### Benefit-Cost Ratio Analysis

```Chapter 9 - Benefit-Cost Ratio
and Other Analysis Methods
Accompany Presentation (optional)
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
EGR 403 - Cal Poly Pomona - SA12
2
Chapter 9 - Other Analysis Methods
•
•
•
•
Future worth analysis
Benefit-cost ratio analysis
Payback period
Sensitivity and breakeven analysis
EGR 403 - Cal Poly Pomona - SA12
3
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
EGR 403 - Cal Poly Pomona - SA12
12.00%
4
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
EGR 403 - Cal Poly Pomona - SA12
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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%
EGR 403 - Cal Poly Pomona - SA12
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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
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
EGR 403 - Cal Poly Pomona - SA12
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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
9
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
EGR 403 - Cal Poly Pomona - SA12
10
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.
EGR 403 - Cal Poly Pomona - SA12
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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
EGR 403 - Cal Poly Pomona - SA12
B
\$ (2,783.00)
\$ 1,200.00
\$ 1,200.00
\$ 1,200.00
\$ 1,200.00
\$ 1,200.00
2.3
B
12
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
EGR 403 - Cal Poly Pomona - SA12
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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
14
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
EGR 403 - Cal Poly Pomona - SA12
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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
EGR 403 - Cal Poly Pomona - SA12
Price of Diesel
would have to
go up to \$.75 to
change decision.
16
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
EGR 403 - Cal Poly Pomona - SA12
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```