Chapter Nine
Project Analysis and Evaluation
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-1
Chapter Organisation
9.1
9.2
9.3
9.4
9.5
9.6
9.7
Evaluating NPV Estimates
Scenario and Other ‘What If’ Analysis
Break-even Analysis
Operating Cash Flow, Sales Volume and Break-even
Operating Leverage
Additional Considerations in Capital Budgeting
Summary and Conclusions
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-2
Chapter Objectives
•
Understand and apply scenario analysis, sensitivity analysis
and simulation analysis to capital project evaluation.
•
Apply break-even analysis, distinguishing between accounting
break-even, cash break-even and financial break-even.
•
Measure the degree of operating leverage of a firm.
•
Discuss the various managerial options in capital budgeting.
•
Outline capital rationing and the difference between soft and
hard rationing.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-3
Evaluating NPV Estimates
The basic problem: How reliable is our NPV estimate?
•
Projected cash flows are based on a distribution of possible
outcomes each period: resulting in an ‘average’ cash flow.
•
Forecasting risk: the possibility of an incorrect decision due to
errors in cash flow projections (GIGO system).
•
Ask: What sources of value create the estimated NPV?
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-4
Scenario and Other ‘What If’ Analysis
•
Base case estimation
– Estimated NPV based on initial cash flow projections.
•
Scenario analysis
– Examine effect on NPV of best-case and worst-case
scenarios.
•
Sensitivity analysis
– Examine effect on NPV by changing only one input
variable.
•
Simulation analysis
– Vary several input variables simultaneously to construct a
distribution of possible NPV estimates.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-5
Fairways Driving Range Example
Fairways Driving Range expects annual rentals to be 20 000
buckets at $3 per bucket. Equipment costs $20 000 and is
depreciated using the straight-line method over five years to a
zero salvage value. Variable costs are 10 per cent of rentals
income and fixed costs are $40 000 per year. Assume no
increase in working capital and no additional capital outlays.
The required rate of return is 15 per cent and the tax rate is
30 per cent.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-6
Fairways Example—Net Profit
Revenues
Variable costs
Fixed costs
Depreciation
EBIT
Taxes (@ 30%)
Net profit
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
$60
6
40
4
10
3
$7
000
000
000
000
000
000
000
9-7
Fairways Example—Base Case NPV
•
Estimated annual cash flow:
$10 000 + $4000 – $3000 = $11 000
•
At 15%, the 5-year annuity factor is 3.3522.
•
The base case NPV is then:
NPV = – $20 000 + ($11 000 × 3.3522)
= $16 874
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-8
Fairways Example—Scenario
Analysis
Inputs for scenario analysis:
Base case: Rentals are 20 000 buckets p.a., variable costs
are 10 per cent of rental income, fixed costs are $40 000,
depreciation is $4000 p.a.
Best case: Rentals are 25 000 buckets p.a., variable costs
are 8 per cent of rental income, fixed costs are $40 000,
depreciation is $4000 p.a.
Worst case: Rentals are 18 000 buckets p.a., variable
costs are 12 per cent of rental income, fixed costs are
$40 000, depreciation is $4000 p.a.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-9
Fairways Example—Scenario Analysis
Scenario
Base case
Best case
Worst case
Rentals Revenues Profit
20 000 60 000
7 000
25 000 75 000 17 500
18 000 54 000
2 464
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
Cash Flow
NPV
11 000 $16 874
21 500 $52 072
6 464
$1 668
9-10
Fairways Example—Sensitivity
Analysis
Inputs for sensitivity analysis:
Base case: Rentals are 20 000 buckets p.a., variable costs
are 10 per cent of rental income, fixed costs are $40 000,
depreciation is $4000 p.a.
Best case: Rentals are 25 000 buckets p.a. All other variables
are unchanged.
Worst case: Rentals are 18 000 buckets p.a. All other
variables are unchanged.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-11
Fairways Example—Sensitivity
Analysis
Scenario
Base case
Best case
Worst case
Rentals
20 000
25 000
18 000
Revenues Profit Cash Flow NPV
60 000 7 000 11 000 $16 874
75 000 16 450 20 450 $48 552
54 000
3 220
7 220 $4 202
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-12
Fairways Example—Sensitivity
Analysis
NPV
Best case
$60 000
NPV = $48 552
x
Base case
NPV = $16 874
x
Worst case
0
NPV = $4 202
x
–$60 000
15 000
20 000
25 000
Rentals per Year
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-13
Break-even Analysis
•
Useful for analysing the relationship between sales volume
and profitability.
•
Break-even point is the sales volume at which the present
value of the project’s cash inflows and outflows are equal 
NPV = 0.
•
Important distinction between variable costs and fixed costs.
•
Accounting break-even is the sales volume that results in a
zero net profit.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-14
Fixed and Variable Costs
•
There are two types of costs that are important in break-even
analysis: variable and fixed.
-Variable costs change when the quantity of output changes
-Total variable costs= quantity × cost per unit
-Fixed costs are constant, regardless of output, over some
time period
-Total Costs = fixed + variable = FC + vQ
Example:
Your firm pays $3000 per month in fixed costs. You also pay $15
per unit to produce your product.
(Total cost if you produce 1000 units = 3000 + 15(1000) = 18 000)
(Total cost if you produce 5000 units = 3000 + 15(5000) = 78 000)
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-15
Average versus Marginal Cost
• Average Cost
- TC/number of units
- Will decrease as number of units increases
• Marginal Cost
- The cost to produce one more unit
- Same as variable cost per unit
•
Example: What is the average cost and marginal cost under
each situation in the previous example?
- Produce 1000 units: Average = 18 000/1000 = $18
- Produce 5000 units: Average = 78 000/5000 = $15.60
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-16
Fairways Example—Accounting
Break-even Analysis
Total cost  variable cost  fixed cost
Total accounting costs  variable cost  fixed cost  dep' n
Rentals Revenue
0
15 000
20 000
25 000
0
45 000
60 000
75 000
Variable
Costs
0
4 500
6 000
7 500
Fixed
Costs
40
40
40
40
000
000
000
000
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
Total
Costs
40
44
46
47
000
500
000
500
Dep’n
4
4
4
4
000
000
000
000
Total
Acct
Costs
44 000
48 500
50 000
51 500
9-17
Fairways Example—Accounting
Break-even Analysis
Total revenues
$80 000
Accounting
break-even point
16 296 buckets
Total accounting
costs
$50 000
Fixed costs
+ Dep’n =
$44 000
Net
Net
Income < 0
Income > 0
$20 000
15 000
20 000
25 000
Rentals per Year
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-18
Fairways Example—Accounting
Break-even Analysis
Solve algebraically for break-even quantity (Q):

Fixed costs FC  Depreciati on D 
Q
Price per unit P   Variable cost per unit v 

$40 000  $4000

$3.00  $0.30
 16 296 buckets
If sales do not reach 16 296 buckets, Fairways will
incur losses in both the accounting sense and the
financial sense.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-19
Accounting of Break-even Point
General expression
Q = (FC + D)/(P – v)
where:
Q
FC
D
P
v
= total units sold
= total fixed costs
= depreciation
= price per unit
= variable cost per unit
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-20
Using Accounting Break-even
• Accounting break-even is often used as an early-
stage screening number.
• If a project cannot break even on an accounting
basis, then it is not going to be a worthwhile
project.
• Accounting break-even gives managers an
indication of how a project will impact accounting
profit.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-21
Summary of Break-even Measures
•
•
•
Accounting break-even
– Q = (FC + D)/(P – v)
– At accounting break-even, net income = 0, NPV is
negative and IRR =0.
Cash break-even
– Q = FC/(p – v)
– At cash break-even, OCF = 0, NPV is negative and IRR =
–100%.
Financial break-even
– Q = (FC + OCF)/(P – v)
– At financial break-even, NPV = 0 and IRR = required
return.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-22
Fairways Example—Break-even
Measures
Accounting

$40 000  $4000 
break - even 
 16 296 units
$3.00  $0.30
IRR  0
NPV   $6 591
$40 000
 14 815 units
$3.00  $0.30
IRR   100% NPV   $20 000
Cash break - even 
Financial break - even 
$40 000  $5966  17 024 units
$3.00  $0.30
IRR  15%
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
NPV  0
9-23
Operating Leverage
•
•
•
The degree to which a firm is committed to its fixed costs.
The higher the degree of operating leverage, the greater the
danger from forecasting risk.
The lower the degree of operating leverage, the lower the
break-even point.
%  in OCF  DOL  %  in Q
FC
DOL  1 
OCF
•
DOL depends on the current sales level.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-24
Fairways Example—DOL
•
Let Q = 20 000 buckets and, ignoring taxes, OCF = $14 000
and FC = $40 000.
$40 000
DOL  1 
 3.857
$14 000
•
•
A 10 per cent increase (decrease) in quantity sold will result
in a 38.57 per cent increase (decrease) in OCF.
Note: Higher DOL equals greater volatility (risk) in OCF and
leverage is a two-edged sword—sales decreases will be
magnified as much as increases.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-25
Managerial Options and Capital
Budgeting
• A static DCF analysis ignores management’s ability
to modify the project as events occur.
• Contingency planning
–
–
–
The option to expand.
The option to abandon.
The option to wait.
• Strategic options
–
–
‘Toe hold’ investments.
Research and development.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-26
Capital Rationing
• A condition which prevents management from
undertaking all acceptable projects because of a
shortage of funds.
• Soft rationing occurs when management limits the
amount that can be invested in new projects during
some specified time period.
• Hard rationing occurs when the firm is unable to
raise the financing for a project.
Copyright  2004 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 3e
Ross, Thompson, Christensen, Westerfield and Jordan
Slides prepared by Sue Wright
9-27