CHAPTER 13
Capital Budgeting: Estimating
Cash Flows and Analyzing Risk
1
Chapter Topics

Estimating cash flows:




Risk Analysis:





Issues in Project Analysis
Depreciation & Tax Effects on Salvage Value
Inflation
Sensitivity Analysis
Scenario Analysis
Simulation Analysis
Decision Trees
Real Options
2
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.
3
Free Cash Flow
FCF  EBIT(1  T)  Deprec & Amort 
 Capital Expenditures  ΔNOWC
Capital Expenditures = FA + Deprec
ΔNOWC = Current Operating Assets
– Current Operating Liabilities
Current Operating Assets excludes Marketable Securities
Current Operating Liabilities excludes Notes Payable
4
Free Cash Flow
FCF  EBIT(1  T)  Deprec & Amort 
 Capital Expenditures  ΔNOWC
FCF  OCF - Investment in Operating Capital
FCF  Investment outlay CF  Operating CF
 NOWC CF  Salvage CF
“Investment outlay CF = CF0
“Operating CF” = Net Income + Non-cash items (deprec) each year
“NOWC CF” = Net working capital requirements each year
“Salvage CF” = After-tax salvage value of assets and NOWC recovery
5
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
6
Depreciation Basics
• Straight Line  Salvage Value
• MACRS  0
•Recovery Period = Class Life
•1/2 Year Convention
7
MACRS Depreciation Classes
TABLE 13.1
8
MACRS Depreciation
TABLE 13.2
9
Annual Depreciation Expense
SCC (Minicase):
Year
1
2
3
4
Equipment cost
Shipping
Installation
% x Basis = Depr
0.33
$ 79.2
$240
0.45
108.0
0.15
36.0
0.07
16.8
(000s)
$200
10
30

Depr
79.2
187.2
223.2
240.0
Book
Value
160.8
52.8
16.8
0
10
Tax Effect on Salvage
• Net Cash flow from sale = Sale proceeds
- taxes paid
• Tax basis = difference between sales price
and book value, where:
Book value = Original basis
- Accumulated depreciation
11
Tax Effect on Salvage
Net Salvage Cash Flow
= SP - (SP-BV)(T)
Where:
SP = Selling Price
BV = Book Value
T = Corporate tax rate
12
Example: If Asset Sold After 3 Years

BV (EOY 3)

IF:
Selling price = $20


= $17
IF:
TCF = $20 - (20-17)(.4) = $18.8
Selling price

= $10
TCF = $10 - (10-17)(.4) = $12.8
13
Adjusting for Inflation

Nominal r > real r


Nominal CF > real CF


The cost of capital, r, includes a premium
for inflation
Nominal cash flows incorporate inflation
If you discount real CF with the higher
nominal r, then your NPV estimate is
biased downward.
14
INFLATION
Real vs. Nominal Cash flows
n
NPV  
t 0
Real
CFt
1  WACC
t
Nominal
15
INFLATION
Real vs. Nominal Cash flows

2 Ways to adjust

Adjust WACC
Cash Flows = Real
 Adjust WACC to remove inflation


Adjust Cash Flows for Inflation

Use Nominal WACC
16
Regency Integrated Chips
A
B
1 Regency Integrated Chips
2
3 Part I: Background Data:
4
5
Building Cost (=Depreciable base)
6
Building MACRS class
7
Equipment Cost (= Depreciable base)
8
Equipment MACRS class
9
Net Operating WC/Sales
10
First year sales (in units)
11
Growth rate in units sold
12
Sales price per unit
13
Variable cost per unit
14
Fixed costs
15
Market value of Building in Year 4
16
Market Value of Equipment in Year 4
17
Tax rate
18
WACC
19
Inflation: growth in sales price
20
Inflation: growth in VC per unit
21
Inflation: growth in fixed costs
C
Chapter 13
$
$
$
$
$
$
$
(000)
Inputs
12,000
39 year
8,000
5 year
10%
20,000
0%
3.00
2.10
8,000.00
7,500.00
2,000.00
40%
12%
2%
2%
1%
17
RIC – Depreciation & Salvage Value
A
B
C
D
23 Part 2: Depreciation Calculations:
24
Building
$
12,000
1
25
MACRS % (Bldg-39 yr))
1.3%
26
Recovery Allowance
$
156
27
Accumulated Depreciation
$
156
28
Book Value
$
11,844
29
Equipment
$
8,000
30
MACRS % (Eqpt-5 yr)
20.0%
31
Recovery Allowance
$
1,600
32
Accumulated Depreciation
$
1,600
33
Book Value
$
6,400
34
35 Part 3: Salvage Values in Year 4
36
Building
37
Market (salvage) Value (Year 4)
$
7,500
38
Book Value (Year 4)
10,908
39
Capital Gain/Loss
(3,408)
40
Taxes
(1,363)
41
Net SV (SV-Taxes)
8,863
42
Total Net Salvage Value
E
F
G
$
$
$
Year
2
2.6%
312 $
468 $
11,532 $
3
2.6%
312 $
780 $
11,220 $
4
2.6%
312
1,092
10,908
$
$
$
32.0%
2,560 $
4,160 $
3,840 $
19.0%
1,520 $
5,680 $
2,320 $
12.0%
960
6,640
1,360
$
Equipment
2,000
1,360
640
256
1,744
10,607
18
RIC – Sales, Costs and NWC
A
B
45
YEAR Number
46 Part 4: Projected Net Cash ($000)
47
Units Sold
48
Sales Price/Unit
49
Fixed Cost
50
Variable Cost per unit
51
Sales
52
NWC Required
10
11
12
13
14
19
20
21
C
D
E
0
$
$
$
$
$
6,000 $
B
First year sales (in units)
Growth rate in units sold
Sales price per unit
Variable cost per unit
Fixed costs
Inflation: growth in sales price
Inflation: growth in VC per unit
Inflation: growth in fixed costs
F
G
1
2
3
4
20,000
3.00
8,000
2.10
60,000
6,120
20,000
3.06
8,080
2.14
61,200
6,242
20,000
3.12
8,161
2.18
62,424
6,367
20,000
3.18
8,242
2.23
63,672
-
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
C
20,000
0%
3.00
2.10
8,000.00
2%
2%
1%
19
RIC – Cash Flow Estimation
A
B
45
YEAR Number
46 Part 4: Projected Net Cash ($000)
54 Initial Investment
55
Building
56
Equipment
57
Net Working Capital
58
Total Investment
59
Sales
60
Variable Costs
61
Fixed Costs
62
Depreciation (Bldg)
63
Depreciation (Eqpt))
64
65
Taxes
66
Net Operating Income
67
Add back Depreciation
68
CASH FLOW from Operations
69
Investment in NWC
70
Recovery of NWC
71
Salvage Value
72
TOTAL PROJECTED CF
C
D
0
E
1
F
2
G
3
4
$
(12,000)
(8,000)
(see below)
(20,000)
$
EBT
(6,000)
$
(26,000) $
60,000 $
42,000
8,000
156
1,600
8,244
3,298
4,946
1,756
6,702
(120)
6,582
$
61,200 $
42,840
8,080
312
2,560
7,408
2,963
4,445
2,872
7,317
(122)
7,194
$
62,424 $
43,697
8,161
312
1,520
8,734
3,494
5,241
1,832
7,073
(125)
6,948
$
63,672
44,571
8,242
312
960
9,587
3,835
5,752
1,272
7,024
0
6,367
10,607
23,999
20
RIC: Cash Flow Analysis
A
B
45
YEAR Number
46 Part 4: Projected Net Cash ($000)
72
TOTAL PROJECTED CF
73
74
Discounted Cash Flows
75
76
77
Cumulative Cash Flows for Payback
78
79
80
Cumulative Discounted Cash Flows
81
82
83
84
85
86
87
88
C
D
0
E
1
F
2
G
3
4
$
(26,000) $
6,582
$
7,194
$
6,948
$
23,999
$
(26,000) $
5,877
$
5,735
$
4,945
$
15,252
$
0
(26,000) $
FALSE
1
(19,418) $
FALSE
2
(12,223) $
FALSE
3
(5,275) $
FALSE
4
18,723
3.22
(26,000) $
FALSE
(20,123) $
FALSE
(14,388) $
FALSE
(9,442) $
FALSE
5,809
3.62
$
NPV
IRR
MIRR
PB
DPB
PI
$
5,809
20.12%
17.79%
3.22
3.62
1.22
21
Excel Functions
83
84
85
86
87
88
C
NPV
IRR
MIRR
PB
DPB
PI
$
D
H
I
5,809
=NPV(C18,D72:G72)+C72
20.12%
=IRR(C72:G72)
17.79%
=MIRR(C72:G72,C18,C18)
3.22
=MAX(C78:G78)
3.62
=MAX(C81:G81)
1.22
=(D83-C72)/-C72
22
A
RIC
Background
Data
Salvage
Value
Basic
Calculations
Cash Flow
Estimation
Cash Flow
Analysis
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
B
C
Regency Integrated Chips
D
E
F
G
H
I
Chapter 13
Part I: Background Data:
Building Cost (=Depreciable base)
Building MACRS class
Equipment Cost (= Depreciable base)
Equipment MACRS class
Net Operating WC/Sales
First year sales (in units)
Growth rate in units sold
Sales price per unit
Variable cost per unit
Fixed costs
Market value of Building in Year 4
Market Value of Equipment in Year 4
Tax rate
WACC
Inflation: growth in sales price
Inflation: growth in VC per unit
Inflation: growth in fixed costs
$
$
$
$
$
$
$
Part 2: Depreciation Calculations:
Building
$
MACRS % (Bldg-39 yr))
Recovery Allowance
Accumulated Depreciation
Book Value
Equipment
$
MACRS % (Eqpt-5 yr)
Recovery Allowance
Accumulated Depreciation
Book Value
(000)
Inputs
12,000
39 year
8,000
5 year
10%
20,000
0%
3.00
2.10
8,000.00
7,500.00
2,000.00
40%
12%
2%
2%
1%
SOURCES
RESULTS
NPV
IRR
MIRR
PB
DPB
PI
$
5,809
20.12%
17.79%
3.22
3.62
1.22
Results recapped from below
$
$
$
1
1.3%
156 $
156 $
11,844 $
Year
2
2.6%
312 $
468 $
11,532 $
3
2.6%
312 $
780 $
11,220 $
4
2.6%
312
1,092
10,908
$
$
$
20.0%
1,600 $
1,600 $
6,400 $
32.0%
2,560 $
4,160 $
3,840 $
19.0%
1,520 $
5,680 $
2,320 $
12.0%
960
6,640
1,360
12,000
("L" = Line)
Data from textbook
Footnote: Page 461
C24 * MACRS recovery % (L25)
C24-Accumulated Depreciation (L27)
8,000
Table on page 461
C29 * MACRS recovery % (L30)
C29-Accumulated Depreciation (L32)
Part 3: Salvage Values in Year 4
Building Equipment
7,500 $
2,000
10,908
1,360
(3,408)
640
(1,363)
256
8,863
1,744
Total Net Salvage Value
10,607
Market (salvage) Value (Year 4)
Book Value (Year 4)
Capital Gain/Loss
Taxes
Net SV (SV-Taxes)
$
YEAR Number
Part 4: Projected Net Cash ($000)
Units Sold
Sales Price/Unit
Fixed Cost
Variable Cost per unit
Sales
NWC Required
0
$
Initial Investment
Building
Equipment
Net Working Capital
Total Investment
Sales
Variable Costs
Fixed Costs
Depreciation (Bldg)
Depreciation (Eqpt))
6,000
1
$
$
$
$
$
20,000
3.00
8,000
2.10
60,000
6,120
$
$
$
$
C15; C16
G28; G33
Market value - Book value (L37-L38)
Gain/loss * tax rate (L39*$C17)
Market value - taxes (L37-L40)
Sum of building + equipment D41+E41
2
3
4
20,000
3.06
8,080
2.14
61,200
6,242
20,000
3.12
8,161
2.18
62,424
6,367
20,000
3.18
8,242
2.23
63,672
-
$
$
$
$
$
$
$
$
$
(12,000)
(8,000)
(see below)
(20,000)
Key
C10
C12 adjusted for inflation (C19)
C14 adjusted for inflation (C21)
C13 adjusted for inflation (C20)
L47 * L48
10% (C9) of next year's sales (L51)
C5
C7
$
Taxes
Net Operating Income
Add back Depreciation
CASH FLOW from Operations
Investment in NWC
Recovery of NWC
Salvage Value
TOTAL PROJECTED CF
$
(26,000) $
6,582
$
7,194
$
6,948
$
63,672
44,571
8,242
312
960
9,587
3,835
5,752
1,272
7,024
0
6,367
10,607
23,999
Discounted Cash Flows
$
(26,000) $
5,877
$
5,735
$
4,945
$
15,252
L72 discounted at WACC (C18)
$
1
(19,418) $
FALSE
2
(12,223) $
FALSE
3
(5,275) $
FALSE
4
18,723
3.22
L45
Cumulative Cash Flows for Payback
0
(26,000) $
FALSE
Cumulative Discounted Cash Flows
$
(26,000) $
FALSE
(20,123) $
FALSE
(14,388) $
FALSE
(9,442) $
FALSE
5,809
3.62
EBT
(6,000)
NPV
IRR
MIRR
PB
DPB
PI
$
60,000 $
42,000
8,000
156
1,600
8,244
3,298
4,946
1,756
6,702
(120)
5,809
20.12%
17.79%
3.22
3.62
1.22
61,200 $
42,840
8,080
312
2,560
7,408
2,963
4,445
2,872
7,317
(122)
62,424 $
43,697
8,161
312
1,520
8,734
3,494
5,241
1,832
7,073
(125)
L51 = L47 * L48
L50 * L47
L49
L26
L31
L59-L60-L61-L62-L63
L64 * tax rate (C17)
L64-L65
L62+L63
L66+L67
=IF(D52=0,0,C52-D52)
=-SUM(C69:G69)
E42
E59+E70+E71+E72+E73
=IF(C77>0,B76+ABS(B77)/C72)
=IF(C80>0,B76+ABS(B80)/C74)
=NPV(C18,D72:G72)+C72
=IRR(C72:G72)
=MIRR(C72:G72,C18,C18)
=MAX(C78:G78)
=MAX(C81:G81)
=(D83-C72)/-C72
23
“Risk” in Capital Budgeting



Uncertainty about a project’s future
profitability
Measured by σNPV, σIRR, beta
Will taking on the project increase the
firm’s and stockholders’ risk?
24
Three types of relevant risk



Stand-alone risk
Corporate risk
Market (or beta) risk
25
Stand-Alone Risk



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.
26
Probability Density
Flatter distribution,
larger , larger
stand-alone risk.
0
E(NPV)
NPV
27
Corporate Risk




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.
28
Project X is negatively correlated to firm’s
other assets → big diversification benefits
Profitability
If r = 1.0, no diversification
benefits. If r < 1.0, some
diversification benefits
Project X
Total Firm
Rest of Firm
0
Years
29
Market Risk




Reflects the project’s effect on a welldiversified 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.
30
Conclusions on Risk



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.
31
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
32
RIC: Sensitivity Analysis
203
204
205
206
207
208
209
210
211
212
B
Deviation
from
Base Case
-30%
-15%
0%
15%
30%
C
Sales
Price
($27,223)
($10,707)
$5,809
$22,326
$38,842
Range
$66,064
D
E
F
G
NPV at Different Deviations from Base
Variable
Growth
Year 1
Nonvariable
Cost/Unit
Rate
Units Sold
Cost
$29,404
($4,923)
($3,628)
$10,243
$17,607
($115)
$1,091
$8,026
$5,809
$5,809
$5,809
$5,809
($5,988)
$12,987
$10,528
$3,593
($17,785)
$21,556
$15,247
$1,376
$47,189
$26,479
$18,875
$8,867
H
WACC
$9,030
$7,362
$5,809
$4,363
$3,014
$6,016
33
RIC: Sensitivity Graph
NPV ($)
$40,000
Sales price
$30,000
Variable cost
Growth rate
$20,000
Units sold
$10,000
Nonvariable cost
$0
WACC
($10,000)
($20,000)
($30,000)
-30%
-15%
0%
15%
30%
Deviation from Base-Case Value (%)
34
Results of Sensitivity Analysis

Steeper sensitivity lines = greater risk


Small changes → 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
35
RIC: Sensitivity Analysis
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
A
% Deviation
from
Base Case
-30%
-15%
0%
15%
30%
B
C
D
WACC
8.4%
10.2%
12.0%
13.8%
15.6%
% Deviation
from
Base Case
-30%
-15%
0%
15%
30%
VARIABLE COSTS
Variable
NPV
Cost
$5,809
$1.47
$29,404
$1.79
$17,607
$2.10
$5,809 Base Case
$2.42
-$5,988
$2.73
-$17,785
% Deviation GROWTH RATE, UNITS
from
Growth
NPV
Base Case
Rate %
$5,809
-30%
-30%
-$4,923
-15%
-15%
-$115
0%
0%
$5,809
15%
15%
$12,987
30%
30%
$21,556
% Deviation
from
Base Case
-30%
-15%
0%
15%
30%
SALES PRICE
Sales
NPV
Price
$5,809
$2.10
-$27,223
$2.55
-$10,707
$3.00
$5,809 Base Case
$3.45
$22,326
$3.90
$38,842
% Deviation NONVARIABLE COSTS
from
Nonvariable
NPV
Base Case
Costs
$5,809
-30%
$5,600
$10,243
-15%
$6,800
$8,026
0%
$8,000
$5,809
15%
$9,200
$3,593
30%
$10,400
$1,376
WACC
NPV
5,809
$9,030
$7,362
$5,809 Base Case
$4,363
$3,014
E
% Deviation
from
Base Case
-30%
-15%
0%
15%
30%
F
G
1st YEAR UNIT SALES
Units
NPV
Sold
$5,809
14,000
-$3,628
17,000
$1,091
20,000
$5,809
23,000
$10,528
26,000
$15,247
36
14-37
Sensitivity Ratio


%NPV = (New NPV - Base NPV)/Base NPV
%VAR = (New VAR - Base VAR)/Base VAR
%NPV
SR 
%VAR
• If SR>0  Direct relationship
• If SR<0  Inverse relationship
RIC: Sensitivity Ratios
Sensitivity Analysis: Sensitivity Ratios
Deviation
from
Base Case
(0.30)
(0.15)
0%
15%
0.30
%ΔNPV
%ΔVAR
SR
Sales
Price
(27,222.63)
(10,706.58)
$5,809
$22,326
38,841.59
284%
15%
18.95
NPV at Different Deviations from Base
Variable
Growth
Year 1
Nonvariable
Cost/Unit
Rate
Units Sold
Cost
29,403.84
(4,922.76)
(3,628.27)
10,243.07
17,606.66
(114.64)
1,090.61
8,026.28
$5,809
$5,809
$5,809
$5,809
($5,988)
$12,987
$10,528
$3,593
(17,784.89)
21,556.34
15,247.22
1,375.88
-203%
124%
81%
-38%
15%
15%
15%
15%
(13.54)
8.24
5.42
(2.54)
WACC
9,030.42
7,361.84
$5,809
$4,363
3,014.07
-25%
15%
(1.66)
38
RIC: Sensitivity Ratios & Graph
%ΔNPV
%ΔVAR
SR
Sales
Price
284%
15%
18.95
NPV at Different Deviations from Base
Variable
Growth
Year 1
Nonvariable
Cost/Unit
Rate
Units Sold
Cost
-203%
124%
81%
-38%
15%
15%
15%
15%
(13.54)
8.24
5.42
(2.54)
NPV ($)
$40,000
Sales price
$30,000
Variable cost
WACC
-25%
15%
(1.66)
Growth rate
$20,000
Units sold
$10,000
Nonvariable cost
$0
WACC
($10,000)
($20,000)
($30,000)
-30%
-15%
0%
15%
30%
Deviation from Base-Case Value (%)
39
Sensitivity Analysis:
Weaknesses


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
40
Sensitivity Analysis:
Strengths



Provides indication of stand-alone risk
Identifies dangerous variables
Gives some breakeven information
41
Scenario Analysis

Examines several possible situations,
usually:




Worst case
Base case or most likely case, and
Best case
Provides a range of possible outcomes
42
RIC: Scenario Analysis
Table 13-4. Scenario Analysis (Dollars in Thousands)
Scenario
Best Case
Base Case
Worst Case
Probability
Sales
Price
Unit
Sales
Variable
Costs
Growth
Rate
25%
50%
25%
$3.90
$3.00
$2.10
26,000
20,000
14,000
$1.47
$2.10
$2.73
30%
0%
-30%
Expected NPV = sum, prob times NPV
Standard Deviation = Sq Root of variance
Coefficient of Variation = Std Dev / E(NPV)
NPV
$146,180
$5,809
($37,257)
Squared
Deviation
Times
Probability
3,366,596,001
295,883,220
1,135,428,840
4797908060
$30,135
$69,267
2.30
43
RIC: Scenario Analysis
a. Probability Graph
Probability
50%
25%
(37,257)
0
30,135
5,809
Most Likely
Mean of distribution
146,180
NPV ($)
44
Problems with Scenario Analysis


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
45
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
46
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
47
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
12%
10%
8%
6%
4%
2%
0%
NPV
48
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
49
Disadvantages of Simulation Analysis


Difficult to specify probability
distributions and correlations
If inputs are bad, output will be bad:
“Garbage in, garbage out”
50
Disadvantages of Sensitivity, Scenario
and Simulation Analysis

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

They measure only stand-alone risk, which may
not be the most relevant risk in capital budgeting
51
Subjective risk factors

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
52
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
53
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?
54
United Robotics Decision Tree
Figure 13-5
55
United Robotics Decision Tree
A
416
417
418
419
t=0
420
421
422
423
424
425
426
0.8
427 ($500)
428
0.2
429
430
431
432
433
B
Cost of capital =
C
D
E
F
G
Join
Probability
H
I
11.5%
t=1
t=2
t=3
t=4
t=5
NPV
Prob.xNPV
$18,000
$18,000
$18,000
0.144
$25,635
$3,691
$8,000
$8,000
$8,000
0.192
$6,149
$1,181
0.144
($10,883)
($1,567)
0.320
($1,397)
($447)
0.200
($500)
($100)
0.3
0.4
($10,000)
0.6
0.3
($1,000)
0.4
Stop
Stop
($2,000)
Stop
1.000 Expected NPV=
$2,758
s=
$10,584
56
Real Options

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
57
Types of Real Options


Investment timing options
Growth options




Abandonment options



Expansion of existing product line
New products
New geographic markets
Contraction
Temporary suspension
Flexibility options
58