Benefit Cost Analysis
•
Typically used for public projects
•
The goal is to determine if benefits exceed
costs:
Benefit / Cost Ratio > 1
•
The goal is NOT to maximize B/C Ratio.
•
Interest rates used are typically lower than
those used by businesses.
• Typically 4% - 8% (6.5% is typical)
• OMB requires 10% (except water proj.)
1
Benefit Cost Analysis
The challenge is to quantify the
benefits and costs.
The equation…
B/C = (Benefits – Disbenefits) to the public
(Costs) to sponsoring agency
You can use NPW, EAW, even NFW
– whichever is easier in a particular problem.
2
Benefit Cost Analysis
Steps:
1. Define the planning horizon.
2. Specify the Discount Rate (MARR) to be used.
3. Develop the cost and benefit-disbenefit profiles in
monetary terms.
4. Compare the benefits to costs using a specified
measure of worth, such as annual equivalent or
present worth.
5. If the B/C ratio is:
>1
project is justified
=1
barely justified – political
<1
not justified
6. Repeat steps 3 – 5 for alternative viewpoints
3
Example
A city library is to be expanded to include meeting rooms,
more electronic volumes, computer facilities, and electronic
check-in and check-out.
The cost of the expansion will be $700,000 and the new
equipment will cost another $175,000.
Maintenance and renewal of the new addition and equipment
will run approximately $100,000/year.
The library is projected to be in operation for 20 years, with a
residual value of 40% of first cost for the physical facilities.
There is no salvage value for the equipment. Discount is 8%.
An estimated 150,000 people will visit the library each year.
How much additional benefit per person, per year, must the
library visitors perceive in order to justify the expansion?
4
Perspective Matters
Suppose the library charged an annual
fee
Suppose the entire county sponsored
The equation…
B/C = (Benefits – Disbenefits) to public
(Initial Investment) by sponsor
What is the viewpoint of a user?
What is the viewpoint of a non-user?
5
Incremental B/C Analysis
MUST be used when there are multiple
alternatives to choose from!
The equation is still…
B/C = (Benefits – Disbenefits) to the public
(Costs) to sponsoring agency
You can use Incr. NPW or Incr. EAW
– whichever is easier in a particular problem.
7
Incremental B/C Analysis
Steps:
1. Define the set of feasible, mutually exclusive, public
sector alternatives to be compared.
2. Define the planning horizon.
3. Develop the cost and benefit-disbenefit profiles in
monetary terms for each alternative.
4. Specify the MARR to be used.
5. Order the alternatives from smallest to largest Cost
6. Compare the alternatives using a specified measure
of worth, such as annual equivalent, capitalized
cost, or present worth (with matching lifetimes).
If the B/C ratio is:
>1
≤1
higher cost project is justified
lower cost project is still justified
8
Incremental Benefit Cost Analysis Example
B
C
174
180
136
4
60
10
Costs
100
120
90
B–D
1.7
Benefits
Disbenefits
C
D
Not Feasible
A
E
F
80
136
178
89
8
10
2
14
80
70
110
50
1.0
1.4
0.9
1.8
Cost Order: G E C A F B
G – DN: (From feasibility, (B – D) / C = 1.5
E – G:
(136 – 89) – (10 – 14) = 51 = 2.55
(70 – 50)
C – E:
A – E:
Upgrade to G
Upgrade to E
Keep Proj. E
20
(174 – 136) – (4 – 10) = 44 = 1.47
(100 – 70)
1.5
20
(136 – 136) – (10 – 10) = 0 = 0
(90 – 70)
1.6
G
30
Upgrade to A
Incremental Benefit Cost Analysis Example
B
C
174
180
136
4
60
10
Costs
100
120
90
B–D
1.7
Benefits
Disbenefits
C
F – A:
E
F
80
136
178
89
8
10
2
14
80
70
110
50
1.0
1.4
0.9
1.8
Cost Order: G E C A F B
(178 – 174) – (2 – 4) = 6 = 0.6
(110 – 100)
B – A:
D
Not Feasible
A
1.5
Keep Proj. A
10
(180 – 174) – (60 – 4) = – 50 = – 2.5
(120 – 100)
1.6
G
20
Best is Proj A
Bonus Problem: B/C Build-Up Example
 Snack Fridge Viability
Data:
110 IE & EngM students
48% will use snack fridge instead of going home
Users average (2) drinks & (1) snack each week
Mark-up is 10%, drink price is $.50, snacks $.75
School year averages 32 weeks
Fridge costs $495, lasts 8 yrs, 8% cpd annually
If they save time & $$ on snacks & drinks, they
can buy books , study more, and expect one of
them to win a $5 500 national scholarship every
4 years. But the vending company will quit
donating $300 per year to their Tech Society
Perform a B/C analysis – IE student perspective