Material Covered
Test #3 Review
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INEN 303
Sergiy Butenko
Industrial & Systems Engineering
Texas A&M University
Breakeven Analysis: Single Project
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The breakeven point for a variable X is
expressed in terms such as units per year or
hours per month.
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Let QBE, be the breakeven amount.
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Use the following decision guideline: accept
project if the estimated quantity is larger than
QBE , and reject it if the estimated quantity is
smaller than QBE.
Breakeven Analysis: Two Projects
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Breakeven Analysis (Chapter 13)
Effects of Inflation (Chapter 14)
Depreciation Methods (Chapter 16)
After-Tax Economic Analysis (Chapter 17)
Sensitivity Analysis and Decision Trees
(Chapter 18)
Breakeven Analysis: Single Project
Breakeven Analysis: Two Projects
For two or more alternatives, determine the
breakeven value of the common variable X by
equating the PW or AW relations and solving for the
parameter in question.
Use the following guideline to select an alternative:
Estimated level of X is below breakeven ⇒ select
alternative with the higher variable cost (larger
slope)
Estimated level of X is above breakeven ⇒ select
alternative with the lower variable cost (smaller
slope)
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Breakeven Analysis: A Typical Problem
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[13.14] Two pumps can be used for pumping a
corrosive liquid. A pump with a brass impeller costs
$800 and is expected to last 3 years. A pump with a
stainless steel impeller costs $1900 and will last 5
years. A rebuild costing $300 will be required after
2000 operating hours for the brass impeller pump
while an overhaul costing $700 will be required for
the stainless steel pump after 8000 hours. If the
operating cost of each pump is $1 per hour, how
many hours per year must the pump be required to
justify the purchase of the more expensive pump?
Use an interest rate of 10% per year.
Effects of Inflation
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Inflation makes the cost of the same
product or service increase over time
This is due to the decreasing purchasing
power of the currency when inflation is in
effect
Terms:
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Today’s dollars or constant-value dollars (CVD)
Future dollars (FD)
Inflated interest rate: if = i + f + i*f
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i : real interest rate
f : inflation rate
Effects of Inflation: A Typical Problem
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[14.26] An engineer deposits $10,000 into an
account when the market interest rate is 10%
per year and the inflation rate is 5% per year.
The account is left undisturbed for 5 years.
(a) How much money will be in the account?
(b) What will be the buying (purchasing)
power in terms of today’s dollars?
(c) What is the real rate of return that is
made on the account?
Breakeven Analysis: A Typical Problem
Solution:
Let x = hours per year
-800(A/P,10%,3) - (300/2000)x -1.0x
= -1,900(A/P,10%,5) - (700/8000)x - 1.0
-800(0.40211) - 0.15x - 1.0x
= -1,900(0.2638) - 0.0875x - 1.0x
0.0625x = 179.532, so x = 2873 hours per year
Effects of Inflation
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PW of a future amount with inflation
considered: P=F(P/F, if ,n)
Future worth of a present amount in
constant-value dollars with the same
purchasing power: F=P(F/P,i,n)
Future amount to cover a current amount with
no interest: F=P(F/P,f,n)
Future amount to cover a current amount with
interest: F=P(F/P, if ,n)
Effects of Inflation: A Typical Problem
Solution:
(a) F = 10,000(F/P,10%,5) = 10,000(1.6105) =
$16,105
(b) Buying Power = 16,105/(1 + 0.05)5 =
$12,619
(c) if = i + 0.05 + (i)(0.05)
0.10 = i + 0.05 + (i)(0.05)
1.05i = 0.05
i = 4.76%
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Depreciation Methods
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Depreciation may be determined for internal
company records (book depreciation) or for
income tax purposes (tax depreciation).
Depreciation does not result in actual cash
flow directly. It is a book method by which the
capital investment in tangible property is
recovered.
The annual depreciation amount is tax
deductible, which can result in actual cash
flow changes.
Depreciation Methods
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Classical methods for book depreciation
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Straight Line (SL) Model
Declining Balance (DB) Model
Modified Accelerated Cost Recovery System
(MACRS) Method
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Method for tax depreciation in the U.S.
Acceptable for book depreciation also.
Depreciation Methods
Depreciation Methods
Depreciation Methods: A Typical Problem
Depreciation Methods: A Typical Problem
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[16.19] A warehouse costs $800,000 to
construct for Ace Hardware. It has a 15-year
life with an estimated resale value of 80% of
the construction cost. However, the building
will be depreciated to zero over a recovery
period of 30 years. Calculate the annual
depreciation charge for years 5, 10, and 25,
using (a) straight line depreciation and (b)
DDB depreciation. (c) What is the implied
salvage value for DDB?
Solution:
B = $800,000; n = 30; S = 0
(a)
Straight line depreciation:
Dt = 800,000 = $26,667 t = 5, 10, 25, and all other years
30
(b)
Double declining balance method: d = 2/n = 2/30 =
0.06667
„ D5 = 0.06667(800,000)(1–0.06667)5-1 = $40,472
„ D10 = 0.06667(800,000)(1–0.06667)10-1 = $28,664
„ D25 = 0.06667(800,000)(1–0.06667)25–1 = $10,183
(c)
BV30 = 800,000(1–0.06667)30 = $100,959
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After-Tax Economic Analysis
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Income tax rates for U.S. corporations and individual
taxpayers are graduated — higher taxable incomes
pay higher income taxes.
A single-value, effective tax rate Te is usually
applied in an after-tax economic analysis.
Taxes are reduced because of tax-deductible items,
such as depreciation and operating expenses.
Because depreciation is not a cash flow, it is
important to consider depreciation only in the TI
computations, and not directly in the CFBT and
CFAT calculations.
After-Tax Economic Analysis
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EVA = net profit after taxes – cost of invested capital
= NPAT – (after-tax MARR)(book value)
= TI – taxes – i(BV)
After-Tax Economic Analysis
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CFBT = gross income – expenses – initial
investment + salvage value
CFAT = CFBT – taxes
= CFBT – (taxable income)(Te)
TI = gross income – expenses – depreciation
+ depreciation recapture
If an alternative’s estimated contribution to
corporate financial worth is the economic
measure, the economic value added (EVA)
should be determined.
After-Tax Analysis: A Typical Problem
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The equivalent annual worth of CFAT and EVA
estimates is the same numerically, due to the fact
that they interpret the annual cost of the capital
investment in different, but equivalent manners
when the time value of money is taken into account.
[17.15] A petroleum engineer with Halstrom
Exploration must estimate the minimum
required cash flow before taxes if the CFAT is
$2,000,000. The effective federal tax rate is
35%, and the state tax rate is 4.5%. A total of
$1 million in tax-deductible depreciation will
be charged this year. Estimate the required
CFBT.
After-Tax Analysis: A Typical Problem
Sensitivity Analysis
Solution:
CFBT= CFAT + taxes = CFAT + TI(Te)
= CFAT + (GI –E – D)Te
= CFAT + (CFBT – D)Te
CFBT = [CFAT – D(Te)]/(1 – Te)
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Te = 0.045 + 0.955(0.35) = 0.37925
CFBT = [2,000,000 – (1,000,000)(0.37925)]/(10.37925)
= 1,620,750/0.62075
= $2,610,955
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We study the sensitivity to variation in one or more
parameters using a specific measure of worth.
When two alternatives are compared, compute and
graph the measure of worth for different values of
the parameter to determine when each alternative is
better.
When several parameters are expected to vary over
a predictable range, the measure of worth is plotted
and calculated using three estimates for a
parameter— most likely, pessimistic, and optimistic.
This formalized approach can help determine which
alternative is best among several. Independence
between parameters is assumed in all these
analyses.
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Sensitivity Analysis
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Decision Trees: A Typical Problem
The combination of parameter and probability
estimates results in the expected value relation
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E ( X ) = ∑ xi P ( X = xi )
i =1
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Decision trees are used to make a series of
alternative selections.
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