1. Appreciate the practical problems of capital budgeting in large corporations.
2. Use sensitivity, scenario, and break-even analyses to see how project profitability would be affected by an error in your forecasts.
3. Understand why an overestimate of sales is more serious for projects with high operating leverage.
4. Recognize the importance of managerial flexibility in capital budgeting.
Chapters 8 and 9 develop a framework for project analysis.
This chapter analyzes the robustness of a project’s value by asking some “What If” Questions.
· Scenario Analysis
· Break Even Analysis
· Real Options and the Value of Flexibility
Capital Budget – The list of planned investment projects.
Capital Budgeting: The Decision Process
1. Stage 1: The Capital Budget
2. Stage 2: Project Authorization
· Outlays required by law or company policy
· Maintenance or cost reduction
· Capacity expansion in existing business
· Investment for new products
Potential Capital Budgeting Problems
· Ensuring forecasts are consistent
· Eliminating conflicts of interest
· Reducing forecast bias
· Proper selection criteria (NPV and others)
What-if Testing
·
Sensitivity Analysis - Analysis of the effects on project profitability of changes in sales, costs, etc.
·
Scenario Analysis - Project analysis given a particular combination of assumptions.
·
Simulation Analysis - Estimation of the probabilities of different possible outcomes.
·
Break-Even Analysis - Analysis of the level of sales at which the company breaks even.
Sensitivity Analysis:
Analysis of the effects on project profitability of changes in sales, costs,
etc.
Why is sensitivity analysis useful?
Sensitivity Analysis – Example
Base Case: Expected cash flows from a new project (with 8% Opportunity Cost of Capital; 40% average tax rate; variable costs are a constant 80% of sales; all numbers in $000s)
NPV = $1,382.47
IRR = 12.7%
Payback Period = 6 years
Profitability Index = .256
Sensitivity Analysis – Example
Possible Range of Variable
Sensitivity Analysis: Changing Sales
(with 8% Opportunity Cost of Capital; 40% average tax rate; variable costs are a constant 80% of sales; all numbers in $000s)
Pessimistic Case—Sales = $14,000 Optimistic Case—Sales = $18,000
NPV = -$426 NPV = $3,191
Note: It is recommended for practice that students calculate the other valuation techniques learned in Chapter 8 (IRR, etc)
Sensitivity Analysis: Changing Fixed Costs
(with 8% Opportunity Cost of Capital; 40% average tax rate; variable costs are a constant 80% of sales; all numbers in $000s)
Pessimistic Case—Fixed Costs = $2,500 Optimistic Case—Fixed Costs = $1,500
NPV = -$878 NPV = $3,643
Note: It is recommended for practice that students calculate the other valuation techniques learned in Chapter 8 (IRR, etc)
Limits to Sensitivity Analysis
· Ambiguous
· How do you consistently define “optimistic” or “pessimistic”?
· Interrelatedness of variables
Scenario Analysis
·
Scenario Analysis - Project analysis given a particular combination of assumptions.
·
Simulation Analysis –Estimation of the probabilities of different possible outcomes, e.g., from an investment project.
Scenario Analysis: Introducing Competition
Assume that it will take two years for competition to enter the market. At this time, sales drop 10% and variable costs increase to 82% (increased labor demand). What happens to NPV under this scenario?
Base Case – No Competition Scenario – Introduce Competition
NPV = $1,382 NPV = -$717
Break-even Analysis
– Analysis of the level of sales at which the project breaks even.
Why is this useful?
Break-Even Analysis: Example
(with 8% Opportunity Cost of Capital; 40% average tax rate; variable costs are a constant 80% of sales; all numbers in $000s)
· Determine the number of units that must be sold in order to break even, on an NPV basis.
· Suppose each unit has a price point of $45,000
· All other variables are at their base case levels
Break-Even Point: Accounting
Break-Even Point (Accounting) - The break-even point is the number of units sold where net profits = $0.
What does the accounting break-even point not account for?
Break-Even Point: Finance
NPV Break-Even Point (Finance):
How can we find the present value of future cash flows? As long as cash flows are equal each year, we can use the Annuity Factor.
NPV break-even point – Level of sales at which project net present value becomes positive.
Break-Even Analysis
Recall: the break-even point is the number of units sold where NPV = $0.
· Note: Think back to discussion of economic value added (EVA) in Chapter 4.
· A project that breaks even on a present value basis will have a positive accounting profit but zero economic value added.
· In other words, it will just cover all its costs, including the cost of capital.
Note: The NPV break-even level of sales will be greater than the accounting break-even level of sales. Why?
Operating Leverage – Degree to which costs are fixed.
Degree of Operating Leverage (DOL) – Percentage change in profits given a 1% change in
sales.
Operating Leverage: Why is it useful?
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Degree of Operating Leverage: Example
Real Options
1. Option to expand
2. Option to abandon
3. Timing option
4. Flexible production facilities
Real Options – Options to invest in, modify, or dispose of a capital investment project
Real Options & the Value of Flexibility
Decision Trees – Diagram of sequential decisions and possible outcomes.
· Decision trees help companies determine their options by showing various choices and outcomes.
· The option to avoid a loss or produce extra profit has value.
· The ability to create an option has value that can be bought or sold.
Decision Trees: Example
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Page 1 of 8
OptimisticCaseYear 0Years 1-12
Investment-5,400
Sales18,000
Variable Costs
Fixed Costs(2,000)
Depreciation(450)
Pretax profit
Taxes
Profit after tax
Operating cash flow
Net Cash Flow-5,400
PessimisticCaseYear 0Years 1-12
Investment-5,400
Sales14,000
Variable Costs
Fixed Costs(2,000)
Depreciation(450)
Pretax profit
Taxes
Profit after tax
Operating cash flow
Net Cash Flow-5,400
OptimisticCaseYear 0Years 1-12
Investment-5,400
Sales16,000
Variable Costs(12,800)
Fixed Costs
Depreciation(450)
Pretax profit
Taxes
Profit after tax
Operating cash flow
Net Cash Flow-5,400
PessimisticCaseYear 0Years 1-12
Investment-5,400
Sales16,000
Variable Costs(12,800)
Fixed Costs
Depreciation(450)
Pretax profit
Taxes
Profit after tax
Operating cash flow
Net Cash Flow-5,400
Year 0Years 1-2Years 3-12
Investment-5,400
Sales16,000
Variable Costs(12,800)
Fixed Costs(2,000)(2,000)
Depreciation(450)(450)
Pretax profit750
Taxes (300)
Profit after tax450
Operating cash flow900
Net Cash Fl
ow-5,400900
Year 0Years 1-12
Investment-5,400
Sales16,000
Variable Costs(12,800)
Fixed Costs(2,000)
Depreciation(450)
Pretax profit750
Taxes (300)
Profit after tax450
Operating cash flow900
Net Cash Flow-5,400900
Year 0Years 1-12
Investment$5,400
Sales45
Var. Cost(36)
Fixed Costs(2,000)
Depreciation(450)
Pretax Profit92,450
Taxes (40%)3.6980
Net Profit5.41,470
Net Cash Flow-5,4005.41,020
X
X
X
X
X
X
´
´
´-
´-
´-
´-
Number of Units Sold
x
=
05.41,470
1,470
X 273 Units
5.4
X
=´-
==
Note: Accounting Break-Even can be expre
ssed in terms of revenue:
fixed costs + depreciation
Break-Even level of revenues =
additional profit from each additional d
ollar of sales
Step 1: PV (Cash Flows) = AnnuityFactor
YearlyCash Flows
1-(1+r)
where Annuity Factor =
t
r
-
´
12
1(1.08)
Example: PV(Cash Flows) = [5.41,020]
.08
X
-
-+
´´-
Step 2: PV (Cash Flows) = Initial Inv
estment
12
1(1.08)
Example-- [5.41,020]5,400
.08
322units
X
X
-
-+
´´-=
=
percent change in profits (pre-tax)
percent change in sales
fixed costs
profits
1
DOL
=+
=
Optimisic SalesYear 0Years 1-12
Investment-5,400
Sales18,000
Variable Costs(14,400)
Fixed Costs(2,000)
Depreciation(450)
Pretax profit1,150
Taxes (460)
Profit after tax690
Operating cash flow1,140
Net Cash Flow
-5,4001,140
Base CaseYear 0Years 1-12
Investment-5,400
Sales16,000
Variable Costs(12,800)
Fixed Costs(2,000)
Depreciation(450)
Pretax profit750
Taxes (300)
Profit after tax450
Operating cash flow900
Net Cash Flow-5,400900
NewOld1,150750
% Change in Profits= .5333
Old750
--
==
18,00016,000
% Change in Sales= .1250
16,000
-
=
% Change in Profits.5333
DOL= 4.27
% Change in Sales.1250
==
Year 0Years 1-12
Investment-5,400
Sales16,000
Variable Costs(12,800)
Fixed Costs(2,000)
Depreciation(450)
Pretax profit750
Taxes (300)
Profit after tax450
Operating cash flow900
Net Cash Flow-5,400900
PessimisticExpectedOptimistic
Sales14,00016,00018,000
Fixed Costs2,5002,0001,500
Range
Variable
BeautifulFlower
Lecture_Note_Chapter_10-Project_Analysis.docx
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