows range of NPVs, the Shows range of NPVs, the
expected NPV, expected NPV, 
NPVNPV, and CV, and CV
NPVNPV..
•Gives an intuitive graph of the Gives an intuitive graph of the
risk situation.risk situation.

54. What are the disadvantages of What are the disadvantages of
simulationsimulation??

Difficult to specify probability distributions Difficult to specify probability distributions
and correlations.and correlations.

If inputs are bad, output will be bad:If inputs are bad, output will be bad:
“Garbage in, garbage out.”“Garbage in, garbage out.”

55. •Sensitivity, scenario, and simulation analyses do Sensitivity, scenario, and simulation analyses do
not provide a decision rule. They do not indicate not provide a decision rule. They do not indicate
whether a project’s expected return is sufficient to whether a project’s expected return is sufficient to
compensate for its risk.compensate for its risk.
•Sensitivity, scenario, and simulation analyses all Sensitivity, scenario, and simulation analyses all
ignore diversification. Thus they measure only ignore diversification. Thus they measure only
stand-alone risk, which may not be the most stand-alone risk, which may not be the most
relevant risk in capital budgeting.relevant risk in capital budgeting.

56. If the firm’s average project has a CV If the firm’s average project has a CV
of 0.2 to 0.4, is this a high-risk project? of 0.2 to 0.4, is this a high-risk project?
What type of risk is being measuredWhat type of risk is being measured??
•CV from scenarios = 0.74, CV from CV from scenarios = 0.74, CV from
simulation = 0.62. Both are > 0.4, this project simulation = 0.62. Both are > 0.4, this project
has high risk.has high risk.
•CV measures a project’s stand-alone risk.CV measures a project’s stand-alone risk.
•High stand-alone risk usually indicates high High stand-alone risk usually indicates high
corporate and market risks.corporate and market risks.

57. With a 3% risk adjustment, should With a 3% risk adjustment, should
our project be acceptedour project be accepted??
•Project r = 10% + 3% = 13%.Project r = 10% + 3% = 13%.
•That’s 30% above base r.That’s 30% above base r.
•NPV = $65,371.NPV = $65,371.
•Project remains acceptable after accounting for Project remains acceptable after accounting for
differential (higher) risk.differential (higher) risk.

58. Should subjective risk factors Should subjective risk factors
be consideredbe considered??
•Yes. A numerical analysis may not capture Yes. A numerical analysis may not capture
all of the risk factors inherent in the project.all of the risk factors inherent in the project.
•For example, if the project has the potential For example, if the project has the potential
for bringing on harmful lawsuits, then it for bringing on harmful lawsuits, then it
might be riskier than a standard analysis might be riskier than a standard analysis
would indicate.would indicate.