PowerPoint Presentation
prepared by
Traven Reed
Canadore College
chapter 11
Cash Flow Estimation and
Risk Analysis
Corporate Valuation, Cash
Flows, and Risk Analysis
CH11
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-3
Topics in Chapter
CH11
• Estimating cash flows:
–
–
–
–
Relevant cash flows
Capital cost allowance
Working capital treatment
Inflation
• Capital budgeting with risk issues
• Project risk analysis
• Managing risk with staged-decision
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-4
Estimating Cash Flows
CH11
• The most important and also most
difficult step in analyzing a capital
budgeting project is the project
cash-flow estimation.
• Project cash flows mean actual
cash to be received or paid.
• Credit policy is invariably ignored in
the capital budgeting process.
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-5
Relevant Cash Flows
CH11
• Additional free cash flow that firms
can expect if they implement the
project.
• Only incremental amounts are
considered.
• FCF/NCF = investment outlay CF +
operating CF + net operating
working capital CF + salvage CF
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-6
CH11
Capital Cost Allowance
(CCA)
• Income Tax Act (ITA) does allow firms to
deduct CCA, which is similar to
amortization for book purposes, in
calculating taxable income.
• CCA calculation is similar to declining
balance amortization for most assets.
• A non-cash expenses involving no actual
cash outflow.
• Have deep cash flow implications.
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11-7
CCA (Cont’d)
CH11
• Apply to tangible assets based on CCA
class specification.
• Pool concept, not concerned with the
economic life and salvage value of any
individual asset.
• Un-depreciated capital cost (UCC) is the
amount remaining to be claimed (i.e.
book value) as CCA for an asset class.
• UCC ≠ market value in general.
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-8
CH11
Effect of CCA Depreciation
on Income and Cash Flow
Company A
Company B
Sales
$100,000
$100,000
Cost of good sold
30,000
30,000
Gross profit
$70,000
$70,000
Operating expenses
50,000
50,000
Depreciation (CCA)
0
10,000
Earning before tax
$20,000
$10,000
Tax @30%
6,000
3,000
Net income
$14,000
$7,000
+ Depreciation
0
10,000
Cash flow
$14,000
$17,000
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-9
Common Asset Classes
CH11
• CCA tax shield = CCA × tax rate
Class
Description
CCA Rate
1
Buildings
4%
8
Machinery, equipment,
furniture
20%
10
Vehicles
30%
12
Computer software
100%
13
Leasehold improvements
Straight line; use
lesser of 5 years
or the lease term
43
Manufacturing assets
30%
45
Computer hardware
45%
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11-10
CCA Calculation
CH11
• Half-year rule allows to include just onehalf of the asset purchase cost for CCA
calculation in the year it is bought.
• This rule is to discourage the last minute
purchase. Regardless when the asset is
actually purchased, deduction is the
same.
• The remaining half of the purchase cost
is added to the asset class in the
subsequent year.
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-11
CCA Calculation (cont’d)
CH11
• If net asset acquisition (purchases
> sales) is positive, the half-year
rule applies(a).
Year
Bgn. UCC
Add/Disp Sales
Proceeds
UCC before
CCA
CCA
@30%
2006
$0
$30,000
--
$30,000
$4,500
2007
$25,500
--
--
$25,500
$7,650
2008
$17,850
$40,000
---
$57,850
$11,355
2009
$46,495
$12,000
$10,000(a)
$48,495
$14,249
$12,000
$20,000(b)
$38,495
$11,549
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11-12
CCA Remarks
CH11
• Half-year rule does not apply to CCA
calculations when there is a net capital
asset disposition(b)
• Adjusted cost of disposal = min [original
cost, sales proceeds]
• Finding the present value of CCA tax
shield is the concern
• In principle, tax savings from CCA go on
even when the project in question ends
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11-13
CH11
Taxation for
Sales/Purchases of Assets
• Recapture occurs when the sale of an
asset creates a negative UCC balance.
CCA recapture is fully taxable.
• Terminal loss arises when the asset pool
is closed, but the UCC is still positive
after selling the last item. Loss may be
deducted from income.
• Capital gain exists when the asset is
sold for more than its initial cost. Gains
are taxed at 50%.
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-14
Proposed Expansion Project
CH11
• $200,000 cost + $10,000 shipping +
$30,000 installation.
• Economic life = 4 years
• Salvage value = $25,000
• CCA class 43 with a 30% rate
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11-15
Project Input Data
CH11
•
•
•
•
Annual unit sales = 1,250
Unit sales price = $200
Unit costs = $100
Net operating working capital
(NOWC) = 12% of sales.
• Tax rate = 40%
• Project cost of capital = 10%
• Inflation = 3%
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-16
What is the depreciation basis?
CH11
Depreciation basis is the capital cost
of the asset established for CCA
calculation
Basis = Cost + Shipping + Installation
= $240,000
Annual CCA deduction = Applicable
UCC × CCA rate
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11-17
Annual Depreciation
Expense (000s)
CH11
Year
%
X
(Initial Basis)
= Depr.
$240
$72.0
1
0.30
2
0.30
50.4
3
0.30
35.28
4
0.30
24.696
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11-18
Annual Sales and Costs
CH11
Year 1
Year 2
Year 3
Year 4
Units
1250
1250
1250
1250
Unit Price
$200
$206
$212.18
$218.55
Unit Cost
$100
$103
$106.09
$109.27
Sales
$250,000
$257,500 $265,225 $273,188
Costs
$125,000
$128,750 $132,613 $136,588
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11-19
Operating Cash Flows
(Years 1 and 2)
CH11
Sales
Costs
EBIT
Taxes (40%)
Op. CF
+ CCA Tax
Shield
Net Op.
Year 1
$250,000
$125,000
$125,000
Year 2
$257,500
$128,750
$128,750
$50,000
$75,000
$51,500
$77,250
$14,400
$60,600
$24,480
$52,770
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11-20
Operating Cash Flows
(Years 3 and 4)
CH11
Sales
Costs
EBIT
Taxes (40%)
Op. CF
+ CCA Tax
Shield
Net Op.
Year 3
$265,225
$132,613
$132,612
Year 4
$273,188
$136,588
$136,588
$53,045
$79,567
$54,635
$81,953
$17,136
$62,431
$ 5,141
$76,812
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11-21
Cash Flows due to Investments in Net
Operating Working Capital (NOWC)
CH11
Sales
Year 0
Year 1
Year 2
Year 3
Year 4
$250,000
$257,500
$265,225
$273,188
NOWC CF Due to
(12% of Investment
sales) in NOWC
$30,000 -$30,000
$30,900
-$900
$31,827
-$927
$32,783
-$956
$0 $32,783
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11-22
Salvage Cash Flow at
t = 4 (000s)
CH11
Salvage Value
Book Value (Assume
full depreciation)
Gain or loss
Tax (40%) on SV
$25
0
Net Terminal CF
$15
$25
10
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11-23
Net Cash Flows for Years 1-3
CH11
Init. Cost
Op. CF
NOWC CF
Salvage CF
Net CF
Year 0
Year 1
Year 2
-$240,000
0
0
0
$60,600
$52,770
-$30,000
-$900
-$927
0
0
0
-$270,000
$59,700
$51,843
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11-24
Net Cash Flows for Years 4-5
CH11
Init. Cost
Op. CF
NOWC CF
Salvage CF
Net CF
Year 3
Year 4
0
0
$62,431
$76,812
-$956
$32,783
0
$15,000
$61,475
$124,595
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11-25
Project Net CFs on a Time Line
CH11
0
1
(270,000) 59,700
2
3
4
51,843
61,475
124,595
Enter CFs in the register and I = 10.
NPV = -$41,595 < 0, reject.
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11-26
Use MIRR to double check
the proposed project
CH11
0
1
(270,000) 59,700
2
51,843
3
4
61,475 124,595
67,623
62,730
79,461
(270,000)
MIRR = ?
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334,409
11-27
Calculator Solution
CH11
• Enter positive CFs in CFLO. Enter I = 10.
Solve for NPV = $228,405
• Now use TVM keys: PV = -228,405,
• N = 4, I = 10; PMT = 0; Solve for FV =
334,409 (This is total of inflows)
• Use TVM keys: N = 4; FV = 334,409;
PV = -270,000; PMT= 0; Solve for I = ?
• I = 5.49% < 10% (WACCproject), reject.
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-28
Determining Project Cash Flows
CH11
• Free (or net) cash flows from operation may
increase because operating sales increase,
operating costs decrease, or both occur
• FCF/NCF = EBIT – Taxes + CCA deduction =
Net income + CCA deduction
• OCF/NCF = (Sales – Cash costs)(1 - Tc) +
(CCA)(Tc) = cash flows from the operating
project + tax savings from the CCA
• Find the PV of each set of CFs independently,
and add them to get the NPV.
• PVTS calculation is tedious.
PV of the CCA tax shield
CH11
• The formula offers a one-step solution
instead of finding separately for each
year’s PV from the CCA tax shield.
• PV of CCA tax shield:
 C  d  Tc  1  0.5r   1   S  d  Tc 
PVTS  

n 




r

d
1

r
(
1

r
)
r

d
 





• The setup assumes the asset class
remains open after the asset is sold (i.e.
UCC > 0).
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11-30
PVTS Formula: Interpretation
CH11
 C  d  Tc  1  0.5r   1   S  d  Tc 
PVTS  

n 




 d  r   1  r   (1  r )   d  r 
 (1)( 2)  (3)( 4)
• (1) calculates the total PV of the tax shield
assuming the asset is held in perpetuity
• (2) accounts for the half-year rule
• (3) discounts the lost tax shield to the present
time
• (4) calculates the PV (at time of sale) of the tax
shield given up from selling the asset
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-31
CH11
PV (CCA Tax Shield)
Computational Formula
 C  d  Tc  1  0.5r   1   S  d  Tc 
PVTS  

n 




d

r
1

r
(
1

r
)
d

r
 





C = $8,000 = capital cost of the asset
d = 30% = CCA rate of the asset class
Tc = 30% = corporate tax rate
r = 12% = discount rate
S = $2,000 = salvage value of the asset
PVTS = $1,350
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11-32
Change in Net Operating Working
Capital (ΔNOWC)
CH11
• The difference between the change in
current assets and current liabilities
associated with a project
• ΔNOWC = ΔCA – ΔCL > or < 0
• Changes in new working capital
merely involve the net build-up or
reduction of current accounts
• All changes will be reverted by the
end of the project’s life.
∆NOWC: Example
CH11
•
•
•
•
A/R:
$150;$170
Δ=$20 (addition)
Inventory:$278;$325
Δ=$47 (addition)
A/P:
$250;$221
Δ=-$29 (addition)
ΔNOWC = ΔCA - ΔCL = [Δ(A/R)+Δ(Inv)][Δ(A/P)] = [(20+ 47)] – (-29) = $96
• We need an extra investment of
$96 in order to get this project
running
Treatment of Financing Costs
CH11
• 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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11-35
Sunk Costs
CH11
• 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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11-36
Opportunity Costs
CH11
• Suppose the plant space could be
leased out for $25,000 a year. Would
this affect the analysis?
• Yes. Accepting the project means we will
not receive the $25,000. This is an
opportunity cost and it should be
charged to the project.
• After-tax opportunity cost = $25,000 (1 T) = $15,000 annual cost.
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11-37
Externalities
CH11
• 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.
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11-38
Incremental CF for a Project
CH11
• A replacement project occurs when
the firm replaces an existing asset
with a new one.
• Project’s incremental cash flow =
(corporate cash flow with the
project) – (corporate cash flow
without the project)
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-39
Timing of CF
CH11
• In theory, CFs should be analyzed
exact as they occur due to the TVM
• In practice, we cannot afford such
degree of detail
• In general, although we assume all
CFs occur at the end of every year.
we may need to estimate mid-year,
quarterly or monthly CFs.
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-40
Why is it important to include inflation
when estimating cash flows?
CH11
• Nominal r > real r. The cost of
capital, r, includes a premium for
inflation.
• Nominal CF > real CF. This is
because nominal cash flows
incorporate inflation.
• If you discount real CF with the
higher nominal r, then your NPV
estimate is too low.
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-41
Inflation (cont’d)
CH11
• Nominal CF should be discounted
with nominal r, and real CF should
be discounted with real r.
• Practically, it is more realistic to find
the nominal CF (i.e., increase cash
flow estimates with inflation) than it
is to reduce the nominal r to a real
r.
Copyright © 2011 by Nelson Education Ltd. All rights reserved.
11-42
Inflation Adjustment
CH11
• Nominal CFt = Real CFt × (1 + i)t
• Fisher equation: (1+rNOM) = (1+ rr)
×(1 + i)
• NPV(with inflation):
N
NCFt
( RCFt )(1  i)t


t
t
t
(
1

r
)
(
1

r
)
(
1

i
)
t 0
t 0
NOM
r
N
• No inflation:
N
( RCFt )
NPV  
t
(
1

r
)
t 0
r
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11-43
What does “risk” mean in
capital budgeting?
CH11
• Uncertainty about a project’s future
profitability.
• Measured by σNPV, σIRR, beta.
• Will taking on the project increase
the firm’s and stockholders’ risk?
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11-44
Is risk analysis based on historical
data or subjective judgment?
CH11
• Can sometimes use historical data,
but generally cannot.
• So risk analysis in capital budgeting
is usually based on subjective
judgments.
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11-45
What three types of risk are
relevant in capital budgeting?
CH11
•
•
•
•
Stand-alone risk
Corporate risk
Market (or beta) risk
They are highly correlated - if the
general economy does well, so will
the firm, and it the firm does well,
so will most of its projects.
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11-46
Stand-Alone Risk
CH11
• The project’s risk if it were the firm’s
only asset and there were no
shareholders.
• Ignores both firm and shareholder
diversification.
• Measured by the σ or CV of NPV,
IRR, or MIRR.
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11-47
Probability Density
CH11
Flatter distribution,
larger , larger
stand-alone risk.
0
E(NPV)
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NPV
11-48
Corporate Risk
CH11
• Reflects the project’s effect on corporate
earnings stability.
• Considers firm’s other assets
(diversification within firm).
• Depends on project’s σ, and its
correlation, ρ, with returns on firm’s other
assets.
• Measured by the project’s corporate
beta.
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11-49
Project X is negatively correlated to firm’s other
assets, so has big diversification benefits.
CH11
Profitability
If r = 1.0, no diversification
benefits. If r < 1.0, some
diversification benefits.
Project X
Total Firm
Rest of Firm
0
Years
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11-50
Market Risk
CH11
• Reflects the project’s effect on a
well-diversified stock portfolio.
• Takes account of stockholders’
other assets.
• Depends on project’s σ and
correlation with the stock market.
• Measured by the project’s market
beta.
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11-51
How is each type of risk used?
CH11
• Market risk is theoretically best in
most situations.
• However, creditors, customers,
suppliers, and employees are more
affected by corporate risk.
• Therefore, corporate risk is also
relevant.
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11-52
How is each type of risk
used? (cont’d)
CH11
• Stand-alone risk is easiest to
measure, more intuitive.
• Core projects are highly correlated
with other assets, so stand-alone
risk generally reflects corporate
risk.
• If the project is highly correlated
with the economy, stand-alone risk
also reflects market risk.
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11-53
Sensitivity Analysis
CH11
• Shows how changes in a variable
such as unit sales affect NPV or
IRR.
• Each variable is fixed except one.
Change this one variable to see the
effect on NPV or IRR.
• Answers “what if” questions, e.g.
“What if sales decline by 30%?”
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11-54
CH11
Evaluating Risk:
Sensitivity Graph
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11-55
Results of Sensitivity
Analysis
CH11
• Steeper sensitivity lines show
greater risk. Small changes result
in large declines in NPV.
• Unit sales line is steeper than
salvage value or r, so for this
project, should worry most about
accuracy of sales forecast.
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11-56
What are the weaknesses of
sensitivity analysis?
CH11
• Does not reflect diversification.
• Says nothing about the likelihood of
change in a variable, i.e. a steep
sales line is not a problem if sales
won’t fall.
• Ignores relationships among
variables.
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11-57
Why is sensitivity analysis
useful?
CH11
• Gives some idea of stand-alone
risk.
• Identifies dangerous variables.
• Gives some breakeven information.
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11-58
Scenario Analysis
CH11
• Examines several possible
situations, usually worst case, most
likely case, and best case.
• Provides a range of possible
outcomes.
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11-59
Best scenario: 1,600 units @ $240
Worst scenario: 900 units @ $160
CH11
Scenario
Probability
NPV(000)
Best
0.25
$279
Base
0.50
88
Worst
.025
-49
E(NPV) = $101.5
σ(NPV) = 116.6
CV(NPV) = σ(NPV)/E(NPV) = 1.15
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11-60
Are there any problems with
scenario analysis?
CH11
• Only considers a few possible outcomes.
• 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.
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11-61
Monte Carlo Simulation
CH11
• 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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11-62
Simulation Analysis (cont’d)
CH11
• 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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11-63
00
30 0)
,0
00
)
60
,
$3 $0
0,
0
$6 00
0,
0
$9 00
0,
$1 000
20
,
$1 000
50
,
$1 000
80
,
$2 000
10
,
$2 000
40
,
$2 000
70
,
$3 000
00
,
$3 000
30
,
$3 000
60
,0
00
($
($
Probability of NPV
Histogram of Results
CH11
12%
10%
8%
6%
4%
2%
0%
NPV
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11-64
What are the advantages of
simulation analysis?
CH11
• 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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11-65
What are the disadvantages
of simulation?
CH11
• Difficult to specify probability
distributions and correlations.
• If inputs are bad, output will be bad:
“Garbage in, garbage out.”
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11-66
Project Risk Conclusions
CH11
• Sensitivity, scenario, and simulation
analyses do not provide a decision rule.
They do not indicate whether a project’s
expected return is sufficient to
compensate for its risk.
• Sensitivity, scenario, and simulation
analyses all ignore diversification. Thus
they measure only stand-alone risk,
which may not be the most relevant risk
in capital budgeting.
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11-67
If the firm’s average project has a CV of 0.2 to
0.4, is this a high-risk project?
What type of risk is being measured?
CH11
• CV from scenarios = 0.74, CV from
simulation = 0.62 Both are > 0.4,
this project has high risk.
• CV measures a project’s standalone risk.
• High stand-alone risk usually
indicates high corporate and market
risks.
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With a 3% risk adjustment,
should our project be accepted?
CH11
•
•
•
•
Project r = 10% + 3% = 13%
That’s 30% above base r
NPV = $65,371
Project remains acceptable after
accounting for differential (higher)
risk.
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Should subjective risk
factors be considered?
CH11
• Yes. A numerical analysis may not
capture all of the risk factors
inherent in the project.
• For example, if the project has the
potential for bringing on harmful
lawsuits, then it might be riskier
than a standard analysis would
indicate.
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CH11
Incorporating Project Risk
into Capital Budgeting
• Risk-adjusted discount rate (RADR)
or project cost of capital is used to
evaluate a particular project
• Each project carries different risk
• The corporate rWACC is based on the
firm’s average risk project
• Adjust rWACC upward/downward for
more/less risky projects
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Decision Trees
CH11
• A form of scenario analysis in which
different actions are taken in
different scenarios.
• The analysis becomes very helpful
whenever new information arrives.
• If investment is made in stages, the
flexibility improves decision making
with decision tree analysis.
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Real option
CH11
• Real options exist when managers can
influence the size and risk of a project’s
cash flows by taking different actions
during the project’s life in response to
changing market conditions.
• Alert managers always look for real
options in projects.
• Smarter managers try to create real
options.
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Types of real options
CH11
• Investment timing options
• Growth options
– Expansion of existing product line
– New products
– New geographic markets
• Abandonment options
– Contraction
– Temporary suspension
• Flexibility options
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