1. Sensitivity and Breakeven Analysis
Lecture No. 29
Professor C. S. Park
Fundamentals of Engineering Economics
Copyright © 2005

2. Chapter 10 Handling Project Uncertainty
Origin of Project Risk
Methods of Describing Project Risk
Probability Concepts for Investment Decisions
Risk-Adjusted Discount Rate Approach

3. In Engineering economics we predict cash flows
How do you know for sure that what you are claiming for interest rate, costs, revenues remain true???
Well for some situations you can be close enough to consider your “single point” analysis to be worthwhile.
For other you need to consider what is called RISK

4. We use the term risk to describe an investment project where cash flows are not known in advanced with certainty.
What to do: Instead of single point analysis, an array of outcomes and their probabilities or odds are to considered.

5. Origins of Project Risk
Risk: (in essence) the potential for loss
Project Risk: variability in a project’s NPW
Risk Analysis: The assignment of probabilities to the various outcomes of an investment project

6. Methods of Describing Project Risk
Sensitivity Analysis: a means of identifying the project variables which, when varied, have the greatest effect on project acceptability.
Break-Even Analysis: a means of identifying the value of a particular project variable that causes the project to exactly break even.
Scenario Analysis: a means of comparing a “base case” to one or more additional scenarios, such as best and worst case, to identify the extreme and most likely project outcomes.

7. Sensitivity Analysis – Example 10.1
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/Yr
Project Life = 5 years
Salvage value = $40,000
Income tax rate = 40%
MARR = 15%

8. Example 10.1 - After-tax Cash Flow for BMC’s Transmission-Housings Project – “Base Case”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
5,575
Taxable Income
$42,137
$29,387
$38,137
$44,387
$54,425
Income taxes (40%)
16,855
11,755
15,255
17,755
21,770
Net Income
$25,282
$17,632
$22,882
$26,632
$32,655

9. (Example 10.1, Continued) 1 2 3 4 5 Cash Flow Statement1 2 3 4 5
Operating activities
Net income
25,282
17,632
22,882
26,632
32,655
Depreciation
17,863
30,613
21,863
15,613
5,575
Investment activities
Investment
(125,000)
Salvage
40,000
Gains tax
(2,611)
Net cash flow
($125,500)
$43,145
$48,245
$44,745
$42,245
$75,619

11. Example 10.1 - 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

12. Sensitivity graph – BMC’s transmission-housings project (Example 10.1)
$100,000
90,000
Unit Price
80,000
70,000
Demand
60,000
50,000
Salvage value
40,000
Base
Fixed cost
30,000
Variable cost
20,000
10,000
-10,000
-20%
-15%
-10%
-5% 0% 5%
10%
15%
20%

13. Example 10.2 - Sensitivity Analysis for Mutually Exclusive Alternatives

14. Capital (Ownership) Cost
Electrical power:
CR(10%) = ($30,000 - $3,000)(A/P, 10%, 7) + (0.10)$3, = $5,845
LPG:
CR(10%) = ($21,000- $2,000)(A/P, 10%, 7) + (0.10)$2, = $4,103
Gasoline:
CR(10%) = ($20,000-$2,000)(A/P, 10%, 7) + (0.10) $2, = $3,897
Diesel fuel:
CR(10%) = ($25,000 -$2,200)(A/P, 10%, 7) +(0.10) $2, = $4,903

15. Annual O&M Cost Electrical power: $500 + (1.60 + 5)M = $500 + 6.6M
LPG:
$1,000 + (12 + 6)M = $1,000 + 18M
Gasoline:
$800 + (13.2 + 7)M = $800  M
Diesel fuel:
$1,500 + (7.7 + 9)M = $1,500 + 16.7M

16. Annual Equivalent Cost
Electrical power:
AE(10%) = 6,345 + 6.6M
LPG:
AE(10%) = 5,103 + 18M
Gasoline:
AE(10%) = 4,697  M
Diesel fuel:
AE(10%) = 6,403 + 16.7M

18. Break-Even Analysis Excel using a Goal Seek function
Analytical Approach

19. Excel Using a Goal Seek Function
NPW
Breakeven Value
Demand

20. Goal Seek
Function
Parameters

21. Analytical Approach Unknown Sales Units (X)1 2 3 4 5
Cash Inflows:
Net salvage
37,389
X(1-0.4)($50)
30X
0.4 (dep)
7,145
12,245
8,745
6,245
2,230
Cash outflows:
Investment
-125,000
-X(1-0.4)($15)
-9X
-(0.6)($10,000)
-6,000
Net Cash Flow
21X +
1,145
21X + 6,245
2,745
245
33,617

22.  PW of cash inflows
PW(15%)Inflow= (PW of after-tax net revenue)
+ (PW of net salvage value)
+ (PW of tax savings from depreciation
= 30X(P/A, 15%, 5) + $37,389(P/F, 15%, 5) $7,145(P/F, 15%,1) + $12,245(P/F, 15%, 2)
+ $8,745(P/F, 15%, 3) + $6,245(P/F, 15%, 4)
+ $2,230(P/F, 15%,5)
= 30X(P/A, 15%, 5) + $44,490
= X + $44,490

23.  PW of cash outflows:
PW(15%)Outflow = (PW of capital expenditure_
+ (PW) of after-tax expenses
= $125,000 + (9X+$6,000)(P/A, 15%, 5)
= X + $145,113
 The NPW:
PW (15%) = X + $44,490
- ( X + $145,113)
= X - $100,623.
 Breakeven volume:
PW (15%) = X - $100,623 = 0
Xb =1,430 units.

24. Demand
PW of
inflow
Outflow
NPW X X
- $44,490 X
+ $145,113 X
-$100,623
$44,490
$145,113
100,623
500
94,773
160,198
65,425
1000
145,055
175,282
30,227
1429
188,197
188,225 28
1430
188,298
188,255 43
1500
195,338
190,367
4,970
2000
245,620
205,452
40,168
2500
295,903
220,537
75,366

25. Break-Even Analysis Chart
$350,000
300,000
250,000
200,000
150,000
100,000
50,000
-50,000
-100,000
Inflow
Break-even Volume
Profit
PW (15%)
Outflow
Loss
Xb = 1430
Annual Sales Units (X)

26. Scenario Analysis Variable Considered Worst- Case Scenario
Most-Likely-Case
Best-Case
Unit demand
1,600
2,000
2,400
Unit price ($) 48 50 53
Variable cost ($) 17 15 12
Fixed Cost ($)
11,000
10,000
8,000
Salvage value ($)
30,000
40,000
50,000
PW (15%)
-$5,856
$40,169
$104,295