T11.1 Chapter Outline
Chapter 11
Project Analysis and Evaluation
Chapter Organization
 11.1 Evaluating NPV Estimates
 11.2 Scenario and Other “What-if” Analyses
 11.3 Break-Even Analysis
 11.4 Operating Cash Flow, Sales Volume, and Break-Even
 11.5 Operating Leverage
 11.6 Additional Considerations in Capital Budgeting
 11.7 Summary and Conclusions
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copyright © 2002 McGraw-Hill Ryerson, Ltd.
T11.2 Evaluating NPV Estimates
I: The Basic Problem
 The basic problem: How reliable is our NPV estimate?

Projected vs. Actual cash flows
Estimated cash flows are based on a distribution of possible
outcomes each period

Forecasting risk
The possibility of a bad decision due to errors in cash flow
projections - the GIGO phenomenon

Sources of value
What conditions must exist to create the estimated NPV?
“What If” analysis
A.
Scenario analysis
B.
Sensitivity analysis
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Slide 2
T11.3 Evaluating NPV Estimates
II: Scenario and Other “What-If” Analyses
 Scenario and Other “What-If” Analyses

“Base case” estimation
Estimated NPV based on initial cash flow projections

Scenario analysis
Posit best- and worst-case scenarios and calculate NPVs

Sensitivity analysis
How does the estimated NPV change when one of the input
variables changes?

Simulation analysis
Vary several input variables simultaneously, then construct a
distribution of possible NPV estimates
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Slide 3
T11.4 Fairways Driving Range Example
 Fairways Driving Range expects rentals to be 20,000 buckets at $3 per
bucket. Equipment costs $20,000 and will be depreciated using SL over 5
years and have a $0 salvage value. Variable costs are 10% of rentals and
fixed costs are $40,000 per year. Assume no increase in working capital nor
any additional capital outlays. The required return is 15% and the tax rate is
15%.
Revenues
Variable costs
$60,000
6,000
Fixed costs
40,000
Depreciation
4,000
EBIT
Taxes (@15%)
Net income
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$10,000
1500
$ 8,500
Slide 4
T11.4 Fairways Driving Range Example (concluded)
 Estimated annual cash inflows:
$10,000 + 4,000 - 1,500 = $12,500
 At 15%, the 5-year annuity factor is 3.352. Thus, the base-case
NPV is:
NPV = $-20,000 + ($12,500 3.352) = $21,900.
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 5
T11.5 Fairways Driving Range Scenario Analysis
INPUTS FOR SCENARIO ANALYSIS
 Base case: Rentals are 20,000 buckets, variable costs
are 10% of revenues, fixed costs are $40,000,
depreciation is $4,000 per year, and the tax rate
is 15%.
 Best case: Rentals are 25,000 buckets, variable costs are
8% of revenues, fixed costs are $40,000,
depreciation is $4,000 per year, and the tax
rate is 15%.
 Worst case: Rentals are 18,000 buckets, variable costs are
12% of revenues, fixed costs are $40,000,
depreciation is $4,000 per year, and the tax
rate is 15%.
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 6
T11.5 Fairways Driving Range Scenario Analysis (concluded)
Revenues
Net
Income
Project
Cash Flow
NPV
$21,250
$25,250
$64,635
Scenario
Rentals
Best Case
25,000
$75,000
Base Case
20,000
60,000
8,500
12,500
21,900
Worst Case
18,000
54,000
2,992
6,992
3,437
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 7
T11.6 Fairways Driving Range Sensitivity Analysis
INPUTS FOR SENSITIVITY ANALYSIS
 Base case: Rentals are 20,000 buckets, variable costs
are 10% of revenues, fixed costs are $40,000,
depreciation is $4,000 per year, and the tax
rate is 15%.
 Best case: Rentals are 25,000 buckets and revenues are
$75,000. All other variables are unchanged.
 Worst case: Rentals are 18,000 buckets and revenues are
$54,000. All other variables are unchanged.
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 8
T11.6 Fairways Driving Range Sensitivity Analysis (concluded)
Revenues
Net
income
Project
cash flow
NPV
$19,975
$23,975
$60,364
Scenario
Rentals
Best case
25,000
$75,000
Base case
20,000
60,000
8,500
12,500
21,900
Worst case
18,000
54,000
3,910
7,910
6,514
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 9
T11.7 Fairways Driving Range: Rentals vs. NPV
Fairways Sensitivity Analysis - Rentals vs. NPV
NPV
Best case
$60,000
NPV = $60,035
x
Base case
NPV = $21,900
x
Worst case
0
NPV = $3,437
x
-$60,000
15,000
20,000
25,000
Rentals per Year
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 10
Break - Even Analysis
 Where the crucial variable for a project and its success is sales volume
- various forms of break-even analysis can be developed essentially
addressing the question of ‘how bad can sales get before we start
losing money’





an understanding of the fixed and variable costs associated with the project
is important in developing the break-even analysis.
Variable Costs - ‘costs that change when the quantity of output changes.’
Variable cost VC = total quantity (Q) * cost per unit (v)
Fixed Costs - ‘costs that do not change when the quantity of output changes
during a particular time period’
• fixed costs are not fixed forever - only for a prescribed period of time; in
the long run all costs are variable
Total Costs TC for a given level of output is the sum of the Variable costs VC
and fixed costs FC
TC = VC+FC or v*Q + FC
Marginal or incremental cost is the change in costs that occurs when there is
a small change in output - what happens to our costs when we produce one
more unit
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Slide 11
Accounting Break-Even
 Accounting break-even is the sales level that results in zero
project net income







P = Selling Price per unit
v = Variable cost per unit
Q = total units sold
FC = Fixed Costs
D = Depreciation
t = Tax rate
VC = Variable cost in dollars
Accounting break-even;
Q =(FC+D)/(P-v)
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Slide 12
Operating Cash Flow, Sales Volume and Break-Even
 Given our focus on cash flow, the next evolution in break-even
analysis is to look at the relationship between operating cash
flow and sales volume
 Cash break-even - the point where operating cash flow (OCF)
is zero

OCF = (P-v) *Q - FC or Q = (FC + OCF)/(P-v)
Cash break-even then is where OCF = 0

Q = (FC + 0)/(P-v)

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Slide 13
Financial Break-Even
 The point where the sales level results in a zero NPV
 the first step is determining OCF for the NPV to be zero
 a zero NPV occurs when the PV of the OCF equals the original
investment - if the cash flow is the same each year we can use the
annuity formula to solve for OCF
• original investment or PV = OCF * annuity future value factor
• OCF = original investment/Annuity future value factor
 the financial break-even is often greater than the accounting
break-even or conversely when a project just breaks even in an
accouning sense it will usually be losing money in a financial or
economic sense
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 14
T11.8 Fairways Driving Range: Total Cost Calculations
 Total Cost = Variable cost + Fixed cost
Rentals
0
Variable
Revenue
cost
$0
Fixed
cost
$0
$40,000
Total
cost
Depr.
$40,000 $4,000
Total
acct. cost
$44,000
15,000
45,000
4,500
40,000
44,500
4,000
48,500
20,000
60,000
6,000
40,000
46,000
4,000
50,000
25,000
75,000
7,500
40,000
47,500
4,000
51,500
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 15
T11.9 Fairways Driving Range: Break-Even Analysis
Fairways Break-Even Analysis - Sales vs. Costs and Rentals
Total revenues
$80,000
Accounting
break-even point
16,296 Buckets
$50,000
Fixed costs + Dep
$44,000
Net
Net
Income < 0
Income > 0
$20,000
15,000
20,000
25,000
Rentals per Year
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 16
T11.10 Fairways Driving Range: Accounting Break-Even Quantity
 Fairways Accounting Break-Even Quantity (Q)
Q = (Fixed costs + Depreciation)/(Price per unit - Variable cost per unit)
= (FC + D)/(P - V)
= ($40,000 + 4,000)/($3.00 - .30)
= 16,296 buckets
If sales do not reach 16,296 buckets, the firm will incur losses in both the
accounting sense and the financial sense .
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 17
T11.11 Chapter 11 Quick Quiz -- Part 1 of 2
Assume you have the following information about Vanover
Manufacturing:
 Price = $5 per unit; variable costs = $3 per unit
 Fixed operating costs = $10,000
 Initial cost is $20,000
 5 year life; straight-line depreciation to 0, no salvage value
 Assume no taxes
 Required return = 20%
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 18
T11.11 Chapter 11 Quick Quiz -- Part 1 of 2 (concluded)
 Break-Even Computations
A. Accounting Break-Even
Q = (FC + D)/(P - V) = ($_____ + $4,000)/($5 - 3) = ______ units
IRR = ______ ; NPV ______ ( = -$______ )
B. Cash Break-Even
Q = FC/(P - V) = $10,000/($5 - 3) = ______ units
IRR = ______ ; NPV = ______
B. Financial Break-Even
Q = (FC + $6,688)/(P - V)
= ($10,000 + 6,688)/($5 - 3) = 8,344 units
IRR = ______ ; NPV = ______
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 19
T11.11 Chapter 11 Quick Quiz -- Part 1 of 2 (concluded)
 Break-Even Computations
A. Accounting Break-Even
Q = (FC + D)/(P - V) = ($10,000 + $4,000)/($5 - 3) = 7,000 units
IRR =
0
; NPV = -$8,038
B. Cash Break-Even
Q = FC/(P - V) = $10,000/($5 - 3) = 5,000 units
IRR = -100% ; NPV = -$20,000
B. Financial Break-Even
Q = (FC + $6,688)/(P - V)
= ($10,000 + 6,688)/($5 - 3) = 8,344 units
IRR = 20% ; NPV = 0
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 20
T11.12 Summary of Break-Even Measures (Table 11.1)
I.
The General Expression
Q = (FC + OCF)/(P - V)
where:
FC = total fixed costs
P = Price per unit
v = variable cost per unit
II. The Accounting Break-Even Point
Q = (FC + D)/(P - V)
At the Accounting BEP, net income = 0, NPV is negative, and IRR of 0.
III. The Cash Break-Even Point
Q = FC/(P - V)
At the Cash BEP, operating cash flow = 0, NPV is negative, and IRR = -100%.
IV. The Financial Break-Even Point
Q = (FC + OCF*)/(P - V)
At the Financial BEP, NPV = 0 and IRR = required return.
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 21
Operating Leverage
 Operating leverage is ‘ the degree to which a firm or project
relies on fixed costs’ - what is the relationship between fixed
and variable costs for the firm or project.




Low operating leverage means low fixed costs as a proportion of
total costs
High operating leverage reflects high fixed costs - often high
investmetn in plant and equipment OR in the ‘new economy high
investment in research and development to develop software for
example.
Once a break-even point is reached, firms or projects with high
operating leverage generate higher cash flow/earnings or NPV for
each additonal unit sold vs firms with low operating leverage conversely lower sales volume can magnify cash flow/earnings or
NPV in the other direction!
The higher the degree of operating leverage the greater the impact
from forecasting risk
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Slide 22
Operating Leverage continued
 The degree of operating leverage (DOL) is’the percentage
change in operating cash flow relative to the percentage
change in quantity sold’


% change in OCF = DOL * % change in Q
DOL = 1+ FC/OCF
 The issue of sub-contracting out certain functions is often a
question of operating leverage - sub-contracting has the effect
of reducing the DOL as more costs become variable and fixed
costs are reduced
 Firms operating in the ‘new economy’ e.g. High tech firms can
have a high DOL as much of the their investment in research
and development is a fixed cost that does not vary with sales
volumes - thus the higher degree of leverage to sales volumes

in today’s economic downturn, we are seeing dramatic reductions
in reported earnings from prior periods - DOL at work!!
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Slide 23
T11.13 Fairways Driving Range DOL
 Since % in OCF = DOL  %  in Q, DOL is a “multiplier” which
measures the effect of a change in quantity sold on OCF.
 For Fairways, let Q = 20,000 buckets. Ignoring taxes,
OCF = $14,000 and fixed costs = $40,000, and
Fairway’s DOL = 1 + FC/OCF = 1 + $40,000/$14,000 = 3.857.
In other words, a 10% increase (decrease) in quantity sold will result in
a 38.57% increase (decrease) in OCF.
 Two points should be kept in mind:
Higher DOL suggests greater volatility (i.e., risk) in OCF;
Leverage is a two-edged sword - sales decreases will be magnified as
much as increases.
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 24
T11.14 Managerial Options and Capital Budgeting
 Managerial options and capital budgeting

What is ignored in a static DCF analysis?
Management’s ability to modify the project as events occur.


Contingency planning
1.
The option to expand
2.
The option to abandon
3.
The option to wait
Strategic options
1.
“Toehold” investments
2.
Research and development
Generally, the exclusion of managerial options from the analysis
causes us to underestimate the “true” NPV of a project.
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 25
T11.15 Capital Rationing
 Capital rationing

Definition: The situation in which the firm has more good
projects than money.

Soft rationing - limits on capital investment funds set within
the firm.
How could this occur in a firm run by rational managers?

Hard rationing - limits on capital investment funds set
outside of the firm (i.e., in the capital markets).
How could this occur in capital markets populated by rational
investors?
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 26
T11.16 Chapter 11 Quick Quiz -- Part 2 of 2
1. What is forecasting risk?
It is the possibility that errors in projected cash flows will lead to
incorrect decisions.
2. What is scenario analysis? Why might this exercise be useful for
decision-makers to perform, even if their estimates ultimately turn out
to be incorrect?
It uses estimates of “Best- and Worst-case” outcomes to see what
happens to NPV estimates if things turn out differently than expected. It
forces decision-makers to think about the possibility of alternative
outcomes.
3. Is it conceivable that the opposite of capital rationing could exist?
Yes - since capital rationing means more good projects than money, the
opposite simply means more money than good projects.
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 27
T11.17 Solution to Problem 11.1
 BetaBlockers, Inc. (BBI) manufactures biotech sunglasses. The
variable materials cost is $0.68 per unit and the variable labor
cost is $2.08 per unit.
 What is the variable cost per unit?
VC = variable material cost + variable labor cost
= $0.68 + $2.08 = $2.76
 Suppose BBI incurs fixed costs of $520,000 during a year when
production is 250,000 units. What are total costs for the year?
TC = total variable costs + fixed costs
= ($2.76)( ______ ) + $ ______ = $ ______
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 28
T11.17 Solution to Problem 11.1
 BetaBlockers, Inc. (BBI) manufactures biotech sunglasses. The
variable materials cost is $0.68 per unit and the variable labor
cost is $2.08 per unit.
 What is the variable cost per unit?
VC = variable material cost + variable labor cost
= $0.68 + $2.08 = $2.76
 Suppose BBI incurs fixed costs of $520,000 during a year when
production is 250,000 units. What are total costs for the year?
TC = total variable costs + fixed costs
= ($2.76)(250,000) + $520,000 = $1,210,000
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 29
T11.17 Solution to Problem 11.1 (concluded)
 If the selling price is $6.00 per unit, does BBI break even on a
cash basis? If depreciation is $150,000 per year, what is the
accounting break-even point?
Qcash = $520,000/($ ______ – $ ______ )
= ______ units
Qacct = ($ ______ + $ ______)/($6.00 – $2.76)
= ______ units
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Slide 30
T11.17 Solution to Problem 11.1 (concluded)
 If the selling price is $6.00 per unit, does BBI break even on a
cash basis? If depreciation is $150,000 per year, what is the
accounting break-even point?
Qcash = $520,000/($ 6.00 – $ 2.76 )
= 160,494 units
Qacct = ($520,000 + $150,000)/($6.00 - $2.76)
= 206,790 units
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 31
T11.18 Solution to Problem 11.7
 In each of the following cases, calculate the accounting break-
even and the cash break-even points. Ignore any tax effects in
calculating the cash break-even.
Unit price
Unit VC
Fixed costs
Depreciation
$1,900
$1,750
$16 million
$7 million
30
26
60,000
150,000
7
2
300
365
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 32
T11.18 Solution to Problem 11.7 (concluded)
Solutions
(1) Qacct = ($16M + $___ )/($1,900 - $1,750) = ______ units
Qcash = $16M/($_____ - $ _____ ) = 106,667 units
(2) Qacct = ($60K + $150K)/($__ - $26) = 52,500 units
Qcash = $______ /($30 - $26) = ______ units
(3) Qacct = ($300 + $365)/($7 - $2) = ___ units
Qcash = $300/($7 - $2) = 60 units
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 33
T11.18 Solution to Problem 11.7 (concluded)
Solutions
(1) Qacct = ($16M + $ 7m )/($1,900 - $1,750) = 153,334 units
Qcash = $16M/($1,900 - $ 1,750) = 106,667 units
(2) Qacct = ($60K + $150K)/($30 - $26) = 52,500 units
Qcash = $60,000/($30 - $26) = 15,000 units
(3) Qacct = ($300 + $365)/($7 - $2) = 133 units
Qcash = $300/($7 - $2) = 60 units
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 34
T11.19 Solution to Problem 11.13
 A proposed project has fixed costs of $20,000 per year. OCF at
7,000 units is $55,000. Ignoring taxes, what is the degree of
operating leverage (DOL)?
 If units sold rises from 7,000 to 7,300, what will be the increase
in OCF? What is the new DOL?
DOL = 1 + ($20,000/$55,000) = 1.3637
%  Q = (7,300 - 7,000)/7,000 = 4.29%
and
%  OCF = DOL(%  Q) = ______ (4.29) = ____ %
New OCF = ($55,000)(_______ ) = $_______
DOL at 7,300 units = 1 + ($20,000/$ _______ ) = _______
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 35
T11.19 Solution to Problem 11.13
 A proposed project has fixed costs of $20,000 per year. OCF at
7,000 units is $55,000. Ignoring taxes, what is the degree of
operating leverage (DOL)?
 If units sold rises from 7,000 to 7,300, what will be the increase
in OCF? What is the new DOL?
DOL = 1 + ($20,000/$55,000) = 1.3637
%  Q = (7,300 - 7,000)/7,000 = 4.29%
and
%  OCF = DOL(%  Q) = 1.3637 (4.29) = 5.85%
New OCF = ($55,000)(1.0585) = $58,218
DOL at 7,300 units = 1 + ($20,000/$58,218) = 1.3435
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 36