Chapter 10
Sensitivity and Breakeven
Analysis
Handling Project Uncertainty

Origin of Project Risk

Methods of Describing
Project Risk
Origins of Project Risk

Risk is to describe investment
project where cash flows are
not known in advance with
certainty. Project risk on the
other hand refer to variability
in a project’s PW. In essence,
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.
Origins of Project Risk
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The decision to make a major capital investment such as introducing a
new product requires cash flow information over the life of a project.
The profitability estimate of an investment depends on cash flow
estimations, which are generally uncertain.
The factors to be estimated include
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continue….
the total market for the product;
the market share that the firm can attain;
the growth in the market;
the cost of producing the product, including labor and materials;
the selling price;
the life of a product;
the cost and the life of equipment needed; and
the effective tax rates.
Many of these factors are subject to uncertainty.
Methods of Describing Project Risk
Fist, 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;
Sensitivity Analysis (SA): Determines the effect on the PW of variations in the
input variables (revenues, operating cost, and salvage value). SA is sometimes
called “what if analysis” because it answers questions such as,
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What if incremental sales are only 1,000 units, rather than 2,00 units? Then
what will be the NPW be?.
SA begins with a base-case situation, which is developed using most-likely values
for each input. A useful way to present results of sensitivity analysis is to plot
sensitivity graphs.
Break-Even Analysis is a technique for studying the effect of variations in output
on a firm’s NPW.
Scenario Analysis is a technique that does consider the sensitivity of NPW to
both changes in key variables and to the range of likely variable values. The
decision maker may consider two extreme cases, a
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“worst-case” scenario (low unit sales, high variable cost per unit, high fixed cost,
and so on) and a
“best-case” scenario to identify the extreme and most likely project outcomes.
Sensitivity Analysis – Example 10.1
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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%
Example 10.1 - After-tax Cash Flow for BMC’s Transmission
Housings Project – “Base Case”
0
1
2
3
4
5
Revenues:
Unit Price
50
50
50
50
50
2,000
2,000
2,000
2,000
2,000
$100,000
$100,000
$100,000
$100,000
$100,000
$15
$15
$15
$15
$15
Variable cost
30,000
30,000
30,000
30,000
30,000
Fixed cost
10,000
10,000
10,000
10,000
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
16,855
11,755
15,255
17,755
21,768
$25,282
$17,632
$22,882
$26,632
$32,651
Demand (units)
Sales revenue
Expenses:
Unit variable cost
Income taxes (40%)
Net Income
Depreciation Calculation
– Cost Base = $125,000
– Recovery Period = 7-year MACRS
N
MACRS
Rate
Depreciation
Amount
Allowed Depreciation
Amount
1
14.29 %
$17,863
$17,863
2
24.49 %
$30,613
$30,613
3
17.49 %
$21,863
$21,863
4
12.49 %
$15,613
$15,613
5
8.93 %
$11,150
$ 5,581
6
8.92 %
$11,150
0
7
8.93 %
$11,150
0
8
4.46 %
$5,575
0
8
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) (Tax Rate)
= $6,533 x (0.40)
= $2,613
9
(Example 10.1, Continued)
Cash Flow Statement
0
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
($125,500)
$43,145
$48,245
$44,745
$42,245
$75,619
Example 10.1 BMC's Transmission-Housings Project
Income Statement
0
Revenues:
Unit Price
Demand (units)
Sales Revenue
Expenses:
Unit Variable Cost
Variable Cost
Fixed Cost
Depreciation
1
2
3
4
5
$
50 $
50 $
50 $
50 $
50
2000
2000
2000
2000
2000
$ 100,000 $ 100,000 $ 100,000 $ 100,000 $ 100,000
$
15
30,000
10,000
17,863
$
15
30,000
10,000
30,613
$
15
30,000
10,000
21,863
$
15
30,000
10,000
15,613
$
15
30,000
10,000
5,581
Taxable Income
Income Taxes (40%)
$ 42,137
16,855
$ 29,387
11,755
$
38,137
15,255
$ 44,387
17,755
$
54,419
21,768
Net Income
$ 25,282
$ 17,632
$
22,882
$ 26,632
$
32,651
25,282
17,863
17,632
30,613
22,882
21,863
26,632
15,613
Cash Flow Statement
Operating Activities:
Net Income
Depreciation
Investment Activities:
Investment
(125,000)
Salvage
Gains Tax
Net Cash Flow
$ (125,000) $ 43,145
32,651
5,581
40,000
(2,613)
$ 48,245
$
44,745
$ 42,245
$
75,619

Is this investment justifiable at a
MARR of 15%?
$75,619

PW(15%) = -$125,000 +
+$43,145(P/F, 15%, 1) + . . . .
+$75,619(P/F, 15%, 5)
= $40,169 > 0
$48,245
$43,145
$44,745 $42,245
0
1
2
3
4
5
Years
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Yes, Accept the Project
$125,000
12
Example 10.2 - Sensitivity Analysis for Five Key
Input Variables
Deviation
Unit price
-20%
$57
-15%
-10%
-5%
0%
5%
10%
15%
20%
$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
40,169
37,152
34,135
31,118
28,101
Fixed cost
44,191
43,185
42,179
41,175
40,169
39,163
38,157
37,151
36,145
Salvage
value
37,782
38,378
38,974
39,573
40,169
40,765
41,361
41,957
42,553
Base
Sensitivity graph – BMC’s transmission-housings project
(Example 10.2)
$100,000
90,000
Unit Price
80,000
70,000
Demand
60,000
50,000
Salvage value
40,000
Fixed cost
Variable cost
Base
30,000
20,000
10,000
0
-10,000
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
Analytical Approach Unknown Sales
Units (X)
0
1
2
3
4
5
Cash Inflows:
Net salvage
37,389
X(1-0.4)($50)
30X
30X
30X
30X
30X
7,145
12,245
8,745
6,245
2,230
-X(1-0.4)($15)
-9X
-9X
-9X
-9X
-9X
-(0.6)($10,000)
-6,000
-6,000
-6,000
-6,000
-6,000
21X +
1,145
21X +
6,245
21X +
2,745
21X +
245
21X +
33,617
0.4 (dep)
Cash outflows:
Investment
Net Cash Flow
-125,000
-125,000
 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
= 100.5650X + $44,490
 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)
= 30.1694X + $145,113
 The NPW:
PW (15%)
= 100.5650X + $44,490
- (30.1694X + $145,113)
= 70.3956X - $100,623.
 Breakeven volume:
PW (15%)
Xb
= 70.3956X - $100,623 = 0
= 1,430 units.
PW of
inflow
PW of
Outflow
NPW
X
100.5650X
- $44,490
30.1694X
+ $145,113
70.3956X
-$100,623
0
$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
Demand
Break-Even Analysis Chart
$350,000
300,000
Break-even Volume
200,000
Profit
Outflow
150,000
Xb = 1430
PW (15%)
250,000
Loss
100,000
50,000
0
-50,000
-100,000
0
300
600
900
1200
1500
Annual Sales Units (X)
1800
2100
2400
Scenario Analysis
Variable
Considered
WorstCase
Scenario
Most-LikelyCase
Scenario
Best-Case
Scenario
Unit demand
1,600
2,000
2,400
Unit price ($)
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