1. Chapter 11 PROJECT ANALYSIS AND EVALUATION
11.1. Evaluating NPV Estimates Scenario and Other What-If Analyses Break-Even Analysis Operating Cash Flow, Sales Volume, and Break-Even Operating Leverage Capital Rationing

2. 11.1. Evaluating NPV Estimates
Suppose we are working on a preliminary discounted cash flow analysis. We identified the relevant cash flows and finally we estimated that the NPV is positive. Are we sure everything is fine? The key inputs into a DCF analysis are projected future cash flows. If the projections are seriously in error the resulting answer can still be grossly misleading.

3. 11.1. Evaluating NPV Estimates
The possibility that errors in projected cash flows will lead to incorrect decisions is called forecasting risk (or estimation risk). One of our goals is to develop some tools that are useful in identifying areas where potential errors exist and where they might be especially damaging.

4. 11.1. Evaluating NPV Estimates
The first line of defense against forecasting risk is simply to ask, “What is it about this investment that leads to a positive NPV?” We should be able to point to something specific as the source of value. For example, if the proposal under consideration involved a new product, then we might ask questions such as the following:

5. 11.1. Evaluating NPV Estimates
Are we certain that our new product is significantly better than that of the competition? Can we truly manufacture at lower cost, or distribute more effectively, or identify undeveloped market niches, or gain control of a market? These are just a few of the potential sources of value. There are many others.

6. 11.2. Scenario and Other What-If Analyses
What happens to the NPV under different cash flows scenarios?
At the very least look at:
Best case – high revenues, low costs
Worst case – low revenues, high costs
Measure of the range of possible outcomes
Best case and worst case are not necessarily probable, but they can still be possible

7. 11.2. Scenario and Other What-If Analyses
New Project Example The initial cost is $200,000 and the project has a 5-year life. There is no salvage. Depreciation is straight-line, the required return is 12% and the tax rate is 34%. Depreciation per year is $40,000 ($200,000/5).

8. 11.2. Scenario and Other What-If Analyses
Base
Lower
Upper
Unit Sales
6000
5500
6500
Price per unit 80 75 85
Variable cost per unit 60 58 62
FC Fixed costs per year
50000
45000
55000

9. 11.2. Scenario and Other What-If Analyses
Base Case Analysis
Sales $ VC FC
50 000
Depreciation
40 000
EBIT
30 000
Taxes (34%)
10 200 NI
19 800
With this information we can calculate the base-case NPV by first calculating net income

10. 11.2. Scenario and Other What-If Analyses
OCF = EBIT + D – Taxes = = $30, ,000 – 10,200 = $59,800 per year. The project has a 5-year life and a 12 percent required return, so the base-case NPV is: NPV= x{1 -[1/(1+0,12)5]/0,12 = = $ NPV is positive and the project looks good.

11. 11.2. Scenario and Other What-If Analyses
Cash Flows
Year
OCF
NCS
CFFA 1
59800 2 3 4 5
NPV
$15.565,62
Base-case NPV = $15.565,62

12. 11.2. Scenario and Other What-If Analyses
The determination of what happens to NPV estimates when we ask what-if Questions is scenario analysis. To get the worst case, we assign the least favorable value to each item. This means low values for items like units sold and price per unit and high values for costs. We do the reverse for the best case.

13. 11.2. Scenario and Other What-If Analyses
Worst Case
Best Case
Unit Sales
5500
6500
Price per unit 75 85
Variable cost per unit 62 58
FC Fixed costs per year
55000
45000

14. 11.2. Scenario and Other What-If Analyses
Worst Case
Sales
412500 VC
341000 FC
55000
Depreciation
40000
EBIT
-23500
Taxes
-7990 NI
-15510

15. 11.2. Scenario and Other What-If Analyses
Year
OCF
NCS
CFFA 1
24490 2 3 4 5
NPV
-$ ,03
Worst-case NPV = -$ ,03

16. 11.2. Scenario and Other What-If Analyses
Best Case
Sales
552500 VC
377000 FC
45000
Depreciation
40000
EBIT
90500
Taxes
30770 NI
59730

17. 11.2. Scenario and Other What-If Analyses
Year
OCF
NCS
CFFA 1
99730 2 3 4 5
NPV
$ ,33
Best-case NPV = $ ,33

18. 11.2. Scenario and Other What-If Analyses
Summary of Scenario Analysis

19. 11.2. Scenario and Other What-If Analyses
Sensitivity Analysis For Unit Sales What happens to NPV when we vary one variable at a time. This is a subset of scenario analysis where we are looking at the effect of specific variables on NPV. The greater the volatility in NPV in relation to a specific variable, the larger the forecasting risk associated with that variable and the more attention we want to pay to its estimation.

20. 11.2. Scenario and Other What-If Analyses
Sensitivity analysis is an investigation of what happens to NPV when only one variable is changed. To illustrate how sensitivity analysis works, we go back to our base case for every item except unit sales. We can then calculate cash flow and NPV using the largest and smallest unit sales figures.

21. 11.2. Scenario and Other What-If Analyses
Sensitivity Analysis For Unit Sales
Base
Lower
Upper
Unit Sales
6000
5500
6500
Sales
480000
440000
520000 VC
360000
330000
390000 FC
50000
Depreciation
40000
EBIT
30000
20000
Taxes
10200
6800
13600 NI
19800
13200
26400

22. 11.2. Scenario and Other What-If Analyses
Cash Flows
Year
Base
Lower
Upper 1
59800
53200
66400 2 3 4 5
NPV
$15.565,62
-$8.225,91
$39.357,14

23. 11.2. Scenario and Other What-If Analyses

24. 11.2. Scenario and Other What-If Analyses
Summary of Sensitivity Analysis for New Project
Scenario
Unit Sales
Cash Flow
NPV
IRR
Base case
6000
59,800
15,567
15.1%
Worst case
5500
53,200
-8,226
10.3%
Best case
6500
66,400
39,357
19.7%

25. 11.2. Scenario and Other What-If Analyses
Simulation Analysis Simulation is really just an expanded sensitivity and scenario analysis. Monte Carlo simulation can estimate thousands of possible outcomes based on conditional probability distributions and constraints for each of the variables. The output is a probability distribution for NPV with an estimate of the probability of obtaining a positive net present value. The simulation only works as well as the information that is entered and very bad decisions can be made if care is not taken to analyze the interaction between variables.

26. 11.2. Scenario and Other What-If Analyses
Making A Decision Beware “Paralysis of Analysis” At some point you have to make a decision. If the majority of your scenarios have positive NPVs, then you can feel reasonably comfortable about accepting the project. If you have a crucial variable that leads to a negative NPV with a small change in the estimates, then you may want to forego the project.

27. 11.3. Break-Even Analysis
Common tool for analyzing the relationship between sales volume and profitability. There are three common break-even measures: Accounting break-even – sales volume at which net income = 0 Cash break-even – sales volume at which operating cash flow = 0 Financial break-even – sales volume at which net present value = 0

28. Total variable costs = quantity × cost per unit
11.3. Break-Even Analysis
There are two types of costs that are important in breakeven analysis: variable and fixed:
Total variable costs = quantity × cost per unit
Fixed costs are constant, regardless of output, over some time period
Total costs = fixed + variable = FC + v×Q

29. 11.3. Break-Even Analysis
Total variable costs (VC) = = quantity (Q) × cost per unit (v) Example: You produce 1000 units and you also pay $2 per unit to produce your product. VC = Q × v = 1000 × 2 = 2000 If you produce 5000 units variable costs: VC = Q × v = 5000 × 2 = 10000

30. 11.3. Break-Even Analysis

31. Example: TC = 8000 + 3×1000= 11000 TC = 8000 + 3×5000= 23000
11.3. Break-Even Analysis
Total costs(TC)=fixed costs(FC)+variable costs(VC)=
TC = FC + v×Q
Example:
Your firm pays $8000 per month in fixed costs. You also pay $3 per unit to produce your product.
What is your total cost if you produce 1000 units?
What if you produce 5000 units?
What if you produce units?
TC = ×1000= 11000
TC = ×5000= 23000
TC = ×10000= 38000

32. 11.3. Break-Even Analysis

33. Average Cost = TC / # of units Marginal Cost
11.3. Break-Even Analysis
Average Cost = TC / # of units
Will decrease as # 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=11000/1000 = $11
Produce 5000 units: Average=23000/5000=$4.60
The marginal cost of producing one more unit is $3.

34. 11.3. Break-Even Analysis
Accounting Break-Even What sales level gives $0 net income (assuming things are the same each year)? This happens when sales equal total costs. P = $5 price per unit v = $3 variable cost per unit Q = 450 # of units or quantity FC = $600 fixed costs D = $300 depreciation, T = 34 % tax rate

35. Accounting Break-Even (Q = 450 units) Sales 2250 VC 1350 FC 600
11.3. Break-Even Analysis
Accounting Break-Even (Q = 450 units)
Sales
2250 VC
1350 FC
600
Depreciation
300
EBIT
Taxes NI

36. 11.3. Break-Even Analysis
Net income = sales – costs – taxes NI = [Q×P – FC – Q×v – D](1 – T) = 0 Divide both sides by ( 1 - T) to get Q×P – FC – Q×v – D = 0 Q×P – Q×v = FC + D Q×(P – v) = FC + D Q = (FC + D) / (P – v) The difference between the selling price and the variable cost (P – v) is often called the contribution margin per unit.

37. 11.3. Break-Even Analysis

38. 11.3. Break-Even Analysis
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.

39. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
We are more interested in cash flow than we are in accounting numbers. As long as a firm has non-cash deductions, there will be a positive cash flow. If a firm just breaks-even on an accounting basis, operating cash flow = depreciation If a firm just breaks-even on an accounting basis, NPV < 0

40. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
To illustrate, suppose the Wettway Sailboat Corporation is considering whether or not to launch its new Margo-class sailboat. The selling price will be $40,000 per boat. The variable costs will be about half that, or $20,000 per boat and fixed costs will be $500,000 per year.

41. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
The Base Case. The total investment needed to undertake the project is $3,500,000. This amount will be depreciated straight-line to zero over the five-year life of the equipment. The salvage value is zero and there are no working capital consequences. Wettway has a 20 percent required return on new projects.

42. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
Wettway projects total sales for the five years at 425 boats or about 85 boats per year. Ignoring taxes should this project be launched? OCF = Sales – Costs – Taxes (Top-Down Approach) OCF = Q×P – Q×v – FC – Taxes OCF = 85×40,000 – 85×20,000 – 500,000 – 0 = =1,200,000 NPV= -3,500, ,200,000×{1-1/(1+0.2)5]}0.2= = -3,500,000 +1,200,000× = 88,720

43. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
Calculate the quantity (Q) necessary for accounting break-even.
Fixed costs = 500,000
Depreciation = 700,000 = 3,500,000/5
Price per unit = 40,000
Variable cost per unit = 20,000
Q = (FC + D) / (P – v)
Q=(500, ,000) / (40,000–20,000)= 60

44. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
If 60 boats are sold, net income will be exactly 0. OCF= NI + Depreciation (Bottom-Up Approach) OCF = NPV= ×{1-1/(1+0.2)5]}/0.2= = = NPV = 0, if IRR = 0. NPV = = 0

45. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
Sales Volume and Operating Cash Flow Cash break-even Again, ignore taxes for simplification: OCF = net income + depreciation OCF = [(P – v) × Q – FC – D] + D = = (P – v) × Q – FC For the Wettway sailboat project OCF = (P – v) × Q – FC = OCF = (40,000-20,000) × Q – 500,000

46. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
Rearrange the OCF equation and solve for Q OCF = (P – v) × Q – FC Q = (FC + OCF) / (P – v) To find the cash break-even point (where OCF =0): Q = FC / (P – v) = 500,000 / (40, ,000) = Q = 500,000 / 20,000 = 25

47. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
Financial Break-Even. To find the financial break-even we have to calculate the sales level that results in a zero NPV. For the Wettway sailboat project: NPV = 0= -3,500, OCF x {1-1/(1+0.2)5]}/0.2 OCF = 1,170

48. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
Q = (FC + OCF) / (P – v) Q = ( ) / ( – ) = = 83,5 So, Wettway need to sell about 84 boats per year to have NPV = 0 The financial break-even for the Wettway sailboat project is 84 boats

49. 11.4. Operating Cash Flow, Sales Volume, and Break-Even

50. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
Summary of Break-Even Measures
I. The General Break-Even Expression
Ignoring taxes, the relation between operating cash flow (OCF) and quantity of output or sales volume (Q) is:
FC + OCF
Q =
P – v
where FC = Total fixed costs; P = Price per unit;
v = Variable cost per unit;
As shown next, this relation can be used to determine the accounting, cash, and financial break-even points.

51. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
II. The Accounting Break-Even Point Accounting break-even occurs when net income is zero. Operating cash flow is equal to depreciation when net income is zero, so the accounting break-even point is: FC + D Q = P – v A project that always just breaks even on an accounting basis has a payback exactly equal to its life, a negative NPV, and an IRR of zero.

52. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
III. The Cash Break-Even Point Cash break-even occurs when operating cash flow is zero. The cash break-even point is thus: FC Q = P – v A project that always just breaks even on a cash basis never pays back, has an NPV that is negative and equal to the initial outlay, and has an IRR of minus 100 percent.

53. 11.4. Operating Cash Flow, Sales Volume, and Break-Even
IV. The Financial Break-Even Point Financial break-even occurs when the NPV of the project is zero. The financial break-even point is thus: FC + OCF* Q = P – v where OCF* is the level of OCF that results in a zero NPV. A project that breaks even on a financial basis has a discounted payback equal to its life, a zero NPV, and an IRR just equal to the required return.

54. 11.5. Operating Leverage
Operating leverage is the degree to which a project or firm uses fixed costs in production. Plant and equipment and non-cancelable rentals are typical fixed cost items. Since fixed costs do not change with sales, they make good situations better and bad situations worse, i.e., they “lever” results.

55. 11.5. Operating Leverage
For example Wettway Corporation can purchase the necessary equipment and build all of the components for its sailboats in-house. Alternatively some of the work could be farmed out to other firms. The first option involves a greater investment in plant and equipment, greater fixed costs and depreciation, and, as a result, a higher degree of operating leverage.

56. 11.5. Operating Leverage
In general, the lower the fixed costs and the degree of operating leverage, the lower is the break-even point. If a project can be started with low fixed costs and later switched to high fixed costs if it turns out well, this is a valuable option.

57. 11.5. Operating Leverage
Measuring Operating Leverage One way of measuring operating leverage is to ask, if quantity sold rises by 5 percent, what will be the percentage change in operating cash flow? Degree of Operating Leverage (DOL) is the percentage change in OCF relative to a percentage change in quantity.

58. 11.5. Operating Leverage
To see this, note that if Q goes up by one unit, OCF will go up by (P - v). In this case, the percentage change in Q is 1/Q, and the percentage change in OCF is (P – v)/ OCF. Given this we have: Percentage change in OCF = = DOL×(percentage change in Q) (P – v) / OCF = DOL × 1/Q DOL = (P – v) × Q / OCF

59. 11.5. Operating Leverage
Based on our definitions of OCF OCF = (P – v) × Q – FC or OCF + FC = (P – v) × Q Thus, DOL can be written as: DOL = (P – v) × Q / OCF DOL = (OCF + FC) / OCF DOL = 1 + FC / OCF
OCF = net income + depreciation
OCF = [(P – v) × Q – FC – D] + D =
= (P – v) × Q – FC

60. 11.5. Operating Leverage
To illustrate this measure of operating leverage we go back to the Wettway sailboat project. Fixed costs were $500,000 and (P - v) was ($40,000 – 20,000) = 20,000 so OCF was: OCF = - 500, ,000 × Q

61. 11.5. Operating Leverage
Suppose Q is currently 50 boats. At this level of output, OCF is - $500,000 +1,000,000 = 500,000 If Q rises by 1 unit to 51, then the percentage change in Q is (51-50) /50 = 0.02, or 2%. OCF rises to $520,000 a change of P - v = $20,000. The percentage change in OCF is ($520, ,000)/500,0000 = 0.04 or 4%. So a 2 percent increase in the number of boats sold leads to a 4 percent increase in operating cash flow.

62. 11.5. Operating Leverage
The degree of operating leverage must be exactly 2.00 We can check this by noting that: DOL = 1 + FC / OCF DOL = ,000 / 500,000 = 2

63. 11.6. Capital Rationing
Capital rationing occurs when a firm or division has limited resources Soft rationing – the limited resources are temporary, often self-imposed Hard rationing – capital will never be available for this project The profitability index is a useful tool when a manager is faced with soft rationing