Chapter 9 - Benefit-Cost Ratio
and Other Analysis Methods
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EGR 403 Capital Allocation Theory
Dr. Phillip R. Rosenkrantz
Industrial & Manufacturing Engineering Department
Cal Poly Pomona
EGR 403 - The Big Picture
• Framework: Accounting & Breakeven Analysis
• “Time-value of money” concepts - Ch. 3, 4
• Analysis methods
–
–
–
–
Ch. 5 - Present Worth
Ch. 6 - Annual Worth
Ch. 7,7A,8 - Rate of Return (incremental analysis)
Ch. 9 - Benefit Cost Ratio & other methods
• Refining the analysis
– Ch. 10, 11 - Depreciation & Taxes
– Ch. 12 - Replacement Analysis
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Chapter 9 - Other Analysis Methods
•
•
•
•
Future worth analysis
Benefit-cost ratio analysis
Payback period
Sensitivity and breakeven analysis
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Future Worth Analysis
• Answers the question, what will the future situation be, if
we take some particular course of action now?
– Example 9.1, FW = P(F/P,i , n), FW = A(F/A, i, n)
Vices
Smoking
Cigarettes
Cigars
Spirits
Beer
Liquor
Wine
Semi-annual
consumption
Semi-annual
in units
Cost/ unit sub total
26
26
$ 15.00 $
$ 1.00 $
26
$ 6.00
6
$ 15.00
13
$ 8.00
Semi-annual total
Present age
Retirement age
Years to retirement
20
65
45
$
$
$
$
FW if saved
FW if invested
in market
390.00
26.00
$128,370.16 $1,225,019.32
$8,558.01
$81,667.95
156.00
90.00
104.00
766.00
$51,348.06
$490,007.73
$29,623.88
$282,696.77
$34,232.04
$326,671.82
$252,132.16 $2,406,063.59
Annual i
5.00%
Compounded semi-annually
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12.00%
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Future Worth Analysis
When constructing a building, the issue is:
• not the dollars out of pocket,
• but the invested cost at start- up.
• Example 9-2: The remodel project costs less out of pocket,
but has a higher “up front” cost. That makes it less desirable.
Interest rate
Purchase site
Design & site preparation
Construction
Equipment installation
Out of pocket costs
FW at start-up
8.00%
Year
0
1
2
3
Alternatives
Remodel
Construct
available
new plant
factory
$
85 $
850
$
200 $
250
$
1,200 $
250
$
200 $
250 Select:
$
1,685 $
1,600 Remodel available factory
$
1,836 $
1,882 Construct new plant
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Benefit-Cost Ratio Analysis
• If the PW of benefits PW of costs 0.
The alternative is
considered acceptable.
• Restated:
Benefit-cost ratio B/C =.
PW of benefit/PW of cost  1.
• Fixed input, maximize B/C.
Example 9-3
Year
0
1
2
3
4
5
PW of:
Cost
Benefit
$
$
$
$
$
$
MARR =
7.00%
Alternative
A
B
(1,000.00) $ (1,000.00)
300.00 $
400.00
300.00 $
350.00
300.00 $
300.00
300.00 $
250.00
300.00 $
200.00
($1,000.00)
($1,000.00)
$ 1,230.06 $
1,257.75
B/C =
1.23
1.26
Select:
B
Other alternatives for comparison:
PW $
230.06 $
257.75
EUAC
$56.11
$62.86
FW
$322.67
$361.50
IRR
15.24%
17.47%
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Benefit-Cost Ratio Analysis
• If the EUAB - EUAC 0.
The alternative is considered acceptable.
• Restated:
Benefit-cost ratio: B/C = EUAB/EUAC  1
Or, using PW: B/C = PWB/PWC 
• Neither input or output fixed - use incremental
B/C.
• Note: Salvage Value is considered a “negative
cost”, not a benefit
• B/C Ratio Analysis is popular in government
• Very easy to use with databases and spreadsheets
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Benefit Cost Ratio Analysis Example
Reject increment if incremental B/C Ratio is < 1
Cost
PWB
B/C
Increment
incr Cost
incr PWB
incr B/C
Keep
D
1000
1340
1.34
B
2000
4700
2.35
A
4000
7330
1.83
C
6000
8730
1.46
E
9000
9000
1
B-D
1000
3360
3.36
B
A-B
2000
2630
1.36
A
C-A
2000
1400
0.70
A
E-A
5000
1670
0.33
A
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Benefit Cost Ratio Analysis Example
First Increment is B-D. Incremental B/C > 1, so choose
higher cost alternative
Cost
PWB
B/C
Increment
incr Cost
incr PWB
incr B/C
Keep
D
1000
1340
1.34
B
2000
4700
2.35
A
4000
7330
1.83
C
6000
8730
1.46
E
9000
9000
1
B-D
1000
3360
3.36
B
A-B
2000
2630
1.36
A
C-A
2000
1400
0.70
A
E-A
5000
1670
0.33
A
EGR 403 - Cal Poly Pomona - SA12
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Benefit Cost Ratio Analysis Example
Reject increment if incremental B/C Ratio is < 1
Cost
PWB
B/C
Increment
incr Cost
incr PWB
incr B/C
Keep
D
1000
1340
1.34
B
2000
4700
2.35
A
4000
7330
1.83
C
6000
8730
1.46
E
9000
9000
1
B-D
1000
3360
3.36
B
A-B
2000
2630
1.36
A
C-A
2000
1400
0.70
A
E-A
5000
1670
0.33
A
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Payback Period:
Important Points
•
•
•
•
Approximate economic analysis method.
Prior to payback the effect of timing is
ignored.
After payback all economic consequences
are ignored.
Will not necessarily produce a
recommended alternative consistent with
equivalent worth and rate of return
methods.
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Payback Period
• The period of time
required for the
profit or other
benefits of an
investment to
equal the cost of
the investment.
• How many years
are required to get
my money back?
9-6
Alternative
Year
0
1
2
3
4
5
Payback:
Select:
A
$ (1,000.00)
$ 200.00
$ 200.00
$ 1,200.00
$ 1,200.00
$ 1,200.00
2.5
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B
$ (2,783.00)
$ 1,200.00
$ 1,200.00
$ 1,200.00
$ 1,200.00
$ 1,200.00
2.3
B
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What is wrong here?
Payback and IRR analysis
do not agree.
Payback Analysis
Example 9-8
Alternative
With alternative A we get our
money back in 4 years but
never make a return on the
investment.
With alternative B we get our
money back in 5 years and
make a return on the investment
of 19%.
How should we make a decision?
1. Liquidity vs. profitability.
2. Life of project.
Year
A
B
0
($30,000.00) $ (35,000.00)
1
$12,000.00 $ 1,000.00
2
$9,000.00 $ 4,000.00
3
$6,000.00 $ 7,000.00
4
$3,000.00 $ 10,000.00
5
$0.00 $ 13,000.00
6
$0.00 $ 16,000.00
7
$0.00 $ 19,000.00
8
$0.00 $ 22,000.00
Salvage
$0.00 $
Payback:
4.00
5.00
Select:
A
IRR =
0%
19%
Select:
B
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Sensitivity and Break-even Analysis
• Economic data represent projections of
expenditures and returns.
• These projections ultimately affect our
decisions.
• To more fully consider our choice of a
decision, we should play a “what if” game to
determine the amount of change in a data
point that might change the decision.
EGR 403 - Cal Poly Pomona - SA12
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Consider Problem 6-21
• Diesel engine is preferred based on values assumed.
• How much would changes in assumptions have to be in order to
change the preferred alternative?
Prob 6-21
Diesel
Gas
Vehicle Cost
13000
12000
Fuel
685.71
910.71
Repairs
300
200
Resale
2000
3000
Insurance
500
500
EUAC
$4,780.22 $5,157.70
n
4
3
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How much would price of diesel fuel
need to go up before Gas would be the
preferred alternative?
Diesel Cost
$0.48
$0.50
$0.55
$0.60
$0.65
$0.70
$0.75
EUAC
$4,780.22
$4,808.79
$4,880.22
$4,951.65
$5,023.08
$5,094.51
$5,165.93
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Price of Diesel
would have to
go up to $.75 to
change decision.
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What is the impact of the variability
of resale value on the analysis?
By varying the resale value, we find that at about $4200 resale
value for the gasoline powered vehicle the EUAC is almost equal
Resale (Gas)
$2,000
$3,000
$4,000
$5,000
$4,200
EUAC
5,471.81
5,157.70
4,843.59
4,529.48
4,780.77
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