# Sensitivity and Breakeven Analysis

Document Sample

L29: Sensitivity and
Breakeven Analysis

ECON 320 Engineering Economics
Mahmut Ali GOKCE
Industrial Systems Engineering
Computer Sciences

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Chapter 10
Handling Project Uncertainty
 Origin of Project Risk
 Methods of Describing
Project Risk
 Probability Concepts
for Investment
Decisions
Rate Approach

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Origins of Project Risk

 Risk: 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

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Methods of Describing Project Risk

 Sensitivity Analysis: a means of identifying the
project variables which, when varied, have the
greatest effect on project acceptability.
 What might have greatest effect on NPW, if changed?
 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.

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Sensitivity Analysis – Example 10.1
Should we or should we not?
   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 at the end of project life.
   Income tax rate = 40%
   MARR = 15%
   Depreciation 7-year MACRS (Check out % depreciation from table 8.5)
for a 5 year project.

 Develop a table for after-tax cash flow table! Then we will assess the
situation under different scenarios
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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
Demand (units)              2,000       2,000       2,000       2,000       2,000
Sales revenue            \$100,000 \$100,000 \$100,000 \$100,000 \$100,000
Expenses:
Unit variable cost              \$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       5,575
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

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(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    32,655

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

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A                 B             C             D           E             F           G
1 Example 10.1 BMC's               Transmission-Housings Project
2
13 Income Statement
14                      0                      1            2           3             4            5
15 Revenues:
16   Unit Price                           \$      50 \$      50 \$      50 \$      50 \$      50
17   Demand (units)                            2000      2000      2000      2000      2000
18   Sales Revenue                        \$ 100,000 \$ 100,000 \$ 100,000 \$ 100,000 \$ 100,000
19 Expenses:
20   Unit Variable Cost                   \$       15   \$       15   \$       15   \$       15   \$       15
21   Variable Cost                            30,000       30,000       30,000       30,000       30,000
22   Fixed Cost                               10,000       10,000       10,000       10,000       10,000
23
24   Depreciation                             17,863       30,613       21,863       15,613        5,581
25 Taxable Income                         \$ 42,137     \$ 29,387     \$ 38,137     \$ 44,387     \$ 54,419
26 Income Taxes (40%)
27                                          16,855       11,755       15,255       17,755       21,768
28   Net Income                           \$ 25,282     \$ 17,632     \$ 22,882     \$ 26,632     \$ 32,651
29
30   Cash Flow Statement
31   Operating Activities:
32      Net Income                            25,282       17,632       22,882       26,632       32,651
33      Depreciation                          17,863       30,613       21,863       15,613        5,581
34   Investment Activities:
35      Investment            (125,000)
36      Salvage                                                                                   40,000
37
38      Gains Tax                                                                                 (2,613)
39 Net Cash Flow          \$ (125,000) \$ 43,145         \$ 48,245     \$ 44,745     \$ 42,245     \$ 75,619
40

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Example 10.2 - 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     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         37,782   38,378    38,974   39,573     40,169    40,765    41,361    41,957    42,553
value

Try to understand what will
happen if estimates on unit                                Base
prices, demand, variable and
fixed cost, salvage value change?

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Sensitivity graph – BMC’s transmission-housings
project

\$100,000
90,000
80,000
Unit Price
70,000
Demand
60,000
50,000
Salvage value
40,000
Base                          Fixed cost
30,000
Variable cost
20,000
10,000
0
-10,000
-20%   -15%   -10%   -5%   0%     5%   10%     15%    20%

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Example 10.2 - Sensitivity Analysis for Mutually
Exclusive Alternatives
Electrical                              Diesel
Power         LPG       Gasoline        Fuel

Life expectancy               7 year      7 years     7 years       7 years
Initial cost                 \$30,000     \$21,000     \$20,000       \$25,000
Salvage value                \$3,000       \$2,000      \$2,000        \$2,200
Maximum shifts per year        260         260         260           260

Fuel consumption/shift       32 kWh       12 gal      11 gal         7 gal

Fuel cost/unit              \$0.05/kWh    \$1.00/gal   \$1.20/gal     \$1.10/gal
Fuel cost/shift               \$1.60        \$12        \$13.20         \$7.7
Annual maintenance cost:
Fixed cost              \$500        \$1,000      \$1,200        \$1,500
Variable cost/shift      \$5           \$6          \$7            \$9

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Capital (Ownership) Cost

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

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REMEMBER L 17 FROM CHAPTER 6 ?
Annual Equivalent Cost
 When only costs are
involved, the AE

Annual Equivalent Costs
method is called the                                Capital
annual equivalent cost.                             costs
 Revenues must cover
+
two kinds of costs:
Operating costs and                                 Operating
capital costs.                                      costs

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REMEMBER L 17 FROM CHAPTER 6 ?
Capital (Ownership) Costs
 Def: Owning an equipment
is associated with two                                                S
transactions—(1) its initial                     0
cost (I) and (2) its salvage                                          N
value (S).
 Capital costs: Taking
these items into                                 I
consideration, we calculate
the capital costs as:                            0 1   2    3          N

CR(i)  I ( A / P, i, N )  S( A / F, i, N )
CR(i)
 ( I  S)( A / P, i, N )  iS

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Annual O&M Cost

Let M be number of shifts per year
 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 + 20.20M
 Diesel fuel:
\$1,500 + (7.7 + 9)M = \$1,500 + 16.7M

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Annual Equivalent Cost

 Electrical power:
AE(10%) = 6,345   + 6.6M
 LPG:
AE(10%) = 5,103   + 18M
 Gasoline:
AE(10%) = 4,697   + 20.20M
 Diesel fuel:
AE(10%) = 6,403   + 16.7M

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12000

10000
Annual Equivalent Cost (\$)

8000
Electrical
LPG
6000
Gasoline
Disel Fuel
4000

2000

0
0
20
40
60
80
100
120
140
160
180
200
220
240
260
Number of Shifts (M)
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Break-Even Analysis

Excel using a Goal Seek function

Analytical Approach

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Excel Using a Goal Seek Function
Goal Seek              ?       X

Set cell:         \$F\$5              NPW

To value:         0                Breakeven Value

By changing cell: \$B\$6             Demand

Ok            Cancel

Can we find demand level for which NPW is 0?

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A                    B             C             D             E             F            G
1    Example 10.3 Break-Even Analysis
2
3    Input Data (Base):                                    Output Analysis:
4
5    Unit Price (\$)           \$        50                  Output (NPW)                         \$0
6    Demand                        1429.39
7    Var. cost (\$/unit)       \$        15
8    Fixed cost (\$)           \$    10,000
9    Salvage (\$)              \$    40,000
10   Tax rate (%)                     40%
11   MARR (%)                         15%
12
13
14                                  0              1            2             3             4             5
15   Income Statement
16   Revenues:
17      Unit Price                            \$     50 \$     50 \$     50 \$     50 \$     50
18      Demand (units)                          1429.39  1429.39  1429.39  1429.39  1429.39
Goal Seek    19      Sales Revenue                         \$ 71,470 \$ 71,470 \$ 71,470 \$ 71,470 \$ 71,470
20   Expenses:
Function     21      Unit Variable Cost                    \$       15   \$       15   \$         15   \$       15    \$       15
22      Variable Cost                             21,441       21,441         21,441       21,441        21,441
Parameters   23      Fixed Cost                                10,000       10,000         10,000       10,000        10,000
24
25      Depreciation                              17,863       30,613         21,863       15,613         5,581
26 Taxable Income                             \$   22,166   \$    9,416   \$     18,166   \$ 24,416      \$   34,448
27 Income Taxes (40%)
28                                                 8,866        3,766          7,266      9,766          13,779
29   Net Income                               \$   13,299   \$    5,649   \$     10,899   \$ 14,649      \$   20,669
30
31   Cash Flow Statement
32   Operating Activities:
33      Net Income                                13,299        5,649         10,899       14,649        20,669
34      Depreciation                              17,863       30,613         21,863       15,613         5,581
35   Investment Activities:
36      Investment                (125,000)
37      Salvage                                                                                          40,000
38
39      Gains Tax                                                                                        (2,613)
40 Net Cash Flow              \$ (125,000) \$       31,162   \$ 36,262     \$     32,762   \$ 30,262      \$   63,636
41

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Analytical Approach
Unknown Sales Units (X) for BMC transm. housing
0         1        2        3          4          5
Cash Inflows:
Net salvage                                                        37,389
X(1-0.4)(\$50)                30X      30X      30X        30X       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      -9X      -9X        -9X        -9X
-(0.6)(\$10,000)              -6,000   -6,000   -6,000     -6,000    -6,000
Net Cash Flow     -125,000   21X +    21X +    21X +      21X +     21X +
1,145    6,245    2,745       245      33,617

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 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

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 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%)      = 70.3956X - \$100,623 = 0
Xb      =1,430 units.

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PW of       PW of
Demand     inflow     Outflow              NPW
X      100.5650X    30.1694X          70.3956X
- \$44,490   + \$145,113        -\$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

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Break-Even Analysis Chart
\$350,000
300,000
250,000
200,000                          Break-even Volume                        Profit

150,000        Outflow
PW (15%)

100,000

Xb = 1430
Loss
50,000
0
-50,000
-100,000

0    300      600   900   1200    1500       1800       2100    2400

Annual Sales Units (X)

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Scenario Analysis
Variable         Worst-    Most-Likely-     Best-Case
Considered        Case        Case           Scenario
Scenario    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

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