1. Chapter 11 Project Analysis and Evaluation
T 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
CLICK MOUSE OR HIT SPACEBAR TO ADVANCE
copyright © 2002 McGraw-Hill Ryerson, Ltd.

2. 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

3. Scenario and Other “What-If” Analyses “Base case” estimation
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

4. 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 $60,000
Variable costs ,000
Fixed costs 40,000
Depreciation ,000
EBIT $10,000
Taxes
Net income $ 8,500

5. T11.4 Fairways Driving Range Example (concluded)
Estimated annual cash inflows:
$10, , ,500 = $12,500
At 15%, the 5-year annuity factor is Thus, the base-case NPV is:
NPV = $-20,000 + ($12,500 3.352) = $21,900.

6. 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 % of revenues, fixed costs are $40,000, depreciation is $4,000 per year, and the tax rate is 15%.

7. T11.5 Fairways Driving Range Scenario Analysis (concluded)
Net Project
Scenario Rentals Revenues Income Cash Flow NPV
Best Case 25, $75, $21, $25, $64,635
Base Case 20, , , ,500 21,900
Worst Case 18, , , , ,437

8. 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.

9. T11.6 Fairways Driving Range Sensitivity Analysis (concluded)
Net Project
Scenario Rentals Revenues income cash flow NPV
Best case 25, $75, $19, $23, $60,364
Base case 20, , , ,500 21,900
Worst case 18, , , , ,514

10. T11.7 Fairways Driving Range: Rentals vs. NPV
Fairways Sensitivity Analysis - Rentals vs. NPV
NPV
Best case
NPV = $60,035
$60,000 x
Base case
NPV = $21,900 x
Worst case
NPV = $3,437 x
-$60,000
15,000
20,000
25,000
Rentals per Year

11. 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

12. 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)

13. 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)

14. The point where the sales level results in a zero NPV
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

15. T11.8 Fairways Driving Range: Total Cost Calculations
Total Cost = Variable cost + Fixed cost
Variable Fixed Total Total
Rentals Revenue cost cost cost Depr. acct. cost
$ $ $40, $40,000 $4,000 $44,000
15, , , , , , ,500
20, , , , , , ,000
25, , , , , , ,500

16. 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
Income < 0
Net
Income > 0
$20,000
15,000
20,000
25,000
Rentals per Year

17. 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)
= ($40, ,000)/($ )
= 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 .

18. 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%

19. 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, ,688)/($5 - 3) = 8,344 units

20. 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 = ; 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, ,688)/($5 - 3) = 8,344 units
IRR = 20% ; NPV = 0

21. 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.

22. 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

23. 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!!

24. 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 =
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.

25. T11.14 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.

26. T 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?

27. 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.

28. What is the variable cost per unit?
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
= $ $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)( ______ ) + $ ______ = $ ______

29. What is the variable cost per unit?
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
= $ $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

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 = $520,000/($ ______ – $ ______ )
= ______ units
Qacct = ($ ______ + $ ______)/($6.00 – $2.76)

31. 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 + $150,000)/($ $2.76)
= 206,790 units

32. 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
, ,000

33. 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

34. 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

35. %  OCF = DOL(%  Q) = ______ (4.29) = ____ %
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) =
%  Q = (7, ,000)/7,000 = 4.29%
and
%  OCF = DOL(%  Q) = ______ (4.29) = ____ %
New OCF = ($55,000)(_______ ) = $_______
DOL at 7,300 units = 1 + ($20,000/$ _______ ) = _______

36. 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) =
%  Q = (7, ,000)/7,000 = 4.29%
and
%  OCF = DOL(%  Q) = (4.29) = 5.85%
New OCF = ($55,000)(1.0585) = $58,218
DOL at 7,300 units = 1 + ($20,000/$58,218) =