1. HANDLING PROJECT UNCERTAINTY CHAPTER 11

2. Handling Project Uncertainty
Origin of Project Risk
Methods of Describing Project Risk

3. Origins of Project Risk
Risk is to describe investment project where cash flows are NOT KNOWN in advance with certainty.
Project risk refer to changeability in a project’s PW. We can see that risk is the potential for loss.
Risk Analysis is the assignment of probabilities to the various outcomes of an investment project.

4. When deciding whether or not to make a major capital investment, such as introducing a new product, a number of issues must be considered and estimated.
The factors to be estimated include
the total market for the product;
the market share that the firm can achieve;
the growth in the market;
the cost of producing the product;
the selling price;
the life of a product;
the cost and the life of equipment needed;
the effective tax rates.
Many of these factors are subject to uncertainty.

5. The total market for the product
The market share that the firm can achieve

6. Methods of Describing Project Risk
First, begin analyzing project risk by determining the uncertainty inbuilt in a project cash flows. We can do this analysis in a number of ways such as the following;
1. Sensitivity Analysis (SA)
is a technique of investment analysis whereby different values of certain key variables are tested to see how sensitive investment results are to possible change in assumptions. SA sometimes called “What if analysis” because it answers questions such as,
If incremental sales are only 1,000 units, rather than 2,000 units? What will be the NPW be?

7. Next, we calculate a new NPW for each of these values.
Sensitivity Analysis begins with a base case situation, which is developed using most-likely values for each input.
We then change the specific variable of interest by several specified percentages above and below the most likely value, while holding other variables constant.
Next, we calculate a new NPW for each of these values.
A useful way to present results of sensitivity analysis is to plot sensitivity graphs.

8. Case # 1 Example of Sensitivity Analysis
Boston Metal company (BMC), a small manufacturer of fabricated metal parts, must decide whether to enter competition to become the supplier of transmission housings (mechanism transferring power to wheels) for Gulf Electric Company that produces the housings in its own in-house manufacturing facility, but that has almost reached its maximum production capacity.
Therefore, Gulf is looking for an outside supplier. To enter competition, BMC must design a new fixture (tool) for the production process and purchase a new furnace. The available details for this purchase are as follows:
The new furnace would cost $125,000.

9. If BMC win the competition gets the order, it may be able to sell as many as 2,000 units per year to Gulf Electric for $50 each. In the case of variable cost, such as direct labor and direct material cost, will be $15 per unit. Fixed cost will amount to $10,000 per year.
The firm expects that the proposed transmission housing project will be about five year. The firm also estimates that the amount ordered by Gulf Electric in the first year will be ordered in each of the following four years.
The initial investment can be depreciated on a MACRS basis over a seven year period, and the marginal income tax rate is expected to remain at 40%. At the end of five years, the furnace is expected to keep a market value of about 32% of the original investment.

10. What Makes BMC Managers Worry:
BMC’s managers are uncomfortable about this project, because too many uncertain elements have not been considered in the analysis:
If it decided to take project, BMC would have to invest in the furnace to provide Gulf electric with some samples as a part of the bidding process.
If Gulf Electric were not like BMC’s sample, BMC would continue to lose its entire investment in the furnace.
If Gulf were like BMC’s sample, then if it was overpriced, BMC would be under pressure to bring the price in line with competing firms. Even the possibility that BMC would get a smaller order must be considered, as Gulf may utilize its overtime capacity to produce some extra units.
Finally, BMC is not certain about its projections of variable and fixed costs.
Recognizing these uncertainties, the managers want to assess the various possible future outcomes before making a final decision.
Put yourself in BMC’s management position, and describe how you may solve the uncertainty associated with the project.

11. Case # 1 Example Sensitivity Analysis summary
Transmission-Housing Project by Boston Metal Company
New investment = $125,000
Number of units = 2,000 units
Unit Price = $50 per unit
Unit variable cost = $15 per unit
Fixed cost = $10,000/Year
Project Life = 5 years
Salvage value = $40,000
Income tax rate = 40%
MARR = 15% Determine the acceptability of the investment

12. Allowed Depreciation Amount
Depreciation Calculation
The firm expects that the proposed project will have five year project life.
Cost Base = $125,000 and Recovery Period = 7-year MACRS N
MACRS
7 - year Rates
Depreciation Amount
Allowed Depreciation Amount 1
14.29 %
$17,863 2
24.49 %
$30,613 3
17.49 %
$21,863 4
12.49 %
$15,613 5
8.93 %
$11,162.5
5,581
TOTAL $ 91,533 6
8.92 %
$11,150 7 8
4.46 %
$5,575 12

13. Cash Flow for BMC’s Transmission Housings Project “Base Case”
Income Statement 1 2 3 4 5
Revenues:
Unit Price 50
Demand (units)
2,000
Sales revenue
$100,000
Expenses:
Unit variable cost
$15
Variable cost
30,000
Fixed cost
10,000
Depreciation
17,863
30,613
21,863
15,613
5,581
Taxable Income
$42,137
$29,387
$38,137
$44,387
$54,419
Income taxes (40%)
16,855
11,755
15,255
17,755
21,768
Net Income
$25,282
$17,632
$22,882
$26,632
$32,651

14. Gains (Losses) associated with Asset Disposal
Salvage value = $40,000
Book Value (year 5) = Cost Base – Total Depreciation = $125,000 – $ 91,533 = $33,467
Taxable gains = Salvage Value – Book Value = $40,000 – $ 33,467 = $6,533
Gains taxes = (Taxable Gains) x (Tax Rate) = $6,533 x (0.40) = $2,613 14

15. Investment activities
(Example Continued)
Cash Flow Statement 1 2 3 4 5
Operating activities
Net income
25,282
17,632
22,882
26,632
32,651
Depreciation
17,863
30,613
21,863
15,613
5,581
Investment activities
Investment
(125,000)
Salvage
40,000
Gains tax
(2,613)
Net cash flow
($125,000)
$43,145
$48,245
$44,745
$42,245
$75,619

17. Is this investment justifiable at a MARR of 15%?
PW(15%) = -$125, $43,145(P/F, 15%, 1) $75,619(P/F, 15%, 5)
= $40,169 > 0
Accept the Project
$75,619
$48,245
$44,745
$42,245
$43,145 1 2 3 4 5
Years
$125,000 17

18. INPUT VALUE OF UNIT PRICE 20% LESS AND OTHERS ARE SAME
INPUT VALUE OF PRICE 20% LESS AND OTHERS ARE SAME

19. Is this investment justifiable at a MARR of 15%?
PW(15%) = -$125,000 + $31,145(P/F, 15%, 1) + $36,245(P/F, 15%, 2) +$32,745(P/F, 15%, 2)
+ $30,245(P/F, 15%, 4) + $63,619(P/F, 15%, 5)
= – $57
No, Do not accept the Project
$63,619
$36,245
$32,745
$30,245
$31,145 1 2 3 4 5
Years
$125,000 19

20. Table - Sensitivity Analysis for Five Key Input Variables
Deviation
-20%
-15%
-10%
-5% 0% 5%
10%
15%
20%
Unit price
$(57)
$9,999
$20,055
$30,111
$40,169
$50,225
$60,281
$70,337
$80,393
Demand
12,010
19,049
26,088
33,130
40,169
47,208
54,247
61,286
68,325
Variable cost
52,236
49,219
46,202
43,186
37,152
34,135
31,118
28,101
Fixed cost
44,191
43,185
42,179
41,175
39,163
38,157
37,151
36,145
Salvage value
37,782
38,378
38,974
39,573
40,765
41,361
41,957
42,553
Base

21. EXERCISE INPUT VALUE OF DEMAND 20% LESS AND OTHERS ARE SAME

22. Is this investment justifiable at a MARR of 15%?
PW(15%) = -$125,000
+$34,745(P/F, 15%, 1)
+$39,845(P/F, 15%, 5) +$36,345(P/F, 15%, 5) +$33,845(P/F, 15%, 5)
+$67,219(P/F, 15%, 5)
= $12,010 > 0
accept the Project
$67,219
$39,845
$36,345
$33,845
$34,745 1 2 3 4 5
Years
$125,000 22

23. Table - Sensitivity Analysis for Five Key Input Variables
Deviation
-20%
-15%
-10%
-5% 0% 5%
10%
15%
20%
Unit price
$(57)
$9,999
$20,055
$30,111
$40,169
$50,225
$60,281
$70,337
$80,393
Demand
12,010
19,049
26,088
33,130
40,169
47,208
54,247
61,286
68,325
Variable cost
52,236
49,219
46,202
43,186
37,152
34,135
31,118
28,101
Fixed cost
44,191
43,185
42,179
41,175
39,163
38,157
37,151
36,145
Salvage value
37,782
38,378
38,974
39,573
40,765
41,361
41,957
42,553
Base

24. Sensitivity graph – BMC’s transmission - housings project
In this graph we can see that the project’s NPW is (1) very sensitive to changes in product demand and unit price, (2) fairly sensitive to changes in variable cost, and (3) relatively insensitive to changes in the fixed cost and salvage value.
$100,000
90,000
Unit Price
80,000
70,000
Demand
60,000
50,000
Salvage value
40,000
Fixed cost
Base
30,000
Variable cost
20,000
10,000
-10,000
-20%
-15%
-10%
-5% 0% 5%
10%
15%
20%
Sensitivity graph – BMC’s transmission - housings project

25. CASE # 2 Example 11.1 Sensitivity Analysis
Capstone Turbine Corporation is the world’s leading provider of micro-turbine based Micro-CHP (combined heat and power) systems for clean, continuous, distributed-generation electricity. The Micro-CHP unit is a compact turbine generator that delivers electricity on-site, or close to the point where it is needed. Designed to operate on a variety of gaseous and liquid fuels, this form of distributed-generation technology first introduced in 1998 for commercial use.
Capstone is considering marketing a modified, but downsized, version of the system unit for residential use, primarily for vacation properties in remote places. The project requires an initial investment of $55 million, but Capstone managers are nervous about this project, because too many uncertain elements have not been considered in the analysis.
Two primary factors that are difficult to estimate are the initial market size and how the market size will grow over the life of the project. The company has prepared the following financial data related to the project:

26. The initial investment can be depreciated on a seven-year MACRS, and the project is expected to have an economic service life of five years. The product life is relatively short, as the technology changes in the energy sector are changing rapidly. The firm’s marginal tax rate is 40%, and its MARR is known to be 15%.
(a) Develop the cash flow series over the project life, based on the assumption of most-likely estimates.
(b) Conduct a sensitivity analysis for each variable and develop a sensitivity graph.

27. CASE # 2 Example 11.1 continue............
Capstone Turbine Corporation
New investment = $55 million
Initial market size (units), year one = 1,500 units
Unit Price = $80,000 per unit
Unit variable cost = $60,000 per unit
Fixed cost = $8,000,000/Yr
Project Life = 5 years
Salvage value = $7,000,000
Income tax rate = 40%
MARR = 15%
Develop the cash flow series over the project life based on the assumption of most-likely estimates.
Conduct a sensitivity analysis for each variable and develop a sensitivity graph.

28. Depreciation Calculation
The firm expects that the proposed project will have five year project life.
Cost Base = $55,000,000 and Recovery Period = 7-year MACRS N
MACRS Rate
Depreciation Amount x 000
Allowed Depreciation
Amount x 000 1
14.29 %
$7,860 2
24.49 %
$13,470 3
17.49 %
$9,620 4
12.49 %
$6,870 5
8.93 %
$4,906
$ 2,453
Total = $ 40,273,000 6
8.92 % 7
$4,911.5 8
4.46 %
$2,453 28

29. Gains (Losses) associated with Asset Disposal
Salvage value = $7,000,000
Book Value (year 5) = Cost Base – Total Depreciation
= $55,000,000 – $ 40,273,000 = $ 14,727,000
Taxable gains (loss) = Salvage Value – Book Value
= $7,000,000 – $ 14,727,000 = – $7,727,000
Tax credits = [Taxable Gains (loss)] (Tax Rate)
= – $7,727,000 x (0.40) = -$3,091,000 29

30. Table Cash Flow for Capstone’s Micro-CHP Project Based on Most-Likely Estimates (Unit: $000; except demand)
Income Statement 1 2 3 4 5
Revenues:
Unit Price 80
Demand (units)
1,500
1,575
1,654
1,736
1,823
Sales revenue
$120,000
$126,000
$132,300
$138,915
$145,865
Expenses:
Unit variable cost
$60
Variable cost
90,000
94,500
99,225
104,186
109,396
Fixed cost
8,000
Depreciation
7,860
13,470
9,620
6,870
2,453
Taxable Income
$14,140
$10,031
$15,456
$19,859
$26,012
Income taxes (40%)
5.656
4,012
6,182
7,944
10,405
Net Income
$8,484
$6,018
$9,273
$11,916
$15,607

31. (Example 11.1 ....... Continued) Cash Flow Statement 1 2 3 4 51 2 3 4 5
Operating activities
Net income
8,454
6,018
9,273
11,916
15,607
Depreciation
7,860
13,470
9,620
6,870
2,453
Investment activities
Investment
(55,000)
Salvage
7,000
Gains tax
3, (add it)
Net cash flow
$16,344
$19,488
$18,893
$18,785
$28,151

32. Cash flow for Capstone’s MicroCHP Project

33. Is this investment justifiable at a MARR of 15%?
PW(15%) = -$55,000, $16,344,000(P/F, 15%, 1) + ……… . +$28,152,000(P/F, 15%, 5)
= $11,107,000 > 0
Yes, Accept the Project
$28,152
$19,388
$18,893
$18785
$16,344 1 2 3 4 5
Years
$55,000 33

34. CASE # 2 SOLUTION
(a) Sensitivity analysis: We begin the sensitivity analysis with a consideration of the base-case situation, which reflects the most-likely estimate (expected value) for each input variable. In developing table next slide, we changed a given variable by 20% in 5% increments above and below the base-case value and calculated new NPWs, while other variables were held constant. Now we ask a series of what-if questions:
What if sales are 20% below the expected level? What if Operating costs rise? What if the unit price drops from $80,000 to $64,000 (20% drop)?
Table, summarizes the results of our varying the values of the key input variables.

35. Base

36. In this graph we can see that the project’s NPW is
(1) very sensitive to changes in unit price and variable cost,
(2) fairly sensitive to changes in demand, and
(3) relatively insensitive to changes in the growth rate, fixed cost and salvage value.

40. INCOME STATEMENT 1 2 3 4 5
Revenues:
Unit price
Demand (units)
Sales Revenue
Expenses:
Unit Variable Cost
Variable cost
Fixed Cost
Depreciation
Taxable Income
Income taxes (40%)
Net Income
CASH FLOW STATEMENT
Net income
Investment
Salvage
Gains (loss) tax
Net cash flow
Total depreciation: ………………………………………………………………………………………………
Book Value: …………….………………………………………………………………………………………..
Taxable gain or (Loss): ………………………………………………………………………………………..
Gain Tax or (Tax credit): ………………………………………………………………………………………..
NPW(15%) = ……………………………………………………………………………………………………

41. INCOME STATEMENT
Inflation
Rate % 1 2 3 4 5
Revenues: 5%
Expenses:
Labor
Material 4%
Overhead
Depreciation
Taxable Income
Income taxes (40%)
Net Income
CASH FLOW STATEMENT
Net income
Investment
Salvage
Gains (loss) tax
Net cash flow
Total depreciation: ……………………………………………………………………………………………………..
Book Value: …………………………………………………………………………………………………………..
Taxable gain or (Loss): …………………………………………………………………………………………………..
Gain Tax or (Tax credit): ………………………………………………………………………………………………..
NPW(15%) = …………………………………………………………………………………………………………

42. PRACTICE PROBLEM SOLUTIONS
2; 15

43. 11.2
Lane Construction Lld. is considering the acquisition of a new dump truck. The truck's base price is $75,000, and it will cost another $15,000 to modify it for special use by the company. This truck falls into the MACRS five-year class. It will be sold after five years for $ The truck purchase will have no effect on revenues, but it is expected to save the firm $35,000 per year in before-tax operating costs mainly in leasing expenses. The firm's marginal tax rate (federal plus stare) is 40%, and its MARR is 15%.
(a) Is this project acceptable based on the most likely estimates given in the problem?

44. Cost basis = $75,000+$15,000=$90,000 D1 = 20% * 90,000 = $18,000
Dep.=18,000+28,800+17,280+10,368+5,184=$79,632
Book value = 90,000 – 79,632 =10,368

45. 11.2) (a) Project cash flows based on most-likely estimates:

47. Cost basis = $8,000,000
D1 = 14.29% * 8,000,000 = $1,143,200
D2 = 24.49% * 8,000,000 = $1,959,200
D3 = 17.49% * 8,000,000 = $1,399,200

48. 11.15) a) Base case scenario:

49. 11.15) b) Best case scenario:

50. 11.15) c) Worst case scenario: